On the Design of Novel Notations and Actions to Facilitate Thinking and Learning

Kenneth R. Koedinger

Abstract

There are certain domains, for example, word problems or high school geometry, which even well-motivated students find particularly difficult. I claim that such domains are enigmatic to students because the problem solving notation used in current instruction does not provide a good reflection of the underlying problem solving processes necessary to be successful in these domains. I argue that some domains are not enigmatic in this sense, like algebra equation solving, and thus, are not good candidates for model-based notation design. However, domains that are enigmatic, like geometry theorem proving, can be made less so by (1) developing a cognitive model of skilled problem solving in the domain and (2) designing novel notations and actions that reify the underlying structures and processes of the model. In previous research, we found that skilled geometry problem solvers plan proofs much differently than the problem solving approach implied by textbook solution examples (and by previous cognitive models). A new cognitive model of this perceptually-based planning approach has been used to design novel geometry notations and actions that facilitate a way of thinking about geometry proofs that is more like the thinking of skilled problem solvers. These notations and actions have been implemented in a computer environment called ANGLE (A New Geometry Learning Environment).