Learning by seeing by doing: Arithmetic word problems

"Learning by doing" in pursuit of real-world goals has received much attention from education researchers but has been unevenly supported by mathematics education software at the elementary level, particularly as it involves arithmetic word problems. In this article, we give examples of doing-oriented tools that might promote children's ability to "see" significant abstract structures in mathematical situations. The reflection necessary for such seeing is motivated by activities and contexts that emphasize affective and social aspects. Natural language, as a representation already familiar to children, is key in these activities, both as a means of mathematical expression and as a link between situations and various abstract representations. These tools support children's ownership of a mathematical problem and its expression; remote sharing of problems and data; software interpretation of children's own word problems; play with dynamically linked representations with attention to children's prior connections; and systematic problem variation based on empirically determined level of difficulty.