How a Chinese teacher improved classroom teaching in Teaching Research Group: a case study on Pythagoras theorem teaching in Shanghai

In China, a school-based teaching research system was built since 1952 and Teaching Research Group (TRG) exists in every school. In the paper, a teacher's three lessons and the changes in each lesson were described, which might show a track of how lessons were continuously developed in TRG. The Mathematical Tasks Framework, The Task Analysis Guide, and Factors Associated with the Maintenance and the Decline of High-level Cognitive Demands developed in the Quantitative Understanding: Amplifying Student Achievement and Reasoning project (Stein and Smith in Math Teach Middle School 3(4): 268-275, 1998; Stein et al. in Implementing stardards-based mathematics instruction. Teachers College Press, NY, pp. 1-33, 2000), were employed in this study. Based on the perspective of Mathematical Task Analysis, changes of three lessons were described and the author provided a snapshot for understanding how a Chinese teacher gradually improved his/her lessons in TRG activities.