• We Want a Statement That Is Always True: Criteria for Good Algebraic Representations and the Development of Modeling Knowledge

    Andrew Izsak
    This article presents a case study in which two eighth-grade students developed knowledge for modeling a physical device called a winch. In particular, the students learned (a) to distinguish equations that are true for any value of the independent variable from    equations that constrain the independent variable to a unique value and (b) to solve the latter type of equation to determine when specific physical events occur. The analysis of how these understandings emerged led to two results. First, the analysis    demonstrated that students have and can use criteria for evaluating algebraic representations.    Second, the analysis led to a theoretical frame that explains how students can develop modeling knowledge by coordinating such criteria with knowledge for    generating and using algebraic representations. The frame extends research on students' algebraic modeling, cognitive processes and structures for using mathematical representations, and the development of mathematical knowledge.