Modelling the Use of Abstraction in Algorithmic Problem Solving
Cruz Izu · 2022
Abstraction plays a key role in efficient problem solving: it helps to identify relationships and properties that support moving from basic brute force approaches towards simpler and more efficient solutions. The ability to abstract in problem solving is a difficult skill that should be nurtured by providing both examples and explicit guidance on how to use abstraction. In order to develop teaching materials we should first have a reasonable estimation of the students' current ability to abstract from the problem description as reflected in their solutions. In this study we have identified a simple problem, "EggCartons" which could be used as an exemplar to model abstraction in the classroom, due to its wide solution space. Its algorithmic solutions move up the ladder of abstraction, from brute force towards mathematical modelling. We visually inspected and classified the problem's solutions written by second year students, in order to explore students' current abstraction skills. The classification helped to identify four levels of abstraction that are relevant to other problems. The insights gained from this analysis provide a possible learning trajectory for abstraction in problem solving which could support undergraduate students to gradually increase the abstraction level of their algorithmic solutions.