Helping Students Make Sense of Algebraic Expressions: The Candy Shop

Abstract

Increasing emphasis on “Algebra for all” (NCTM 1997a, 1997b) compels educators to identify and address fundamental ideas that build the foundations for algebraic thinking and reasoning. Identifying these foundational concepts and developing appropriate instructional approaches are the focuses of our work. One area in which students often experience difficulty is adding and subtracting algebraic expressions. Although students may be able to memorize a procedure, such as “distribute the negative” when subtracting algebraic expressions, they are often unable to make sense of this procedure. Our work suggests that part of students' difficulty in this area is that they do not conceptualize an algebraic expression as a composite unit. In the paragraphs below, we explain what is meant by composite units and how this construct helped frame our development of an instructional sequence to help students make sense of, and find meaning in, algebraic expressions and operations on algebraic expressions.