Teaching using contextualised and decontextualised representations: examining the case of differential calculus through a comparative judgement technique

An ongoing debate concerns whether novel mathematical concepts are better learned using or decontextualised representations. A barrier to resolving this debate, and to progress in the discipline, has been the paucity of validated methods of measuring’ understanding of mathematical concepts. We developed an innovative and efficient for measuring, in experimental settings, students’ understanding of any mathematical using comparative judgement. We demonstrate the method by applying it to the of learning outcomes from two teaching conditions. Participants (260 15-16 year across six schools) were introduced to differential calculus using contextualised or representations. We then assessed participants’ comparative conceptual of derivatives. We found evidence that contextualised and decontextualised were equally effective at promoting student learning in this context. The method yielded valid and reliable results, suggesting that it offers a robust and approach for the problem of assessing conceptual understanding in experimental or comparative settings