Task Comprehension Strategies in Proof Construction – Methodological and Educational Issues

Kirsten, K.; Neuhaus-Eckhardt, S.

Abstract

Many students have difficulty constructing proofs. To overcome these difficulties, developing a rich mental representation of the proving task could be helpful. Thus, using task comprehension strategies that support building such a mental representation could relate positively to proof construction. However, it is an open question how the use of these strategies can be measured in a large sample. Therefore, we addressed (a) methodological issues of measuring task comprehension strategies, before investigated the relationships between task comprehension strategies and (b) prior knowledge, and (c) performance on proof construction. Our results from a sample of 152 second-semester university students in Germany, who had already taken two proof-based courses, indicate that students' self-reports of their strategy use and performance tests on their strategy use measure different abilities. In addition , we found that prior knowledge influences performance on more advanced task comprehension strategies, such as inferring or evaluating examples, and proof construction. However, we could not confirm our hypotheses regarding the relation between strategy use for both measurements and performance on proof construction. In discussing these results and the limitations of our study, practical implications are also highlighted.