|Results from the 2007 TIMSS showed the grim reality that the United States did not measure up to other industrialized countries in both fourth- and eighth-grade results in geometry (Mullis, Martin, & Foy, 2008). Furthermore, Clements (2003) concluded from literature on teaching and learning geometry in kindergarten through twelfth grade (K-12) that the U.S.’s curriculum and teaching are weak. Since teacher knowledge impacts student achievement, it is pertinent to study teacher knowledge as a subset of the solution to improving student achievement in geometry.
Case studies were conducted to see what connections there are between two high school geometry teachers’ specialized content knowledge, knowledge of content and students, and knowledge of content and teaching (Hill, Ball, & Schilling, 2008) shown during the planning of lessons and the teachers’ actual execution of the lessons. The three types of knowledge were collectively called Teachers’ Applied Content Knowledge (TACK) for this study.
The two teachers chosen for the case study were dubbed as exemplary geometry teachers by the researcher. Each teacher participated in interviews and observations involving two units of her choice. One teacher was observed for 7 lessons, and the other, 6; all lessons were also of their choosing. Interviews and classroom observations were video taped and audio recorded. Classroom observations were recorded with a video camera and with a voice recorder that the teachers carried with them. Qualitative data analysis was done through case study and grounded theory. These exemplary teachers’ ability to execute what was planned with additional geometry TACK shown during observations was based on knowledge accumulated from many sources, but the most commonly referenced were professional development and reflections from previously taught lessons.