Using Multiple Mathematical Representations and Facilitating Meaning Making: A Study Analyzing Mathematics Lessons in Urban Chinese High Schools

• 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. Quality of mathematics teaching is a major factor influencing student mathematics learning and this assumption has been driving US mathematics teaching reform over the years (Romberg et al., 2005) with little effects on high school student performances (Kloosterman, 2010). Recently, useful mathematics representation and skillful facilitation of mathematics discourse are among eight important teaching practices assumed crucial for effective mathematics teaching (National Council of Teachers of Mathematics, 2014). Chinese high school students are the top mathematics performers in the world (Fleischman et al., 2010) and thus, their lessons may reflect such practices. This study examines whether and to what extent Chinese high school teachers are able to help students develop useful mathematics representations and facilitate their mathematics learning discourse.
Theoretical Framework. The sociocultural assumption of learning that tool use, social interaction, and assisted performances shape what and how one learns frames this study (Vygotsky, 1978b). This study considers mathematics representations as a useful tool mediating mathematical learning (Leinhardt, Zaslavsky, & Stein, 1990) and classroom interactions on mathematics representations valuable in promoting students’ conceptual understanding and appropriating their mathematical communication (Sfard, 2008). It assumes teachers’ modeling mathematics problem solving and scaffolding students to reason important to lead students to the learning level beyond their own efforts (Collins, Brown, & Newman, 1998).
Methodology. Three lessons on geometry, algorithm, and probability respectively from different Chinese urban high schools were analyzed in this study for the characteristic of mathematics representations for the real-life yet problematic situations using general mathematical equations and problem-specific representations as suggested (Erickson, 2006). Then, they were analyzed in a top-down manner for recurring instructional discourses (Jordan & Henderson, 1995). Lesson plans and interviews were also analyzed to triangulate with findings from the lesson analysis.
Results. All the teachers were able to elicit students’ representations about the real life problem in the lessons by helping them notice the useful clues as suggested (Lobato, Rhodehamel, & Hohensee, 2012). For instance, one teacher assisted students to notice the equation ‘S = 70x + 50y’ to improve their representations of flat area, All lessons ended with teachers having students come up representations for the problem different from those they developed through the lessons with teachers’ assistance to reinforce students’ experience about multiple representations of a mathematics problem (Sfard, 2008). In addition, they rephrased students’ ideas to help the whole class understand and used the questions, “why are you doing this,” “why are you making this drawing,” or “why do you think this graph would work?” to facilitate students’ discourses around the ideas in public frequently. Such discourses echo the sociocultural contexts helpful for students mathematics learning (Engle & Conant, 2002; Michaels, O’Connor, & Resnick, 2008).
Significance. This study helps develop a micro level understanding about the mathematics and pedagogical characteristics of Chinese high school mathematics lessons little known in the literature (Fan, Wong, Cai, & Li, 2004). Thus, this understanding contributes to the knowledge base for developing effective policy initiatives and practices in mathematics education in China and other places.

Author

• Sihan Xiao, University of California - Los Angeles