Can Chinese Students' Mathematics Success Be Demystified Through Analysis of Mathematics Lessons and Relevant Activities?

• In Event: 60.023 - Content Representations and Pedagogical Moves in Chinese and U.S. Mathematics Classrooms: Lesson Video Analyses at Elementary, Middle, and High School Levels

Abstract

Objectives: The direct instruction featuring teacher introducing the new concepts followed by students’ practices is seen ineffective for students mathematics learning (Smith, 1996) because it fails to reflect how students construct mathematics ideas (Fennema & Others, 1996), nature of mathematics (Lampert, 1990), and how mathematics is practiced in the real world (Lave, 1988). Consequently, the persistent high mathematics performances of Chinese students in various international studies (Wang & Lin, 2009, 2013), especially in PISA (Fleischman, Hopstock, Pelczar, Shelley, & Xie, 2010), become a myth since Chinese mathematics teaching can be easily characterized as direct instruction based on the observations of both outsiders (Bracey, 1993, 1999) and insiders (Ma, Lam, & Wong, 2006). This study explores this myth by analyzing the alignment of mathematics connections, pedagogical sequence, curriculum, and assignments in Chinese urban middle schools.
Theoretical Framework: The zone of proximal development theory (ZPD) (Vygotsky, 1978; 1994) frames the focus, data collection, analysis, and interpretation of this study. According to this theory, teaching activities central to effective mathematics learning should focus at the level that students are unable to reach by themselves without a series of carefully structured instructional scaffoldings over time.
Methodology: The data sources for this study included 10 lessons on angles and triangles from Grade 6-9 classrooms in different urban schools in China, which were analyzed to identify the concepts representations, connections, and pedagogical sequences. Interviews with each teacher on his and her lessons and relevant teaching and learning activities were analyzed for the mathematics and pedagogical connections between the lesson and the activities. Mathematics curriculum materials, students’ practice book, teachers’ lesson plans, and students’ assignments were also coded for their mathematics and pedagogical connections to the relevant lessons.
Findings and Discussions: The preliminary analysis identified a coherent system of scaffolding instructional activities in all the lessons and the relevant teaching and learning activities beyond the lessons, which supported students to solve increasingly more challenging problems using flexible mathematics connections and varied approaches. It started with pre-lesson homework to help students review and prepare the relevant concepts for the lesson. The lesson stared with direct instruction introducing the new concept through teacher-led interactions built on pre-lesson preparation. The multiple practice sections on the concept using varied approaches and flexible concept connections with constant public examinations of the results and processes. Finally, the after school homework involved the concept learned in the lesson and other concepts necessary for solving more challenging problems, which also prepared for the next lesson. The curriculum materials and students’ practice books were aligned with each stage of this scaffolding sequence with clear expectations, multiple examples, specific suggestions, and practice items. This system is consistent with the ZPD process (Vygotsky, 1978; 1994).
Significance: The study indicates that the carefully structured direct instruction focusing concept connection and varied approaches can be effective for students mathematics learning (Huang & Leung, 2005). It challenges the dichotomized view of mathematics teaching as either ineffective direct instruction or effective one following the constructivist perspective (Watkins & Biggs, 2001).

Authors

• Xiangming Huang, East China Normal University

• Tainian Zheng, East China Normal University

• Yiping Huo, East China Normal University