Research in Brief - December 2007 - Volume 107 (8)

Examining and Understanding Mathematics Classroom Instruction and Possible Contributing Factors through a Cross-National Lens

Yeping Li
p. 308

American classroom instruction has been dominated by a format and procedure almost unchanged for the past several decades (National Commission on Mathematics and Science Teaching for the 21st Century, 2000). The quality of mathematics classroom instruction had not been a major concern of policy makers and educators until it was compared to other educational systems (e.g., Silver, 1998). Especially with recent TIMSS classroom video studies, a teaching gap has been revealed between U.S. mathematics classrooms and classrooms in other education systems (Hiebert et al., 2003; Stigler & Hiebert, 1999, 2004). In particular, U.S. mathematics teachers tended to state the mathematical concepts and procedures introduced, and decrease cognitive demands of the mathematical tasks being used. In contrast, teachers in Japan (Stigler & Hiebert, 1997, 2004) and Hong Kong (Stigler & Hiebert, 2004) tended to make connections among mathematical ideas and maintain high cognitive demands of the mathematical tasks that were used. Stigler and Hiebert (1997) also reported that over 60% of U.S. teachers believed that mathematical skills (e.g., solving specific kinds of problems or using specific formulas) are important, whereas over 70% Japanese teachers believed that mathematical thinking (e.g., exploring and understanding mathematical ideas or inventing new ways to solve problems) is important. More surprisingly, the 1995 TIMSS video study revealed that U.S. mathematics teachers teach in a similar way, but different from either Japanese or Germany teachers (Stigler & Hiebert, 1999). Simply put, teaching is fundamentally a cultural activity (Stigler & Hiebert, 1999), and it can be difficult to view it differently without a cross-national lens.

Efforts to pursue high-quality classroom instruction in the United States have also led to the increased interest in exploring teachers' instructional practices in high-achieving education systems in East Asia, including China. A comparison with Chinese classroom instruction is especially interesting, as Chinese students are taught with a traditional style of lecture, a form of classroom instruction that is not advocated in the United States. Large numbers of students, often around 40-70, sit in one classroom (Ding, Li, Li, & Kulm, in press). Although large class size can be detrimental to effective instruction in mathematics (e.g., Rice, 1999), existing research has revealed some other factors that are believed to contribute to the quality of mathematics instruction in China (e.g., An, Kulm, & Wu, 2004; Ma, 1999; Perry, 2000; Stevenson & Lee, 1997; Stigler, Lee, & Stevenson, 1987; Stigler & Stevenson, 1991).

In a cross-national study that included selected first- and fifth-grade mathematics classrooms in the United States, Japan, and Taiwan, Stigler et al. (1987) found that Chinese teachers make increasingly good use of class time for academic activities. Moreover, Chinese teachers often teach with conceptual and procedural variations in classroom instruction (Gu, Huang, & Marton, 2004). Classroom activities focus on discussing and solving mathematically challenging problems (Stigler & Stevenson, 1991), and engage students in solving problems with multiple solutions and justification (Fan, Wong, Cai, & Li, 2004). Consistently, Chinese teachers offer students many direct and complex explanations during classroom instruction (Perry, 2000). Mathematics lessons, overall, are coherent and polished (Stigler & Stevenson, 1991) in the form of well-organized whole-class teaching (Stevenson & Lee, 1997).

To understand what may contribute to high quality instruction in mathematics classrooms, Ma (1999) provided a partial explanation through her cross-national comparative study. She interviewed a group of Chinese elementary school teachers to explore their knowledge and teaching of elementary school mathematics, and compared their responses to the data from a group of U.S. elementary school teachers. Based on this study of Chinese and U.S. elementary school teachers, Ma (1999) argued that Chinese teachers' understanding of mathematics content knowledge and of the ways that elementary mathematics can be presented to students contributed to students' high achievement. Ma's findings suggested that teachers' knowledge of subject matter and pedagogy content are a key factor in making quality classroom instruction possible. Similar results were also obtained in a recent cross-national study on number and operations between elementary and middle school teachers in the U.S. and China (An, Kulm, & Wu, 2004). However, most Chinese elementary school teachers are content specialists whereas U.S. teachers are not. Different job assignments certainly can provide Chinese in-service elementary teachers some advantages in developing their competence in mathematics and pedagogy over time. If both U.S. and Chinese teachers were content specialists, it remains to be further explored whether teachers' competence would differ cross-nationally.

Researchers also tried to look at teachers' work outside of their classrooms. One of the key factors might be teachers' lesson planning and interactions that happen before and after classroom instruction (e.g., Paine & Ma, 1993; Stigler & Hiebert, 1999; Stigler & Stevenson, 1991). If teachers can design well-thought-out and high quality lesson plans, as a process of curriculum planning at the micro level, they will build a solid base for classroom implementation. Quality instruction is, therefore, more likely to occur. In fact, researching U.S. teachers' lesson planning is not a new endeavor (e.g., McCutcheon, 1980; Shavelson, 1983; Yinger, 1980). The results from studies on U.S. expert and novice teachers' cognition indicated that variations in teacher's planning relate to their classroom teaching behavior (e.g., Hogan, Rabinowitz, & Craven, 2003; Leinhardt & Greeno, 1986). Cross-nationally, a recent study on the topic of arithmetic average revealed that U.S. teachers' lesson plans are extremely varied even for teachers in the same school, and differ from their Chinese counterparts whose plans share many similarities (Cai, 2005). Our on-going investigation has been focusing on U.S. and Chinese mathematics teachers' thinking about curriculum and instruction, how teachers make use of curriculum materials in the process of curriculum planning, and how they enact curriculum as planned (e.g., Li, Kulm, Huang, & Ding, in press).

Mathematics teachers in the United States may face greater challenges in carrying out the task of teaching, as less professional development time is available (U.S. Department of Education, 1998). A solution may require going beyond an assumed increase of professional development time alone. In particular, it becomes critical to understand what U.S. mathematics teachers already know and what they are required to do (Li, in press), and how competent they are now in the process of planning and enacting curriculum, before we know how to better help them.

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Author Note: Preparation of this paper was supported in part by a research grant from the Spencer Foundation. However, any opinions expressed herein are those of the author and do not necessarily represent the views of the Spencer Foundation.