Exploring students’ conceptual understanding through mathematical problem solving: students’ use of and shift between different representations of rational numbers

One way to stimulate conceptual considerations is through mathematical problem solving, which requires students to construct new solution methods, potentially including new representations. Hence, this study focuses on students’ use of and shift between representations during problem solving, specifically regarding the fundamental and often challenging concept of rational numbers. Swedish elementary school students were observed when tackling mathematical problems in pairs. The findings revealed that the students’ considerations concerned several conceptual properties of rational numbers through the use of different representations. However, students tended to use the representations presented in the problem, favouring the most familiar representation rather than constructing their own. As a result, they may have overlooked opportunities to explore a wider range of representations which could have deepened their understanding of the concept. This suggests a potential opportunity to design problems that require students to transfer between representations and grapple with unfamiliar ones.