QUANTITATIVE OPERATIONS AS A BASIS FOR ALGEBRAIC REASONING AND TEACHING PRACTICES

Abstract

We present initial analysis of data from a long-term constructivist teaching experiment whose purpose is to understand how middle grade students can build algebraic reasoning out of their evolving quantitative operations and quantitative reasoning. We taught 4 pairs of 6th graders at a rural middle school in Georgia from October 2003 to May 2004 and will work with them through AY 2004-2005. Teaching episodes occurred biweekly, lasted thirty minutes, were videotaped, and included the use of computer software—TIMA: Sticks and Javabars. For this presentation we focus on 2 pairs of students, describing how they built a quantitative scheme that we believe underlies the construction and solution of basic linear equations (i.e., of the form ax= b.) In this process we discuss the connection between quantitative schemes and basic linear equations, a hallmark of algebra.