Sources of Differences in Children's Understandings of Mathematical Equality: Comparative Analysis of Teacher Guides and Student Texts in China and the United States

Abstract

This study reports findings from comparative samples of sixth-grade Chinese and U.S. students' interpretations of the equal sign. Ninety-eight percent of the Chinese sample correctly answered 4 items indicating conceptions of equality and provided conceptually accurate explanations. In contrast, only 28% of the U.S. sample performed at this level. We examine how teacher preparation materials, students' textbooks and teachers' guidebooks treat equality in each country. U.S. teacher preparation textbooks rarely interpreted the equal sign as equivalence. On the contrary, Chinese textbooks typically introduced the equal sign in a context of relationships and interpreted the sign as “balance,” “sameness,” or “equivalence” and only then embedded the sign with operations on numbers.

ACKNOWLEDGMENT

Special thanks to Charles M. and Amira Molina Capraro for their patience and assistance in the editing of the final version of this manuscript.