Matches or Discrepancies? Student Perceptions and Teacher Intentions in Chinese Mathematics Classrooms

• In Event: Culturally Specific Perspectives on Quality Mathematics Teaching

Abstract

This presentation explores quality teaching by examining the relationship between student and teacher perceptions of classroom instruction in China with respect to a particular structural characteristic of quality Chinese teaching: The Three-point Approach. Li, Chen, and Kulm (2009) found that Chinese teachers paid considerable attention to three essential content points in the lesson: the important point, the difficult point, and the critical point; that is, the important content identified in the curriculum standards or teachers’ instructional goals; the content that is typically difficult for students to understand and master and which might easily lead to student mistakes or confusion; and, finally, the critical point referring to any content that plays a decisive role in student learning, helping the student navigate the mathematical terrain, achieving the learning goals, while avoiding or overcoming the pitfalls that might arise. Quality teaching involves helping students understand and master important points through overcoming difficult points and making use of critical points. We hypothesised that it would be important for students to recognize those lesson events that are closely related to the three points.

We selected Mr Zhang, recognized as an effective teacher by a group of local Chinese mathematics educators. His class included 55 seventh-grade students and utilized the unified official textbook in Shanghai. Data sources were teacher interviews, student interviews, and lesson plans. We asked Mr Zhang to identify three important lessons from the sequence of 15 lessons. Interviews on each of the three selected lessons asked Mr Zhang to describe his intentions in each lesson, identify the important events, and share his perception of what he did, thought, and felt during the lessons. For each lesson, two students followed the same video-stimulated interview protocol. Lesson plans were also analysed.

Analysis was two-tiered: We first examined whether students realised the importance of the different stages within mathematics lessons and the correspondence with the teacher intended important events. The second level addressed the nature of the shared important events. We investigated whether the identified important events were closely related to addressing the Three Points.

The students in this study recognised the importance of events commonly associated with Chinese classroom routines. These student-perceived important events included introducing new concepts or procedures, practicing new knowledge and skills, sharing students’ work, and summarising key points. In comparing student and teacher important events, for each of the three lessons there were more matches than discrepancies. During the shared important events the teacher facilitated and supported students in achieving the learning goals by specifically dealing with the difficult points with a focus on mastering the important content points.

This case study engages the learner’s perspective to assist in interpreting mathematics classroom learning in China. Our findings highlight the value of “Three Points” as a tool of quality mathematics classroom instruction in China.

References
Li, Y., Chen, X., & Kulm, G. (2009). Mathematics teachers’ practices and thinking in lesson plan development: a case of teaching fraction division. ZDM - The International Journal on Mathematics Education, 41, 717-731.

Authors

• Rongjin Huang, Middle Tennessee State University

• Angela T Barlow, Middle Tennessee State University