Developing Students’ Algebraic Thinking in Earlier Grades: Lessons from China and Singapore

Abstract

In this chapter, we discuss how algebraic concepts and representations are developed and introduced in the Chinese and Singaporean elementary curricula. We particularly focus on the lessons to be learned from the Chinese and Singaporean practice of fostering Early algebra learning, such as the one- problem-multiple-solutions approach in China and pictorial equations approach in Singapore. Using the lessons learned from Chinese and Singaporean curricula, we discuss four issues related to the development of algebraic thinking in earlier grades: (1) To what extent should we expect students in early grades to think algebraically? (2) What level of formalism should we expect of students in the early grades? (3) How can we help students make a smooth transition from arithmetic to algebraic thinking? and (4) Are authentic applications necessary for students in early grades?

Authors’ note: The preparation of this paper has been supported by grants from the National Science Foundation (ESI-0114768; ESI-0454739). Any opinions expressed herein are those of the authors and do not necessarily represent the views of the National Science Foundation. This chapter is a revised version of an article published in ZDM (Cai, J., Lew, H. C., Morris, A., Moyer, J. C., Ng, S. F. & Schmittau, J. (2005). The Development of Students’ Algebraic thinking in Earlier Grades: A Cross-Cultural Comparative Perspective. Zentralblatt fuer Didaktik der Mathematik (International Journal on Mathematics Education), 37(1), 5–15, DOI 10.1007/BF02655892), where we summarized findings from analyses of Chinese, Russian, South Korean, Singaporean, and U.S. elementary curricula. In this chapter, we only focused on the Chinese and Singaporean curricula. We are grateful for the productive collaboration with Drs. H. C. Lew, A. Morris, & J. Schmittau.