CHAPTER 10: Some Highlights of the Similarities and Differences in Intended, Planned/Implemented, and Achieved Curricula Between China and the United States

It is widely accepted that a major goal of educational research is to improve learning opportunities for all students. In order to improve students’ learning, it is necessary to understand the developmental status of their thinking and reasoning. Thus, the more information teachers obtain about what students know and think, the more opportunities they create for student success (Darling-Hammond, 1994). Teachers’ knowledge of students’ thinking has a substantial impact on their classroom instruction, and hence, on students’ learning (Fennema & Franke, 1992; Gardner, 1999; Wittrock, 1986). Cross-national comparisons of curriculum and instructional practices provide a unique perspective for understanding what students know and think, as well as seeing how we should help students learn mathematics with understanding. Such an international perspective can increase educators’ and teachers’ experiences when they try to address the issues and challenges facing students’ learning of mathematics with understanding (Cai, 2001; Gardner, 1989; Ma, 1999; Stigler & Hiebert, 1999). In other words, cross-national comparisons of curriculum and instruction not only can reveal what topics are or are not treated in different curricula, but they also can show how the same topics are treated.