Computer Environments for Proof Construction

Abstract

Does the presentation and use of the search space matter for complex problem solving tasks? We address these questions for the construction of proofs in sentential logic. Using a fully computerized logic course, we isolated crucial features of computer environments and assessed their relative pedagogical effectiveness. After being given a pretest for logical aptitude, students were divided into three matched groups, each of which used a distinct computerized environment to construct proofs. All students were presented with identical course material on sentential logic for approximately five weeks.

Students completed more than one hundred exercises during those five weeks and took a midterm at the end of the period. The group using the most informative and most flexible interface performed substantially better on the midterm— the difference was particularly striking for hard problems. In two follow‐up experiments we added strategic problem solving help; student performance improved again (entirely on the difficult problems). Our interpretation is, first, flexibility in traversing the search space leads students to see the global structure of the search space and to develop effective heuristics; second, strategic help reinforces and extends these heuristics.

Additional information

Notes on contributors

Wilfried Sieg

We thank Ken Koedinger for many helpful discussions and some needed encouragement. We also thank Virginia Hoage, who collected the data, and Chris Walton, who performed the programming miracles that made this study possible.