The development of studients' algebraic thinking in earlier grades

We analyzed how algebraic concepts and representations are introduced and developed in the Chinese, South Korean, and Singaporean elementary curricula, and in selected Russian and U.S. elementary curricula. In all five curricula, the main goal for learning algebraic concepts is to deepen students' understanding of quantitative relationships, but the emphases and approaches to helping students deepen their understanding of quantitative relationships are very different. Based on the analyses of the five curricula, we discuss four issues related to the development of algebraic thinking in earlier grades: (1) To what extent do curricula 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?