Introducing the Variable through Pattern Exploration Pattern Exploration

摘要

Variables are the basic tool for expressing generalizations. An understanding of the concept of variable is fundamental to our students' success with algebra. Yet this concept is more sophisticated than we realize and is often the stumbling block in our students' algebraic development (Leitzel 1989; NCTM 1989). Traditionally, a students' first encounter with a variable has been in an equation, where it represents an unknown number. Textbooks that follow this approach offer students few opportunities to investigate, explore, and experience the construction of algebra. In recent years, we have begun to question this traditional approach. Curriculum documents now recommend informal, concrete activities in which students investigate patterns in shape and number, formulate verbal rules to describe these patterns, and then look for ways to generalize the situation (Booth and Blane 1992; Morelli 1992; NCTM 1989). Our purpose here is to review this alternative patterning approach and to highlight the difficulties that it can present to students when they lack the requisite skills and knowledge of processes. We then offer some recommendations for establishing these important understandings.