Action to process: constructing functions from algebra word problems

Abstract

Abstract The ability to build a mathematical model of a situation described in ordinary language has always been an important goal of school mathematics teaching. This paper gives one explanation for the difficulties many students experience with certain stylized modeling tasks (solving algebra word problems) and puts these difficulties in the context of a theory about the acquisition of the concept of mathematical function. It also describes a visual programming language that can act as a bridge, and in some sense an alternative, to formal algebraic notation as a language for describing situations. Tracing the author's classroom experiments and his reflections on those experiments, the paper suggests a method for helping students.