Teachers' mathematical understanding of proportionality: Links to curriculum, professional development, and support

The Proportional Relationship Study was designed to investigate whether using a standards-based middle school mathematics curriculum, together with professional development and followup support, can lead to increased teacher content knowledge and pedagogical content knowledge of proportionality. From the literature, it is clear that what teachers do in the classroom affects what students learn, and that what teachers know affects their actions in the classroom. Teachers need strong personal content knowledge and pedagogical content knowledge in order to teach mathematics well; therefore, the question is an important one.; Seven sites participated in a statewide implementation effort during 1996--1999 that included Connected Mathematics Project (CMP) curriculum professional development experiences for teachers plus additional district and/or campus support. As part of this study, the Proportional Reasoning Exercise (PRE) was given to seventh-grade teachers three times: before CMP professional development, after a year of teaching with CMP materials, and again after a second year of teaching with the materials. Teacher responses were coded for correctness and for problem-solving strategy; group responses were compared for all three PREs. In addition, group and individual interviews were conducted with CMP teachers.; Data from the three PREs anti group and individual interviews of seventh-grade teachers showed growth in performance and understanding of proportional relationships over the two-year period. Analysis of each of the PRE problems revealed an increase in the percent of teachers who correctly answered the problems and a tendency toward using more sophisticated proportional relationship strategies. However, choice of strategy appeared to depend on the context of the problem. Participants also tended over time to record multiple and more diverse strategies, increase the depth and detail of their written explanations, and include units along with numbers.; Interviews after the first year confirmed that experienced teachers placed in a new situation, with new curriculum and expectations of using new instructional approaches, often revert to "novice" status, concerned primarily with survival (Borko & Livingston, 1989). However, individual interviews conducted after the second year showed that teachers were then ready to focus on student understanding of mathematics and were themselves learning new and important mathematics.