## ABSTRACT

This chapter provides a shared road map of algebra in the elementary grades and an historical perspective on why the authors might need such a road map. Recognizing the algebra problem and crafting a solution that spans grades K–12 introduces another complexity, namely, defining "algebra" and "algebraic reasoning," especially as an object of thinking in the elementary grades. Solving the algebra problem involves deep curriculum restructuring, changes in classroom practice and assessment, and changes in teacher education—each a major task. Through the 1980s, research in algebraic thinking and learning focused on student errors and constraints on their learning, especially developmental constraints. The underlying premise is that conventional forms can not only express, but also enrich and deepen algebraic reasoning in students. Mathematicians and mathematics educators differ in their views of which of the two core aspects of algebra is more central to defining algebra.