Learning to solve story problems—supporting transitions between reality and mathematics

Abstract

Applying mathematics to real problems is increasingly emphasized in school education; however, it is often complained that many students are not able to solve mathematical problems embedded in contexts. In order to solve story problems, a transition from a textual description to a mathematical notation has to be found, intra-mathematical calculations have to be performed, and the results have to be interpreted with respect to the described situation. On the one hand, it is often suggested to consider problems which are embedded in a context from the very beginning; on the other hand, step-by-step procedures at the beginning of learning processes are widely proposed. In the present work, it was tested experimentally whether starting a learning process in a “pure” intra-mathematical way (thus, without a textual description of a context) is more beneficial than starting a learning process with problems providing a very short context or with problems providing a detailed context, both with respect to objective measures and with respect to subjective measures. The results indicate that starting with intra-mathematical problems and starting with detailed story problems can both be very effective; however, interaction effects with prior knowledge have to be taken into account. With respect to motivational aspects, the results indicate that intra-mathematical problems and focused story problems are substantially more appreciated by the learners than detailed story problems.