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Curriculum & cognition: a study on math problems.

Article Excerpt
Abstract

Analyzing textbook problem provides a unique opportunity for exploring students' problem-solving experience, as textbook problems embody cognitive expectations for students in a specific system. In this study, we examined mathematical problems in algebra chapters of selected textbooks from Mainland China, Singapore, and the United States. The results revealed some substantial variations between the U.S. textbooks and the textbooks from Asia, which extends what we can possibly learn from textbook analysis in large-scale international studies.

Introduction

Educational knowledge is a major regulator of the structure of students' experience (Bernstein, 1975). The selection, classification and transmission of educational knowledge are generally outlined in the form of curriculum. Curriculum thus envisions a body of organized knowledge that can contribute to students' cognitive development. With a focus on identifying curricular influence on students' academic achievement, researchers have come to the understanding that cross-system similarities and differences in curriculum can provide partial explanations to cross-system discrepancy in students' academic performance, especially in mathematics (Fuson, Stigler, & Bartsch, 1988; McKnight et al., 1987; Schmidt et al., 1997; Schmidt et al., 2001). In particular, when compared to the curriculum materials from some high achieving education systems in East Asia, researchers have revealed that the U.S. curriculum materials failed to provide challenging mathematics content (e.g., Schmidt, McKnight, & Raizen, 1997) and devoted more page space to student practice than to content instruction (e.g., Carter, Li, & Ferrueci, 1997; Mayer, Sims, & Tajika, 1995).

Because textbooks are often the curricular materials that are the most influential to what happens in classrooms (e.g., McKnight et al., 1987), textbooks have attracted more and more research attention from the international mathematics education community in the past two decades. In particular, the Third International Mathematics and Science Study (TIMSS) was the first time, in the history of large-scale international studies conducted by the International Association for the Evaluation of Educational Achievement (lEA), to include the analysis of textbooks and other curriculum materials from about 50 participating education systems as a major part of the study (Schmidt et al., 1997). However, large-scale international comparisons with a focus on students' mathematical performance often included broad measures of the differences and similarities in mathematics curricula but not an analysis of problems in mathematics textbooks. As students develop their mathematical skills and abilities through solving mathematics problems, problems in the textbooks should be taken as the embodiments of content and performance expectations for students in a specific system. Several cross-national studies on mathematical textbooks have conducted fruitful comparisons of mathematical problems presented in textbooks (e.g., Li, 2000; Stigler et al., 1986; Sugiyama, 1987; Zhu & Fan, 2006). The results from these studies have confirmed the feasibility of textbook problem analysis for exploring students' learning experience through problem solving. To extend what we...