Supporting the development of algebraic thinking in middle school: a closer look at students’ informal strategies

Abstract

This study investigated how 31 sixth-, seventh-, and eighth-grade middle school students who had not previously, nor were currently taking a formal Algebra course, approached word problems of an algebraic nature. Specifically, these algebraic word problems were of the form x + ( x + a) + ( x + b) = c or ax + bx + cx = d. An examination of students’ understanding of the relationships expressed in the problems and how they used this information to solve problems was conducted. Data included the students’ written responses to problems, field notes of researcher–student interactions while working on the problems, and follow-up interviews. Results showed that students had many informal strategies for solving the problems with systematic guess and check being the most common approach. Analysis of researcher–student interactions while working on the problems revealed ways in which students struggled to engage in the problems. Support mechanisms for students who struggle with these problems are suggested. Finally, implications are provided for drawing upon students’ informal and intuitive knowledge to support the development of algebraic thinking.