Creating Connections: Promoting Algebraic Thinking with Concrete Models

The recent “Algebra for all” era has meant “the best of times and the worst of times” in many middle schools. At one extreme, many adolescents delight in the opportunity to study algebra or algebraic thinking and perform well in this course of study. At the other extreme, too many adolescents encounter serious challenges as they delve into fundamental ideas that make up this essential mathematical subject. Instead of viewing algebra as a natural extension of their arithmetic experiences, significant numbers of adolescents do not connect algebraic concepts with previously learned ideas. For instance, data from the Third International Mathematics and Science Study (TIMSS) showed that at the international level, only 47 percent of the seventh graders and only 58 percent of the eighth graders were able to recognize that m + m + m + m was equivalent to 4m (Beaton et al. 1996).