Correspondence-based analogies for choosing problem representations in mathematics and computing education
Problem-solving is the centrepiece of mathematics and computing curricula: students learn new concepts and fortify their expertise by working through prescribed problems. The representation of a problem—be it through algebra, diagrams, or code—is key to understanding and solving it. Multiple-representation interactive environments are a promising approach to mathematics and computing education, showing the same object in different representations and levels of abstraction. However, the burden of choosing an appropriate representation is largely placed on the user. What if we could choose a good representation automatically?
We propose a new method to recommend representations based on correspondences: conceptual links between domains. Correspondences can be used to analyse, identify, and construct analogies even when the analogical target is unknown (a departure from previous work in analogical reasoning). In this paper we: explain how correspondences build on probability theory and Gentner’s structure-mapping framework; propose rules for semi-automated correspondence discovery; and describe how correspondences can be used to both explain and construct analogies. We exemplify this by considering how we might re-represent a simple mathematics problem