AN EXPLORATORY STUDY OF THE FACTORS ASSOCIATED WITH THE
MATHEMATICS ACHIEVEMENT OF SIX TENTH GRADE
AFRICAN AMERICAN STUDENTS
Except where reference is made to the work of others, the work described in this
dissertation is my own or was done in collaboration with my advisory
committee. This thesis does not include proprietary
or classified information.
____________________________
Sarah Kathryn Westbrook
Certificate of Approval:
___________________________ ___________________________
W. Gary Martin Marilyn E. Strutchens, Chair
Professor Associate Professor
Curriculum and Teaching Curriculum and Teaching
___________________________ ___________________________
Kimberly King-Jupiter Chris Rodger
Associate Professor Professor
Educational Foundations, Leadership Mathematics and Statistics
and Technology
___________________________
Stephen L. McFarland
Dean
Graduate School
AN EXPLORATORY STUDY OF THE FACTORS ASSOCIATED WITH THE
MATHEMATICS ACHIEVEMENT OF SIX TENTH GRADE
AFRICAN AMERICAN STUDENTS
Sarah Kathryn Westbrook
A Dissertation
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of
Requirements for the
Degree of
Doctor of Philosophy
Auburn, Alabama
December 16, 2005
iii
AN EXPLORATORY STUDY OF THE FACTORS ASSOCIATED WITH THE
MATHEMATICS ACHIEVEMENT OF SIX TENTH GRADE
AFRICAN AMERICAN STUDENTS
Sarah Kathryn Westbrook
Permission is granted to Auburn University to make copies of this dissertation at its
discretion, upon request of individuals or institutions and at their expense.
The author reserves all publication rights.
___________________________
Signature of Author
___________________________
Date of Graduation
iv
DISSERTATION ABSTRACT
AN EXPLORATORY STUDY OF THE FACTORS ASSOCIATED WITH THE
MATHEMATICS ACHIEVEMENT OF SIX TENTH GRADE
AFRICAN AMERICAN STUDENTS
Sarah Kathryn Westbrook
Doctorate of Philosophy, December 16, 2005
(M. A., Auburn University, 2005)
(M.Ed., Florida A & M University, 1976)
(B. S., Auburn University, 1972)
188 Typed Pages
Directed by Marilyn E. Strutchens
Using observations and interviews, six African American students were followed
through their tenth grade year in mathematics class. All of the students were enrolled in
regular, college preparatory geometry. An assessment of the factors affecting the
mathematics achievement of these students also included interviews with teachers and
parents. These students? success in mathematics was found to be linked to self-
confidence, self-motivation, parental influence and educational level, school mathematics
placement and assessment practices, teacher support and expectations, and classroom
procedures and practices. Furthermore the issue of dysconscious racism at the school
v
level and its effects on students? mathematics achievement was addressed in this study.
Recommendations which resulted from this study are focused on empowering, instead of
filtering out African American students through mathematics instruction. With a goal of
challenging the existing status quo of who is successful in mathematics and changing
current practices which adversely affect African American students? success in
mathematics, teacher and institutional practices must be addressed.
vi
ACKNOWLEDGEMENTS
I would like to thank my major professor and major supporter, Dr. Marilyn
Strutchens, for her critiques, endless hours of editing, requests for rewrites, and thousands
of sticky notes. I would also like to thank my other committee members: Dr. Kimberly
King-Jupiter, Dr. Gary Martin, and Dr. Chris Rodger for their encouragement and
feedback
The students and teachers in this study were most cooperative and
accommodating and a heartfelt thanks goes to each of them. The students let me invade
their business and their lives which I thoroughly enjoyed. The teachers accommodated
my every request for information and classroom observation time. The school personnel
and district superintendents were most helpful in locating students, providing interview
space, and assisting me wherever possible.
I would like to thank my fellow graduate students for their encouragement and
willingness to listen to complaints and woes. In particular a big thank you to Joy Black,
fellow older graduate student, and my good friend.
Also, I would like to thank my best friend, my husband who never complained
about the long hours his spouse spent in front of the computer or buried under papers.
And a special thank you to my mother who financially and emotionally supported me
through this process.
vii
TABLE OF CONTENTS
LIST OF TABLES ix
LIST OF FIGURES x
CHAPTER I
STATEMENT OF THE PROBLEM 1
Purpose of the study 2
Significance of the study 3
Framework and Research Questions 5
CHAPTER II
REVIEW OF RELATED LITERATURE 7
African American Student?s Achievement in Mathematics 8
Barriers to Mathematics Learning 26
Theoretical Basis for Study 55
CHAPTER III
DESIGN OF THE STUDY 64
Methodology 65
Participant Selection 66
School and Community Setting 69
Teachers 72
Instrumentation 78
Procedure 81
Data Analysis 82
CHAPTER IV
RESULTS OF THE STUDY 84
Jasmine 84
Danielle 90
Jonathan 95
Tony 99
Josh 103
Amber 107
CHAPTER V
ANALYSIS AND INTERPRETATION 112
Community and Cultural Influences 116
Educational Institution 122
Classroom Practices 127
Student Attitude 132
CHAPTER VI
SUMMARY AND RECOMMENDATIONS 135
viii
Limitations 136
Implications of the Study 139
Final Remarks 151
BIBLIOGRAPHY 153
APPENDICES
A. Interview guides 165
B. Permission forms 168
ix
LIST OF TABLES
Table 1. Average Score for 2002 Calculus AB and BC Exams by Selected
Racial/Ethnic Groups
16
Table 2. Percentage of Students by Racial/Ethnic Group for the 1994 and
2002 AB Calculus Exam
17
Table 3. Percentage of Graduate Students, Masters Level by Race/Ethnicity
24
Table 4 . Summary of Student Demographics and Testing Performance
69
Table 5. Demographics of Central City and Jackson for 2003 (United States
Census Bureau, 2003)
70
Table 6. SAT-10 and AHSGE Pass Rate for Central City High, Jackson High,
and State
72
Table 7. Codes Words Used and Frequency
114
Table 8. Answers to the question: ? On a scale of one to ten, with one being
the worse math student and ten being the best math student, how would you
rate ____??
116
x
LIST OF FIGURES
Figure 1. Average NAEP mathematics score for 9 year old students by
race.
9
Figure 2. Average NAEP mathematics score for 13 year old students by
race
10
Figure 3. Average NAEP mathematics score for 17 year old students by
race
10
Figure 4. 1973-1999 average score differences on NAEP mathematics for
9 year old students.
11
Figure 5. 1973-1999 average score differences on NAEP mathematics for
13 year old students.
12
Figure 6. 1973-1999 average score differences on NAEP mathematics for
17 year old students.
12
Figure 7. Gain or loss by NAEP question type for 1992 to 2000 (Silver et
al., 1997; Strutchens & Silver, 2000)
14
Figure 8. Spheres of Influence on Student Behaviors and Achievement.
27
Figure 9. Comparison of National average eighth mathematics scores
with Alabama eighth grade average scores.
152
1
CHAPTER 1
STATEMENT OF THE PROBLEM
The cover story for the March 2004 issue of U.S. News and World Report was
Fifty Years After ?Brown V. Board Of Education? Unequal Education: Why So Many
Kids Are Still Being Cheated ("50 years after Brown," 2004). The 1954 Supreme Court
ruling in Brown v. the Board of Education of Topeka, Kansas officially ended the practice
of separate but equal public facilities for African American citizens. Apparently, unequal
education remains for many African American students, even though more than fifty
years have passed since the Supreme Court?s ruling. The answer is not straight-forward
nor is the solution imminent (Secada, 1995).
The National Assessment of Educational Progress (NAEP), dubbed the Nation?s
Report Card, is a congressionally-mandated testing assessment of a sample of United
States students. The test is conducted in mathematics, reading, science, writing, history,
and several other subjects (U.S. Department of Education, 2005). The 2004 NAEP results
indicate a continuation of a pattern that has been apparent since NAEP achievement
testing began in 1969 (U.S. Department of Education, 2005). White students consistently
and significantly outscore African American students in mathematics. Results from other
achievement tests such as the Scholastic Assessment Test (SAT), Advanced Placement
exams, and the ACT (formerly American College Testing) show similar trends (ACT
Inc., 2003; The College Board, 2003). Many well respected and well known researchers
2
have examined this pattern and established the fact that African American students as a
racial group score lower than other racial groups on standardized and norm-referenced
mathematics achievement tests used in the United States (Berry, 2003; D'Amato, 1992;
Delgado & Stefancic, 2000; Delpit, 1988; Fordham, 1988; Hoffman, Llagas, & Snyder,
2003; Jacobson, Olsen, Rice, Sweetland, & Ralph, 2001; Ladson-Billings, 1997; Martin,
2000; Moses & Cobb Jr., 2001; Ogbu & Matute-Bianchi, 1986; Perry, 2003; Rech &
Stevens, 1996; Schoenfeld, 2002; Shulman, 2002; Silver, Strutchens, & Zawojewski,
1997; Singham, 2003; Sleeter, 1997; Strutchens, Lubienski, McGraw, & Westbrook,
2004; Strutchens & Silver, 2000; Tate, 1997; Weissglass, 2002). Furthermore, even
though improvements in test scores on many of the assessment instruments reviewed in
the previously mentioned studies have occurred over the past years, striking differences
between racial/ethnic groups remain. Finding and addressing the cause of this
discrepancy is not as straight forward as confirming that achievement gaps exist.
Purpose of the Study
In answering the question as to why this achievement gap exists, researchers have
posited several theories. These include teacher expectations and biases (Delpit, 1988;
Rousseau & Tate, 2003; Sleeter, 1993), socioeconomic status (Roscigno, 1998; Tate,
1997), lack of parental or community support (Perry, 2003), social and historical factors
resulting in cultural differences and resistance theories (Martin, 2000; Ogbu & Matute-
Bianchi, 1986), inadequate teaching and lack of school resources (Oakes, 2002; Perry,
2003; Roscigno, 1998), negative peer pressure or regarding academic success as being
White (Fordham, 1988; Kunjufu, 1988), and teaching methods and assessment measures
which do not match the learning styles of the students (Banks, 1993; Berry, 2003; Delpit,
3
1988; Ladson-Billings, 1995a; Lee, Smith, & Croninger, 1997; Singham, 1998). This
study sought to extend existing research by encouraging a few African American students
to speak for themselves of their schooling experiences, their attitudes towards learning
mathematics, and their interpretations of peer, parent, and teacher influences. While
much of the research reviewed in this study focused on the broad picture of achievement
pattern differences between African American students and other racial groups, this study
sought to examine the mathematical learning experiences of a small number of African
American students through their own, personal perspectives. Focusing on a small number
of students allowed more in-depth information to be obtained, and learning experiences
could be viewed through the student lens. The purpose of this study was to examine the
mathematics experiences of several African American students through their eyes and
their voices. More specifically, what did the students believe influenced their
performance and achievement and how did they react to those influences? In addition to
extending existing research on African American students? mathematics achievement,
suggestions are offered to help eliminate barriers to educational attainment for African
American students.
Significance of the Study
Ladson-Billings (1997) and Moses and Cobb (2001) argued that greater
mathematics knowledge and skill attainment is tied to better life chances. Having
mathematics and science skills allows students to succeed in advanced high school
mathematics and science classes thereby allowing the opportunity for college enrollment
(Moses, Kamii, Swap, & Howard, 1989). In the classroom, mathematics has been used as
a sieve or gatekeeper to select a few top students to advance. This filtering approach has
4
tracked many African American students into the lower level mathematics classes, out of
school, and into lower level jobs (Ladson-Billings, 1997; Oakes, 2002). Moreover,
schooling tends to reproduce societal inequalities (Roscigno, 1998).
Furthermore, while math illiteracy is not unique to African Americans, it affects
some African Americans and other minorities more than Whites (Moses & Cobb Jr.,
2001). The amount of schooling that an individual has can affect his or her life chances
and the choices available to them. African Americans have higher school drop-out,
suspension, and incarceration rates than Whites (Ladson-Billings, 1997). If one accepts
that life chances are improved by attaining higher levels of education, and that
mathematics is one of the major hurdles in access to higher levels of education, then we
must focus on African American students? mathematics education (Ladson-Billings,
1997).
Recently, a major educational reform project, Equity 2000, focused on increased
mathematics experiences for students by ensuring exposure to algebra and geometry early
in school and providing support for success in these classes (Green, 2001). The premise
for Equity 2000 was that increased exposure to early higher level mathematics
experiences would close the achievement gap between minority or disadvantaged
students and their non-disadvantaged peers (Green, 2001). The basic premise of this
paper was that African American children deserve to have the same life chances and
opportunities as other children.
5
Framework and Research Questions
In this study, multiple-single individual case studies were conducted through
extensive student interviews, classroom observations, and parent and teacher interviews.
Six students were considered as individual case studies, even though the students,
teachers, and parents were interviewed with the same initial set of questions, the result
can be described as multi-single units. Students were interviewed concerning their beliefs
about the importance of taking mathematics courses and the practical value of the
mathematics they were learning in school. Questions for the students attempted to discern
whether or not they felt that the education offered to them in mathematics was sufficient
and equitable. Through interviews, observations, and clarifications, it was hoped that
students voiced the positive and negative influences and hindrances which affected their
mathematics experiences. Additionally, it was hoped that the students in this study would
offer practical suggestions on addressing the issues which were barriers to their
education, whether it was the teacher, the curriculum, peer pressure, or the students?
interpretation of parental involvement levels.
Research Questions
1. How do African American students in this study view their mathematics
experiences currently and in their past?
2. Do the African American students in this study consider mathematics important to
learn? Do they see a relationship between mathematics acquisition and future job
opportunities or education? Do they view mathematics as an empowering tool?
3. Are parents, guardians, community, and peers influential sources for the African
American students in this study in achievement and specifically mathematics
6
achievement? For the students in this study, where or what is their primary
source of influence?
4. How do the African American students in this study interact with their
mathematics teacher? Do the students perceive their teacher as encouraging, and
knowledgeable? Is there a relationship of mutual respect and admiration between
the student and the teacher?
5. To be successful in mathematics, must one adopt the culture and behaviors of the
White students? If this is the case, does it hold true for African American
students whether they are the minority or majority in school? Are there other
coping mechanisms for these students to employ when dealing with racial issues
which confront them in situations at school so that access to mathematics
education is not an issue?
6. Does gender affect the African American students? view of mathematics? If this
is the case, in what ways does gender affect the student?s relationship with school
officials, parents and society at large, with respect to mathematics learning?
7
CHAPTER II
REVIEW OF RELATED LITERATURE
This literature review begins with an examination of African American students?
mathematics achievements and trends of achievement over the past 30 years. Available
data from the National Assessment of Educational Progress, the College Board testing
programs, U.S. Census Bureau, Scholastic Assessment Test, and ACT assessments were
examined to assess the status, and document the changes in the mathematics achievement
of African American public school children. In addition to these test scores, college
enrollment and high school drop-out rates were reviewed, and differences between racial
groups were noted. The second part of the literature review was devoted to a discussion
of the research and theories on why this discrepancy exists. The theories range from
cultural influences and peer pressure to classroom practices, from school tracking policies
to inadequate curriculum, and from the tendency of some teachers to stereotype to
assessment practices. To assess the current situation in mathematics education, it is
important to look at trends in achievement tests over the last several decades. As
discussed below, in spite of the fact that improved test scores were found on many of the
assessment instruments reviewed here, striking differences between racial/ethnic groups
remain.
8
African American Student?s Achievement in Mathematics
National Assessment of Educational Progress Results
To examine the question of how African American students are doing in
mathematics, one could consider how African American students are doing in
comparison to other racial/ethnic groups in the United States. Looking at national testing
results is one method of examining the trends in mathematics achievement. The National
Assessment of Educational Progress (NAEP) long-term trend assessment was designed to
gauge levels of and trends in educational achievement for students across the nation
(Jacobson et al., 2001). This long-term data set is used to indicate how well students are
achieving computational skills in mathematics. NAEP scores range from 0 to 500 with
level 150- the basic arithmetic facts, level 200- beginning skills and understanding, level
250- basic operations and beginning problem-solving, level 300- moderately complex
procedures and reasoning, and level 350- multi-step problem solving and algebra (Tate,
1997). It should be noted that the problem-solving reflected here is different from that
which the National Council of Mathematics (NCTM) has defined in the Principles and
Standards for School Mathematics (National Council of Teachers of Mathematics, 2000),
but rather was developed in 1973 as consistent with the terminology used at that time
(Tate, 1997).
The National Assessment of Educational Progress (NAEP) provides long-term
mathematics achievement data for ten of the years between 1973 and 2004 at randomly
selected intervals ranging from two to five years. The test is administered nationwide to
selected samples of students aged 9, 13, and 17 (U.S. Department of Education, 2005).
The following figures, 1, 2, and 3, depict the reported scores by year for African
American, White, and Hispanic students, and indicate that the scores of African
American students increased more than White or Hispanic students? scores from 1973 to
2004 for the three age groups with one exception. Hispanic 17 year-old students showed
a greater increase than African American students.
NAEP Average Scale Scores: Age 9
180
200
220
240
1
9
7
8
1
9
8
2
1
9
8
6
1
9
9
0
1
9
9
2
1
9
9
4
1
9
9
6
1
9
9
9
2
0
0
4
African American
White
Hispanic
Figure 1. Average NAEP mathematics scores for 9 year old students by race (U.S.
Department of Education, 2005).
9
NAEP Average Scale Scores: Age 13
210
230
250
270
290
1
9
7
8
1
9
8
2
1
9
8
6
1
9
9
0
1
9
9
2
1
9
9
4
1
9
9
6
1
9
9
9
2
0
0
4
African American
White
Hispanic
Figure 2. Average NAEP mathematics scores for 13 year old students by race (U.S.
Department of Education, 2005).
10
NAEP Average Scale Scores: Age 17
260
270
280
290
300
310
320
1
9
7
3
1
9
7
8
1
9
8
2
1
9
8
6
1
9
9
0
1
9
9
2
1
9
9
4
1
9
9
6
1
9
9
9
2
0
0
4
African American
White
Hispanic
Figure 3. Average NAEP mathematics scores for 17 year old students by race (U.S.
Department of Education, 2005).
How the gap between racial/ethnic groups changed has changed over the last 30
years: More important than studying the achievement gap is to examine how this gap has
changed over the years. As measured by the NAEP long-term mathematics assessment, is
the gap between racial/ethnic groups for mathematics achievement decreasing? The next
three figures, 4, 5, and 6 depict the differences between African American and White
students, between Hispanic and African American students, and between Hispanic and
White students.
Differences Between White & African American,
Hispanic & African American, White & Hispanic:
Age 9
-5
5
15
25
35
1
9
7
3
1
9
78
1
9
82
1
9
86
1
9
9
0
1
9
9
2
1
9
9
4
1
9
9
6
1
9
9
9
2
0
0
4
African American-
White
Hispanic-African
American
White-Hispanic
Figure 4. 1973-2004 average score differences on NAEP mathematics for 9 year old
students (U.S. Department of Education, 2005).
11
Differences Between White & African American,
Hispanic & African American, White & Hispanic:
Age 13
0
10
20
30
40
50
1
9
7
3
1
9
7
8
1
9
8
2
1
9
8
6
1
9
9
0
1
9
9
2
1
9
9
4
1
9
9
6
1
9
9
9
2
0
0
4
White-African
American
Hispanic-African
American
White-Hispanic
Figure 5. 1973-1999 average score differences on NAEP mathematics for 13 year old
students (U.S. Department of Education, 2005).
Differences Between White & African American,
Hispanic & African American, White & Hispanic:
Age 17
-8
2
12
22
32
42
1
9
7
3
1
9
7
8
1
9
8
2
1
9
8
6
1
9
9
0
1
9
9
2
1
9
9
4
1
9
9
6
1
9
9
9
2
0
0
4
White-African
American
Hispanic-African
American
White-Hispanic
Figure 6. 1973-1999 average score differences on NAEP mathematics for 17 year old
students (U.S. Department of Education, 2005).
In summary, it appeared that while the achievement scores for African Americans
increased fairly consistently from 1973 until 2004, the achievement gap between African
12
13
American and White students did not decrease significantly during this same time period.
The achievement gap decreased for the three age levels reported from 1973 until 1986,
but this gap has not changed appreciably for 9 or 13 year olds since 1986, and for 17 year
olds since 1990. In fact, the difference in achievement between African American and
White students increased for 13 year olds from 1986 until 1999 and for 17 year olds from
1990 until 1999. The differences between the scores for White and Hispanic students
were significant but were less than those for White and African American students. And
the differences between African American and Hispanic might be increasing for 17 year
old students but overall appeared to be small for all the ages tested.
Critical thinking skills. A second NAEP data set provides information on how
well students are doing on problem-solving and application skills which is radically
different from the basic skills on the trend assessment (Tate, 1997). The types of
questions include some which require an extended response, not just multiple choice
items. Strutchens et al.(2004) found that in 2000, just over 1 in 4 White 4th grade
students scored at or above proficient while only 1 of 20 African American 4th grade
students scored at this level. For 12th grade students, 1 in 5 White students and 1 in 25
African American students scored at or above the proficient level.
NAEP questions are either multiple choice, short constructed response, or
extended constructed response (Silver et al., 1997; Strutchens et al., 2004; Strutchens &
Silver, 2000). For the extended response questions which reflect more critical thinking
skills, both the 8th and 12th grade students increased the percentage of correct responses
across all racial groups 1992, 1996, and 2000. Examining only the data for 8th grade
students by question type for the years 1992 and 2000, one can see some interesting
results depicted in Figure 7 (Silver et al., 1997; Strutchens et al., 2004). Overall, 8th
grade students gained in the percentage correct on multiple choice and extended response
items, with greater gains on the extended response questions. African American students
made greater gains on multiple choice items, while White students made greater gains on
extended response questions. All students lost percentage points from 1992 to 2000 on
short constructed response test items with the White students having the largest drop,
followed by the Hispanic students. African American students had the least drop in
percent correct for the short constructed response questions from 1992 to 2000.
Average Gain or Loss for NAEP Question Type
1992-2000 Eighth Grade
-8
-6
-4
-2
0
2
4
6
8
10
Multiple Choice Short Constructed Extended
Response
White
African American
Hispanic
Nation
Figure 7. Gain or loss by NAEP question type for 1992 to 2000 (Silver et al., 1997;
Strutchens & Silver, 2000).
Reporting on the 1996 NAEP data, Strutchens and Silver (2000) stated that 8th
grade African American students performed about 70 percent as well as White students
on multiple choice items, but only 20 percent as well on extended response questions.
14
15
From the 2000 NAEP data, they report that 8th grade African American students
performed 72.5 percent as well as White students on the multiple choice and 31 percent
as well as White students on extended response questions. Results from the 2000 NAEP
data indicated that African American students are more often assessed with multiple
choice tests than White students (Strutchens et al., 2004). One might hypothesize that
African American students will score lower on constructed response test items because
they have had less experience with this question type (Strutchens et al., 2004). In 2000
however, the percentage correct for African American students on extended response
questions increased, and this increase held and was greater than increases for other
reporting groups.
Advanced Placement Exams
Because calculus is the highest level of mathematics that is offered at the high
school level in the United States, the Advanced Placement (AP) Calculus exam is a valid
indicator of mathematics achievement (Tate, 1997). The College Board offers two levels
of the Advanced Placement Calculus exam. Calculus AB is equivalent to the first
semester of college calculus, and Calculus BC is equivalent to a full year of single
variable integration and differentiation. Scoring on the AP exams is on a 5 point scale to
determine whether or not the candidate should receive credit for the college equivalent
course: 5 is extremely well qualified; 4 is well qualified; 3 qualified; 2 possibly qualified;
and 1 no recommendation (The College Board, 2003). Using data from The College
Board (2005) Table 1 was created comparing the average exam score for the reporting
racial/ethnic groups in 2004. (The College Board uses the classification Chicano
American in contrast to the NAEP classification of Hispanic).
16
Table 1
Average Scores for 2004 Calculus AB and BC Exams by Selected
Racial/Ethnic Groups
2004 AB
2004 BC
All students taking the exam
2.96
3.65
White 3.06 3.68
African American 2.00 2.79
Chicano American 2.06 2.82
(The College Board, 2005)
It is apparent from the table that African American and Chicano American
students score significantly lower than the average of all students taking the exam and
even lower than the White students taking the exam in 2004. Although African American
students scored significantly lower than White students on both the AB and BC exams,
African American students scored only slightly lower than Chicano American students.
Of all the students who took the Calculus AB exam in 2004, only 62.3 percent of the
White students, 31 percent of the Chicano American students, and 30 percent of the
African American students scored at or above a 3 (The College Board, 2005). This means
that approximately 70 percent of the African American students who took the calculus
exam in 2004 did not score well enough to be considered qualified to have completed one
semester of college calculus.
17
Another statistic apparent from an analysis for the work done by Tate (1997) and
more recent data from The College Board (2005) showed the percentage of students who
have taken the calculus exams by reported racial/ethnic group, see Table 2. From 1994 to
2004 the percentage of African American students taking the Calculus AB exam
remained at 4 percent. The percentage of African American students taking the Calculus
BC exam was 2 percent for 2004 (The College Board, 2005). So, while the number of
African American students taking this exam has increased, as well as the percentage
scoring a 3 or higher, the proportion of the students taking the exam who are African
American has not increased over the last 10 years.
Table 2.
Percentage of Students by Racial/Ethnic Group for the 1994 and 2004
AB Calculus Exam.
Reported racial/ethnic group
1994 AB Exam
2004 AB
Exam
White
67
68.5
African American 4 4
Chicano American 2 3.8
(The College Board, 2005)
Scholastic Assessment Tests and ACT exams
In addition to NAEP, the Scholastic Assessment Test (SAT) and the ACT,
formerly the American College Testing assessment, are designed to measure academic
18
achievement. But in contrast to NAEP, the SAT and the ACT are designed to predict
academic performance in colleges and are administered to a self-selected group of college
bound high school students (Jacobson et al., 2001). Since neither the SAT nor the ACT
are taken by all students, caution should be urged in interpreting the scores, although the
trends might be of interest. From 1975 to 1995, the combined mathematics and verbal
score on the SAT rose 8 percent for African American youth while remaining fairly
constant for White youth (Jacobson et al., 2001). This trend led some to believe that the
gap between the scores of the White and African American students was closing
(Jacobson et al., 2001). But during this same time period, the number of African
Americans taking the SAT dropped by 9 percent (Jacobson et al., 2001), and from 1992
to 2002, the mathematics portion of the SAT indicated an 8 point increase in the scores
for African American youth and an 18 point increase for White youth (The College
Board, 2003). Mexican American test takers had no increase in scores for the time period,
while Puerto Rican students had a 13 point gain (The College Board, 2003). Apparently,
the earlier trends closing the gap between White and African American students have not
continued for students taking the SAT over the last ten years. Of the one and a half
million students taking the SAT in 2004, 9 percent were African American; in 1992, 10
percent were African American (The College Board, 2003, 2005). While the actual
number of African American students taking the SAT has increased, the percentage of
students taking the SAT who are African American has not increased over the last 10
years.
The average composite score on the ACT was just less than 21 for all students
taking this test in 2003 (ACT, 2004). For the high school graduating classes of 2003,
19
African American students? average score was 16.7, White students averaged 21.3,
Mexican- Americans averaged 18.3, and other Hispanics averaged 18.9 in mathematics
(ACT, 2004). Twelve percent of the slightly more than one million students who took the
ACT in 2003 were African Americans, similar to the percentage taking the SAT in 2003.
The percentage of African American students taking advanced placement
mathematics tests has not increased over the past decade nor the percentage of African
Americans taking college entrance examinations. Furthermore, the difference between
African American and White students? scores on advanced placement and college
entrance exams is considerable. Advanced placement exam, SAT, and ACT scores are all
indicators of college preparation and predictors of students? success in college level
mathematics classes. Fewer African American students nationwide participate in
advanced placement, SAT, and ACT testing than White students, and on average African
American students score significantly lower on each of these measures. The results from
these assessment tools indicate that African American students are not being prepared to
compete with other students in college matriculation.
School Retention and Expulsion
For students to have access to higher level mathematics, they have to remain in
school and progress to higher level classes. Students who are repeatedly retained on grade
level, are suspended, faced with expulsion, or who have dropped-out altogether have little
chance for success in higher level mathematics.
For seven of the years between 1990 and 2003, the National Household Education
Surveys Program (NHES) was used by the National Center for Educational Statistics
(NCES) to collect data on educational issues which were not addressed with the school
20
level data (National Center for Education Statistics, 2004). Through computer assisted
telephone interviews, households spanning the United States are surveyed about issues
such as adult education, early childhood program participation, parental involvement in
education, and before or after-school programs (NCES, 2004). From the 1999 NHES,
Hoffman et al. (2003) found that 18 percent of African American students in grades K-12
have repeated a grade compared to 9 percent of White and 13 percent of Hispanic
students. In grades 7 through 12, 35 percent of the African American students report ever
being suspended or expelled compared to 15 percent of the White students and 20 percent
of the Hispanic students (Hoffman et al., 2003). It is shockingly clear that African
American youth are being retained, expelled, and suspended more from school than other
racial/ethnic groups. And certainly, being expelled or suspended must have a negative
effect on mathematics achievement.
High School Dropout and Completion Rates
As stated earlier, for students to have access to higher level mathematics, they
have to remain in school and progress to higher level classes. Hispanic students are much
more likely to drop-out of school than African Americans, and African American
students are slightly more likely to drop-out of high school than White students (Hoffman
et al., 2003). In 1974, the high school drop-out rate for African Americans was twice the
corresponding rate for Whites (Jacobson et al., 2001). By 1997 the dropout rate was 3.6
percent for African Americans and 5.0 percent for Whites, thus the dropout rates became
more similar over the 23 year time span (Jacobson et al., 2001). Data from the Bureau of
the Census reveal even higher rates for high school dropouts. The Bureau of the Census
reports for the year 2000, that the percent of 16- to 24- year-olds who were high school
21
dropouts was approximately 28 percent for Hispanics, 12 percent for African Americans,
and 7 percent for Whites (Hoffman et al., 2003). Data for all three racial/ethnic groups
indicate a decrease from 1972 until 2000, with the African American and White
decreases being fairly consistent in contrast to the reported Hispanic rate which shows
great fluctuations over the same time period of nearly thirty years.
From the Bureau of the Census 1972 through 2000 data, high school completion
rates are up for all racial/ethnic groups since 1972, but the changes since 1982 are not
significant (Hoffman et al., 2003). The rates of high school completion for 2000 are 84
percent, 92 percent, and 64 percent for African American, White and Hispanic students
respectively (Hoffman et al., 2003). Analysis of data from another source indicated
similar trends. Used by the National Center for Education Statistics, the National
Educational Longitudinal Study of 1988 (NELS:88) began with a baseline of 8th grade
students in 1988 and conducted follow-up of these students in 1990, 1992, 1994, and
2000 (NCES, 2004). NELS:88 was designed to collect trend data about the transitions
that students face and to supplement existing testing administered by schools and states
(NCES, 2004). For the initial 1988 sampling, NELS:88 used student, teacher, school, and
parent questionnaires along with four cognitive tests (NCES, 2004). An analysis of the
NELS:88 data by Jacobson et al. (2001) revealed that the gap between African American
and White completion rates had narrowed substantially between 1975 and 1998 from 16
to 6 percentage points (Jacobson et al., 2001). This data included both high school
graduation and the high school completion equivalency exam the GED (General
Educational Development) certificate. An analysis of this data indicates that high school
22
completion is not as large a problem for African American students as it currently is for
Hispanic students.
College Enrollment and Completion
A higher percentage of African Americans attended college or a university in
2000 than in 1980. In 1980, 19 percent of all 18 to 24-year-old African Americans were
enrolled as compared to the 31 percent enrolled in college in 2000 (Hoffman et al., 2003).
Of all high school graduates, the proportion of African Americans enrolled in college
increased from 28 to 39 percent from 1980 to 2000 (Hoffman et al., 2003). Of the total
students enrolled in college, the percent of African Americans, during this same 24-year
period, increased from 9 to 11 percent (Hoffman et al., 2003).
Interestingly the percent of White college and university students declined from
81 percent in 1980 to 68 percent in 2000 (Hoffman et al., 2003). And the percentage of
Hispanic students rose from 4 to 10 percent over the same 20 years (Hoffman et al.,
2003). Comparing the increases in percentage of Hispanic and African American
students, it is apparent that the college enrollment increase for Hispanic students is much
greater that the percent increase of African American students.
The top three declared majors for undergraduate African Americans in 1999-2000
were business management, health related, and other technical fields. For undergraduate
White students, the top three declared majors were listed as arts and humanities, business
management, and social and behavioral sciences (Horn, Peter, & Rooney, 2002). Less
than one percent of the 1999-2000 college students either White or African American
declared a mathematics undergraduate major. Of those who received degrees in 1999-
2000, the top three majors for all students were business management, social and
23
behavioral sciences, and humanities (Bradburn, Berger, Li, Peter, & Rooney, 2003). Of
the Bachelor degrees awarded in 1999-2000, only 1.1 percent and 0.2 percent were given
in mathematics to White and African American students respectively. For those subjects
which rely most heavily on mathematics, physical sciences and engineering, the
percentage of all degrees awarded were low for all students, with African American
students consistently lower in numbers and percent than White students.
The percentage of graduate students in 2000-2001 who listed African American
as their race was similar to the percentage of undergraduate students, 11 percent. More
interesting is the change in percent enrolled in graduate school from 1976 until 2000 as
presented in Table 3 (Snyder & Hoffman, 2003). The proportion of Hispanic students
increased the most during this period whereas the proportion of White students at the
masters degree level declined.
Table 3.
Percentage of Graduate Students, Masters Level by Race/Ethnicity.
1976
2000
African American
6.6
8.2
White 84 68.4
Hispanic 1.9 4.6
(Snyder & Hoffman, 2003)
24
At the doctoral level, there were 2,207 African American students in 2000 as compared to
27,454 White students (Snyder & Hoffman, 2003). The top two fields for all doctoral
students in 2000 were education and psychology with less than 1 in 50 White students,
and less than 1 in 100 African American students studying mathematics. In considering
United States population demographics, it is clear that African Americans are not
proportionally represented at the post secondary academic level, nor in mathematics-
related fields of study, and considering the trends presented and discussed earlier on the
data from elementary and secondary mathematics education, this pattern of African
American student achievement in mathematics at the post secondary level is not
surprising.
Summary of Achievement Trends
While there are positive trends in mathematics achievement for African
Americans in the past 30 years of available statistics, many inequities remain. There is
evidence to suggest that some of the reported gaps in achievement between White and
African American students are not decreasing and in fact might be increasing over the
last 10 years of analysis of NAEP testing results (Strutchens et al., 2004; U.S.
Department of Education, 2005). On extended response type questions, 8th grade African
American students performed about 31 percent as well as White students in 2000, which
was an increase from 20 percent in 1992, and 18 percent and 1996 (Strutchens et al.,
2004; Strutchens & Silver, 2000).
African American students continue to make up larger than expected proportions
of all students who are retained in grades, suspended, or expelled (Hoffman et al., 2003;
Jacobson et al., 2001). More African American students are taking advanced mathematics
25
exams each year. But examining the percentage of students taking these exams who are
African American, the numbers remain constant (Tate, 1997; The College Board, 2005).
Additionally, there had not been an increase in the percent of African American students
scoring proficiently on these exams (Tate, 1997; The College Board, 2005). The
proportion of African American students taking SAT and ACT tests has not changed
appreciably in the last 10 years (ACT Inc., 2003; Tate, 1997; The College Board, 2003).
Although the high school dropout rate for African American students is less than that of
Hispanic students, it continues to surpass the rate for White students (Jacobson et al.,
2001). Perhaps the most positive bit of data is the indication that a larger percentage of
the 18 to 24- year old student population of African Americans was enrolled in college in
2002 compared to 20 years earlier (Hoffman et al., 2003). To summarize, if higher
educational access and national assessment measures such as NAEP are valid measures
of mathematics achievement, then African American students continue to be underserved
by the educational system in the United States.
For the purposes of this study, the question remains: How does all of the above
data relate to the actual classroom performance and mathematics achievement of African
American students. National trends indicate performance differences but do not suggest
how the students themselves are affected by these trends.
Barriers Suggested by Research Which Limit African American Students? Access to
Mathematics Learning
The focus of research has too often been to compare African American students to
White middle class students when measuring achievement (Singham, 1998). Even an
26
examination of the achievement gap between African American and White students
assumes that the standard is what the White students are achieving (Ladson-Billings,
1999). It is clear that caution should be used in ascribing failure or setting standards for
acceptance.
In an attempt to analyze the factors affecting student learning, and determine the
category which has the most potential for change within the education community,
several spheres of influence are offered for consideration. Borrowing from models used
by Weissglass (2002) and Martin (2003), the following spheres of influences, as depicted
in Figure 8, will be considered: community and culture, educational institution, classroom
practices, and finally, student attitudes. Although these spheres of influence are depicted
in Figure 8 as cleanly divided, and non-overlapping; in reality this would not be the case.
The neat division of the spheres, with the exception of culture, are made purely for
organizational reasons. Culture, as interpreted by the author, permeates the other spheres
of influence for the student.
Community
Educational
Institution
Classroom
Practices
STUDENT
Culture
Figure 8. Spheres of Influence on Student Behaviors and Achievement.
First, the focus on the wider community of the student includes issues of parental
influence, peer pressure, culture, and language. The term community is used here to mean
the social, historical, and political influences on the student other than those from the
educational system; therefore, culture will be addressed along with community issues.
Narrowing the sphere of student influence to the institutional practices, the second set of
issues such as course offerings, tracking, curriculum decisions, and funding will be
discussed. Next, specific classroom strategies and resources such as teacher attitudes and
behaviors, assessment practices, resources available, and curriculum implementation will
be addressed.
27
28
Community and Cultural Influences
Caste-like minority theory and rejection of the dominant culture. Community and
cultural influences received much attention from John Ogbu (1986) in his writings on
how minorities react differently to oppression. Ogbu coined the term ?Caste-like
minority? to partially explain why African Americans are less likely to be successful
academically than some other minorities in the United States educational system (Ogbu
& Matute-Bianchi, 1986). Caste-like minorities are those minorities which are
involuntarily and permanently incorporated into a society through slavery or colonization
and then relegated to menial status (Ogbu & Matute-Bianchi, 1986). Immigrant
minorities are those who come to the country voluntarily and respond differently than
caste-like minorities to similar treatment (Ogbu & Matute-Bianchi, 1986). Voluntary
immigrant minorities do not necessarily subscribe to the morays of the dominant culture
and might not internalize the negative effects of discrimination (Ogbu & Matute-Bianchi,
1986). For immigrant minorities, self-advancement is strong enough to overcome the
obstacles imposed on them by the host country (Ogbu & Matute-Bianchi, 1986). For
caste-like minorities, such as Mexican Americans and African Americans, success in
school is not linked to success in life (Ogbu & Matute-Bianchi, 1986). Thus some caste-
like minorities do not respond to the educational system as do voluntary immigrant
minorities (Ogbu & Matute-Bianchi, 1986). Having been historically denied access to
equal education, some African Americans are not prepared to compete for the better jobs,
and for those minorities who do enter the job force, some meet job ceilings, real or
perceived, and because they are African American cannot advance to upper status jobs.
Even for those African American parents who do value education, the reality of their life
29
experiences of being denied opportunities afforded Whites can dampen enthusiasm for
the educational experience for their children, and consciously or unconsciously transmit
these feelings of education being meaningless to their children (Martin, 2000). Children
might interpret their parent?s lack of involvement in school events as telling them that
education and mathematics is unimportant. Community responses to school experiences
can have a negative or a positive impact on student beliefs about school and mathematics.
Martin (2000) argued that community forces have as much or more influence on student
achievement as societal or school influences. Delgado (2000) stated that racial
stigmatization can negatively impact parenting practices of minorities to the point that
tradition of failure is perpetuated. Possible behavior responses range from feelings of
isolation, humiliation, and self-hatred to psychological effects as severe as mental illness
and physical illnesses such as high blood pressure (Delgado, 2000).
Negative peer pressure. According to Ogbu and Matute-Bianchi (1986), caste-like
minorities seek to establish an identity separate from the dominant group, developing a
collective distrust described as ?cultural inversion.? Cultural inversion refers to a set of
practices for the minority which is oppositional to the dominant group and employed as a
strategy for demonstrating this opposition (Ogbu & Matute-Bianchi, 1986). Cultural
inversion also implies a rejection of some behaviors as not acceptable for their group
because they are characteristic of Whites (Ogbu & Matute-Bianchi, 1986). As an
example, being successful in school is synonymous with ?acting White? for some African
American students (Fordham, 1988; Kunjufu, 1988). By examining several successful
African American students, Fordham (1988) found that these students had assumed a
raceless persona in order to achieve academic success, that is being African American
30
while rejecting the ethos of the African American community. The students in Fordham?s
two year study, 1982-1984, responded in several different modes of racelessness. The
female participants adopted an attitude of isolation, dropping their friends and dropping
selected activities which were usually attributed to members of their community, whereas
the male students generally chose to remain with their peers, keeping their academic
successes hidden, and rejecting the upper academic tracts. Fordham (1988, p.80)
maintained that to be academically successful, these students must internalize their
oppression and appear to become raceless. While recognizing that the males and females
in the study differed considerably in their reactions, Fordham (1988) labeled both as a
form of raceless behavior adoption.
Steele (1995) used the term ?stereotype threat? to identify a behavior response for
those students who value academics. Recall the study by Steele and Aronson (1995,
2004) where African American students responded with performance at a lower level
than they were capable of when they internalized the stereotypes that permeated their
culture. This self-condemnation contributes to students demoralization, and with
continued threat over time, students might disidentify with school achievement (Ladson-
Billings & Tate, 1995b; Steele & Aronson, 1995). Thus some forms of peer influence can
be oppositional to academic achievement for African American children (Fordham, 1988;
Kunjufu, 1988; Martin, 2003; Ogbu & Matute-Bianchi, 1986).
Cultural capital. While acknowledging that Ogbu?s (1986) caste-like minority
theory has merit for explaining some of the current academic status of African
Americans, Perry (2003) argued that Ogbu?s theory does not take into account the
positive cultural traditions. Perry (2003) stated that African Americans have a strong and
31
powerful academic tradition of freedom for literacy, and literacy for freedom, racial
uplift, citizenship and leadership. Those who follow Ogbu?s caste-like minority theory
completely might be tempted to place the blame for student failure on the African
American parents and the community.
Instead of focusing on the failures of African American children in school,
perhaps the real question should be: How have so many African Americans become
successful facing so much opposition? For African American minorities, the task of
academic achievement is distinctive (Perry, 2003). These distinctions include dealing
with racism, cultural behaviors which cause misunderstanding, irrelevant curriculum,
inappropriate pedagogy, tracking and other school issues which limit educational access.
Citing cultural mechanisms of behavior and language patterns, Perry (2003) maintained
that some African American students do not speak or act as Whites, and these cultural
differences create misunderstandings.
Adapting to the dominant culture appears, in many instances, to be a precursor to
skill acquisition in the American educational system (Perry, 2003). For example, Perry
(2003) described the 1978 case of Martin Luther King Jr. v. Ann Arbor School Board.
Two-thirds of the children from the local housing development and attending the Martin
Luther King Jr. school were labeled learning disabled by the school (Perry, 2003). None
of the fifteen plaintiffs, children up to age eleven, could read above the second grade
level. It was determined that the barrier denying the children access to learning was
language. Perry (2003) defined African American English as a distinct, rule-based
language which is culturally based with different discourse rules than standard American
English. The discourse rules can be problematic for children when they involve different
32
ways of asking questions, expressing emotions, and exercising control. Therefore, while
non-standard English is not a barrier to education for African American children in itself,
the problem results from teacher reaction and responses to the non-standard English
(Perry, 2003).The children?s home language in the case of Martin Luther King Jr. v. Ann
Arbor School Board was African American English not standard English. Not only did
the school not acknowledge African American English, but the teachers did not have the
training to understand the language differences. The teachers equated African American
English with being learning disabled. The point is that not only was there a mismatch
between the minority and dominant cultures, but that students first had to adapt to the
dominant culture before they could receive learning skills. Cultural capital is the term
Perry (2003) used, borrowing from French social theorist Bourdieu, to mean the socially
inherited cultural competence that facilitates learning in school. To Bourdieu, capital
meant simply a resource that yields power (Calhoun, 1993).
In addition to language differences, cultural capital can include social behaviors
that are inherited and learned through an individual?s culture (Perry, 2003). For example
there are some African American communication styles which can influence a teacher?s
judgment about the student?s intellectual capacities when the teacher does not understand
cultural differences (Perry, 2003). An African American student might sound loud and
argumentative to the teacher by merely voicing his/her opinion. Perry (2003)
hypothesized that the cultural capital offered by whiteness includes the ability to be
reserved, suppress emotions, and present a disciplined exterior while for some, to be
African American is to be lazy, criminal, emotional, rebellious, and disrespectful of
authority. If one accepts that schools transmit knowledge in cultural and linguistic codes
33
then those who know the codes before attending school will out-perform those children
who do not know the codes (Perry, 2003).
Summary of community and culture. In summary, community cultural influences
conflict with goals for academic success for African American students according to
Ogbu & Matute-Bianchi (1986), Martin (2000), and Fordham (1988). While for Perry
(2003) and Singham (2003) the conflict arises from misunderstandings of cultural
differences. Fordham (1988) maintained that for African American students to be
academically successful, some feel they must assume a raceless persona, but Singham
(2003, p. 587) argued that African American and White students share similar social
costs and benefits of academic success. Therefore, Singham (2003) cast doubt on the
negative peer pressure theory. One might hypothesize that whether you subscribe to
Ogbu?s (1986) caste-like minority theory, Perry?s (2003) theories on cultural capital
acquisition, or Fordham?s (1988) raceless adaptation mechanisms, race plays a major role
in all of United States society and especially in educational institutions (Ladson-Billings,
1999; Martin, 2003).
Racism
Ignatiev (1996), Lopez (2000), and others have asserted that Whiteness is a social
construction and not a natural one. Greater genetic variation exists within populations
labeled as African American or White than between these populations (Lopez, 2000). The
racial spectrum in the United States is White on one end and African American on the
other, with all other races in between (Ignatiev, 1996; Perry, 2003). Racism supports the
notion that the traits and abilities of Whites is the admirable or correct end of the
spectrum and as such, where does that leave all the ?others?? W.E.B. Du Bois described
34
the difficulty of being African American in 1898 as a balancing act, a double
consciousness (Perry, 2003). African Americans must perform this balancing act by
trying to function as members of society and as outsiders: citizen without the rights and
privileges of full citizenship (Perry, 2003).
Racism is the most prevalent theme that African Americans must face in
educational access and is cited directly by Ladson-Billings (1999), Martin (2003), Perry
(2003), Singham (1998), and Weissglass (2002). Whiteness as a social construction is not
a natural one, and Whiteness is in opposition to Blackness (Ignatiev, 1996). Just as
racism is pervasive in our society, so is the notion for some that being African American
means inferior intelligence (Perry, 2003). A high school teacher told Malcolm X that
being a ?nigger,? he could not expect to become a lawyer: rather he needed to be realistic
in his life goals (Perry, 2003). Malcolm?s response to this prejudicial behavior was to
reject Whites and schooling altogether, possibly a cultural inversion tactic which he later
regretted. Gwendolyn Parker met a similar response from an English teacher, but reacted
differently from Malcolm X (Perry, 2003). When her family moved from the segregated
south to the integrated north for better educational opportunities, they met school
personnel who did not believe that a person of color could perform on the same level as a
White person. Gwendolyn?s English teacher accused her of plagiarizing a poem she
wrote, stating that a ?Negro? could not have possibly written something that good (Perry,
2003). Her response was the opposite of Malcolm?s, Gwendolyn set out to prove that
being African American was not being intellectually inferior. Perry (2003) asserted that
African American students need to have support from their community to overcome the
negative forces which they face in school and society. Malcolm X and Gwendolyn Parker
35
are only two examples of what many more African Americans have faced at some point
in their lives. If being smart is oppositional to being African American, and African
American children are faced with these attitudes and responses from others daily, weekly,
and yearly, then how can we equip these children to handle this and persevere?
Educational Institution
To discuss this overview of research, the following are included under educational
institution: school issues and reports such as dropout, suspension, retention rates; school
population descriptions as pertaining to socioeconomic factors; course-taking patterns
and tracking; and high stakes testing. Many of these issues are credited with affecting
student learning. The school population can be described in terms of racial/ethnic and
socio-economic status as measured by free or reduced lunch participation. Data from
NAEP gives some insight into classroom experiences, as reported by the students, in
instructional time, homework assigned, types of assessment, and type of courses taken. In
surveys conducted by the U.S. Census Bureau, one can find data relating to grade
retention and school suspension or expulsion as reported by racial groups.
Socioeconomic factors. Low mathematics achievement patterns typically begin in
the early school years and are often associated with poverty (Oakes, 2002). Children of
poverty fail in disproportionate numbers (Singham, 1998). There is evidence supporting
this, as well as evidence that African American children are disproportionately
represented in the lower socioeconomic classes and schools (Strutchens et al., 2004).
Because most states fund schools based on property tax, the better funded schools tend to
be in the higher priced neighborhoods. Ladson-Billings (1999) maintained that this
school level inequality is another form of institutional and structural racism. Evidence
36
from the 2000 National Assessment of Educational Progress indicated that 34 percent of
African American versus 3 percent of White students attend schools in which over 75
percent of the students qualify for free or reduced lunches (Strutchens et al., 2004). Most
African American students attended public schools where minorities represent the
majority of the student population in 1999 (Hoffman et al., 2003). Of African American
4th grade students, 73 percent attended schools where more than half the students receive
free or reduced lunch costs (Hoffman et al., 2003). Poorer schools provide fewer
resources for the children, attract less qualified teachers, and serve a disproportionate
number of African American students (Roscigno, 1998).
It is important to note that African American students score lower on standardized
mathematics tests even when controlling for socioeconomic status (Singham, 2003;
Strutchens et al., 2004). However instead of addressing racism, many educators ascribe
educational success to socioeconomic factors, and in doing so, they are putting the blame
on the students and their families (Rousseau & Tate, 2003). By blaming the students and
their families, the social and economic injustices perpetuated by schools have been
avoided instead of addressed.
High stakes testing. Attaching high stakes, such as graduation, grade retention or
track placement, to achievement tests can disadvantage those who do not have the
training to be good test-takers or a chance to learn the material ahead of time (Edley,
2002; National Research Council, 2000). In 1972, Moses v. Washington Parish School
Board, the supreme court ruled that using standardized tests for track placement
disadvantaged African Americans and denied these children their educational benefits,
therefore established as unconstitutional (Tate & Rousseau, 2002). By placing African
37
American children disproportionately in the lower tracks, they were experiencing inferior
education as compared to the academic tracks (Oakes, 1994a, 1994b). The National
Council of Teachers of Mathematics issued a position statement on high stakes testing in
2002, making two critical arguments against testing which is tied to promotion,
graduation, course credit, or placement in special groups. First, tying a single assessment
to a crucial decision about a child?s future is unfair, inaccurate, and not aligned with
movement toward equity or equality (National Council of Teachers of Mathematics,
2002). Secondly, attaching inflated importance to any high stakes test can cause the
curriculum and instructional methods to become narrowly defined to follow the
objectives of that test (National Council of Teachers of Mathematics, 2002; Schoenfeld,
2002). Schoenfeld (2002) claimed that a large part of a test score reflects the preparation
that the student has undergone, not what the student actually knows, or what the test
purports to measure. The important decisions made with serious consequences for a child
should encompass multiple means of assessment (National Council of Teachers of
Mathematics, 2002).
Tracking. Tracking is a form of segregation (Tate & Rousseau, 2002). Because
schools decide who takes what classes and what classes are offered, tracking is one of the
principal barriers to academic access in American schools. Tate & Rousseau (2002)
found tracking to be a primary barrier to academic access in American schools, yielding
mixed results on the relationship between track placement and race in a number of
studies. An explanation for these mixed results was offered by Oakes (1994a, 1994b)
who claimed that the large scale assessment tools mask the subtleties found by examining
the racial make-up of the school. Oakes (1994a, 1994b) and Useem (1992) argued that
38
the mixed results were the result of the differences in racial makeup of the school
districts, for example, an African American student in the top track of a minority school
would not necessarily be assigned to the top track in a predominantly White school.
Wells and Oakes (1996) found in 1994 that the racial placement patterns varied
dramatically by school. Through teacher interviews, Wells and Oakes (1996) learned that
the teachers studied equated race with intellectual potential and made recommendations
aligned with their beliefs. Additionally, parents with political and social power are the
ones who can work the system for their children, insisting that their children receive
something extra from the school (Wells & Oakes, 1996). Pushing the school to enroll his
or her child in more advanced classes takes a self-confident person, and parents with
higher levels of education have been linked to involvement with their child?s placement
(Useem, 1992). This means that the best educational assets will remain beyond the reach
of all but the ?chosen few? who were placed by birth on the top of our stratified social
system (Wells & Oakes, 1996).
Tracking is the post Civil Rights form of segregation (Tate & Rousseau, 2002).
The supreme court of the United States decided in Hobson v. Hansen (1967) that African
American children in the Washington D.C. school system were placed in the lower tracks
in disproportionate numbers (Tate & Rousseau, 2002). While one would hope that better
qualified teachers and higher quality instruction would join forces in the lower tracks
where supposedly the students need more help, this is not what actually takes place.
Oakes (1994a, 1994b) found in her studies that the higher mathematics tracks had the
more qualified teachers, more resources and an overall better learning environment
(O'Neill, 1992). Similar findings were reported in 1998 by Roscigno. In the lower tracks
39
the teachers were less qualified and held lower expectations of achievement for their
students (Roscigno, 1998). Oakes (1994a, 1994b) claimed that the type of instruction
typically found in the low level tracks can make knowledge less accessible to students.
This instruction typically includes drill and practice, worksheets, as well as instructor-
student interactions which are quiet and few; in other words, not the type of instruction
recommended for students who are having difficulties in school (Oakes, 1994a, 1994b;
O'Neill, 1992).
High school course taking. Tracking in the elementary grades determines what
courses the student takes in high school. A child who is placed in a low level track early
in her school career cannot hope to complete high school having taken the higher level
college preparatory mathematics classes (Spade, Columba, & Vanfussen, 1997). Parents
from higher socioeconomic classes are more involved in determining which classes
students take, whereas in schools where mostly working class children attend, the
decision is contained within the guidance department (Spade et al., 1997). Course-taking
matters (Gutierrez, 2000; Strutchens et al., 2004; Tate & Rousseau, 2002). African
American students are less likely than White students to take advanced mathematics
courses in high school (Hoffman et al., 2003; Strutchens et al., 2004). White students are
more likely to take algebra in the eighth grade and geometry in the ninth (Strutchens et
al., 2004); therefore, White students are more likely than African American students to be
on the college preparatory track to take calculus or other college preparatory mathematics
courses in high school.
While African American students high school graduates completed more
academic courses in 1982 than in 1992, the total credits for these African American
40
students lagged behind their White peers (Hoffman et al., 2003). The number of
vocational credit totals for African American students was higher than the number of
vocational credits for White students in 1998 for graduating students (Hoffman et al.,
2003). African American students earned about the same number of academic credits as
Hispanic students in 1982 as in 1998 (Hoffman et al., 2003).
Challenging and relevant curriculum. A challenging curriculum has been linked
to the mathematics achievement of students (Gutierrez, 2000; Lee & Smith, 1993, 1995a,
1995b; Lee et al., 1997; Schoenfeld, 2002). Perry (2003) insisted that African American
students who do not have a challenging curriculum will not only be shortchanged, but
will believe that those who selected this curriculum think that they are not as capable as
other students. Encouraging students by telling them they are smart and then offering
them a watered down curriculum does not indicate to the students that you have faith that
they are actually capable (Perry, 2003). One successful program offering students a
challenging mathematics curriculum is the QUASAR project, an educational reform
project aimed at economically disadvantaged middle school students (Silver & Stein,
1996; Tate & Rousseau, 2002). The project established partnerships between selected
middle schools in various cities and local colleges and universities, and these partners
worked together to address the needs of their students (Williams & Baxter, 1997). One of
the purposes of QUASAR was to use challenging mathematical tasks to engage students
and to help their understanding. The results for those students who participated in this
project have been very promising with many of them taking and passing algebra in the
ninth grade at higher rates than before the project (Tate & Rousseau, 2002).
41
On the high school level the Interactive Mathematics Program (IMP) provides
students with a challenging and integrated mathematics curriculum. Comparative
evidence from several studies indicated IMP students completed more years of high
school mathematics, took more advanced mathematics classes in high school, and scored
as well as or higher on the traditional standardized tests than did the students enrolled in
traditional college preparatory mathematics classes (Merlino & Wolff, 2001; Webb,
2003). IMP content, which differs from the traditional college preparatory mathematics
classes, includes an increased emphasis on statistics and probability, and helping students
become more effective at problem solving. When IMP students are compared with other
students on problem solving, probability or statistics, the IMP students outperform the
students from the traditional mathematics classes (Webb, 2003).
In addition to being challenging, the content must be relevant to the students out-
of-school life (Martin, 2003). For a student to learn new mathematical ideas, they must be
able to relate it to previously learned material (Heibert & Carpenter, 1992). The degree of
understanding that a student has is directly related to the number of connections the
student can make with their own knowledge and personal experiences (Heibert &
Carpenter, 1992). The culture of the student structures the learning environment so that
relationships between in-school mathematics and out-of-school knowledge are
strengthened. Students who do not see a connection between what they are learning in
school and what skills are needed for their life goals will likely have little motivation for
continuing to attend to their education (Carey, Fennema, Carpenter, & Franke, 1995).
Schools should help students develop the skills they need to analyze the social
injustices that they encounter (Sleeter, 1997). Frankenstein (1995) argued that
42
empowering students mathematically requires teachers to include a component of
investigating socioeconomic class issues in their curriculum. To challenge inequitable
practices, one has to understand them. For example, suppose the working class person
understood percentages and that the tax burden faced by them is much greater than that
faced by the richest Americans (Frankenstein, 1995). Frankenstein (1995) found that
most working class people do not have the time to reflect and analyze when they are just
getting by and that it is the responsibility of educators to enable this analysis.
Supportive environment and addressing racism. Gutierrez (2000) analyzed
several high schools which were effective in teaching minority students and found that
common components were a rigorous curriculum, reform-oriented instructional practices,
and a strong teacher collective believing in and committed to mathematics success for all
students. These schools had administrative support, particularly department chairs, who
were committed to and supportive of a teacher collective (Gutierrez, 2000). There was no
evidence that these teachers helped their marginalized students address racism and
become critical of social issues, rather the goal appeared to be assimilating the students
into mainstream mathematics (Gutierrez, 2000). Furthermore, Gutierrez (2000) wondered
what more these schools could have accomplished for their minority students beyond
academic advancement if the collective goal had included critical thinking of social
issues and inequalities.
Perry (2003) used the term ?racial socialization? for the process of preparing
children to deal with racism and other obstacles that they might face in school. The
playing field is not always equal, and letting children know how to persevere is essential
to empower them for society. To develop strong intellectual identity among African
43
American students, Perry (2003) suggested using a model such as one developed by the
Association of Independent Schools, called the Multicultural Assessment Plan. Perry
(2003) explained that the Multicultural Assessment Plan is an external review process in
which schools are assessed on whether they reproduce the ideology of African American
intellectual inferiority, and how schools can address this issue and move in another
direction. Several schools in the Northeast have successfully used this plan to change the
direction of their schools to a more supportive environment. African American students
need affirmation that their racial heritage is synonymous with being intellectual and an
achiever (Perry, 2003). Weissglass (2002) also argued that the racist practices in schools
can be alleviated through a complex process of reflection and re-evaluation of existing
practices and understanding. Furthermore, it is suggested that the new paradigm for our
schools should be one of a healing community, and that it is our responsibility as
educators to heal ourselves from the damage that racism has done (Weissglass, 2002).
Reform efforts attempting to reduce the achievement gap which do not address
racism/classism will be doomed to failure (Weissglass, 2002).
Banks (1993) argued that for education to be effective for marginalized
populations, students should be taught that knowledge is culturally and situationally
constructed. Students should be afforded the opportunity to explore these biases and
cultural assumptions that influence knowledge construction, for example, consider how
the Eurocentric paradigm reproduces the notion that Columbus discovered America
ignoring the indigenous population and their claim to the land (Banks, 1993; Ladson-
Billings, 2003).
44
Classroom Practices
While teacher-student interactions may be the most influential factor in student
achievement for classroom practices, there are other factors in the classroom which can
also exist as barriers to mathematics achievement for African American children
(Singham, 2003). Some of these include irrelevant curriculum, lack of resource materials,
types of assessment, teacher attitudes and beliefs, and instructional practices which do not
match the learning style of the student (Tate & Rousseau, 2002).
Classroom resources. In resource materials, the argument might be made that the
implementation of available resources is at least as important as the amount and type of
materials available (Schoenfeld, 2002). If one accepts this, then the available data does
not tell us much about whether or not resources might be a barrier to achievement for
African American students. Results from NAEP 2000 indicated that even when
accounting for socio-economic status, African American students are less likely to have
teachers who report having all or most of the resources that they need (Strutchens et al.,
2004). For instance, African American students are less likely to have access to
calculators, and calculator access does correlate positively with mathematical proficiency
(Strutchens et al., 2004). African American students are equally likely as White students
to have access to and use of computers, although how the computers are used for
instruction differs by the race of the student. More teachers of African American students
reported using computers for drill and practice as opposed to simulations or
demonstrations of concepts (Strutchens et al., 2004). Recall additionally that African
American children are disproportionately assigned to lower tracks in mathematics and
that students in the lower tracks have access to fewer resources and usually poorer quality
45
of instruction (Oakes, 2003). Again the author hypothesizes that implementation of the
curriculum and resources may be more important for student achievement than the
accessibility of the resources.
Curriculum implementation. While teachers do not often have the option of
selecting the mathematics curriculum, teachers do have options in implementation of the
selected curriculum. Ladson-Billings (1999, p. 21) described the curriculum in stark
terms, with its distortions, omissions, and stereotypes, as a cultural artifact designed to
maintain a White supremacist master script. For example, Rosa Parks is usually portrayed
as a tired seamstress instead of a longtime participant in social justice endeavors, and
Martin Luther King, Jr. is portrayed as a sanitized folk hero supported by all Americans
instead of the disdained scholar and activist that he was (Ladson-Billings, 1999). One
might argue that in mathematics class, this misrepresentation would not take place, as
mathematics is supposedly culture-free. Weissglass (2002) disavowed this notion in his
report of a popular 1998 eighth grade mathematics textbook. In an attempt to situate
mathematics in history and give meaning to mathematics, the textbook misrepresents the
indigenous people of California and the events surrounding the acquisition of California
from Mexico (Weissglass, 2002). The societal, structural status quo is maintained by a
curriculum which distorts the facts and encourages the acceptance of students? relative
oppressed positions (Weissglass, 2002). Teachers mediate and interpret curriculum
materials for students (Banks, 1993). Additionally, there is evidence that textbook
publishers will avoid putting controversial issues, such as racism, classism, and poverty,
in their books for fear of losing sales to school districts (Banks, 1993). So even if teachers
do not have input in selecting the course objectives and textbooks, they can and should be
46
aware that repeating stereotypes and distortions disadvantages learning for many
students; and the curriculum should be carefully examined for distortions.
Implementation of the curriculum might be as important as the curriculum itself
(Schoenfeld, 2002). Assessing the results of a successful standards-based reform effort in
Pittsburgh schools, Schoenfeld (2002) noted the differences between teachers who
implemented the curriculum in the manner intended with those who had a weak
implementation. For those students who were in classes with a strong implementation of
this curriculum, achievement scores rose, and the gap between White and African
American students decreased (Schoenfeld, 2002).
Another program, Cognitively Guided Instruction (CGI) was developed by
researchers at the University of Wisconsin under the premise that if teachers increased
their understanding of how students learned, then their teaching practices would become
more effective (Carey et al., 1995; Tate & Rousseau, 2002). Research studying the effects
of CGI summer training for teachers found that teachers who changed their
implementation methods by focusing on more problem solving improved the
mathematics achievement of their largely African American student population (Tate &
Rousseau, 2002). Improved teaching practices coupled with higher level task
requirements of their students result in better student performance (Schoenfeld, 2002).
Assessment strategies. Assessment strategies used for evaluation are another area
of the mathematics classroom which can disadvantage the African American child. The
type of assessment can favor a particular individual because of the cultural practices
which it incorporates (Weissglass, 2002). For example, timed tests and multiple choice
tests advantage those students who have learned particular test-taking strategies.
47
Strutchens et al. (2004) found that African American students are more likely than White
or Hispanic students to take multiple choice tests. And the more often a student reported
having been assessed with multiple choice tests, the lower their mathematical proficiency
score (Strutchens et al., 2004).
The test taking environment can also work to the disadvantage of some students
by causing different levels of anxiety (Weissglass, 2002). Steele and Aronson (1995)
found that African American students scored much worse on a standardized test when
informed that the test was evaluating their intellectual abilities. When the same test was
presented as a non-evaluative problem-solving test, African American students performed
about as well as White students who had equivalent performance records (Sackett,
Hardison, & Cullen, 2004; Steele & Aronson, 1995, 2004). Steele and Aronson (1995)
termed this phenomenon ?stereotype threat,? whereas Weissglass (2002) used the term
?internalized oppression? for the phenomenon where people believe the messages that
they receive about themselves from society.
Ladson-Billings (1999) argued that traditional assessment measures tell us what
the child does not know but do not tell us what the child does know. She included an
example of a 10-year-old African American girl labeled as a poor math student by her
teacher. This child was responsible for all of the household budgeting and bill paying in
an attempt to keep the welfare agent unaware of problems within the household.
Apparently the girl?s mother was incapable of maintaining the home due to a drug
addiction problem. A girl who could not do fourth grade math was doing fine keeping the
household going. The mathematics that the teacher was assessing was not the
mathematics that the student could do, and some might argue, not the mathematics that
48
the student needed. Traditional assessment methods are a method of maintaining the
inequitable power structure (Weissglass, 2002).
Teacher beliefs, differential treatment of students, and culturally relevant
teaching. In education, the immediate point of contact and influence for students and
their educational achievement is the teacher and what occurs within the classroom.
Studies conducted in the 1990s indicated that teacher beliefs, expectations, and
stereotypes play a role in maintaining the inequitable status of the classroom (Gutierrez,
2000; Levy, Plaks, Hong, Chiu, & Dweck, 2001). Teacher attitudes and beliefs influence
how the teacher responds to the students (Levy et al., 2001). For many teachers,
instructional practices presume that the African American child is deficient (Ladson-
Billings, 1999). Historical narratives from several African Americans consistently
include instances in which students are bluntly or subtly told that they are not capable
because of their race (Perry, 2003). Differential treatment of students is one of the results
of teachers connecting race, gender, or ethnic group to the intelligence of the individual.
Students in the same room, using the same materials, with the same teacher, have very
different learning experiences based on differential treatment from the teacher (Sadker &
Sadker, 1986). Perry (2003) asserted that many people stereotype African Americans as
having inferior intellect. If this belief is held by teachers, then teachers would
automatically expect less of African American students, possibly interact less with these
students, or recommend that African American students be place in lower tracks. Lower
track placement can result in instructional methods and resources limiting mathematics
skill acquisition (Oakes, 2002). Differential treatment patterns of students exist for
49
whatever reason and African American children seem to be shortchanged in teacher
interactions.
Color-blindness on the part of the teacher is a form of dysconscious racism
(Ladson-Billings, 1994). Probably unintentionally, this form of racism indicates that the
teacher is unaware of the fact that she created an environment where some children are
privileged while others are disadvantaged (Ladson-Billings, 1994; Rousseau & Tate,
2003). Teachers who claim not to notice the race of their students and purport to treat all
students the same might be suffering from this form of racism. Color-blindness ignores
students? important features and makes students wonder if they should be ashamed of
their color (Rousseau & Tate, 2003). Teachers who do not address the issue of racism
with their students, are not empowering their students to effectively confront racism in
society (Martin, 2003; Rousseau & Tate, 2003). Marva Collins and Jaime Escalante are
two teachers who practiced a method of addressing racism with their students (Ladson-
Billings, 1995). They reminded their students that society expected them to fail, and as
such, the students had to work even harder to overcome this oppression and be
successful. Teachers can empower their students to confront racism in society through
examples, discussions, and research.
Sleeter (1993) argued that the race of the teacher matters; not only are African
American teachers generally more effective for African American students, but it is
inadequate to address racism by educating White teachers on equity issues. The school
population is increasingly diverse, while the teacher population continues to be
predominately White. Sleeter (1993) argued that while multicultural education improves
White teachers? attitudes immediately after receiving instruction, there are no lasting
50
changes. From 1987 through 1989, Sleeter (1997) studied the impact of professional
development on 30 teachers from 18 schools. The study involved observing the training
sessions, interviewing the teachers, and making three to five classroom observations over
one and a half years. Other than increasing cooperative learning classroom time, Sleeter
(1997) reported that the teachers studied did not sustain the benefits of their professional
development as it was intended. Furthermore, Sleeter (1993) argued that teachers give
one or two different explanations as to why students of color are not as successful as
White students. Either teachers deny race altogether or they define students of color as
?immigrants.? Furthermore, by denying race, teachers are trying to suppress the negative
images that they attach to those of other races (Sleeter, 1993).
In her book Dreamkeepers, Ladson-Billings (1994) contradicts Sleeter?s (1993)
assertion that African American teachers are the only teachers who can effectively teach
African American students. Ladson-Billings (1994) described successful teachers of
African American students who are not African American themselves. Ladson-Billings
(1994) used the term ?culturally relevant pedagogy? to describe the kind of teaching that
is needed to ensure success for the disadvantaged child. The culturally relevant teacher
has the following characteristics. First, the teacher sees knowledge as changing and must
be viewed critically, not accepted at face value but examined for misrepresentations,
stereotypes, and omissions (Ladson-Billings, 1994). Secondly, teachers help the student
acquire prerequisite skills rather than expecting them to come to class equipped with
them. Additionally, culturally relevant teachers are passionate about content and
encourage students to learn collaboratively (Ladson-Billings, 1994). In the classroom the
teacher develops a community of learners where students are respectful and responsible
51
for each other. The culturally relevant teacher believes that all students can succeed, and
it is her job to help the student make connections to the community, the nation and the
world (Ladson-Billings, 1994). Maintaining the status quo is not a goal for this teacher,
but teaching goals do include achieving excellence and access. Sleeter (1997) used
similar categories to describe a good multicultural teacher, one who is effective with
minority students.
Ladson-Billings (1997) believed that the best chance for changing the success
rates of African American students is through changing teacher practices. In her book,
Dreamkeepers, Ladson-Billings (1994) observed and interviewed several successful
teachers who model what Ladson Billings described as culturally relevant teaching.
Margaret Rossi is one the teachers described in Dreamkeepers (Ladson-Billings, 1994,
p.119):
From a pedagogical standpoint, I saw Margaret make a point of getting
every student involved in the mathematics lesson. She continually assured
students that they were capable of mastering the problems. They cheered each
other on and celebrated when they were able to explain how they arrived at their
solutions. Margaret's time and energy were devoted to mathematics.
Margaret moved around the classroom as students posed questions and
suggested solutions. She often asked, "How do you know?" to push students'
thinking. When students asked questions, Margaret was quick to say, "Who
knows? Who can help him out here?" Margaret helped her students understand
that they were knowledgeable and capable of answering questions posed by
themselves and others?
All of Margaret's students participated in algebra, even though it was
beyond what the district's curriculum required for sixth grade. Margaret
scrounged an old set of algebra books from the district's book closet and
exempted no one from the rigors of the class. One of Margaret's students was
designated a special needs student. However, Margaret determined that with a few
accommodations the student could remain in the classroom and benefit from her
instruction. James performed well in the classroom. He participated in class
discussions, posed problems as well as solved them, and accepted help from
classmates when he struggled. By the end of the year, Margaret had convinced the
principal that James had no need for services outside the classroom.
52
Contrast this description of Margaret?s class with that found in a typical
mathematics classroom where maintaining order and control is the teacher?s focus.
Effective teachers help students make mathematical connections in contexts that they
know and understand. School mathematics cannot be divorced from what students
experience everyday (Ladson-Billings, 1997). Furthermore, directive, controlling
classrooms appeal to teachers who have low expectations for or who fear children of
color or poverty (Ladson-Billings, 1997). A dysfunctional curriculum in combination
with a lack of instructional innovation will result in poor performance for some minority
students, especially African American children (Ladson-Billings, 1999).
Tate (1997), Rech and Stevens (1996), Sleeter (1993), Berry (2003), and Ladson-
Billings (1994, 1997) addressed the learning styles of children and effective teaching
practices. Tate argued that the traditional mathematics classroom emphasizes whole class
lectures followed by students working alone on large problem sets or workbooks/sheets.
This instructional practice is a cultural artifact, a default cultural policy which is designed
to produce students who can correctly answer a set of narrowly defined problems (Tate,
1997). Similarly Rech and Stevens (1996) found a statistically significant correlation
between learning styles, gender, and achievement of the African American eighth graders
in their study. Interestingly, for fourth grade African American students the correlation
was not as strong, but the variables which correlated were mathematics attitude,
socioeconomic status, and achievement (Rech & Stevens, 1996). The learning style of the
majority of the students tested was described as field dependent and oppositional to the
manner used by most teachers. Field dependent learning styles include the use of
manipulatives, verbalization, and a global perspective (Rech and Stevens, 1996). Berry
53
(2003) described the learning style of most African American students as a relational
style of learning. A relational learning style is characterized by divergent thinking,
freedom of movement, variation, creativity, and inductive reasoning with a focus on
people (Berry, 2003). African American students prefer to use concrete imagery and base
learning on making holistic connections between items and ideas (Berry, 2003). The
learning style of the mathematics classroom is typically analytical, in which object
relations are approached in a logical, diagnostic, impersonal fashion (Berry, 2003). While
urging teachers to adopt culturally relevant teaching practices, Berry (2003) also warned
of ethnic stereotyping: all African American students do not prefer or benefit from
teaching practices recommended for relational or field dependent learners.
Empowering traditionally underserved students is a primary theme of Ladson-
Billings (1994, 1995, 1997, 1999, 2003), Schoenfeld (2002), Perry (2003) and others.
Empowering students goes beyond matching teaching practices to learning styles. The
teacher is the primary contact person for children in school and can impact positively a
child?s self confidence and desire for learning. There are many examples of teachers who
empower their students with relevant mathematics. Assigning his students a project on
housing costs, mathematics teacher Gutstein (Martin, 2003) required students to use
mathematics to examine housing costs to determine whether or not there was evidence of
racism.
Gutierrez (2000) found some encouraging results from her study of several
successful high schools. Selecting several high school mathematics departments which
were chosen based on their success with their working class and ethnically diverse
students, Gutierrez (2000) correlated the organizational structure of the mathematics
54
department with student achievement over a six year period. School site visits were
conducted in 1994 where observations and interviews were conducted, questionnaires
were administered, and school documents were examined (Gutierrez, 2000). While not all
teachers within the departments were on board with the reform practices being used in the
schools, Gutierrz (2000) noted several interesting phenomena. Teachers who did not
believe that students would respond to reform-oriented classroom practices were
surprised by how much their students achieved (Gutierrez, 2000). These teachers adopted
the teacher practices that were implemented collectively in their school before buying
into the practices, but the results were so impressive that the teachers became believers in
the practices. None of the teachers adopted practices aimed at confronting social
inequalities and injustices, but because they did adopt reform-oriented practices such as
rigorous curriculum, cooperative learning, and use of manipulatives their students
experienced success (Gutierrez, 2000). The conclusion is that teachers can be taught how
to be more effective in the classroom without their buying into the ideal, and with more
successful students, the teachers will become believers.
Ladson-Billings (1994, 1997), Berry (2003), Sleeter (1997), Tate (1997), and
Schoenfeld, (2002), Lee and Smith (1993, 1995a, 1995b,1997), and Gutierrez (2000)
gave convincing arguments that effective teaching styles and standards-based curriculum
can make a difference in mathematics learning. Results from several standards-based
reform curriculum implementations in Pittsburgh, Michigan, Philadelphia,
Massachusetts, and other locations indicate that a well-designed standards-based
approach appears to work (Berry, 2003; Schoenfeld, 2002). Not only did more students
do well, but the racial performance gap, although not eliminated, was reduced.
55
Student Attitudes
Kim (1998) found that the attitudes of the students towards learning mathematics
appeared to be a major factor in determining achievement for African Americans as well
as Whites although this study used data collected in 1981-1982 for the Second
International Mathematics Study (Kim, 1998). Similarly and more recently, Rech and
Stevens (1996) found that the strongest predictor of mathematics achievement for fourth
grade students in their study was their attitude about mathematics. Rech and Stevens
(1996) administered standardized tests to 251 fourth and eighth grade students from city
schools with largely African American student populations. The standardized instruments
used were the California Achievement Test to measure mathematics achievement, the
Mathematics Attitude Inventory to measure attitudes towards mathematics, the Group
Embedded Figures Test to measure learning style in terms of field dependence; and the
Piers-Hams Children?s Self Concept Scale to measure the self-concepts of students (Rech
& Stevens, 1996). Rech and Stevens (1996) then correlated the results from the four tests
using multivariate analysis of variance and established that the strongest correlation
factor was between mathematics achievement and student?s attitude towards
mathematics.
A student who fears mathematics or thinks that only certain people can
understand the subject might be inclined to have a negative attitude towards the subject.
Often mathematics is feared and revered as a subject only understood through innate
ability (Ladson-Billings, 1997). Confirmation of this belief in how and who can learn
mathematics is found in studies by Levy, Plaks, Hung, Chiu, and Dweck (2001), and by
Signer, Beasley and Bauer (1997) which supported the evidence that less successful
56
students viewed intelligence as fixed and innate. Less successful students in the study
believed that if a person is good at something, then they do not have to work hard at it;
therefore, if effort is involved then low ability is implied (Signer, Beasley, & Bauer,
1997). The more successful students indicated the belief that intelligence could be
obtained through hard work and persistence. In contrast, low achieving students often
believed that their ability level is fixed and the cause of failure (Signer et al., 1997).
Signer, Beasley and Bauer (1997, p. 387-389) found some interaction between ethnicity
and beliefs about ability, and advised teachers to examine classroom practices that lead to
?learned helplessness.?
From the 1996 NAEP data, the largest difference in attitudes towards mathematics
found between African American and White students was in the belief that mathematics
is merely a matter of memorization (Strutchens & Silver, 2000). Many more African
American than White students maintain that mathematics is a matter of memorization.
The authors suggested that this might be a reflection of course taking, since more White
students reported taking the college preparatory mathematics classes (Strutchens &
Silver, 2000). In a NAEP mathematics achievement study by Strutchens et al. (2004), the
percent of all students who liked math had decreased; and while more African American
students have reported liking mathematics at a higher percentage than others, by 2000 for
twelfth grade students the difference between the reporting racial/ethnic groups was
almost non-existent. In response to the statement that learning mathematics is mostly
memorizing facts, more African American students consistently agreed with this
statement from 1990 through 2000 (Strutchens et al., 2004). While the overall numbers of
students agreeing that mathematics is mostly memorization has decreased, the difference
57
in percentages between the number of African American and White students who agree
with the statement has increased (Strutchens et al., 2004).
D?Amato (1992) contended that schools themselves are responsible for student
resistance due to three factors: First, school is compulsory and the element of compulsion
and resulting unequal power struggle is a source of contention between the teacher and
student (D'Amato, 1992). Secondly, instruction involves assessment with the teacher as
the evaluator; meaning students must vie with each other for teacher awards (D'Amato,
1992). And lastly, by teaching children as a group, the resistance developed by peer
relationships is a natural consequence from teacher expectations of group norms and
group duty (D'Amato, 1992). When schooling has a primarily negative meaning for a
child, and the child does not have an acceptably cultural or self-developed rationale for
attending, then resistance occurs and very little learning takes place. One might argue that
the caste-like minority theory as discussed by Ogbu and Matute-Bianchi (1986) explains
why some individuals develop a rationale of striving for school success and others do not.
Summary of Barriers to Mathematics Achievement
The issue of racism and its devastating effects is in all of the spheres of influence
for students. From teacher attitudes, beliefs, and stereotypes, through curriculum
distortions, tracking, language, and behavior traits of the student?s culture; racism seems
to be the major obstacle for African American children to overcome in attaining
educational access. Martin (2003) insisted that if one accepts that mathematics is the
gatekeeper for higher education and higher status jobs, then equity for education implies
correcting the unequal power structure which currently exists and prevents some
minorities from attaining the same educational access as the White, middle class male.
58
Teachers who are committed to learning for all students can make a difference in
their classrooms by addressing issues of equity. Educational institution policy makers
have to make conscious choices to address issues of equity for teacher action to have a
sustained effect. Ideally the teacher, school personnel, parents, and community should
work together to reach goals of equal educational access and empowerment. Cohen
(National Research Council, 2000) argued that children are delegates from the outside
world and, as such, one must consider their social environment and their community.
Additionally for mathematics achievement, one cannot address any of the components
listed above separately as the students community and social environment can be linked
to student perception of classroom activities and success (National Research Council,
2000). Research concerning barriers to educational access for African American children
mandates a challenging curriculum, supportive school environment, and teacher
professional development to learn innovative instructional methods, methods of
addressing racism, and culturally relevant pedagogical techniques. To summarize and
borrow a quote from Christopher Edley, Jr., research tells us that ?to improve student
achievement, pick better students; failing that, do better and more teaching of the students
you are stuck with? (Edley, 2002).
Theoretical Basis for Study
A critical social theory concerns issues of power and justice and the ways in which
race, class, gender, education, religion and other social and cultural dynamics interact to
construct a social system (Kincheloe & McLaren, 2003). Critical emancipation is an
attempt to gain control by those who seek to control their own lives and critical research
59
attempts to expose those forces that prevent individuals from making their own decisions
(Kincheloe & McLaren, 2003).
Traditional educational theory takes the existing society as a given, even
desirable, and not changeable in any major way (Weiler, 1988). On the other hand,
critical educational theorists argued that the exploitative and oppressive society is capable
of being changed (Weiler, 1988). In critical education theory there are production
theorists who are concerned with the processes that allow social structures to maintain
and reproduce, and reproduction theorists who are concerned with how individuals
interpret their experience and resist the forces imposed on them (Weiler, 1988). For many
production and reproduction theorists, schools are the primary means of transmitting the
culture (Weiler, 1988). According to French social theorist, Bourdieu, children of the
dominant classes are successful in school, not because of their natural intelligence, but
because they already know what is valued in society (Weiler, 1988). Additionally, school
language and knowledge is middle-class language and as such has restricted access for
working-class children (Banks, 1993). Production theorist Gramsci?s central concern was
the ways that the dominant classes impose their reality on all subordinate classes, and the
possible ways that the oppressed create understanding of this oppression (Weiler, 1988).
As discussed earlier, different minorities respond to their oppression in different manners,
some of these methods seem to be more beneficial to individual achievement than others.
Racism and Critical Race Theory
For theory and research, the natural response to racism is critical race theory.
Critical race theory evolved from critical legal studies, a movement that challenged the
traditional legal scholarship focusing on doctrine and policy analysis in favor of law
60
which focuses on individuals in social and cultural contexts (Ladson-Billings, 2003;
Ladson-Billings & Tate, 1995b). Earlier work from the production theorist Gramsci
questions the continued legitimacy of the oppressive American societal structures and
contributes to the ideology of critical legal studies (Ladson-Billings, 2003; Ladson-
Billings & Tate, 1995b). In that critical legal studies were not concerned with racism as a
primary issue, something more was needed. Derrick Bell?s and Alan Freeman?s
frustration with the slow pace of racial reform in the 1970?s fueled the emergence of
critical race theory (Delgado & Stefancic, 2000; Ladson-Billings, 2003; Ladson-Billings
& Tate, 1995b).
Critical race theory scholars maintain that our nation was founded not on
individual rights, but on property rights (Bell, 2000; Delgado & Stefancic, 2000; Ladson-
Billings, 2003). This property rights notion is from England, where only those who
owned the land could make decisions about the country. Our founding fathers did not
conceive of individual rights apart from property, therefore belief in liberty and justice
could coexist with oppression of African Americans, indigenous peoples, and women
(Bell, 2000). Additionally, this notion of property ownership and the rights of ownership
has developed into thinking that what Whites own is valuable (Ladson-Billings, 1999).
Many African Americans are naturally less enthusiastic about U.S. citizenship than
Whites because their experiences of citizenship are not the same as the White experience.
And with differential treatment in school and job ceilings, African American students
will be less convinced that success in academics is related to higher status job access
(Ladson-Billings, 1999).
61
Features of critical race theory include acknowledging that, in our society, racism
is accepted as normal and not aberrant (Delgado, 2000). A former Congresswoman,
Shirley Chisholm, stated in 1970 that racism is so widespread and deep-seated that it is
invisible in this country (Weissglass, 2002). Critical race theory is concerned with
understanding how a regime of white supremacy and subordination of people of color
developed and is being maintained (Kincheloe & McLaren, 2003; Ladson-Billings, 1999,
2003). Without this understanding, one cannot hope to make the sweeping changes
needed to combat racism.
Other important concerns of critical race theory are challenging the bonds
between racial power and law (Kincheloe & McLaren, 2003; Ladson-Billings, 1999,
2003), acknowledging that the civil rights legislation has benefited Whites primarily
(Bell, 2000), and giving voice to people of color (Delpit, 1988). With regards to
education, beyond exposing racism and proposing radical solutions for addressing it,
critical race theory makes several claims addressing issues of curriculum, assessment,
instruction, funding, and desegregation. These areas are identified as sources of inequity
for many minority children and, as such, need to be examined for contributing to the
problem of addressing educational access for African American children which, in turn,
affects mathematics achievement.
Storytelling is an often-used feature of critical race theory which can help heal the
wounds of racial oppression (Ladson-Billings & Tate, 1995b). Stories can help the
storyteller put order to experiences, understand how the oppression came to exist, and
stop internalizing the stereotypic images created by society to maintain the power
structure (Ladson-Billings & Tate, 1995b). The oppressor will also be affected by the
62
stories and will have cause to reexamine their rationalization of their contribution to the
injustices inflected on the marginalized groups (Ladson-Billings & Tate, 1995b). To
analyze the educational system, voices from African Americans are needed (Delpit, 1988;
Ladson-Billings & Tate, 1995b). Secada (1995) warned that implicit in the idea of giving
voice is that an individual can speak for himself, but not necessarily for the group. Not
only can one person not capture the complex behaviors or response of the group, but
within the group are many different ways of interpreting and responding (Secada, 1995).
In summary, critical race theory seeks to uncover color-blindness and the
presumably race-neutral practices of public education which maintain and perpetuate the
power structure (Kincheloe & McLaren, 2003). With an emancipatory agenda, critical
race theory uses methods such as story-telling to give voice to people of color (Denzin,
2003). Seeing the world through the eyes of the person of color, one will reject the
Eurocentric paradigm and the postpositivist view (Denzin, 2003). The Eurocentric
paradigm developed from the colonization of other countries by European countries and
postulates that everything progressive has developed from European male thinking. The
Eurocentric paradigm brings into being the notion of the White European male as the
self-proclaimed dominant species, and the sole owner of rational thinking, learning, and
mathematics (Denzin, 2003). A tenet of postpositivistism states that we can never
understand or describe reality only approximate it (Denzin, 2003). Whereas through
story-telling offered by critical race theory, reality is true for the story-teller (Denzin,
2003). In Martin?s (2003) sociohistorical forces, Ogbu?s (1986) caste-like minorities, and
Perry?s (2003) historical narratives, reality exists as interpreted by the individual, and this
is the reality that the individual acts upon. Buying into the Eurocentric paradigm
63
reinforces the belief that European descendents have innate intellectual abilities that other
races do not have (Sleeter, 1997).
64
CHAPTER III
DESIGN OF THE STUDY
Overall Approach and Rationale
The author believes as do Moses and Cobb Jr. (2001), that equitable schooling is a
civil rights issue and as Ladson-Billings (1997, 1994) wrote, that more African American
than White children are limited in their life choices because of current schooling practices
in the United States. Furthermore, the author believes that the same issues which prevent
many African American children from being successful in mathematics and taking more
higher level mathematics courses are the issues that cause many children to be
unsuccessful in mathematics. Even if you believe our society to be racially equitable in
job accessibility, students who are not successful in mathematics are severely limited in
their life choices and chances for attaining the more technical, higher-salaried jobs
(Ladson-Billings, 1997; Moses & Cobb Jr., 2001).
While it appears that critical race theory, with its emphasis on the devastating
effects of racism, is the most appropriate theory for this study, certainly elements from
the other theories reviewed are important. For example according to reproduction theory,
one acknowledges that schooling reproduces our society, and with production theory, one
has hope for helping empower students to deal with oppression. Cultural reproduction
theory adds an important dimension in examining the student?s cultural reference.
Additionally, Martin?s (2003) sociohistorical and community forces, as well as Ogbu?s
(1986) minority classifications and Perry?s (2003) insistence on strong academic
65
traditions, expand this discussion. Certainly critical race theory can not just explain the
existing conditions but also encompasses all of these as it seeks to make significant
changes in the educational system.
Methodology
This study consisted of six multi-individual case studies. Creswell (1998)
described the focus of a case study to be an in-depth analysis of a single or multiple
cases, bounded by time and place. For this study, the cases are six African American high
school geometry students studied within a time frame of six months, which is the length
of the semester of tenth grade mathematics. Data collection for case studies consists of
multiple sources to include documents, interviews, observations, archival records, and
physical artifacts (Creswell, 1998). The data sources included in this study consisted of
interviews with students, three per student; classroom observations, a minimum of four
per student; interviews with mathematics teachers, a minimum of three times during the
semester; interviews with former mathematics teachers for five of the six students; and a
minimum of one parent interview for five of the six students. Artifacts examined included
each student?s notebook which they maintained for geometry class, and the student?s
cumulative record for test scores and previous mathematics grades. Additionally, the
context of the school and community setting are described and discussed. The purpose of
this study was to examine the mathematics experiences of several African American
students through their eyes and through their voices, and to address the research questions
which examined potential barriers to mathematical success for African American
students.
66
Participant Selection
Six students were selected for this study from the population of tenth grade
African American mathematics students at two public schools, Central City and Jackson
High School, located in a southeastern state. At both of the schools, geometry is taught in
a single course with the label ?regular geometry?, or divided into two parts to be taught
as two courses, geometry part A and geometry part B. By splitting geometry into two
courses, the class can be taught at a slower pace. A tenth grade student who is enrolled in
regular geometry class is on the college preparatory track culminating in an advanced
diploma. Only students enrolled in regular geometry as tenth graders were considered as
prospective participants for this study. A ninth grade student enrolled in geometry is on
an accelerated track because he or she took algebra in the eighth grade. Very few
geometry students at Central City and none of the geometry students at Jackson had the
opportunity to be at this accelerated level, and therefore, ninth grade geometry students
were not considered as candidates for this study.
Using data from the National Longitudinal Survey of Youth, 1980, the National
Education Longitudinal Survey, 1988, population surveys of 1970, 1975 and 1990, and
the National Assessment of Educational Progress, researchers from the RAND institute
found the highest correlation between student achievement and family demographics in
the following four areas: parental education level, household income, family size, and age
of mother at birth of child (Grissmer, Kirby, Berends, & Williamson, 1994). Therefore,
for this study, students from middle to upper household income levels were sought, as
well as students from lower income levels. Lower income levels were determined by
whether or not the student participated in a government subsidized lunch program.
67
Within these two income groupings, lower and middle, students who have been
successful in mathematics as well as students who have not been successful were
recruited. Successful students were defined as those who were taking college preparatory
mathematics classes, were on track for college, passed the State High School Exit Exam,
scored at or above the average Stanford Achievement Test-version 10 percentile in eighth
grade, and had done well in previous mathematics classes. Students who are not
successful were those whose eighth grade standardized test scores (Stanford Achievement
Test-version 10) indicated that the student might not be successful in mathematics class,
those who had not passed the State High School Exit Exam, or those who were generally
not performing at expected levels in mathematics.
Stanford Achievement Test-version 10 (SAT-10) scores, and the State High
School Graduation Exam (SHSGE) mathematics pass rate were used in this study as a
general comparison of mathematics proficiency. The SAT-10 was administered to all
students in this state in grades three through eight in the school year 2002-2003, and the
results for the two schools are recorded in Table 6. A second means of assessing
mathematics proficiency was the mathematics portion of the State High School
Graduation Exam (SHSGE). The SHSGE is administered to all students in the eleventh
grade and to selected students in the tenth grade, dependent upon the school district
policy and student class selection. Students must retake the SHSGE or portions thereof
which they did not pass. Table 6 contains the SHSGE pass rate data from the schools, and
Table 4 contains the individual test results of the six participants in this study.
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In an effort to measure the effects of gender, it was necessary to include both
males and females. Participants were selected to include male and female, weak and
strong past performance in mathematics as measured by their SAT-10 eighth grade
mathematics score, and students who received government subsidized lunch, as well as
those who did not. Students were selected from both single and two parent homes and
included three females: Danielle, Amber, and Jasmine, and three males: Tony, Jonathan,
and Josh. Only one of the six students, Jasmine, had not passed the high school exit exam
in mathematics. The students? SAT-10 eighth grade mathematics scores ranged from
Jasmine?s 14 to Josh?s 90 percentile. Four of the six students, Danielle, Amber, Tony,
and Jonathan, participated in government subsidized lunch. A summary of demographics,
school, and testing performance for the six participants is included in Table 4.
Pseudonyms have been used for all students, teachers, and schools included in this study.
69
Table 4
Summary of Student Demographics and Testing Performance
Previous
math
grades
8th grade
SAT-10
math
score
SHSGE
math
portion
Other
school
grades
2005 Lunch
status: Free
indicates
government
subsidized
Type of
household
Josh A 90 Pass A-B Paid Single: Recently
widowed
Danielle A 29 Pass A-B Free Single parent
Amber A-B 56 Pass A Free Single parent
Tony B 86 Pass C-D Free Two parent
Jonathan B-C 61 Pass B-D Free Single parent
Jasmine C 14 Fail C Paid Two parent
School and Community Setting
The six students selected for this study attended two different schools in two
different school districts. The first school, Central High, was located in a small town with
a population of approximately 15,000 and the second school, Jackson High, was located
in a rural community with a population of approximately 3,000 (U.S. Census Bureau,
2004). In both locations, the median family income was below that of the rest of the state,
and was significantly lower than the median family income in the United States. While
more than 80 percent of the people in the United States in 2003 had completed high
school, this number dropped to 70 percent for Central City and 60 percent for Jackson
70
(U.S. Census Bureau, 2004). For 2003, the percent of the population which was African
American was 28 percent for Central City and 45 percent for Jackson (U.S. Census
Bureau, 2004).
Table 5
2003 Demographics of Central City and Jackson
2003
Population
Estimate
2003
Median
household
income
Percent of
Population
who are
White
Percent of
Population
who are
African
American
Education:
percent of
population
completing
high school
Central City 14,832 $29,309 70 28 70
Jackson 3,212 $25,266 53 45 60
State 4,385,446 $35,158 71 26 79
United States $43,564 75 12 84
(United States Census Bureau, 2003)
The demographics of the two schools shared some characteristics and were
strikingly different in other characteristics. The median household income for the cities in
which the two schools were located was comparable, with both being well below the
national median household income. Both districts had lower than national average
percent of population who had completed high school. The most notable difference
between the two schools was the classrooms themselves. The rooms in Jackson High
were small, dirty, not well-lit, and with poor heating and air conditioning. Central City
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High had many of its class rooms renovated, so that they were spacious, well-lit, with
good heating, and air-conditioning.
More striking differences between Central City and Jackson High student
populations were found in student mathematics achievement as measured by SAT-10
mathematics scores, and the State High School Graduation Exam (SHSGE) mathematics
pass rate. Central City students averaged higher than the state average on SAT-10 scores
and on pass rates for the mathematics portion of the exit exam. Jackson High students
scored significantly lower than state averages on SAT-10 and mathematics pass rate for
the exit exam. Table 6 summarizes this data.
72
Table 6
SAT-10 and AHSGE Pass Rate for State, Central City, and Jackson High
2004 SAT-10 8th grade
average percentile
2004 SHSGE 11th grade
mathematics portion pass rate
State average 50 78
White 59 85
African Amer. 34 65
Central City 57 88
White 69 92
African Amer. 40 78
Jackson High 25 59
White 27 69
African Amer. 21 45
(* State Department of Education, 2004a)
Teachers
There were four regular geometry sections at Central City, three of which had the
same instructor. There was only one regular geometry class at Jackson High. Four of the
students in this study were from Central City, with Mrs. Smith as their teacher; and two
students attended Jackson High, with Mrs. Basswood as their instructor. A brief
description of each teacher and their typical geometry class follows.
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Mrs. Smith
A twelve-year veteran of high school mathematics teaching, Mrs. Smith lived all
of her life in the same region of the state and has spent all of her career at Central City.
Mrs. Smith majored in mathematics for her undergraduate studies and completed a
Masters in Applied Mathematics from a nearby state university. Although she has taught
geometry from another text, Mrs. Smith stated that this was only her second year teaching
geometry from the textbook used at that school.
Mrs. Smith?s classroom had been recently renovated, and it was clean and well-
organized. The walls of her classroom were covered with inspirational posters, such as
?Strive to do your best? and ?You can be successful.? Along one wall were all of the
geometry terms covered in class. As the chapters from the geometry book were covered
and new terms were introduced, Mrs. Smith printed the geometry vocabulary on brightly
colored paper and pasted them onto the geometry wall of terms. The classroom was
meticulously organized with all of the transparencies, worksheets, homework checks,
tests, and assignments placed where Mrs. Smith could readily place her hands on them.
Students had access to two bookshelves in the back of the classroom where Mrs. Smith
kept a classroom set of textbooks and workbooks, so that the students would not be
required to bring their own mathematics book to class.
When asked to describe herself as a teacher, Mrs. Smith, who is White, stated that
most important for her is to break down mathematics so that her students can understand
the material. Mrs. Smith described a college mathematics professor who lectured so that
no one in the class could understand; Mrs. Smith was determined to do just the opposite
and make mathematics easy for her students.
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A typical geometry class in Mrs. Smith?s room. (Tony and Jonathan were in one of
Mrs. Smith?s classes, and Amber and Josh were in another.) When the bell rang, students
went to their assigned seats. Mrs. Smith put prepared transparencies with answers to the
even problems from the homework of the previous night on the overhead projector. She
set a timer for ten minutes and allowed the students to ask questions on those problems
that they did not understand. Mrs. Smith explained to me that the timer helped keep her
on track so that there was time for her to cover the new material. If a student had a
question at the end of the ten minutes, Mrs. Smith would reset the timer for a few more
minutes. Amber is the only one of Mrs. Smith?s students in this study who asked
questions about homework. Tony and Josh never asked questions about the homework,
and only on one occasion did Jonathan ask about a problem.
At the end of the question period, Mrs. Smith passed out a half sheet of paper with
a homework quiz on it. The questions on the short quiz were similar to the homework
that the students had been assigned to do the previous evening. Jonathan was the last
student or one of the last students to complete his homework quiz at every observation.
According to Mrs. Smith, she explained her assumption that Jonathan was trying to figure
out how to do the quiz problems, because he had not done his homework.
After the quiz, Mrs. Smith passed out a double-sided sheet of main ideas for the
next section or two of the book. This paper was to be used as a guide for the students to
take notes and organize the lecture and book material. During the first observation, which
took place the second week of the semester, most of the students appeared to be taking
notes on this paper. On subsequent visits, fewer and fewer students were taking notes as
Mrs. Smith lectured, but most of the students were quiet and mannerly. Of the four
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students from this study in Mrs. Smith?s geometry classes, only Amber continued to take
notes throughout the semester. Josh was busy doing geometry but not taking notes or
paying much attention to Mrs. Smith. Tony did not take any notes during observations,
and Jonathan took notes occasionally. Jonathan would often quietly talk to another
student in front of him when Mrs. Smith was not facing his direction. Of the four students
in this study in Mrs. Smith?s class, Jonathan had the most trouble sitting still, paying
attention, not talking, and taking notes for 90 minutes.
Other than when the students were taking a quiz or a test, Mrs. Smith lectured for
most of the 90 minute block. A student occasionally asked a question or volunteered an
answer when a question was presented to the class. Amber was one of the few students in
the class who was not shy about volunteering an answer or asking questions. Mrs. Smith
called upon students who volunteered and only rarely called on a student who did not
volunteer. When this occurred, it was frequently to correct or interrupt a student?s
behavior.
During my visits to Mrs. Smith classes, I observed no deviations from the routine
described except on two occasions. Near the end of the second observation with less than
ten minutes remaining in the class period, Mrs. Smith directed groups of four students
whose desks were the closest together to work on a problem or two and to compare their
solutions. At another time, after Mrs. Smith changed the seating arrangement, students
had different groups that they worked with. During this period, Josh sat with his assigned
group, but he did not share his solutions unless someone in his group asked him directly
what answer he had gotten. Amber appeared to be the group leader in her groups and
used the time to work on the problem assigned. Jonathan used the group time to do some
76
chatting with whomever was in his group and did not appear to be discussing geometry,
as he watched Mrs. Smith closely and stopped talking when she came near his group.
Tony politely sat with his group, but it appeared as if he had nothing to offer and did not
work on the assigned problem. The group-work on these two occasions lasted no more
than 5-10 minutes, and the groups did not share with the class the results of their group-
work.
Mrs. Basswood
Mrs. Basswood was a thirteen-year veteran of high school teaching who had
graduated from a state university with a degree in mathematics education and history, and
who later returned to the same university to complete a Masters in Mathematics. Mrs.
Basswood was White and had grown up in a small town less than 50 miles from where
she currently taught and resided. All of her family lived in this same area for years, and
she did not expect to live anywhere else.
Mrs. Basswood?s classroom was typical of those at Jackson High, which was an
old building in need of repair. The classrooms were heated with radiators and cooled by
window units which did not always work. Other repairs were needed in the classroom.
There were missing tiles in the floor, desks which were covered with scratches and nicks,
and bent metal support on the desk chair backs resulted in very uncomfortable seating.
Mrs. Basswood?s room was decorated with very old trophies, prom paraphernalia from
previous years, and old student-created posters and drawings. Everything in the room was
covered with dust. Mrs. Basswood stated that any cleaning done in the room usually had
to be done by her since the janitorial staff was understaffed. Adding to the clutter in Mrs.
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Basswood?s room were club fundraiser items, such as boxes of candy or pencils for sale,
since Mrs. Basswood was the sponsor of several school clubs.
When asked to describe herself as a teacher, Mrs. Basswood stated that it is most
important to understand the people that you teach. ?That is the first thing I learned when I
went, when I started teaching, was that if they break up with their boyfriend, that they
really don?t care what?s going on in algebra and geometry.? Since Jackson is a very
small town, Mrs. Basswood was very knowledgeable of each student and his or her
family. Mrs. Basswood taught both Jasmine and Danielle. The previous year, Mrs.
Basswood was Danielle?s algebra teacher. This was Mrs. Basswood?s second year to
teach geometry, and she stated that she was much more comfortable with the material this
year.
A typical geometry class in Mrs. Basswood?s room. Even though the atmosphere
in Mrs. Basswood?s room was more relaxed than in Mrs. Smith?s, the teaching method
was still predominantly traditional. After the students were seated in their assigned seats,
Mrs. Basswood began by reviewing the homework or the answers to a quiz or test. Mrs.
Basswood used the overhead projector to draw a copy of the sketches from the book, and
explained how the solution was obtained. After this review time, Mrs. Basswood began
the next section of the book and explained the new material. After an explanation,
students worked out some of the problems either individually or in pairs. At the
beginning of the semester even if Mrs. Basswood had not explicitly asked the students to
share their work, many would ask each other about their answers. By the end of the
semester, the majority of the students were still doing the required tasks, but the level of
cooperation from the students to complete the assigned tasks was diminished. Danielle
78
was very attentive and cooperative at the beginning of the semester, but by mid-semester,
she no longer eagerly participated. Jasmine did not participate, ask questions, or share
work with other students except on one occasion discussed later.
Mrs. Basswood occasionally gave the class a notebook quiz. Students found
specific problems in their notebooks and then copied the problems and solutions directly
from their notebooks onto the quiz. Additionally, Mrs. Basswood used worksheets
created by the textbook publisher, which Mrs. Basswood felt were a more ?fun? version
of the problems in the text. Danielle usually worked on whatever was assigned in class
and completed the quizzes; whereas on many occasions Jasmine appeared to be doing
nothing and would turn in partially completed work.
When students were assigned to work in groups, the typical assignment consisted
of problems from the text or workbook. Students were instructed to solve the problems
and compare solutions with their group members. Students did not share their groups?
work with the class, nor were they required to justify their solutions. Groups were not
assigned open-ended problems or projects. Danielle appeared to enjoy group-work,
particularly when the group contained some of her basketball teammates. Jasmine did not
seem to enjoy group-work any more than any other activity that occurred in geometry
class.
Instrumentation
Interviews
At the initial interview of each student, parent, and teacher, a predetermined list of
questions was used to ensure that those interviewed were asked the same questions and
that all of the planned topics were covered. The interview questions are included in
79
Appendix A. Subsequent interviews consisted of clarifications of earlier statements made
at the initial interviews, discussions of classroom observation notes, and updates on the
semester?s progress.
The student interview questions were designed to determine how they rated their
efficacy as mathematics students, and their perceptions of teacher, parent, and peer
support and expectations. Questions were used to determine if the students thought
mathematics was useful, important, and necessary to be successful in life. Student
participants were asked to analyze the reasons for their current mathematics grade and
whether they were performing as well as they could. Students were asked if they liked
mathematics and their mathematics teacher. Additionally, students were asked if they
thought that their mathematics teacher expected them to do well, if their teacher
encouraged them, and what manner of encouragement the teacher used. Students were
questioned about whether or not they had homework and whether or not they completed
their homework. Information obtained from students which could be confirmed by
observations included asking students to describe their typical classroom performance,
specifically whether they took notes, paid attention in class, interacted with the teacher or
others, and whether or not the students asked questions.
Teachers were asked to analyze the students? performance in geometry class, their
typical classroom behavior, typical homework assignments turned in by the students, and
the types of interactions that they, as teachers, had with students. Questions were asked to
determine what the teachers perceived as the students? attitudes towards mathematics, if
the students appeared to be interested in class, and if the students volunteered or asked
questions. Teachers were asked if they believed that the students were working up to their
80
potential in mathematics and what the students might do to improve performance in math
class. In subsequent interviews classroom observation notes were discussed with the
teachers with regards to the behavior of the students in class, and the students? responses
to their respective teachers and the assigned tasks.
Parents were asked to analyze their child?s performance in school and specifically
in mathematics. Parents were questioned about their child?s attitude towards
mathematics, why the child had this attitude, and where the child might have obtained his
or her attitude. Specifically, parents were asked what motivated their child to do well in
mathematics and whether the parents thought their child was doing the best that he or she
could. Parents were questioned about their interactions with their child?s mathematics
homework, interactions with their child?s mathematics teacher, and what expectations the
parents had for the child?s success in mathematics. Additionally, for students who had
siblings, parents were asked if they had the same expectation for success in mathematics
for all of their children as for the child in this study.
Observation Protocol
Observations of the mathematics classrooms were conducted to determine the
type and level of interactions that the students had with their respective teachers and their
peers. All of the classes observed were approximately ninety minutes in length unless
interrupted by planned events such as school assemblies or fire drills. During the
observation, notes were taken documenting each student?s behavior, note-taking patterns,
response to teacher questions, group participation, and perceived level of interest.
Additionally, notes were taken on the arrangement of the classroom, the classroom
procedure, the lesson discussed, the pacing of the lesson, the seating patterns of the
81
students, the demeanor and actions of the teacher, and the interactions of the students
even if they were not related to the lesson. The level and types of student participation in
the mathematics classroom were noted and discussed with each student at subsequent
individual student interviews.
Procedure
During the semester prior to the 2005 spring semester, school superintendents and
principals were contacted and meetings were arranged in which the purpose and direction
of this study were discussed. Permission to proceed was obtained from these principals
and superintendent; see Appendix B for copies of the consent forms used as well as an
introductory letter given to the principals. The second task completed before the semester
began was to locate the regular geometry classes and the potential tenth grade African
American students for the study. Students were approached at each of the schools in the
study, the planned procedure of the study was discussed with possible student
participants, and permission from the students was obtained to contact parents for
approval to proceed. Next, the parents of each of the selected students were contacted, the
study explained, and permission obtained to conduct student interviews and classroom
observations. Permission to conduct classroom observations and teacher interviews was
obtained from each classroom teacher and their respective school principals; examples of
the consent forms given to the teachers and parents are included in Appendix B.
After permission was obtained from the parents or guardians of the students, each
student was interviewed individually on at least three separate occasions during the
spring 2005 semester. All interviews were audio-taped and later transcribed. Classroom
observations were conducted of the students? mathematics classrooms at least four times
82
during the semester. Interviews with parents followed initial student interviews and
classroom observations. Teacher interviews were conducted before and after classroom
observations, and teachers were contacted via email almost weekly throughout the
semester.
Data Analysis
Interviews of students, parents, and teachers, as well as classroom observations,
were employed in this study as a method of triangulation of the data sources.
Triangulation can be described as a method of adding layers to the data source, using
multiple items to measure the same construct (Fine, Weis, Weseen, & Wong, 2003). In an
attempt to triangulate the data sources, some identical questions were asked of the
student, teacher, and parent for each case. For example, one question asked of the
students, teachers and parents, was to rate the student on a numerical scale of one to ten
with one being the worst mathematics student and ten being the best mathematics student.
Other data sources for this study included accessing cumulative records of the six
students and examining the students? current geometry mathematics notebooks. Data was
obtained from the students? cumulative records which included past grades for
mathematics courses and overall performance, eighth grade SAT-10 mathematics score,
and whether or not the student had passed the mathematics portion of the SHSGE. From
students? geometry notebooks, observations were made as to the students? organization,
and absence or presence of classroom notes, quizzes, tests, and homework assignments.
Geometry notebooks were examined with the students present in order for students to be
able to explain what was in the notebook, what was missing, how the notebook was
organized, and whether or not the student used the notebook to study.
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All interviews, which were audio-taped, and observation notes were transcribed
into word processing documents and subsequently loaded into a software package,
ATLAS-ti. This qualitative data analysis software was used to code data so that similar
responses could be noted and discussed. The major categories and codes obtained from
the analysis using ATLAS-ti are discussed in detail in the results and analysis chapter of
this document.
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CHAPTER IV
RESULTS OF THE STUDY
Jasmine
Past Performance in Mathematics
Based on past performance in mathematics classes and previous test results,
Jasmine was the lowest performing student in this study. One of 25 regular geometry
students at Jackson High, Jasmine was the only student in the class who did not pass the
State High School Graduation Exit Exam. With a SAT-10 mathematics score of 14th
percentile, Jasmine fell below the average SAT-10 score at Jackson High of 25
percentile, and well below the state average of 50 percentile (* State Department of
Education, 2004a). Jasmine?s previous mathematics grades were consistently in the
average range, and even though Jasmine stated that mathematics was her worse subject,
her past mathematics grades were fairly consistent with her other school grades. Taking
into account Jasmine?s SHSGE failure, her SAT-10 score, and past performance in
mathematics classes, one might predict that Jasmine would not be successful in
Geometry, or at least not as successful as other students in the study.
Family Structure and Influence
Jasmine did not participate in the government subsidized lunch program, and
lived with her two parents in a modest brick home in Jackson. Jasmine was a much
younger sibling of two others who quit school before graduating. Jasmine?s mother
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believed that Jasmine was more capable academically than her other two children.
According to Jasmine?s mother, ?I expect more from her (than the other two children), as
my other two kids were born in the 70?s and had changed a lot. I want more for her
(Jasmine).? Jasmine stated that both of her parents expected her to do well in school, not
just in mathematics, and that they planned for her to go to college. Jasmine?s mother
seemed to be very influential in instilling in Jasmine the importance of doing well in
school and made an appointment to talk with Jasmine?s teacher when Jasmine brought
home a low grade on a progress report. Stating that she herself was not good in
mathematics, Jasmine?s mother said that she helped Jasmine when she could. On a scale
of one to ten with ten being the best mathematics student, Jasmine?s mother rated her as
an eight because Jasmine usually got all of her work done and finished her assignments.
Jasmine volunteered information about her father when asked about her shyness.
Jasmine stated,
I think it (shyness) is genetic. Because other people in my family are shy, not all
of them. I guess I get it from my Dad. He is really shy, but it depends on who he
is around. My mom is not shy at all. People in my Dad?s family are not really shy,
but he is.
Neither of Jasmine?s parents had attended college, but they expected Jasmine to attend
college.
School Level Factors
Jasmine belonged to both the girl?s basketball team and the track team at Jackson
High. While Jasmine?s mother related that Jasmine was often discouraged during
basketball season because Jasmine sat on the bench most of the time instead of getting to
play, Jasmine stated that she preferred basketball to track. When asked if she might
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qualify for an athletic scholarship, Jasmine stated, ?I might. I don?t really know. In
basketball, I?m not the best. . .maybe in track. Well, I like basketball better than track. It
is something I really enjoy.?
Classroom Dynamics
Jasmine was a very quiet, cooperative young person, who would only speak when
she was asked a question directly. I never witnessed Jasmine volunteer a comment in
class, during our interviews, or when I met with her in small groups or in her home.
When asked what Jasmine could do to improve her work, her teacher, Mrs. Basswood
specifically mentioned wanting Jasmine to speak up in class, find someone with whom to
work, and ask questions. Although Jasmine stated that she would seek help by phone
from one of her friends or maybe from Mrs. Basswood if she needed it, I never witnessed
her asking for help except on one occasion at the end of the semester. At this point
Jasmine had received a D on her progress report for the second nine-week period, and her
mother had been to the school to speak with Mrs. Basswood.
During this class, each student was assigned to a group of three. Jasmine was
placed in a group which included another African American female and a White male.
The other female student proceeded to work on her own and not speak to Jasmine or the
third group member. This third group member was a very bright boy, not very popular
among the class members, but insightful and talented. He had written only the answers to
the problems assigned and passed those over to Jasmine, then got out a paperback book to
read. Jasmine looked at the answers to the assigned problems, interrupted his reading, and
asked him to explain how to do several of the problems.
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As a mathematics student, Mrs. Basswood rated Jasmine as a three out of ten and
stated that Jasmine was a very weak math student. During the year, Mrs. Basswood asked
for a parent conference several times but did not get a response from Jasmine?s mother
until Jasmine brought home a D on her progress report. Mrs. Basswood expressed
surprise and pleasure when Jasmine had a grade of a high C at mid-semester and believed
that was a good grade for Jasmine in view of her weak foundation in earlier mathematics
courses.
On one occasion, when the geometry class was learning about angle bisectors,
altitudes, medians, centroids, incenters, orthocenters, and perpendicular bisectors, Mrs.
Basswood had the students use patty paper and fold the different triangle attributes.
Jasmine was very confused about what to do and spent much of the time just sitting and
watching other students fold their triangles. Other students asked me to help them as Mrs.
Basswood could not help all of the students individually, so I asked Jasmine if she
wanted me to help her, and she said that she did not. At the end of class, I interviewed
Jasmine and talked to her about what was going on in the class. She reluctantly got out
the patty paper, and we folded each of the triangle bisectors, median, and altitudes. Many
of the basic geometric terms covered earlier in the term seemed to be meaningless to
Jasmine. For example, she could not respond to directions of folding a 90 degree angle,
or questions such as ?if an angle is bisected and one of the resulting angles is 40 degrees,
what is the measure of the other angle??
Personal Beliefs about Mathematics
Jasmine expressed her dislike of mathematics because she ?did not get it? a lot of
the time. Jasmine stated that she is frustrated when she does not understand and will quit,
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but then try to force herself to start to work again. On a scale of 1 to 10, Jasmine rated
herself as a 5, because she considered herself to be ?in the low range of the smart
people.? Jasmine believed that she could change the 5 to a higher number if she made
herself understand it. Questioning Jasmine about her reluctance to seek help, the
conversation was as follows.
Interviewer: Is it hard for you to ask, to talk in front of other people, the class?
Jasmine: mmm, hmmm
Interviewer: Why do you suppose it is hard?
Jasmine: Because you are afraid of what people will think- of your answer and
maybe laugh if it is wrong.
Interviewer: That would be embarrassing.
Jasmine: Yeah.
Interviewer: Is there a time when you could ask for help outside of class?
Jasmine: Yes, but I wouldn?t. I would ask my friends.
Interviewer: Do you see other people in the class asking for help when they don?t
know what is going on?
Jasmine: Yes.
Interviewer: Plenty of people do, don?t they?
Jasmine: Yep.
Interviewer: But you wouldn?t do that?
Jasmine: Yep.
Interviewer: Explain that.
Jasmine: I don?t know, I am a shy person.
Interviewer: Are you that way in every class?
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Jasmine: Yes, well not in Biology. It depends on the class and the teacher.
Interviewer: What is different about Biology?
Jasmine: I got a good grade in that class- and so I know what is going on.
Throughout the semester, Jasmine maintained that mathematics is important, that
she needed to take mathematics. She wanted to be a part of this college track class, but
was having trouble passing tests and understanding the material. Even at the end of the
semester, with her low grade average, Jasmine maintained that geometry was important
to learn for many fields of study and that she planned to attend a state university and
possibly become a lawyer.
Jasmine?s geometry notebook was disorganized and incomplete, consisting of the
work done in class that day and partially completed homework assignments. Jasmine
stated that she never used her notebook to study or to understand how to do a problem
from her notes. In reviewing the problems in her notes, it seemed that Jasmine did not
recognize when she was close to a solution or when she was completely on the wrong
track. For example, she correctly set up a triangle proportionality problem which
involved algebraic equations. Jasmine solved the algebraic equations correctly until the
final step of the solution when she divided by four instead of two. In her notes, she made
another complete copy of the problem, starting over because she got it wrong. Jasmine
did not realize that she made a small calculation error which could have been easily
corrected instead of starting at the beginning to repeat many of the steps which she had
done correctly.
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Summary of Performance in Geometry
Jasmine appeared to have little success with geometry and struggled to maintain a
passing grade throughout the semester. In class, Jasmine never volunteered solutions,
comments, or questions. As a general rule, Jasmine did not seek help from her teacher,
Mrs. Basswood, nor from others in the class. Jasmine did not enjoy geometry and seemed
to have very little understanding of mathematical terms. Jasmine completed geometry
with a D average. Jasmine is scheduled to take Algebra II in her 11th grade year.
Danielle
Past Performance in Mathematics
Danielle was an honor roll student from the time she entered school until the time
of this study, consistently maintaining high grades in all of her subjects. At the beginning
of the semester her geometry teacher, Mrs. Basswood, described Danielle as a sponge,
the perfect math student, and on a scale of one to ten: a ten plus. Mrs. Basswood taught
Danielle the previous year and so felt that she knew her fairly well. Mrs. Basswood stated
that she would love to have a class full of Danielles; that Danielle is just that good.
Danielle passed the SHSGE mathematics portion, but only scored in the 29th
percentile on the SAT-10. The average SAT-10 for Danielle?s high school was 25th
percentile, so Danielle scored just above the average for her school, but well below the
state average of 50 percentile.
When Danielle was asked to rate herself as a mathematics students, she stated ?I?d
say probably a five. I?m not saying that I?m the lowest, I?m not saying I?m the best.?
When asked if maybe she was underrating herself, Danielle responded, ?I try not to, you
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know, I try not to have a big head about myself.? Clarifying her statement later, Danielle
added,
?that just makes other people think like, oh she?s just thinking more of herself,
she don?t care about anybody else, you know. Care about if we know how to do it
or if I know how to do it. It?s, I just don?t do that. I try to put myself in a position
where I don?t try to brag on myself. If I know how to do it, then , yeah I know
how to do it, but if I see someone else struggling then I?m gonna try to pick them
up.
Danielle took two semesters of algebra during her ninth grade year so that she could be in
regular geometry in her tenth grade. Danielle stated ?Well, mainly because if I like took
Algebra A the first semester then I may need to take it again. I wouldn?t have
remembered some of the stuff that I took.? When asked if someone encouraged her to
double up on her mathematics, Danielle stated that she figured it out for herself.
Family Structure and Influence
Even though Danielle lived in the housing project, she came to school dressed
nicely and similar to most of the other students at Jackson High. More than half of the
student population at Jackson High, including Danielle, received free or reduced lunch.
Danielle lived with her mother in Jackson?s only housing project and although Danielle?s
mother signed the permission form allowing me to interview her daughter, she never
responded to my requests for an interview. According to Mrs. Basswood, Danielle?s
family never attended any of the basketball games in which Danielle played, nor any
other school function. Mrs. Basswood stated that Danielle would not allow Mrs.
Basswood to give her a ride home following school activities. Rather Danielle rode home
with other friends of hers from the school. Mrs. Basswood believed that Danielle did not
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want Mrs. Basswood to see where she lived or to meet her mother. The only information
that I obtained about Danielle?s family was from Danielle herself.
It is interesting to note that when asked who influenced her the most, Danielle
noted her most influential source was a certain friend whom she has known for many
years. When Danielle began experiencing problems in geometry and her grade dropped,
she told me that her friend encouraged her and told her not to give up.
When I did want to give up, because I couldn?t take it all. But they encouraged me
to keep on. If you want to really reach your goals, then it will settle down some
day. I have to keep on.
School Level Factors
Danielle was a member of the Jackson High girls basketball, volleyball, and track
teams. Midway through the semester, Danielle took a job working at the local grocery
store and dropped off of the track team. At the end of the semester, Danielle stated that
she was back on the track team for the final week of school. When asked how this
happened, Danielle responded, ?My coach needed, she was like, needed someone for the
relay.? Apparently Danielle was a good athlete and needed by her coach for a final track
meet so that she was allowed to compete even though she had not been to practice.
Classroom Dynamics
At the beginning of the semester, Danielle was attentive, responsive, cooperative,
prepared, and helpful to other students. By mid-semester, this was not the case, Danielle
remained cooperative, but she was not as responsive in class, did not have all of her
work, and seemed tired and distracted. During this time, Danielle took the job at the local
grocery store and worked several days a week. Mrs. Basswood was concerned that
Danielle had a boyfriend and her driver?s license, and was no longer as interested in her
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studies. Danielle denied both of these things when asked. While Danielle was very polite
and answered every question that I asked, I did not feel that Danielle shared her thoughts
and feelings with me or Mrs. Basswood. For example, a conversation about her drop in
grades follows.
Interviewer: You have had a lot of changes this year. I see a difference from the
time I first started talking to you until now. What do you think? Do you see a
difference?
Danielle: Yes.
Interviewer: What do you see as a difference?
Danielle: About how I am always on the go?
Interviewer: That and geometry, I see a difference. What do you think?
Danielle: I don?t know.
Interviewer: What do you see as different?
Danielle: (silent)
Interviewer: Do you want me to tell you what I see as different?
Danielle: Yes
Interviewer: I see that you are a really top-notch student and back in January, I
noticed that you smiled a lot and really paid attention. Now you are tired and you
don?t smile as much and you seem distracted. I think some things have happened
this year to make a change. Something is different.
Danielle: Well, I?m not trying to let work get in the way. . .not sleeping well, with
all the work to do.. . .I don?t know, I be paying attention, but it just doesn?t click
with me.
Personal Beliefs about Mathematics
Danielle stated that mathematics was important: ?I think more jobs today, you
know, require more math. Cuz, you know, technology and stuff, you need good math.. .
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You need math to get through life.? Additionally, Danielle stated that mathematics is
something that could be used every day. For example, Danielle stated that geometry is
important because ?
when you are playing sports, you have to draw out the plays. You have to be at a
certain angle to the goal to make it. Or when you are running track and you have
to know the circumference of the track.
As Danielle experienced the changes in her grades through the semester, she
continued to tell me that she was fine, everything was fine, and that the geometry was just
getting a little harder. Danielle continued to state that she might get a scholarship to
college by way of her athletic abilities and her good grades.
Danielle?s ambition was to be a cosmetologist, but she was not sure what she
would have to study to become a cosmetologist. While she indicated that there were
many people who depended on her to do well in school and in sports for a college
scholarship, she was frightened about going off to college and not at all sure that this was
what she wanted to do with her life.
Summary of Performance in Geometry
Danielle clearly had circumstances in her life which affected her normal
classroom behavior. Danielle was an honor roll student making excellent grades in
mathematics up until this year. Danielle did not have a parent or sibling who went to
college, and no one from her family attended school functions. Instead, Danielle seemed
to receive her encouragement and support from her friends and her teachers. In addition
to being an excellent student before this semester, Danielle was also a strong athlete on
the basketball, volleyball and track teams. It seemed as if working at the local grocery
store was replacing some of her involvement in school activities and her homework time.
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Danielle seemed to have lost her focus to be one of the top students at Jackson High and
to remain on the scholarship track. Danielle finished the year with a D average in
geometry.
Jonathan
Past Performance in Mathematics
Jonathan?s grades in mathematics prior to geometry were in the average range.
Jonathan passed the SHSGE in the ninth grade and scored in the 61 percentile on the
SAT-10 in the eighth grade. The SAT-10 average for Jonathan?s school, Central City,
was 57 overall with African American students averaging 40 and White students
averaging 69. Jonathan?s ninth grade teacher described him as very bright but moody,
that he responded inappropriately in class either by showing off or putting other students
down. According to his ninth grade algebra teacher, Jonathan was suspended during his
freshmen year in high school for fighting, and she believed that he had gotten in trouble
again earlier in his tenth grade year. Other teachers labeled Jonathan as disruptive in class
and disrespectful to the teacher.
Jonathan indicated to me that he thought math was his favorite subject, important
to learn, and that he was a good math student, 8 out of 10. When asked why he rated
himself an 8, he responded:
Cuz I can?t rate myself a ten, cuz I?m not really, really good at it like people
making 98?s and all. I ain?t that good at it, and I wouldn?t rate myself a one, cuz I
know, I know how to do math better than that, give myself a one?I just
connected with math so good. I just catch on real fast, or at least know what the
teacher say and then I know how to do it once I heard it.
Jonathan said that he could be a ten if he put his mind to it ?if I put more and more effort
into it, I probably could.?
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Family Structure and Influence
Jonathan participated in the government subsidized lunch program and lived with
his mother and brother in a well kept trailer on the edge of Central City. The community
where Jonathan and his mother lived consisted of modest homes and trailers and would
probably be considered as lower middle class.
Jonathan?s mother rated Jonathan a 10 as a math student and believed that he is
very smart, motivated to do well, and that school is easy for him. Jonathan?s mother
believed that Jonathan did the best that he could and that he liked mathematics.
Jonathan?s mother stated that Jonathan finished his homework at school, and so she did
not usually see him do homework and did not get involved with his homework. When
Jonathan was asked what his mother would do if he brought home a D or an F in
mathematics, Jonathan responded:
Mom would just get mad. She?d be like, I know you can do better than this. What
you doing with this grade? She?d be asking me questions, are you getting it, is the
teacher teaching you right? Get to asking me, so I try to make good so she won?t
have to ask me if the teacher teaches right.
School Level Factors
Jonathan did not participate in any official extracurricular activities at Central
City. Jonathan?s behavior of fighting with other students continued into his tenth grade
year and caused him to be on suspension on at least one occasion during his semester of
geometry.
Classroom Dynamics
Early in the semester, Jonathan usually had his head down on the desk, did not
appear to be listening to the geometry lecture, and could not have been taking notes.
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Jonathan?s geometry teacher, Mrs. Smith rated Jonathan a three or four out of ten and
indicated that he often scored a C on the chapter tests, but on the homework checks and
mastery tests, he made lower grades. Mrs. Smith stated that Jonathan rarely brought items
which he needed for class and usually did not pay attention. But there were periods of
time during the semester when his behavior changed, and during observations late in the
semester, Jonathan paid closer attention and took notes. Mrs. Smith believed that the
progress reports spurred Jonathan into facing reality and that he tried harder for a short
period of time.
Jonathan had behavior issues in class and at school. According to Mrs. Smith,
Jonathan lost his privilege of going to the bathroom during class, because he disappeared
for long periods of time instead of returning to class in an appropriate amount of time.
During the second nine weeks, Jonathan was suspended from school for three days.
According to school regulations, when a student was suspended, they were not allowed to
make up the missed work.
Jonathan chose to prepare his notebook before he shared its contents with me.
Jonathan removed all traces of any graded work or progress reports and rearranged the
order of his notebook before he would let me examine it. Surprisingly, Jonathan?s
geometry notebook revealed handwriting that was extremely neat and meticulous, and
consisted of quite a few days of class lecture notes. Not surprisingly, there were no
homework assignments in his notebook. Jonathan was quite pleased with what he shared.
Personal Beliefs about Mathematics
Jonathan believed that mathematics was important to learn and useful in dealing
with prices and knowing what to charge people:
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?know how to count money. Like say you be working at a restaurant or
something, don?t have a calculator and you count back their change in your
head? Cuz, like somebody might ask you what?s this and you?d be able to tell
them. Or like they ask you something, multiply by something and you?d know
how to tell them the answer.
Jonathan thought it was important to do well in mathematics so that it would look good
on his diploma. Although Jonathan did not know exactly what he wanted to do upon
graduation, he mentioned that he and his brother might move to another state to work
with his cousin painting automobiles. Jonathan stated that he tried for good grades, ?so
that it looks like I know math real good. That?s why I try to get A?s and B?s in math, so it
will look like I know how to do math real good.? When asked who this would look good
for, Jonathan responded, ?Hm? For a college or something like that.?
Summary of Performance in Geometry
Jonathan appeared to be quite capable of doing well in mathematics, as
recognized by his mother, his algebra and geometry teachers, and himself. Jonathan was
not truthful about the work he did, what grades he was making, or what was happening to
him in geometry. Additionally, Jonathan had behavior problems which caused him to
miss class from time to time. It seemed as if Jonathan believed that he could catch onto
the mathematics without actually having to do any work outside of class. Jonathan
completed the term with a D in geometry. At Central City High, this meant that he passed
geometry, but he would not be recommended to take Algebra II; Jonathan would be
assigned to Algebraic Connections, a lower class level than Algebra II and no longer on
the advanced diploma track.
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Tony
Past Performance in Mathematics
Tony made a B in his ninth grade algebra class, passed the SHSGE, and scored in
the 86th percentile on the SAT-10, well above both his school and state average scores.
Tony?s ninth grade mathematics teacher described him as a good student, whose
attendance problems hampered his performance in mathematics. In ninth grade Tony was
described by his former teacher as a cooperative student who tried to do his work. Tony?s
ninth grade mathematics teacher stated:
he participates?if something?s bothering him or if something?s upsetting him
um, he might not participate as much but he would (participate). He was typically
one of those that wanted to go to the board, you know, kind of like to show out.
Cuz, he knew what we were talking about.
Tony stated that he took Algebra I twice:
I took it in the eighth grade and I took it again in the ninth grade. I don?t know
why, I think they just placed me in it. My teacher advised me before that year was
over to take it again, because algebra was to be so much of future math. Whatever
you do you are gonna use Algebra I. So that is why I took it over again.
Family Structure and Influence
Tony lived with two parents, several siblings, and occasionally cousins in
government-subsidized housing in Central City, and he received free lunches through the
government school lunch program. Tony seemed to be very close to his family and spoke
of his mother and father several times. In discussions of the importance of mathematics,
Tony mentioned his father and other family members.
Well, my daddy, he used to say it was always important, you know, and um, my
auntie was like my auntie goes, was in college, and my cousin?s in college now
for accounting, and he always does math, and he says how important it is.
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Tony was planning on attending college with a scholarship to study computer science and
possibly play basketball or softball.
Tony?s mother apparently had serious health issues resulting in open heart surgery
during Tony?s tenth grade year, the semester of this study. Immediately preceding the
first interview, Tony missed a week of school while his mother was in the hospital in a
city about 80 miles from their home.
School Level Factors
In addition to days missed from school due to family and personal illness, Tony
missed school because he participated on the football, basketball and baseball teams.
Discussing how many days he missed from school, Tony stated that he might not be able
to take Algebra II the following year. ?They probably won?t let me take it (Algebra II)
since I been so lazy this year?That is I want to take it, I need to focus. I have been all
out of focus this year.? Tony broken his wrist playing basketball earlier in the year so
that ? somebody else had to write for me since I am left handed and that?s the one I
broke. And then my mom had open heart surgery.? Tony again acknowledged in a later
conversation, ?I always have an attendance problem, I get sick all the time.?
Classroom Dynamics
Mrs. Smith rated Tony as a potential seven or eight out of ten as a mathematics
student. Mrs. Smith believed that Tony could be a better student if he did not miss so
many assignments. Tony indicated that he liked his current mathematics class because the
class did not contain any students who were disruptive or rude; ?we have no clowns or
nothing so that?s why she has a good class. No one?s talking out loud or nothing like that.
Everyone?s listening to what she?s saying.? Tony liked his math teacher, liked all the
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math teachers that he has ever had, and believed that Mrs. Smith was ?real good.? Tony
stated that you do not have to do the homework in Mrs. Smith?s class, because she goes
over how to do it before you take the homework quiz.
Tony was a handsome young man with a charming smile and agreeable
disposition, who appeared to get along very well with other class members. If there was a
chance to interact with other students in the class, Tony appeared very comfortable
talking with whomever was in his group.
By mid-semester, Tony had missed quite a number of days and appeared to be
confused about what was being presented in class as well as behind in his homework.
During a classroom observation near mid-semester, Tony placed his head in his hands
during the note-taking time of the lecture and when he did look up, he kept his hands in
his lap. There was no evidence that Tony participated by taking notes or asking questions.
Several times, he appeared to have fallen asleep during the class period.
At the end of the semester, Tony had much the same classroom behavior: he did
not appear to be taking notes nor did he appear to know what was going on in the class.
Tony was behind in much of his work. Interestingly, he was very optimistic about his
grades; he stated that he was going to make it up and make a good grade on the final.
With a D the first nine weeks and a D on his progress report, he stated that he hoped to
make a C in the class. He was confident in his ability in math and continued to state that
his poor attendance caused his low grades. Tony explained:
See when I miss school, I always get behind, and I never really catch up. I never
make up all of my work. I get a lot of zeros out of 10 and can never get it all made
up, and they always bring my grade down.
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After being gone from class, Tony explained what it was like coming back and trying to
catch up with the geometry.
You have to figure it out yourself? It is kind of hard. She (teacher) gives you the
notes, but it?s just a whole lot different without her explaining it? And then you
have that night?s homework.
Tony described his normal schedule, ?during season, you practice, get home late, eat, do
homework,? and consequently he is too tired to get everything done. Tony went on to
state that:
if you know the work in Mrs. Smith?s class, you don?t have to do the
homework?She goes over it right before you take the homework check?And I
always manage to figure it out before a chapter test.
Personal Beliefs about Mathematics
Tony believed that mathematics was important to learn, primarily so that you
would get into college and possibly get a scholarship. Tony planned to do both, and was
taking advice from his cousin who was attending college and involved with sports.
Summary of Performance in Geometry
Tony had the ability to do quite well in geometry, based on his past performance,
his standardized test scores, and teacher assessments of his ability. Tony had a history of
missing many days of schools. Even when Tony was in the first grade, he missed more
than 25 days of school. His official attendance for geometry class listed only 8 days
absent due to the nature of the reporting system. Any excused absences would not be
recorded as absent, so when he missed for basketball games, had doctor?s notes or
checked out of school early, these did not count as absences. Of approximately a dozen
visits to Central City, Tony was absent on three occasions and checked out early by his
mother on two other occasions. As a consequence, Tony stayed behind in his work and
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barely managed to pass geometry. Tony planned to take Algebra II in his junior year in
high school, but he will be placed in Algebraic Connections, because he completed
geometry with a D average.
Josh
Past Performance in Mathematics
Josh was at the 90th percentile on the SAT-10 mathematics, the highest score of
those included in this study. Josh passed the SHSGE and made an A in algebra the
previous year. Josh?s ninth grade teacher described him as very quiet, very conscientious,
attentive, and a student who completed all of his homework. Therefore, Josh?s former
mathematics teacher rated him a 9 out of 10 as a mathematics students. Additionally,
Josh?s former teacher stated that she would have rated Josh as a 10, but he had a habit of
working ahead on future homework assignments during the class instead of being on task.
Her concern was that Josh might be missing important information because he liked to do
the homework for the next section during class while she was covering earlier material.
Josh stated that he did not like mathematics, although his mother stated that
mathematics and science were his favorite subjects. Josh claimed that he never studied
because it was not necessary for him to do so, and that he was good in mathematics.
Rating himself an 8 out of 10, Josh stated that he could be a 10, but that he did not have a
passion for doing mathematics. Josh explained that he would have taken geometry in the
ninth grade but he had a really bad eighth grade mathematics teacher, whom he did not
like, and consequently he made a 79 in her class. He explained that to not repeat Algebra
I in ninth grade, he needed to make an 80 in eighth grade.
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Family Structure and Influence
Josh did not receive free or reduced lunch and lived with his recently-widowed
mother in a brick home in Central City. When I first interviewed Josh in his home, I
noticed the respect that Josh and his mother had for each other and the way that Josh?s
mother listened intently to what Josh was saying. Josh?s father was an engineer by
profession, who died during Josh?s ninth grade year in school. When interviewing Josh
alone or with his mother, he was not reluctant to speak about his experiences and feelings
about mathematics and mathematics class.
Josh?s mother was very concerned with his progress in school and seemed to
make every effort to be available to the school and to his teachers. His ninth grade
algebra teacher remarked that Josh?s parents consistently responded to progress reports
and were the only parents from his mathematics class to attend open house at the school
during Josh?s ninth grade year.
Josh stated that his mother wanted him to be an engineer, and he planned on
attending a college or university. According to Josh: ?I really wanted to be a race car
driver,? even though his mother does not like it. To clarify, Josh said that this would have
to be his side job, and that he would do something else to earn his money so that he could
race. Josh stated:
You have to have something to fall back on if that does not work. . .engineering
will help, but I don?t want to be an engineer.. . I would rather do something
outside.. . I think of an engineer as being stuck inside.
Josh did not know where he got this interest in racing cars, because he did not drive,
never saw car races first hand, and had no relatives who raced, but he had seen some
races on television.
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School Level Factors
Josh did not participate in official extracurricular activities at the school. Josh did
not indicate that he was interested in participating in school activities, nor did he indicate
that he was adverse to the idea.
Classroom Dynamics
Josh was a neatly-dressed young man who was very small for his age and had a
high-pitched, soft voice. According to Josh?s ninth grade teacher, she tried to protect him
when other students picked on him because he was so small and vulnerable. Josh?s
algebra teacher described his classroom behavior as ?quiet, he didn?t say a word. He
didn?t like to call attention to himself but he would?put stuff on the board. He was one
of those that he just didn?t like to be the center of attention.? In his geometry class, Josh
did not volunteer or speak to others in the class.
While describing Josh as an introvert, Mrs. Smith rated him a 9 or a 10 on a scale
of 10, because he always completed his homework, and always did the required
assignments. Josh stated, ?I do my homework while Mrs. Smith is talking unless she is
looking directly at me.? Apparently Mrs. Smith gave her students the list of homework
assignments before she covered each chapter, and so Josh worked on the assignments
while Mrs. Smith was talking; the result was he did not have to do any homework at
home. When Josh did homework at home, he might work ahead. ?Last night I did my
homework for, well it was for today and I started, um, for tomorrow.? Questioning Josh
about what might happen if he misses something important by working on homework
instead of listening, he stated, ?I might have to stop and listen. Or figure out how to do
the problem by myself?There are examples in the book.?
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Josh stated ?I do not study for anything. I probably should, but I don?t like to
study.? As an explanation of why he had good grades, Josh stated ?I do my homework,
and I understand everything.? Although, Josh was not as sure of himself when he took
algebra the first time, ?now that I?ve gotten into it more, I understand it?well, I felt like I
understood it before, but the test did not show it. And now I am doing better on the tests.?
Josh?s geometry notebook was completely disorganized, containing all of his
other school work in with his geometry work. Josh thought that it was amusing that he
was disorganized and that he could not find old papers. Josh laughed about the state of
his notebook and shared that his notebook was missing a zipper on it and caused him to
lose some of his papers from time to time, as the papers would fall out.
Personal Beliefs about Mathematics
Josh stated that mathematics was not his favorite subject and that he did not like
mathematics, but it was apparent that he was probably not exactly truthful when he made
that statement. Josh?s mother stated that Josh did enjoy mathematics. Josh was very
playful in his comments during the interview process. For example, he told me that he
was stating exactly whatever he thought I wanted him to say. Josh was clever and
challenging in his short concise comments.
While acknowledging that mathematics was important, Josh did not see the
connection between geometry and what he expected to do with his life. Josh seemed to
trust that the school knew what he needed to take to be successful. As Josh expected to do
well in mathematics, both he and his mother were quite surprised when he did not earn an
A for the semester.
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Summary of Performance in Geometry
Josh had the potential to make excellent grades in mathematics and he did the
work that he thought was necessary to make a good grade in geometry. While admitting
that he did not study for tests and did not pay attention in class, he did not see a conflict
because he understood the material. Josh made a B for his final average because of his
final exam on which he earned a D. In a telephone conversation with Josh and his mother,
after school had ended, Josh stated that he did not understand how the final exam average
was calculated, as there was not a particular test given in his class which was called a
final exam. I explained to Josh and his mother that Josh was correct, and that the final
exam for his geometry class consisted of an accumulation of quizzes given throughout
the semester. It is hard to imagine that Josh would have made such a low grade on the
accumulation of these quizzes, when his other grades were very good.
Amber
Past Performance in Mathematics
Amber passed the SHSGE and scored in the 56th percentile on the SAT-10, which
was close to the average mathematics SAT-10 for Amber?s school, Central City. Amber
consistently made As and Bs in mathematics other than her 6th grade year. In the 6th
grade, Amber indicated that she had a D average in mathematics and that her mother had
subsequently gotten her a tutor. As a result, in the seventh grade, Amber stated that she
had the highest mathematics average in the class. Amber cited the following reasons for
her success:
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?it was the tutoring and it was me, cuz I studied a lot. When I got to middle
school everything changed cuz I think I started studying more? And I was
getting older. Maybe I?m make (take) some more responsibilities. A little more.
Amber?s ninth grade teacher said that Amber started the year thinking that she
was not a good mathematics student, and enrolled in Algebra A, the first semester of
Algebra I. By the end of her semester of Algebra A, Amber had become quite proud of
what she could do. Amber then enrolled in Algebra B for the first semester of her tenth
grade, doubling up on her mathematics to be able to take regular geometry for the second
semester of tenth grade. Amber?s algebra teacher believed that Amber was a very good
student, an 8 out of 10, who understood the connections in mathematics and did not just
memorize the algorithms. According to her algebra teacher, Amber always sought to
understand the mathematics, often came early to class to ask questions, listened in class,
and generally did all that she could do as a mathematics student.
Family Structure and Influence
Amber participated in the government subsidized lunch program at school and
lived with her mother in Central City. Amber spoke often of her mother, ??well my
mama, she?s in college right now, and I help her with her math.? Amber was a vivacious,
competent student who credited her academic success to her family and her personal
goals for her success. She stated that other students might not be successful because ?they
didn?t push theirself (themselves) to their goals,? or have family support: ?maybe their
family can?t put them through college.? Amber seemed very close to her mother and
stated that ?if your mama don?t care about what you do, why should you??
Amber?s mother saw the need for a strong mathematics background and wanted
Amber to do better than she had done herself in school. Amber?s mother believed that
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Amber was at least an 8 out of 10 as a mathematics student. Amber?s mother believed
that the only reason Amber was not a 10 was that Amber did not have the confidence
herself that she was a great mathematics student.
School Level Factors
Amber played on the girls basketball team, was a member of the flag team during
football season, was a part of the concert band, and was nominated to be a class officer at
Central High. Amber was conscientious about putting her school work first and did not
allow her extracurricular activities to interfere with her academics. Furthermore, Amber
stated that she planned on taking her next mathematics course during football season
rather than during basketball season so that she would not miss so many classes.
According to Amber, ?I ain?t takin it (during basketball season). I?m sure about that. It?s
gonna always be on Friday with football. It ain?t as bad as basketball ?cuz you have every
Monday, Wednesday, (and) Thursday (for games or practice).?
Classroom Dynamics
When I first contacted Amber?s mother, she said that she was glad that I was
talking to Amber because Amber complained about her geometry teacher, stating that
Mrs. Smith did not explain things well. Amber stated:
I still don?t like the way Mrs. Smith teach. But I?m not the only one.. . There is
something about her I?m not used to, but maybe that help me out in the long run
since she don?t break thing down like I think she could.
Amber indicated to me that she really loved algebra and her algebra teacher, but she did
not think that Mrs. Smith was a good geometry teacher. However, Amber believed that
Mrs. Smith wanted all of her students to do well, because she had posters all over her
room which told you to be excellent and to try your best. Amber said that she checked
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with her friends and believed that Mrs. Smith was the best geometry teacher at Central
City ?. . and basically I think that?s (she?s) the best teacher it (there) is from what they
say.?
Amber was observed to always do exactly what was being required in her
geometry class; she took notes, and paid attention. When the class was invited to ask
questions, Amber was one of only three or four in the class to ask questions, and Amber
asked as many questions as she could. Amber sought help from her teacher and from
friends when she did not understand a concept. Mrs. Smith rated Amber an 8 out of 10 as
a mathematics student and could not think of ways for Amber to improve.
Personal Beliefs about Mathematics
Amber believed that mathematics was important and that she needed to do well in
mathematics class. Amber stated:
Without math skills, you probably can?t get too far. Cuz if you like, want to make
a lot of money. McDonald?s, you don?t need math. . .if you?re at the cash register
it tell you how much money to give them back when it pop up?The way the
world is today, you need it (math).
Amber planned on getting scholarships and becoming ?a physical therapist, an x-
ray technician, or a pharmacist,? any of which, according to Amber, would probably
require mathematics. Amber stated, ?I want to be something in the medical field and you
got to know math for that.?
On a scale of 1 to 10, Amber initially rated herself a 5, ?cuz, I ain?t gonna say I?m
the best math student, but I know I?m not the worst. But if I had another choice, maybe a
7. I can help out my friends.? Then Amber upped that to an 8 in the next sentence and
rated herself, not in comparison to others as a 10. Overall Amber concluded with rating
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herself an 8, based on the fact that she paid attention in class and did what the teacher
said. Amber stated that other students fell asleep or just talked during class, while she did
what she was suppose to do.
Summary of Performance in Geometry
Amber did the work that was required of her in geometry and class and if she was
absent from school for any reason, she made sure that she made up the missed work.
Amber finished the semester with a B average. Amber stated that her grade was:
?89, I think?I been doing my homework, so-so. I been making good on my
homework checks and we took a chapter test today and yesterday we took a
formula test and I know I made 100 on that ?cuz I knew all them formulas. I think
I did good on the test.
Amber still believed that it was important to make good grades in mathematics
and that she wanted to remain on the advanced diploma track, but she was no longer sure
of the usefulness of geometry. Amber stated that ?It might be, but I don?t think it got
nothing to do with what I want to be. I want to be, um, an x-ray technician, and I don?t
think it got nothing to do with that.? Amber had advice to give future teachers of
mathematics.
Don?t go as fast as Ms. Smith, go at a slow pace. The homework check?is a
good thing, but if you don?t get it, then there go your grade. Do like Mrs. Johnson
(another math teacher) and give a grade if you try it, and then learn how to do
it?Go over it slowly?We only get in groups on certain days and you don?t get
to pick your group. If I could, I would get in a group with Coot (a friend),
and?Don?t do homework checks and do as many worksheets as you can to get
lots of practice.
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CHAPTER V
ANALYSIS AND INTERPRETATION
Interpretation and analysis of interviews, observations, interactions with the six
students, their parents and teachers in this study was done with the aid of Atlas-ti (Muhr,
1991), a qualitative computer software program . After all taped interviews and
observation notes were transcribed, they were loaded as separate path documents into the
software. That is, each document was linked to the software and accessed through the
link, therefore the document could not be altered by the software. Atlas-ti allows the user
to code text in any size segments into hermeneutic units, which is simply a means of
naming a unit of text documents. A single word or a paragraph from several documents
could be coded or labeled with a phrase which referred to the meaning attributed to the
words. For example, each student, parent, and teacher discussed the students? study
habits and these words or phrases were all coded with the words ?study habit?. Identical
phrases or parts of phases might be coded with more than one code; as study habits might
include ?homework? or ?peer influence?. Subsequently, a selected code will yield all text
associated with that code, and to which document the code belongs.
After reading each of the documents, response pattern emerged and similarities
were noted which led to the development of code lists. In that all initial interviews with
students, parents, and teachers followed a defined script, it was not difficult to find
similar response categories even if the responses were different. For example, five of the
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students gave responses which revealed elements of confidence in their ability to do
mathematics. These five students contrasted with the one student who was very unsure of
her ability in mathematics and her frustration in not ?getting it?. As each document was
reread, any response which referred to self-confidence or lack of self confidence was
coded with the term ?self confidence?. Other codes were developed as the documents
were read. These included codes such as personal goal, family education, reference to
peers, and understanding (as in the importance of understanding mathematics).
In that the review of current research was presented in categories labeled as
spheres of influence for the student and the interview protocols were developed from
these spheres, it seemed important to attempt to locate evidence of these categories within
the student, teacher, and parent responses. The spheres of influence included the
community and culture of the students, their educational institutions, and their
mathematics classrooms. For example, in the review of research there were theories
discussed which offer a rejection of the dominant culture by African American students
and the associated negative peer pressure (Kunjufu, 1988; Ogbu & Matute-Bianchi,
1986). In response to this research, a code of peer influence was developed and a student
response such as ?I call up my friends? or ?they think it is hard, was coded with the
words ?peer influence?. There were a total of 52 responses from the students which were
coded with ?peer influence?. Interestingly, none of these resulted in what would have
been classified as negative peer influence.
Teachers and parent interviews and classroom observations were used to
triangulate the data obtained from the students. There were no new codes developed from
the analysis of the teacher, parent interviews and the observations. The list of codes
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follows in Table 7 with the number of times each code was used after all the documents
were coded.
Table 7
Codes Words Used and Frequency
Codes Frequency
Advanced diploma
Agree with interviewer
Attendance
Behavior issues
Classroom dynamics
Confidence
Cooperative
Family education
Group work
Homework
Importance of math
Like or dislike
Parental pressure
Pay attention in class
Peer influence
Personal goal
Prepare for college
9
2
11
15
33
98
25
13
16
38
45
30
6
29
52
50
16
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Table 7 continued
Codes Words Used and Frequency
Codes Frequency
Scholarship
Seeks help
Study habits
Takes notes
Teacher support
Understanding
Want better for child
7
40
43
24
29
67
4
With 98 responses resulting in ?confidence in ability?, it was apparent that
confidence was a major category for all of the six students. Furthermore, as an example
of the triangulation of data, students, parents and teachers were asked the same question.
Students, parents, and teachers were asked: ?On a scale of 1 to 10 with 1 being the worst
math student and 10 being the best math student, how would you rate ____?? The results
obtained from this question are summarized in table 8 and will be discussed further in the
analysis of results.
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Table 8
Answers to the question: ?On a scale of one to ten, with one being the worst math
student and ten being the best math student, how would you rate ____??
Jasmine Tony Jonathan Amber Josh Danielle
Student 5 8 8 7 8 6
Mother 7-8 8-9 10 8 9 -
Geometry teacher 3 7-8 5-6 8 8 10
Algebra teacher - 7-8,10 5-6 8 9-10 10
One can see from the table that most of students were fairly confident in their ability and
that the ratings given by student, teacher, and parent are generally not too far apart.
Using Atlas-ti allowed for an efficient and accurate count of selected codes so that
in the analysis it could be easily determined which issues were the most often mentioned
by the students, their teachers and parents. For example, interview text from the six
students resulted in ?understanding mathematics? being coded 67 times while ?parental
pressure? was only mentioned six times.
Community and Cultural Influences
Whereas, the verbal evidence from students and parents indicated strong support
for Perry?s (2003) argument that African Americans have a strong and powerful
academic tradition, the actions of some of the parents tended to support the rejection of
education ascribed to caste-like minorities by Ogbu and Matute-Bianchi (1986) or Martin
(2000). According to every student and parent in this study, success in school and in
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mathematics was important and linked to success in life by way of attending college and
possibly receiving scholarships to support college attendance. Amber and Josh were the
only students in the study with parents who attended or graduated from college, but all of
the interviewed parents stated that they were confident that their children could be
successful in mathematics, would attend college, and would exceed what they as parents
had accomplished in school.
Martin (2000) maintained that even for those African American parents who
value education, the reality of their lived experiences of being denied opportunities
afforded Whites can dampen enthusiasm for the educational experience for their children.
Furthermore, these adults might consciously or unconsciously transmit these feelings of
meaningless education to their children (Martin, 2000). It is conceivable that Danielle and
Jonathan might have sensed this from their families, as their families did not participate
in school activities, nor did they respond to poor progress reports from geometry class.
Danielle, in particular, appeared to receive the least support from her mother and
expressed this family conflict by avoiding talk of her mother, hindering contact attempts
with her mother, and stating that her main support was from her good friends and from
members of the basketball team. Jonathan?s mother might not have been aware of how
poorly Jonathan was doing in geometry until late in the semester, as Jonathan might have
implied otherwise to his mother as he did in his interviews. On several occasions during
our interviews, Jonathan was not honest when he reported his grades or classroom
behavior to me. Danielle and Jonathan continued to state that education, mathematics,
and geometry in particular were important for them to learn. They felt it was important to
make good grades, even when their grades were not good. Thus, if Jonathan, Jonathan?s
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mother, or Danielle, consciously or unconsciously believed that education was
meaningless, they did not verbally confirm this.
Tony?s family was directly responsible, at least partially, for his lack of success in
geometry. Based on the number of days Tony stayed home or was checked out of school
early, attending school was not a high priority for Tony?s parents. Interestingly, Tony?s
absences from school, which were consistent and chronic through all of his school years,
did not seem to interfere with his grades in his early grades compared to what occurred
during his tenth grade in geometry. Tony?s parents had been able to keep Tony at home
many times prior to his high school years without causing him to make poor grades. It is
probable that the combination of days missed due to family and days missed due to
playing sports was finally taking toll on Tony?s academics.
The mothers of these six students were the most vocal, the most visible, and the
most often mentioned by the students. Josh talked about his father occasionally when
questioned, whereas Jonathan and Danielle never mentioned their fathers. Jasmine?s
mother was vocal in her support of Jasmine?s education, and her actions reinforced this
support when she met with Mrs. Basswood after Jasmine brought home her progress
report. Jasmine?s mother was confident that Jasmine was going to college and that she
was a good student who could earn a scholarship. Amber?s mother provided tutors for
Amber when she needed help and was always aware of Amber?s struggles in school and
how she was doing in mathematics.
Several of the students mentioned other family or community members who were
supportive of their educational efforts. Tony discussed his father, cousin, and ?auntie,?
who talked to him about going to college. Although, as noted earlier, his family?s
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behavior obstructed his academic success. Amber stated that while her mother supported
and influenced her, her biggest supporter was her grandmother. Amber?s grandmother
had not been to college herself, but encouraged and taught Amber that it was important to
go to college to be successful and to do what she wanted with her life.
Useem (1992) interviewed 86 parents of middle school students to study the
correlation between parent educational levels and ability level placements of students in
mathematics class. The results of the study indicated that parents pass their educational
advantage on to their children (Useem, 1992). The more educated the parent, the more
the parent understands the placement process of the school, and the more involved the
parent is in school activities. Therefore the more educated the parent the more likely the
parent is to intervene in the placement process (Useem, 1992). The results also indicated
that the more educated parent encouraged the higher level placement of their children in
mathematics class (Useem, 1992). The two most successful students, Josh and Amber,
had parents who had either had been or were currently enrolled in college. Furthermore
while all of the parents verbally supported their children in school and encouraged them
to do their best, the evidence supported Useem?s finding that the higher educated parents
were more knowledgeable about their child?s mathematics placement. In particular Josh
and Amber seemed to have inherited an educational advantage, whereas Tony, Jonathan,
Jasmine, and Danielle did not. Specifically, Tony?s success in mathematics was
undermined by his family?s actions as they caused him to miss many days of school.
There was no evidence that family members of Jonathan or Danielle contacted the school,
participated in school activities, or questioned their child?s placement in mathematics
class.
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Negative Peer Pressure
It should be noted that the students in this study were selected from a pool of
students who were already on the advanced diploma, or college track in their
mathematics coursework. These six students had been fairly successful in their
mathematics career thus far, and therefore the conclusions on negative peer pressure
might not be applicable to a wider population of students.
There was no evidence of pressure from these six students? peers to not be
successful academically, and there was no evidence that being successful was not
synonymous with acting White as described by Fordham (1988). All six students stated
that their friends thought mathematics was important to learn, and being successful in
school and specifically in mathematics was important. Amber mentioned older friends
who had passed geometry, but did not like it, as well as friends who had to repeat algebra
in summer school, and did not like it. All of her friends thought mathematics was
important, but did not like it because they did not understand it. Amber seemed to be
proud of the fact that she could help her friends with their mathematics and would
arrange study sessions for them. Danielle stated that she competed with her friends for
the highest grades on mathematics tests and if she needed help, she would call up her
friends. Danielle relied on her friends for support, and she indicated that they expected
her to be successful in mathematics and overall in school. Jasmine agreed with others that
her friends who understood math, liked it; and those who did not understand it and
therefore did not do well, did not like math. Jasmine stated that even her friends who did
not like math, thought it was important to learn. Tony stated that his cousin liked math
like he did, and his cousin was also his friend because they hung around together. Tony
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stated that he competed with another friend in his geometry class for the better grades.
Josh stated that he did not talk to his friends about mathematics, but that he knew that his
friends thought it was important to learn.
Jonathan had the least positive relationship with his peers, as evidenced by his
school suspensions which resulted from fighting in school. In ninth grade, Jonathan acted
inappropriately in his algebra class by teasing or putting other students down. Jonathan?s
algebra teacher believed that Jonathan possibly did this to make himself look better in
front of his peers. In geometry class, he did not mind asking questions which might have
sounded foolish or giving answers that might not be correct. Jonathan did not indicate
that he was bothered by appearing to his friends as if he understood mathematics, and his
peers did not influence him to hide his talent.
In summary, the evidence from interviews of the students, their parents, and
classroom observations supported Perry?s (2003) viewpoint, in that these African
American students appeared to have a strong cultural academic tradition. Furthermore,
the task for academic achievement is distinctive for African American students. The
distinctions listed by Perry (2003), many of which will be discussed later, include:
dealing with racism and cultural behaviors which cause misunderstanding, irrelevant
curriculum, inappropriate pedagogy, tracking, and other institutional and school practices
which limit educational access. While the evidence indicated a strong academic tradition
for these students, some of the actions or inactions by some of the parents did not support
student success.
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Educational Institution
Socioeconomic Factors
With children of poverty the pattern of low mathematics achievement often
begins in the early years, and these children continue to fail in disproportionate numbers
(Oakes, 2002; Singham, 1998). Whereas four of the six students in this study qualified
for the government-subsidized lunch program, it was unclear how their poverty level
affected their success in mathematics. It was evident that the total number of African
American students in each of the geometry classes observed was not proportional to the
number of African American students in the school. Moreover, most of the students
eligible for this study were eligible for government subsidized lunch. Tony and Danielle
resided in different housing projects, but both were well liked and respected by their
classmates and did not appear to have trouble relating to other students. Additionally,
both Jackson and Central City had median household income levels below the state
average and well below the national average, but it was not clear that this affected the
success of these students in geometry.
It was apparent that school resources were more abundant in Central City than in
Jackson, but all of the students had access to qualified and experienced teachers, new
textbooks and workbooks, and the supplies that they needed for school. Neither of the
geometry teachers in this study utilized their schools computer labs, but both teachers had
calculators available for their students to use in class. Both Central City and Jackson
High offered mathematics classes designed to prepare the students for college.
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High Stakes Testing, Tracking, And Course Taking
Track placement based on a single assessment measure often disadvantages
African American children (Edley, 2002; National Research Council, 2000; Oakes,
1994a, 1994b; Tate & Rousseau, 2002). While it was not clear to me that a single
assessment placed the students in the college preparatory track, four students in this study
mentioned how they came to be on the college track with their mathematics courses.
These four students stated that it was a result of taking pre-algebra in seventh or eighth
grade, and what their final grade was in each of those classes. Josh stated that he made a
79 when 80 was the cut off to be allowed to take algebra in the eighth grade. Jonathan
and Tony acknowledged that they were good in math in junior high, and therefore they
were allowed to take geometry in the tenth grade. According to Amber, she was not
encouraged to take pre-algebra in the seventh grade and later learned that not taking pre-
algebra early was a mistake. Amber stated that she doubled up in mathematics, taking
two mathematics classes her tenth grade year so that she could get an advanced diploma.
Amber commented that students should be required to take pre-algebra in the seventh
grade, and algebra in the eighth grade, so that when they got to high school they would
not be behind. Without her mother and grandmother pushing her, Amber stated that she
would not have known to take the mathematics that she did. Course-taking matters
(Gutierrez, 2000; Strutchens et al., 2004; Tate & Rousseau, 2002), as Amber stated very
ably.
According to Mrs. Smith, passing geometry did not qualify a student to take
Algebra II. Students from Central City High were recommended for Algebra II if they
earned a 70 percentage average in geometry calculated by taking their two 9-week
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averages as 50 percent and their final exam as 50 percent. Mrs. Smith stated that this was
a departmental decision and applied to all of the mathematics classes offered at Central
City High. This meant that a student who did poorly on the final exam would be assigned
to take Algebraic Connections instead of Algebra II. None of the students in Mrs. Smith?s
class understood or acknowledged knowing this policy. Additionally, Tony, Jonathan,
Amber, and Josh did not understand that the mastery quizzes which they took throughout
the semester would accumulate to become the final exam grade.
Challenging and Relevant Curriculum
The degree of understanding that a student has is directly related to the number of
connections that the student can make with personal knowledge and experience (Heibert
& Carpenter, 1992). In addition to being challenging, the content must be relevant to the
students? out-of-school life (Martin, 2003). All of the students in this study acknowledged
the importance of geometry, but rarely could any of the students state any connection to
out-of- school experience. Danielle stated that geometry was needed in sports, ?You have
to draw out the plays. You have to be at a certain angle to the goal to make it. Or when
you are running track, and you have to know the circumference of the track.? So
Danielle made connections from the geometry vocabulary to sports, but she did not need
geometry for any future work other than to make a good grade in class. Jasmine stated
that you needed geometry only if you were to become an architect or some similar
profession. All of the students determined that the mathematics of the class itself was not
important other than for counting out or adding money, but it was important in that they
could receive an advanced diploma and thus go to college.
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In all of the classroom observations, it was apparent that those students who were
most successful- Josh by focusing on his future homework and Amber by taking notes-
could remain focused on the material being presented by the teacher even though the
curriculum did not appear to be relevant or connected to life outside of the classroom.
Danielle was focused on the teacher lecture early in the semester, but not later as her
grades began to drop. Jasmine, Tony, and Jonathan often had trouble remaining focused
for the ninety-minute block of geometry theorems, postulates and proofs.
Supportive Environment and Addressing Racism
Gutierrez (2000) analyzed several high schools which were effective in teaching
minority students and found that common components were a rigorous curriculum,
reform-oriented instructional practices, and a strong teacher collective believing in and
committed to mathematics success for all students. These schools had administrative
support, particularly department chairs, who were committed to and supportive of a
teacher collective (Gutierrez, 2000). There was no evidence in the two schools involved
that either administration was committed to a teacher collective or to ensuring success for
students who had traditionally not been successful in school. When asked if I might work
individually with one of the students who was struggling in geometry, the principal of
Central City responded that there was plenty of after-school help offered at the school in
which the student should participate and that offering special services to that student was
not necessary.
The four year projected dropout rate is the percent of students in grade nine for
the academic year 2002-2003 who would be projected to leave school prior to graduation
in 2006 (* State Department of Education, 2004b). The projected dropout rate, not
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reported by racial/ethnicity groups, for Central City was just over 20 percent, and for
Jackson High, 33.5 percent (* State Department of Education, 2004b). Both of these
dropout rates are extremely high as evidenced by the overall state dropout rate of 13
percent, which earned this state the rank of 47 of the 50 United States in the percent of
people who complete high school (* State Department of Education, 2004b; U.S. Census
Bureau, 2004). So while the projected dropout rate is not reported by race, it is apparent
from examining the racial makeup of the freshmen and senior classes at each of the two
schools in this study that more African American students dropout than White students
from both Jackson and Central City High Schools. None of the six students in this study
appeared to be considering dropping out of school, but as stated above the
administrations at the school was not committed to addressing this issue for their African
American students.
The geometry curriculum at Jackson High and Central City High was identical in
content, both teachers using and following the same textbook, chapter by chapter.
Instructional practices were traditional and non reform-oriented for both Mrs. Smith and
Mrs. Basswood, and both appeared to operate independently of their respective
departments. The teachers seemed to be committed to treating all students equally, but
did not appear to be committed to ensuring that their minority students would be
empowered mathematically to overcome any injustices that these minority students might
experience because of their race. Mathematics was viewed as a stepping stone on the
college path, but not as a tool to empower students as described by Sleeter (1997),
Ladson-Billings (1995), Frankenstein (1995), and Guiterrez (2000). The students in this
study were not challenged to investigate the connection between mathematics and
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society, and therefore did not have the opportunity to learn to deal with obstacles which
can limit their success.
Classroom Practices
Classroom practices which can serve as barriers to mathematics achievement for
African American students include irrelevant curriculum, lack of resource materials, and
types of assessment which do not match the learning style of the student (Singham, 2003;
Tate & Rousseau, 2002).
Classroom Instructional Practices
The classroom practices of Mrs. Smith and Mrs. Basswood were not aligned with
the best practices recommended by the National Council of Teachers of Mathematics and
described in their documents, the Professional (1991) and Assessment Standards (1995)
and the Principles and Standards for School Mathematics (2000). Effective teaching
practices can make a difference in mathematics learning, therefore it is informative to
examine the methods used by Mrs. Basswood and Mrs. Smith.
Analysis of Classroom Strategies
Ladson-Billings (1994, 1997), Berry (2003), Sleeter (1997), Tate (1997), and
Schoenfeld, (2002), Lee and Smith (1993, 1995a, 1995b,1997), and Gutierrez (2000)
gave convincing arguments that effective teaching styles and standards-based curriculum
can make a difference in mathematics learning. Not only do more students do well, but
the racial performance gap, although not eliminated, could be reduced (Berry, 2003;
Schoenfeld, 2002). As stated earlier, neither Mrs. Smith nor Mrs. Basswood used a
standards-based curriculum but relied heavily on their textbook, incorporating very little
group work, no student discourse, no student investigations, and no justifications of
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student work. The vision for the mathematics classroom as described by the Principles
and Standards for School Mathematics (National Council of Teachers of Mathematics,
2000) had not been realized in these two classrooms. Four of the six students in this study
completed geometry with a D average. If success in mathematics is measured by grades,
then these four were not successful. But if success in mathematics is seen as
empowerment, relevance, and training for future work and society situations, then one
might hypothesize that none of the students were successful. The two students who made
grades above D did not view geometry acquisition as having importance beyond going to
the next level of mathematics and on to college.
Assessment Strategies
There was no evidence in either Mrs. Basswood or Mrs. Smith?s room that
assessment consisted of measuring the students? critical thinking skills. Ladson-Billings
(1999) argued that traditional assessment measures tell us what the child does not know
but do not tell us what the child does know. Furthermore, traditional assessment methods
are ways of maintaining the inequitable power structure (Weissglass, 2002).
In Mrs. Smith?s class, student assessment consisted of homework checks, which
mimicked the problems of the textbook; mastery check quizzes, given over the semester
and totaling to become the final exam score; and graded homework assignments when a
student or Mrs. Smith was absent. There was no evidence of investigative work, projects,
or group-work which was graded.
Mastery quizzes in Mrs. Smith?s classes were one-fifth of the students final grade.
These quizzes were scheduled to be taken over the course of the semester and as much as
several weeks after the material had been covered. For example, the class might be
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working in chapter seven, section three, and take a short mastery quiz on section one,
chapter six, on the same day. A student could arrange to retake a mastery quiz, but the
two quizzes, the original and the make-up, would be averaged for the final mastery quiz
grade. None of the four students in Mrs. Smith?s class: Tony, Jonathan, Amber, or Josh
understood how these mastery quizzes were scored or that they would sum to become
the final exam grade.
Another grade component of Mrs. Smith?s class was the homework check, or in
case of absences, graded homework. The students took a homework grade or quiz on the
material to which they had been introduced the previous day. Amber stated concisely,
?The homework check is a good thing, but if you don?t get it, there go your grade.?
Amber continued with the recommendation, ? do like Ms. Johnson (another mathematics
teacher) and give a grade if you try it, and then learn how to do it?go over it slowly.?
Amber?s recommendation was to give a homework grade for effort instead of correctness
and then review the new concept a second time.
Student assessment in Mrs. Basswood?s class consisted of notebook quizzes,
where the students used their notebooks to find and copy a previously assigned problem
onto the quiz; chapter tests taken from textbook material; and points given for effort on
class or group work. Again there was no evidence in Mrs. Basswood?s room of
investigative work or projects. Jasmine, with her disorganized and incomplete notebook,
had a particularly difficult time with notebook quizzes.
Therefore the only means of determining success in mathematics for the six
students were more traditional forms of assessment, the final class averages, and whether
or not they would be allowed or encouraged to move to the next level in mathematics. As
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a result of the assessment practices used in their respective schools, Jasmine, Amber,
Josh, and Danielle are eligible to take Algebra II in their junior year in high school, and
Tony and Jonathan are only eligible to take Algebraic Connections, a lower level of
mathematics. Amber and Josh would be the only two students in this study to be deemed
successful by their final grade averages.
Teacher Beliefs and Differential Treatment of Students
Perry (2003) asserted that if teachers stereotype African Americans as having
inferior intellect then these teachers would automatically expect less of African American
students, possibly interact less with these students, or recommend that African American
students be place in lower tracks. There was no evidence from classroom observations or
statements made by students that either of the two teachers involved in this study
expected less from these students as African American than they did for their students of
other races. But on the other hand, there was no evidence to suggest that either Mrs.
Basswood or Mrs. Smith was committed to ensuring the success of their minority
students.
Danielle and Jasmine were students in Mrs. Basswood class, and both of them
stated that they liked their teacher and felt supported by her. Mrs. Basswood did not
expect Jasmine to make a good grade in geometry because Jasmine failed the SHSGE
mathematics portion. Mrs. Basswood saw Jasmine as a weak geometry student and
ranked her as a 3 out of 10. When Danielle made unexpectedly low grades, Mrs.
Basswood?s response was to write notes on Danielle?s tests encouraging her to do better.
Danielle seemed to respect Mrs. Basswood, but she did not communicate to Mrs.
Basswood any reason why her grade was dropping. Neither Danielle nor Jasmine would
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seek extra help from Mrs. Basswood, and Mrs. Basswood clearly had different
expectations for Jasmine and Danielle.
The two students who made the highest grades, and the two students who made
the lowest grades in geometry were in Mrs. Smith?s class. Mrs. Smith seemed to have no
particular expectations for most of her students. She did not know anything about their
home situations, or study habits, or friends. She was unable to identify any reasons which
may have caused them to behave as they did. For example, Mrs. Smith did not know why
Tony missed so much school, and she did not know that Josh had recently lost his father.
Mrs. Smith did not expect Jonathan to do well, and commented on Jonathan?s behavior
both in her class when he lost bathroom privileges, and when he got suspended and could
not make up the work. Mrs. Smith was not enthusiastic about any of the students? work
when I interviewed her. She usually did not know how the students were doing in her
class until she got out her grade sheets. Mrs. Smith?s response to low grades was to send
home the school-mandated progress report and expect her students to improve their
performance.
Neither Mrs. Basswood nor Mrs. Smith made a practice of calling the homes of
their students. Direct parental contact by both teachers was maintained through the
progress reports or was initiated by the parent. Any information about the student?s home
circumstances either was told to the teacher by others at the school or by the students
themselves.
Color-blindness on the part of the teacher is a form of dysconscious racism
(Ladson-Billings, 1994). The teacher who claims that she does not see children as
African American, White, or Hispanic, but sees them only as children, is unaware of the
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fact that she created an environment where some children are privileged while others are
disadvantaged (Ladson-Billings, 1994; Rousseau & Tate, 2003). Both Mrs. Smith and
Mrs. Basswood, who were White, appeared to treat all of their students equally and most
probably would fall into the category of acting color-blind. There was nothing done
proactively by either teacher to ensure success by their African American students nor to
empower these students in or through mathematics.
Student Attitude
Students? attitudes towards learning mathematics appears to be a major factor in
determining achievement (Kim, 1998; Rech & Stevens, 1996). Mathematics is feared and
revered as a subject only some can understand through innate ability (Ladson-Billings,
1997). Tony, Jonathan, Amber, and Josh believed strongly in their self-efficacy as
mathematics students. Jasmine struggled with the notion that she was not particularly
good in math, but believed that if she pushed herself then she could possibly understand
more. Danielle seemed fairly confident of her ability at the beginning of the semester, but
unsure of her ability by the end of the semester as her grade dropped. Danielle did not
acknowledge that she was not attentive in class, in contrast to her behavior earlier in the
year.
According to a study by Signer, Beasley, and Bauer (1997), many students
believe that if a person is good at something than they should not have to work hard at it.
Therefore, if effort is involved, then low ability is implied. On the other hand, more
successful students indicated that intelligence could be obtained through hard work and
persistence (Signer et al., 1997). Tony and Jonathan continued to believe that they could
finish the year with C averages because they were good in math and could do well on the
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tests. Both Jonathan and Tony did do remarkably well on the chapter tests and homework
quizzes, despite having done none of the homework and being absent on numerous
occasions. There were several chapter tests on which either or both Jonathan and Tony
made as high as a B. In contrast, Jasmine seemed to be experiencing what Signer,
Beasley, and Bauer (1997) termed as ?learned helplessness?, where students believe that
their ability level is fixed and the cause of their failure. Observing Jasmine in class, it was
apparent on many occasions she gave up, would not ask questions, and accepted that she
was not going to understand.
Student Reactions to Marginality
Forham (1988) described how some African American students assume a raceless
persona when faced with confrontation from peers and teachers. Grant and Reese (1997)
offered several more categories for describing response behaviors, some being
detrimental to learning, such as withdrawn or affected; and some being beneficial to
learning, such as emulative, emissarial, and balanced. As all six of the students in this
study were chosen based on the fact that they were in regular college-track geometry, and
none of the six were found to have adapted behavior detrimental to their mathematics
learning as a response to racism. None of the students appeared to reject their race nor
their African American friends; they were not defiant or withdrawn, two of the categories
found by Grant and Reese (1997). It is possible that Josh rejected his friends, but he did
not seem to want to be friendly with any of the other students in the class, choosing to
work by himself. Amber stated that it would be helpful to her if she were allowed to
select her own group in geometry so that she could work with some of her friends whom
she believed were doing well. Furthermore, on several occasions Amber mentioned
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working with her friends on their mathematics, even those who were not taking
geometry. All six students commented that their friends and family believed being
successful in mathematics and in school was important.
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CHAPTER VI
SUMMARY AND RECOMMENDATIONS
The purpose of this study was to use a student lens to assess the mathematical
experiences, attitudes towards mathematics, expectations of peers, parents and teachers,
and to assess how these perceptions affected the mathematics performance of six tenth
grade African American students as expressed by the students, each student?s classroom
behavior and performance, and the students? parents and teachers. The general research
questions were:
1. How do African American students in this study view their mathematics
experiences currently and in their past?
2. Do the African American students in this study consider mathematics important to
learn? Do they see a relationship between mathematics acquisition and future job
opportunities or education? Do they view mathematics as an empowering tool?
3. Are parents, guardians, community, and peers influential sources for the African
American students in this study in achievement and specifically mathematics
achievement? For the students in this study, where or what is their primary
source of influence?
4. How do the African American students in this study interact with their
mathematics teacher? Do the students perceive their teacher as encouraging, and
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knowledgeable? Is there a relationship of mutual respect and admiration between
the student and the teacher?
5. To be successful in mathematics, must one adopt the culture and behaviors of the
White students? If this is the case, does it hold true for African American
students whether they are the minority or majority in school? Are there other
coping mechanisms for these students to employ when dealing with racial issues
which confront them in situations at school so that access to mathematics
education is not an issue?
6. Does gender affect the African American students? view of mathematics? If this
is the case, in what ways does gender affect the student?s relationship with school
officials, parents and society at large, with respect to mathematics learning?
Specifically the purpose of this study was to examine the mathematics experiences of
six African American tenth grade students through their eyes, their actions, and their
voices. What did the students believe influenced their performance and achievement and
how did they react to these influences? This study supplemented existing research on
African American students? mathematics achievement, and echoed the appeals made by
many researchers for changes in curriculum and instructional practices so that barriers to
mathematics attainment for African American students could be reduced. Additionally,
this study reinforced the idea that parental support and cooperation must be maintained to
maximize student learning and achievement.
Limitations
Although a multi-single unit case study was selected as the most appropriate
method for this study, there are several limitations. A major limitation of this study is in
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assuming applications to a wider population than these six high school students. Using a
few case studies allows in-depth information to be obtained on these few students at the
sacrifice of breadth. A second limitation of this study is in generalizing characteristics of
populations along racial/ethnic lines. Not only do different assessment tools use different
classifications for race/ethnic groups, but there exist subgroups within racial groups
adding the need for further caution in applying generalizations about racial groups (Tate,
1997). Tate (1997) warned of the difficulty in classifying racial/ethnic groups,
recognizing that the literature reviewed is limited by not defining the subgroups within
the classifications used. Additionally, it is important to recognize that individuals are not
just African American or White, Hispanic or Asian, but gendered, and gender differences
do exist. Acknowledging these differences and maintaining that overall the gender
differences were outweighed by racial/ethnic differences, this paper does not further
address gender issues.
A further limitation with this study was in determining whether or not these six
students were successful in mathematics. To the students, their parents, and teachers,
success was passing geometry and making a good grade. According to Principles and
Standards of School Mathematics (2000), geometry should enable students to analyze and
understand structures in the world. Students should be able to problem solve, make
conjectures, justify their position mathematically, and apply their learning to new
situations (National Council of Teachers of Mathematics, 2000). For these six students,
the kind of mathematics learning recommended by the National Council of Teachers of
Mathematics was not assessed. Schoenfeld (2002) warned that often the kind of
knowledge being tested is not aligned with the kind of mathematics that we want our
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students to be learning. The type of assessment that would more closely measure
mathematics which reflected problem solving skills beyond basic computation have been
expensive for school systems as well as hard for the public to understand (Schoenfeld,
2002). Therefore these tests, which actually measured useful and relevant mathematical
skills, were not likely to be used by school systems in general and specifically were not
used for these six students.
Finally, and possibly most importantly among the limitations, was the subjectivity
of the researcher in being a participant as well as an observer in these case studies. While
a script was used for all initial observations, and the analysis resulted from the use of
available software to code common themes, there was an interpretive component to this
qualitative research in which a degree of subjectivity was involved. The researcher was
occasionally involved in the classroom dynamics during observations, and always a
participant in the interviews. Interpretive research requires the researcher to continually
reflect critically on self and the components of self which the researcher brings to the
research setting (Lincoln & Guba, 2003). One necessary component of the required
critical reflection was the fact that the students were African American and the researcher
was White. Some would argue that a researcher who is not African American can not
interpret research results of African Americans critically or effectively (Bergerson, 2003).
It is possible that a White researcher would have the opportunity to analyze this research
in a manner differently than an African American, but there is arguably validity in both.
Therefore, recognizing that some of the student interviews might have revealed more to a
researcher who shared the student?s race, there was considerable self reflection done
while analyzing the results of this study.
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Implications of the Study
Amber and Josh took responsibility for their mathematics learning. Amber asked
questions in class, completed her homework assignments, engaged a tutor when needed,
and enrolled in two mathematics classes during her sophomore year. Josh completed
most of the homework assigned, read and understood the textbook, and usually paid
attention in class. While Danielle, Tony, Jonathan, and Jasmine did not take the essential
steps to ensure successful completion of geometry, student inactions should not excuse
parents, counselors, coaches, and teachers from allowing these students to fail. Educators
can and should affect change in the classroom to enable students, and specifically
students who have been underserved, to become successful and empowered by
mathematics. Therefore the greater part of the implications discussed in this chapter are
school level issues.
Implications for Parents
Three of the students in this study, who were not successful in geometry, had
families whose actions or non-actions interfered with their children?s success in
mathematics. Tony?s family was mostly responsible for his chronic absentee problem.
Jonathan?s mother stated that she did not get involved with the school because Jonathan
was smart and could do his work. Danielle?s mother did not attend school functions,
would not respond to requests for conferences, and might have been responsible for
Danielle dropping off the basketball and track team to take a job at the local grocery
store.
The two most successful students in the study had parents or other family
members who were directly involved with their school work, and were aware of what
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mathematics courses their child was taking, and who their child?s mathematics teacher
was. Josh?s mother was present at the school?s open house and met his mathematics
teacher. Amber?s mother was aware of what Amber thought about mathematics and her
mathematics class and teacher. Additionally, Amber?s mother furnished a tutor for
Amber when it was indicated that she needed additional help.
Josh and Amber were the only two students whose parents had or were attending
college. Parents with higher levels of education or those from higher socioeconomic
levels often have higher levels of involvement in their child?s education (Spade et al.,
1997; Useem, 1992; Wells & Oakes, 1996). The parents in this study support previous
research results, as evidenced by the parents of Josh and Amber who appeared to be the
most positively involved in their children?s schooling.
In summary, parents need to be aware that they have the power to hinder or
support the schools efforts on behalf of their children. A student whose family places
school attendance as a low priority will negatively effect the students ability to be
successful in mathematics. Parents who detach themselves from their child?s school or
academics send a message to the child that schooling has to be handled without the
parental support. For some children, being successful in mathematics is not supported by
parents? actions.
Implications for Schools
Parents as partners. It is the responsibility of the school to ensure that parents are
involved in their child?s schooling at an early age so that major educational decisions are
not left solely to the schools guidance department or worse not made at all. It should not
be assumed that all parents are equipped with the tools necessary to effectively support
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the educational endeavors of their children. If that assumption is made then school
personnel through inaction allow the failure of some disadvantaged children.
Teacher collective. While Mrs. Smith?s mathematics department worked together
to decide what standards they would collectively use to recommend students for
placement the following year in mathematics class, they did not work together to ensure
the success of their students. At Mrs. Basswood?s school, the math teachers usually
worked individually in their respective classrooms. Neither Mrs. Smith nor Mrs.
Basswood had time scheduled for their respective mathematics departments to work
collaboratively.
As stated previously, the effective components for schools to ensure success for
minority students include a rigorous curriculum, reform-oriented instructional practices,
and a strong teacher collective believing in and committed to mathematics success for all
students (Gutierrez, 2000). Teachers working individually might be successful with
students for the term or year, but to support long term results, schools must ensure
collaborative efforts of all the teachers and administrators. Ladson-Billings (1994)
described a situation when a student of a culturally relevant teacher faced a setback the
following year when confronted with a teacher who did not acknowledge the students?
mathematical abilities (Ladson-Billings, 1994). When the administration and teachers
work together in a committed collaborative effort, situations such as those faced by this
student would be avoided.
Ideally, the coaches and counselors from the school would be a part of the teacher
collective focused on academic success for all students. Four of the six students in this
study participated in school sports and three of those students experienced less than
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desirable success in their mathematics courses. There was no evidence that the athletic
staff from the students? teams were involved with the students? academic endeavors.
Similarly, there was no evidence that the schools? counselors were involved with student
academic achievement or with student course selection and placement.
There are several approaches which school counselors can use to increase the
number of African American students who are successful in mathematics.
Recommendations from the United States Department of Education include holding high
expectations for all students and recognizing that taking advanced mathematics courses in
school is essential to increase opportunities for students in career selection and higher
education (U.S. Department of Education, 1996). Counselors should have a system to
communicate the necessity of mathematics course-taking to parents and to tap
professional organizations to provide role models for students (Shoffner & Vacc, 1999;
U.S. Department of Education, 1996). Further recommendations for counselors include
working with teachers and administrators to address perceptions and the relationship
between attitudes and achievement (Shoffner & Vacc, 1999).
Cohesive challenging curriculum. The students in this study were not exposed to
a challenging relevant geometry curriculum. A challenging curriculum has been linked to
students? mathematics achievement (Gutierrez, 2000; Lee & Smith, 1993, 1995a, 1995b;
Lee et al., 1997; Schoenfeld, 2002). Perry (2003) insisted that African American students
who do not have a challenging curriculum will not only be shortchanged, but will believe
that those who selected this curriculum think that they are not as capable as other
students. Successful programs such as the QUASAR project and the Interactive
Mathematics Program (Merlino & Wolff, 2001), serve as models for how to offer
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challenging mathematics curriculum to students who are primarily African American and
economically disadvantaged (Silver & Stein, 1996; Tate & Rousseau, 2002).
Tracking and course-taking. Central City High had a method of placing students
into advanced mathematics classes that was not easily understood by the students in this
study. Furthermore, Amber would not have been on college track in mathematics if she
had not taken the initiative herself to double the mathematics courses she took during the
school year. Neither Tony nor Jonathan understood how they were placed in geometry in
the tenth grade. At Jackson High, Danielle was encouraged by her teachers to take
college track mathematics as she had been an excellent student through the years. On the
other hand Jasmine?s mother was the one who pushed her to take the college preparatory
classes and maintain a decent grade.
Schools must be mindful of their open or subtle tracking procedures, and who or
what influences the students in selecting which courses to take. Tracking can start as
early as elementary grades and can determine what courses the student takes in high
school (Spade et al., 1997). Additionally, the parents with political and social power are
the ones who make the system work for their children, insisting that their children receive
something extra from the school (Wells & Oakes, 1996). Pushing the school to enroll
their child in more-advanced classes takes a self-confident person, and parents with
higher levels of education have been linked to increased involvement with their child?s
placement (Useem, 1992). Parents from higher socioeconomic classes are more involved
in determining which classes students take, whereas in schools where mostly working
class children attend, the decision is contained within the guidance department (Spade et
al., 1997). Course-taking matters and African American students have been less likely
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than White students to take advance mathematics courses in high school (Gutierrez,
2000; Hoffman et al., 2003; Strutchens et al., 2004; Tate & Rousseau, 2002). Schools
must carefully evaluate how they encourage or discourage students from taking specific
mathematics courses.
Preparing students to address racism and social inequities. While some might
argue that the mathematics classroom is not the place to address issues of social
injustices, others would argue that there is no better place than in mathematics. Both
Ladson-Billings (1997) and Moses and Cobb (2001) argued that more mathematics
knowledge and skill attainment is tied to better life chances. Furthermore, educational
reform efforts which attempt to reduce the achievement gap but do not address
racism/classism will be doomed to failure (Weissglass, 2002). Perry (2003) used the term
racial socialization, for the process of preparing children to deal with racism and other
obstacles that they might face in school. The playing field is not always equal and helping
children learn how to cope and persevere is essential to empowering them to function as
citizens. Perry (2003) suggested using a model such as one developed by the Association
of Independent Schools, called the Multicultural Assessment Plan. Perry (2003)
explained that the Multicultural Assessment Plan is an external review process in which
schools are assessed for how they reproduce the ideology of African American
intellectual inferiority and how schools can address this issue and move in another
direction. Several schools in the Northeast have successfully used this plan to change the
direction of their schools to a more supportive environment. African American students
need affirmation that their racial heritage is synonymous with being intellectual and an
achiever (Perry, 2003). Weissglass (2002) argued that the racist practices in schools can
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be alleviated through a complex process of reflection and re-evaluation of existing
practices and understanding. Furthermore, it was suggested that the new paradigm for our
schools should be one of a healing community and that it is our responsibility as
educators to heal ourselves from the damage that racism has done (Weissglass, 2002).
Implications for the Classroom
Relevant standards-based curriculum. Culturally relevant teaching as described
by Ladson-Billings (1994, 1995a) was not available to these six students in geometry
class. If these six students, who seemed to have the potential to do fairly well in
mathematics, had been exposed to mathematics which was culturally relevant and
empowering for them, what would have been the outcome? Research indicated that
effective teaching coupled with a standards based curriculum could make a difference
(Berry, 2003; Gutierrez, 2000; Ladson-Billings, 1995a, 1997; Lee & Smith, 1993, 1995a,
1995b; Lee et al., 1997; Rousseau & Powell, 2005; Schoenfeld, 2002; Sleeter, 1997;
Tate, 1997).
Using the same textbooks and supplemental workbooks, Mrs. Basswood and Mrs.
Smith employed very traditional teaching styles. Lesson plans for both Mrs. Smith and
Mrs. Basswood consisted of textbook chapter numbers, and test and quiz dates. Lessons
in these two classrooms did not flow from student conjectures and student discussions.
Therefore, the students were often bored and not paying attention. These students were
not participants in their learning.
For a student to learn new mathematical ideas, they must be able to relate it to
previously learned material (Heibert & Carpenter, 1992). Moreover, the students? culture
affects the students? perception and interpretation of the learning environment.
146
Additionally, the degree of understanding that a student has is directly related to the
number of connections the student can make with their knowledge and personal
experiences (Heibert & Carpenter, 1992). Students who do not see a connection between
what they are learning in school and what skills are needed for their life goals will have
no motivation for continuing to attend to their education (Carey et al., 1995). The
curriculum used in the classrooms in this study did not allow for connections to the
students experiences or personal knowledge. The opportunity to learn of students?
culture, experiences, or personal knowledge was not possible in these two classrooms as
little or no student discourse took place.
Standards based curriculum is focused on student?s conceptual understanding and
reasoning rather than rote learning and memorization (National Council of Teachers of
Mathematics, 1989, 2000). Features of a standards based curriculum include meaningful
mathematics which is accessible to all students, empowering them to become
mathematically literate for the workplace or for college, and to function as informed
citizens in a democratic society (National Council of Teachers of Mathematics, 1989).
Standards based curriculum emphasizes problem solving, higher-order thinking, and
student inquiry through investigations, conjectures, and justifications. While both
geometry teachers expressed wanting all of their students to be successful in
mathematics, there was a conspicuous absence in either classroom of higher order
thinking through problem solving and no student investigations, conjectures, or
justifications. Of the six students only Josh and Amber stayed on track with homework
through the semester. There was not an opportunity for any of the six students in this
147
study to experience standards based curriculum or teaching practices aligned with the
recommended standards.
Effective pedagogy. Standards based teaching includes selecting worthwhile
mathematical tasks, knowing and understanding mathematics, understanding students as
learners, knowing what the students bring to class from their culture and past
mathematics learning, providing a challenging and supportive environment, knowing
how to orchestrate student discourse, and being reflective about instructional practices
(National Council of Teachers of Mathematics, 1991, 2000). To both Mrs. Smith and
Mrs. Basswood teaching meant that they should explain all of the material very carefully
to the students. Both Mrs. Smith and Mrs. Basswood wanted to make mathematics as
understandable and simple as possible, going over an example of each kind of problem
which their students would encounter in the chapter being studied. The students depended
on their teachers to translate the mathematics textbook for them. Mathematics being
similar to a foreign language. Indeed, very few students could read the examples in the
textbook, nor were they able to proceed unaided with an assignment when either Mrs.
Basswood or Mrs. Smith was absent. Danielle depended on Mrs. Basswood to explain or
translate the material for her, and Jasmine stated that she did not understand most of what
was explained but could understand more with help from Mrs. Basswood than when left
to her own devices with her textbook. Amber believed that she needed a teacher to
explain math to her, but Josh would teach himself from examples in the text. The type of
instruction which took place in the two geometry classrooms in this study included drill
and practice, worksheets, as well as instructor-student interactions which were few and
148
required only short responses; in other words, not the type of instruction recommended
for students who are having difficulties in school (Oakes, 1994a, 1994b; O'Neill, 1992).
Not all African American students can be categorized as a particular type of
learner, although research indicated that many African American children are relational
or field dependent learners (Berry, 2003; Rech & Stevens, 1996). Effective teaching for
field dependent learning styles includes the use of manipulatives, verbalization, and a
global perspective (Rech and Stevens, 1996). A relational learning style is characterized
by divergent thinking, freedom of movement, variation, creativity, and inductive
reasoning with a focus on people using concrete imagery (Berry, 2003). Traditional
teaching styles are not effective for relational, field dependent learners and were
described by Tate (1997) as a cultural artifact designed to produce students who can
answer a narrowly defined problem set. Furthermore, by allowing some students to fail,
traditional methods of instruction served to maintain the status quo, reinforcing white
privilege (Rousseau & Tate, 2003).
Rousseau and Tate (2003) identified two barriers to teachers reflection about their
teaching and changing teaching practices, and these were the teachers? view of equity and
the teachers disposition toward color blindness. Color blindness, while probably
unintentional, is described as a form of dysconscious racism (Ladson-Billings, 1994). The
teacher is unaware of the fact that she created an environment where some children are
privileged while others are disadvantaged (Ladson-Billings, 1994; Rousseau & Tate,
2003). Teachers who do not address the issue of racism with their students, are not
empowering their students to effectively confront racism in society (Martin, 2003;
Rousseau & Tate, 2003). Culturally relevant teaching which respects and utilizes the
149
culture of the student and empowers the student to face societal injustices does not allow
for color blindness. Culturally relevant teaching ensures the success of the disadvantaged
child (Ladson-Billings, 1994). While both Mrs. Smith and Mrs. Basswood believed that
they were doing the best job that they could to teach geometry to their students and to
treat all of their students fairly and equally, neither recognized the need to use unequal
means to ensure equitable outcomes for their unique students.
On one occasion in Mrs. Basswood class, two students, both White males,
returned graded quizzes to their peers. These two students commented on whatever grade
was on the paper as they returned the paper to its owner. Jasmine, along with several
other students, was distinctly uncomfortable with having her grades analyzed by another
student. Mrs. Basswood did not seem to notice that these two boys were humiliating other
students. Parsons (2005) had several suggestions for helping teachers to become
culturally relevant caring teachers. The first step for the teacher is to disrupt the
dominance of any students which might prevent access to learning for other students
(Parsons, 2005). The second step is for the teacher to recognize the abilities of the
students, and provide assistance to students not as remediation but in the spirit of pride
and supportive accomplishment (Parsons, 2005). The third step requires teachers to seek
opportunities to reinforce African American students competencies and encourage them
to support their peers (Parsons, 2005). Parsons (2005) insisted that teachers, and
particularly white teachers, can and must disrupt the existing order of white privilege by
empowering their African American students in the classroom.
A classroom which incorporates cooperative learning, another aspect of standards
based teaching, can have a positive effect on African American students (Ladson-
150
Billings, 1994). Controlled, directed classrooms appeal to teachers who have low
expectations for poor or minority students (Ladson-Billings, 1997). Gutierrz (2000) found
common threads present at schools which had been successful in teaching minority
students. Teachers who adopted reform-oriented practices such as rigorous curriculum,
cooperative learning, and use of manipulatives, found that their students experienced
success (Gutierrez, 2000). Gutierrez (2000) concluded that teachers can be taught how to
be more effective in the classroom without them buying into the ideal, and with more
successful students as a result, the teachers will become believers. In this study, Amber
recognized the benefit of working with other students, and stated that she wished Mrs.
Smith would let her pick her own group to work with in class. Amber wanted to work
with three other African American students who she believed understood geometry.
Amber stated that they could communicate with each other better than listening to the
teacher lecture. A standards vision for teaching changes the focus of instruction from
teacher centered with lecture and demonstration, to student centered with active
participation and managed student discourse (National Council of Teachers of
Mathematics, 1991). The teacher?s role should be one of facilitator, making sure that all
students participate in classroom discourse surrounding mathematically appropriate tasks
designed to further student learning.
Assessment practices. Traditional assessment measures are another means to
maintain the inequitable power structure (Weissglass, 2002). Amber was correct when
she acknowledge that Mrs. Smith?s assessment plan penalized those students who do not
understand the homework the first time they are exposed to it. Amber stated that some
151
students needed to be taught in a different manner and not tested on material until they
had the opportunity to learn the material.
Assessment practices in the mathematics classroom must reflect what is valued
for mathematics learning. Assessments should address the students? full mathematical
power not isolated skills (National Council of Teachers of Mathematics, 1995). The kind
of assessment practices which are fundamental in a standards based classroom include the
use of multiple sources, allow for open-ended tasks, and are seamless with instruction
(National Council of Teachers of Mathematics, 1989, 1995, 2000). Assessment practices
should allow students to fully express themselves, their thinking, and their problem-
solving processes using varied forms of communication (National Council of Teachers of
Mathematics, 1989, 1995, 2000). Assessment should not be used as a filter to select
certain students away from learning opportunities, but should enhance the learning
process (National Council of Teachers of Mathematics, 1995).
Summary of Recommendations
Explicitly, schools must evaluate their output: who is being successful, who is
being empowered by the system, and who is not making acceptable grades; who is not
enrolled in the college-track classes, and who is not graduating and heading off to higher
education. It is not sufficient for schools to offer mathematics courses to students and
assume the position that ensuring the success of the students is the student?s or parent?s
job. There are effective models in place, such as the QUASAR project and the Interactive
Mathematics Program, but school administration must be committed to disrupting the
failure patterns of African American and other minority students. The collective goal of
152
the school must be to empower all students through a rigorous, challenging, and relevant
curriculum.
To effectively transform traditional classroom teaching practices to standards
based practices as recommended by the National Council of Teachers of Mathematics,
teachers must make substantial changes. Recommended teaching practices which include
higher order thinking, cooperative learning, problem solving, conjectures and
justifications, effective student discourse, assessment which does not focus on isolated
skills, are necessary but not sufficient changes. Teachers need to critically reflect on their
practices with regards to color-blindness, and equality versus equity. Additionally,
teachers must actively disrupt the existing power structure and failure patterns which are
experienced by many African American students in the mathematics classroom.
Final Remarks
Recommendations which could eliminate barriers to mathematical success for
African American students could have a positive effect on mathematics learning for all
students. Whereas this study was situated in a southeastern state, the achievement gaps
for African American students reflect the national picture with the exception of the
statistics for Hispanic students. In addition to the achievement gaps between African
American and White students, NAEP data obtained from the National Center for
Educational Statistics (2004) indicated that in comparison to national scores, the overall
mathematics achievement was quite low for most students in this southeastern state.
Therefore while the study was situated in a southeastern state, the implications and
recommendations described in this study are not limited to this state.
Eighth Grade Mathematics
Achievement
200
215
230
245
260
275
290
1990 1992 1996 2000 2003
Year
Average Scale Score
African
American/National
White/National
African
American/State
White/State
Figure 9. Comparison of National average eighth mathematics scores with State
eighth grade average scores. (U.S. Department of Education, 2005).
Reference (*State Department of Education, 2004a, 2004b)
(Alabama State Department of Education, 2004a, 2004b)
153
154
BIBLIOGRAPHY
50 years after Brown. (2004, March 22, 2004). U.S. News & World Report, 136, 64-66.
ACT Inc. (2003). ACT national and state scores. Retrieved July 5, 2004, from
http://www.act.org/news/data.97/t5-6-7.html
Alabama State Department of Education. (2004a). Accountability. Retrieved July 15,
2005, from http://www.alsde.edu/Accountability/Accountability.asp
Alabama State Department of Education. (2004b). Student demographics. Retrieved
August 4, 2004, from http://www.alsde.edu/
Banks, J. A. (1993). The canon debate, knowledge construction, and multicultural
education. Educational Researcher, 22(5), 4-14.
Bell, D. A., Jr. (2000). Property rights in whiteness: Their legal legacy, their economic
costs. In R. Delgado & J. Stepfancic (Eds.), Critical race theory: the cutting edge
(second ed., pp. 71-79). Philadelphia: Temple University Press.
Bergerson, A. A. (2003). Critical race theory and white racism: Is there room for white
scholars in fighting racism in education? International Journal of Qualitative
Studies in Education, 16(1), 51-63.
Berry, R. Q., III. (2003). Mathematics standards, cultural styles, and learning preferences:
The plight and the promise of African American students. Clearing House, 76(5),
244-250.
155
Bradburn, E. M., Berger, R., Li, X., Peter, K., & Rooney, K. (2003). A descriptive
summary of 1999-2000 Bachelor's degree recipients 1 year later. Retrieved
October 15, 2004, from http://nces.ed.gov/pubs2003/2003165.pdf
Calhoun, C. (1993). Habitus, field, and capital: The question of historical specificity. In
C. Calhoun, E. LiPuma & M. Postone (Eds.), Bourdieu: Critical perspectives (pp.
61-88). Chicago: The University of Chicago Press.
Carey, D., Fennema, E., Carpenter, T. P., & Franke, M. L. (1995). Equity and
mathematics education. In W. Secada, E. Fennema & L. B. Adajian (Eds.), New
directions for equity in mathematics education (pp. 93-125). New York:
Cambridge University Press.
Creswell, J. W. (1998). Qualitative Inquiry and Research Design: Choosing Among Five
Traditions. Thousand Oaks: Sage Publications.
D'Amato, J. (1992). Resistance and compliance in minority classrooms. In E. Jacobs & C.
Jordan (Eds.), Minority education: Anthropological perspectives (pp. 181-207).
Norwood, NJ: Ablex Publishing.
Delgado, R. (2000). Words that wound: A tort action for racial insults, epithets, and
name-calling. In R. Delgado & J. Stepfancic (Eds.), Critical race theory: the
cutting edge (Second ed., pp. 131-140). Philadephia: Temple University Press.
Delgado, R., & Stefancic, J. (2000). Introduction. In R. Delgado & J. Stefancic (Eds.),
Critical race theory: the cutting edge. Philadelphia: Temple University Press.
Delpit, L. D. (1988). The silenced dialogue: Power and pedagogy in education other
people's children. Harvard Educational Review, 58(3), 280-298.
156
Denzin, N. K. (2003). The practices and politics of interpretation. In N. K. Denzin & Y.
S. Lincoln (Eds.), Collecting and interpreting qualitative materials (second ed.,
pp. 458-498). Thousand Oaks, CA: SAGE Publications.
Edley, J., Christopher. (2002). Education reform in context: Research, politics, and civil
rights. In T. Ready, J. Edley, Christopher & C. Snow (Eds.), Achieving high
educational standards for all. Washington, D.C.: National Academy Press.
Fine, M., Weis, L., Weseen, S., & Wong, L. (2003). For whom? Qualitative research,
representations, and social responsibilities. In N. K. Denzin & Y. S. Lincoln
(Eds.), The landscape of qualitative research: Theories and issues (second ed.,
pp. 167-207). Thousand Oaks, CA: Sage Publications.
Fordham, S. (1988). Racelessness as a factor in Black students' school success: Pragmatic
strategy or Pyrrhic victory? Harvard Educational Review, 58(1), 54-84.
Frankenstein, M. (1995). Equity in mathematics education: Class in the world outside the
class. In W. Secada, E. Fennema & L. B. Adajian (Eds.), New directions for
equity in mathematics education (pp. 165-190). New York: Cambridge University
Press.
Green, R. S. (2001). Closing the achievement gap: Lessons learned and challenges ahead.
Teaching and Change, 8(2), 215-224.
Grissmer, C. W., Kirby, S. N., Berends, M., & Williamson, S. (1994). RAND: Student
achievement and the changing American family. Santa Monica: RAND Institute
on Education and Training.
157
Gutierrez, R. (2000). Advancing African-American, urban youth in mathematics:
Unpacking the success of one math department. American Journal of Education,
109, 63-111.
Heibert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D.
A. Grouws (Ed.), Handbook of research on mathematics teaching and learning
(pp. 65-97). New York: Macmillan.
Hoffman, K., Llagas, C., & Snyder, T. D. (2003). Status and trends in the education of
Blacks (No. NCES 2003-034). Washington DC: U.S. Department of Education,
National Center for Education Statistics.
Horn, L., Peter, K., & Rooney, K. (2002). Profile of undergraduates in U.S.
postsecondary education institutions: 1999-2000. Retrieved October 15, 2004,
from http://nces.ed.gov/das/epubs/2002168/profile2b.asp
Ignatiev, N. (1996). Immigrants and whites. In N. Ignatiev & J. Garvey (Eds.), Race
traitor. New York: Routledge.
Jacobson, J., Olsen, C., Rice, J. K., Sweetland, S., & Ralph, J. (2001). Educational
achievement and Black-White inequality (No. NCES 2001-061). Washington DC:
U.S. Department of Education, National Center for Education Statistics.
Kim, S. (1998). Racial differences in eighth-grade mathematics: Achievement and
opportunity to learn. Clearing House, 71, 175-179.
Kincheloe, J., & McLaren, P. (2003). Rethinking critical theory and qualitative research.
In N. K. Denzin & Y. S. Lincoln (Eds.), The landscape of qualitative research:
Theories and issues. Thousand Oaks, CA: Sage publications.
158
Kunjufu, J. (1988). To be popular or smart: The Black peer group. Chicago: African
American Images.
Ladson-Billings, G. (1994). The dreamkeepers: Successful teacher of African American
children. San Francisco, CA: Jossey-Bass.
Ladson-Billings, G. (1995a). But that's just good teaching! The case for culturally
relevant pedagogy. Theory into Practice, 34(3), 159-165.
Ladson-Billings, G. (1997). It doesn't add up: African American students' mathematics...
Journal for Research in Mathematics Education (Vol. 28, pp. 697): National
Council of Teachers of Mathematics.
Ladson-Billings, G. (1999). Just what is critical race theory and what's it doing in a nice
field like education? In L. Parker, Deyhle, D., Villenas, S. (Ed.), Race is . . . race
isn't; Critical race theory and qualitative studies in education (pp. 7-30).
Boulder, Colorado: Westview Press.
Ladson-Billings, G. (2003). Racialized discourses and ethnic epistemologies. In N. K.
Denzin & Y. S. Lincoln (Eds.), The landscape of qualitative research (second ed.,
pp. 398-432). Thousand Oaks, CA: SAGE Publications.
Ladson-Billings, G., & Tate, W. F., IV. (1995b). Toward a critical race theory of
education. Teachers College Record, 97(1).
Lee, V. E., & Smith, J. B. (1993). Effects of school restructuring on achievement and
engagement of middle-grade students. Sociology of Education, 66(3), 164-187.
Lee, V. E., & Smith, J. B. (1995a). Effects of school restructuring on the achievement
and engagement. Sociology of Education, 68(4), 241-270.
159
Lee, V. E., & Smith, J. B. (1995b). Effects of high school restructuring and size on early
gains in achievement and engagement. Sociology of Education, 68(4), 241-270.
Lee, V. E., Smith, J. B., & Croninger, R. (1997). How high school organization
influences the equitable distribution of learning in mathematics and science.
Sociology of Education, 70(2), 128-150.
Levy, S. R., Plaks, J. E., Hong, Y., Chiu, C., & Dweck, C. S. (2001). Static versus
dynamic theories and the perception of groups: Different routes to different
destinations. Personality and Social Psychology, 5(2), 156-168.
Lincoln, Y. S., & Guba, E. G. (2003). Paradigmatic controversies, contradictions, and
emerging confluences. In N. K. Denzin & Y. S. Lincoln (Eds.), The Landscape of
Qualitative Research: Theories and Issues (Second ed., pp. 253-291). Thousand
Oaks, CA: Sage Publications.
Lopez, I. F. H. (2000). The social construction of race. In R. Delgado & J. Stepfancic
(Eds.), Critical race theory: the cutting edge (second ed., pp. 163-175).
Philadelphia: Temple University Press.
Martin, D. B. (2000). Mathematics success and failure among African-American youth:
The roles of sociohistorical context, community forces, school influence, and
individual agency. Mahwah, NJ: Lawrence Erlbaum Associates.
Martin, D. B. (2003). Hidden assumptions and unaddressed questions in 'Mathematics for
All' rhetoric. The Mathematics Educator, 13(2), 7-21.
Merlino, F. J., & Wolff, E. (2001). Assessing the costs/benefits of an NSF "standards-
based" secondary mathematics curriculum on student achievement. The
Philadephia experience: Implementing the Interactive Mathematics Program
160
(IMP). Part I. Retrieved October 10, 2005, from
http://www.gphillymath.org/StudentAchievement/Reports/SupportData/Part1Intro
.pdf
Moses, R. P., & Cobb Jr., D. E. (2001). Radical equations: Math literacy and civil rights.
Boston: Beacon Press.
Moses, R. P., Kamii, M., Swap, S. M., & Howard, J. (1989). The Algebra Project:
Organizing in the spirit of Ella. Harvard Educational Review, 59(4), 423-443.
Muhr, T. (1991). Atlas.ti. Retrieved November 10, 2005, from
http://www.atlasti.com/index.php
National Center for Education Statistics. (2004). Programs of the National Center for
Education Statistics. Retrieved July 29, 2004, from
http://nces.ed.gov//programs/coe/2004/notes/n03.asp
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation
standards for school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics. (1991). Professional standards for
teaching mathematics. Reston VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (1995). Assessment standards for school
mathematics. Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (2000). Principles and standards for
school mathematics. Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (2002). High-stakes testing. Retrieved
October 4, 2002, from
http://www.nctm.org/about/position_statements/highstakes.htm
161
National Research Council. (2000). Achieving high educational standards for all. Paper
presented at the Achieving high educational standards for all, Washington, D.C.
Oakes, J. (1994a). More than misapplied technology: A normative and political response
to Hallinan on tracking. Sociology of Education, 69(2), 84-89.
Oakes, J. (1994b). One more thought. Sociology of Education, 69(2), 91-92.
Oakes, J. (2002). Tracking in mathematics and science education. In Readings in
education (pp. 299-311). Boston: Pearson Custom Publishing.
Ogbu, J. U., & Matute-Bianchi, M. E. (1986). Understanding sociocultural factors:
Knowledge, identity and school adjustment. In Beyond language: Social and
cultural factors in schooling language minority students (pp. 73-142). Los
Angeles: Evaluation, Dissemination, and Assessment Center.
O'Neill, J. (1992). On tracking and individual differences: A conversation with Jeannie
Oakes. Educational Leadership(October), 18-21.
Parsons, E. C. (2005). From caring as a relation to culturally relevant caring: A White
teacher's bridge to Black students. Equity & Excellence in Education, 38, 25-34.
Perry, T. (2003). Up from the parched earth: Toward a theory of African-American
achievement. In T. Perry, C. Steele & A. G. Hilliard III (Eds.), Young, gifted, and
Black (pp. 1-108). Boston: Beacon Press.
Rech, J., & Stevens, D. J. (1996). Variables related to mathematics achievement among
Black students. Journal for Research in Mathematics Education, 89(6), 346-351.
Roscigno, V. J. (1998). Race and reproduction of educational disadvantage. Social
Forces, 76, 1033-1062.
162
Rousseau, C., & Powell, A. (2005). Understanding the significance of context: A
framework to examine equity and reform in secondary mathematics. High School
Journal, 88(4), 19-31.
Rousseau, C., & Tate, W. F. (2003). No time like the present: Reflecting on equity in
school. Theory into Practice, 42(3), 210-217.
Sackett, P. R., Hardison, C. M., & Cullen, M. J. (2004). On interpreting stereotype threat
as accounting for African American-White difference on cognitive tests.
American Psychologist, 59(1), 7-13.
Sadker, M., & Sadker, D. (1986). Sexism in the classroom: From grade school to
graduate school. Phi Delta Kappan, 67(7), 512-512.
Schoenfeld, A. H. (2002). Making mathematics work for all children: Issues of standards,
testing, and equity. Educational Researcher, 31(1), 13-25.
Secada, W. (1995). Social and critical dimensions for equity in mathematics education. In
W. Secada, E. Fennema & L. B. Adajian (Eds.), New directions for equity in
mathematics education (pp. 146-164). New York: Cambridge University Press.
Shoffner, M. F., & Vacc, N. N. (1999). Careers in the mathematical sciences: The role of
the school counselor. (No. ED435950). Greensboro, N. C.: The Educational
Resources Information Center.
Shulman, L. S. (2002). Making differences. Change, 34(6), 36.
Signer, B., Beasley, T. M., & Bauer, E. (1997). Interaction of ethnicity, mathematics
achievement level, socioeconomic status, and gender among high school students'
mathematics self-concepts. Journal of Education for Students Placed at Risk,
2(4), 377-393.
163
Silver, E. A., & Stein, M. K. (1996). The QUASAR project. Urban Education, 30(4),
476-522.
Silver, E. A., Strutchens, M. E., & Zawojewski, J. S. (1997). NAEP findings regarding
race/ethnicity and gender: Affective issues, mathematics performance, and
instructional context. In P. A. Kenney & E. A. Silver (Eds.), Results from the sixth
mathematics assessment of National Assessment of Educational Progress (pp. 33-
60). Reston, VA: National Council of Teachers of Mathematics.
Singham, M. (1998). The canary in the mine: The achievement gap between Black and
White students. Phi Delta Kappan, 9-15.
Singham, M. (2003). The achievement gap: Myths and reality. Phi Delta Kappan, 84(8),
586-592.
Sleeter, C. E. (1993). How White teachers construct race. In C. McCarghy & W.
Crichlow (Eds.), Race identity and represetation in education. New York:
Routledge.
Sleeter, C. E. (1997). Mathematics, multicultural education, and professional
development. Journal for Research in Mathematics Education, 28(6), 680-696.
Snyder, T. D., & Hoffman, C. (2003). Postsecondary education. Retrieved October 15,
2004, from http://nces.ed.gov/pubs2003/2003060c.pdf
Spade, J., Columba, L., & Vanfussen, B. (1997). Tracking in mathematics and science:
Courses and course selection procedures. Sociology of Education, 70(2), 108-127.
Steele, C. M., & Aronson, J. (1995). Stereotype threat and the intellectual test
performance of African Americans. Journal of Personality and Social
Psychology, 69(5), 797-811.
164
Steele, C. M., & Aronson, J. (2004). Response to Sackett, Hardison and Cullen. American
Psychologist, 59(1), 47-48.
Strutchens, M. E., Lubienski, S., McGraw, R., & Westbrook, S. K. (2004). NAEP
findings regarding race/ethnicity: students' performance, school experiences,
attitudes and beliefs, and family influences. In P. Klooterman & F. K. Lester, Jr.
(Eds.), Results and interpretations of the 1990 through 2000 mathematics
assessments of the National Assessment of Educational Progress. Reston, VA:
National Council of Teachers of Mathematics.
Strutchens, M. E., & Silver, E. A. (2000). NAEP findings regarding race/ethnicity:
Students' performance, school experiences, and attitudes an beliefs. In E. A.
Silver & P. A. Kenney (Eds.), Results from the seventh mathematics assessment of
the National Assessment of Educational Progress (pp. 45-72). Reston, VA:
National Council of Teachers of Mathematics.
Tate, W. F. (1997). Race-ethnicity, SES, gender and language proficiency trends in
mathematics achievement: An update. Journal for Research in Mathematics
Education, 28(6), 652-679.
Tate, W. F., & Rousseau, C. (2002). Access and opportunity: The political and social
context of mathematics education. In L. D. English (Ed.), Handbook of
international research in mathematics education (pp. 271-299). Mahwah, New
Jersey: Lawrence Erlbaum Associates.
The College Board. (2003). SAT national reports. Retrieved July 5, 2004, from
http://www.collegeboard.com/sat/cbsenior/yr2000/nat/natbk200.html
165
The College Board. (2005). Summary Reports: 2004. Retrieved June 26, 2005, 2005,
from http://www.collegeboard.com/student/testing/ap/exgrd_sum/2004.html
U.S. Census Bureau. (2004, March 18, 2004). U.S. interim projections by age, sex, race
and Hispanic origin. Retrieved July 7, 2004, from
http://www.census.gov/ipc/www/usinterimproj/
U.S. Department of Education. (1996). What schools can do to improve math and science
achievement by minority and female students. (Educational Resources
Information Center No. ED 462 253). Washington DC: Office for Civil Righs.
U.S. Department of Education. (2005). The nations reportcard. Retrieved July 25, 2005,
from http://nces.ed.gov/nationsreportcard.
United States Census Bureau. (2003). American community survey: 2003 ranking tables.
Retrieved May 15, 2005, 2005, from
http://www.census.gov/acs/www/Products/Ranking/index.htm
Useem, E. (1992). Middle schools and math groups: Parent's involvement in children's
placement. Sociology of Education, 65(4), 263-279.
Webb, N. L. (2003). The impact of the Interactive Mathematics Program on student
learning. In S. L. Senk & D. R. Thompson (Eds.), Standards-based school
mathematics curricula: What are they? What do students learn? (pp. 375-398).
Mahwah, NJ: Lawrence Erlbaum Associates.
Weiler, K. (1988). Critical education theory. In Women teaching for change (pp. 1-26).
New York: Bergin & Garvey.
Weissglass, J. (2002). Inequity in mathematics education: Questions for educators. The
Mathematics Educator, 12(2), 34-39.
166
Wells, A. S., & Oakes, J. (1996). Potential pittfalls of systemic reform: Early lessons
from research on detracking. Sociology of Education(Extra Issue), 135-143.
Williams, S. R., & Baxter, J. A. (1997). Dilemmas of discourse-oriented teaching in one
middle school mathematics classroom. The Elementary School Journal, 97(1), 25-
39.
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APPENDIX A
Interview Guides
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Parent
1. What subjects are easiest for your son/daughter? What subjects are the most
difficult? What subjects does he/she like the most?
2. Does your son/daughter like mathematics? Why do you think this?
3. Do you think that your son/daughter does well in school, in math?
4. Do you have the same expectations for this child in school and in mathematics as
you did your other children? Do you think that your child knows what you
expect?
5. On a scale of one to ten with ten being the very best mathematics student, and one
being the worse, how would you rate your son/daughter? Why do you think this?
6. Does your son/daughter have math homework?
7. How do you get involved with your son/daughter?s math homework?
8. What grades does your son/daughter make in math? Are you okay with those
grades?
9. Do you think your son/daughter is motivated to do well in mathematics?
10. What do you think influences your child the most in how he/she does in math?
11. What do you think is your child?s attitude about mathematics? Where did he/she
get this attitude?
12. Do you think that your son/daughter does the best that he/she can in math class?
Teacher
1. First tell me about yourself. Where did you go to school? How long have you
been teaching and where? Do you live in the area?
2. Describe yourself as a teacher, your approach to teaching.
3. Describe __student name_ as a mathematics student.
4. How does he/she typically behave in class?
5. What kind of class and homework does he/she do?
6. On a scale of one to ten, with ten being the very best mathematics student, and
one being the worse, how would you rate __student name_? Why do you think this?
7. How often do you interact with this __student name____? Describe the typical
interaction.
8. Does __student name__ volunteer in class?
9. How often do you call upon __student name____ ? (When he/she volunteers or other
times?)
10. Does __student name__ seem interested in math?
11. Does __student name__ ask for help?
12. What do you think is __student name__?s attitude towards math? Why do you think
this?
13. Do you believe that __student name__ is working to his/her full potential in math?
Why do you think this?
14. What could __student name__ do to improve his/her performance in math class?
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Student
1. How would you define mathematics?
2. Who could become a mathematician? Could you?
3. What do you want to do when you finish school? Does it involve math?
4. Is mathematics useful in the real world?
5. Do you need math to be successful in life?
6. Is it important to do well in math in school?
7. Do your parents talk about the importance of math?
8. How do your friends feel about math? Do they like math? Do they think it is
important to learn?
9. Would you take math if you did not have to?
10. Do you like mathematics? Your math teacher?
11. How did you decide what math course to take? What were your choices?
12. On a scale of one to ten with one being the worse math student and ten being the
best math student, how do you rate yourself? Why do you think this?
13. How do you compare to other students in your math class?
14. Describe a typical math class. What would I see happen? What would I see you
do?
15. Do you think that your teacher expects you to do well in math?
16. Do you think that your teacher encourages you? How?
17. When the teacher asks a question do you raise your hand?
18. Does your teacher call on you even if you don?t raise your hand?
19. What grades do you try for in your classes and in math class?
20. What is the reason for your current math grade?
21. What would happen if you brought home a D or F in math?
22. Do you have math homework? Do you do it? Why or why not?
23. If you need help in math, what do you do?
24. Are you doing as well as you can in math? Why do you think this?
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APPENDIX B
Permission Forms
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Information letter for Principal
One of the goals of TEAM-Math is to address the mathematics achievement of students
who have not been performing on the same levels as other students. As a graduate
student, I am interested in learning why some African American students have been
successful in mathematics and some have not. Standardized test results for the United
States indicate that overall African American children do not perform as well as White
students in mathematics achievement. Additionally, fewer African American students are
enrolled in college track mathematics courses than are White students. Research has
suggested several theories for this discrepancy, including- income level, parental
involvement, negative peer pressure, low expectations of teachers, and low motivational
levels on the part of students.
The research that I intend to conduct focuses on the mathematics achievement of six
African American high school students. My methodology will be to closely follow
several successful students as well as students who have not been successful. By
focusing on only a few students, no more than six, more in-depth information can be
obtained. Following recommendations from your school personnel, several students from
the tenth grade will be approached about participating in this study. Permission will be
sought from both the students and guardians to conduct interviews and observations.
Initially, the students and parents/guardians will be interviewed individually to talk about
their expectations for mathematics learning. Next, the mathematics teachers of the
students will be interviewed to obtain information on the student?s level of performance
in class. In assessing whether or not the student is performing at expected levels, previous
standardized tests scores for the individual students will be examined. The students will
be observed in their mathematics class at least three times during the next semester with
minimal intrusion into the class. Following the observations and interviews, it is expected
that students and possibly teachers will be interviewed again to verify the information
collected and clarify any misunderstanding or misinterpretations on my part.
Enclosed are copies of the permission forms and interview questions which will be used
with the teachers, parents, and students. Thank you and your teachers for allowing me to
conduct this research, and I will be happy to share the results with you.
S. Kathy Westbrook
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