2134/11494206.v1
Marie-Josée Bisson
Marie-Josée
Bisson
Camilla Gilmore
Camilla
Gilmore
Matthew Inglis
Matthew
Inglis
Ian Jones
Ian
Jones
Teaching using contextualised and decontextualised representations: examining the case of differential calculus through a comparative judgement technique
Loughborough University
2020
Mathematical Sciences
decontextualised representations
calculus
conceptual understanding
contextualised representations
randomised controlled trial
Education
2020-01-07 14:10:09
Journal contribution
https://repository.lboro.ac.uk/articles/journal_contribution/Teaching_using_contextualised_and_decontextualised_representations_examining_the_case_of_differential_calculus_through_a_comparative_judgement_technique/11494206
An ongoing debate concerns whether novel mathematical concepts are better learned using
contextualised or decontextualised representations. A barrier to resolving this debate, and
therefore to progress in the discipline, has been the paucity of validated methods of measuring
students’ understanding of mathematical concepts. We developed an innovative and efficient
method for measuring, in experimental settings, students’ understanding of any mathematical
concept using comparative judgement. We demonstrate the method by applying it to the
comparison of learning outcomes from two teaching conditions. Participants (260 15-16 year
olds across six schools) were introduced to differential calculus using contextualised or
decontextualised representations. We then assessed participants’ comparative conceptual
understanding of derivatives. We found evidence that contextualised and decontextualised
representations were equally effective at promoting student learning in this context. The
assessment method yielded valid and reliable results, suggesting that it offers a robust and
efficient approach for the problem of assessing conceptual understanding in experimental or
other comparative settings