Measuring conceptual understanding in mathematics

A major challenge for mathematics education research is how to measure pupils’ conceptual understanding with acceptable validity and reliability. Furthermore, opinion is often divided on whether abstract or concrete representations are better at supporting pupils’ conceptual understanding.

This study will develop a measure of conceptual understanding using the Comparative Judgement (CJ) approach, and demonstrate the application of CJ to this debate. It builds on previous work, including a study by the same researchers, and a recent pilot study demonstrating how CJ could be used to measure learners’ understanding of mathematical concepts.

The research will involve two teaching experiments with Year 11 and Year 5 students. In each experiment students will be randomly allocated into two groups and taught an unfamiliar mathematical concept. One group will be taught using abstract representations, the other using concrete representations. The researchers will then use CJ to establish whether the abstract or concrete representations led to a more sophisticated mathematical understanding of the target concept in each experiment.

The project aims to provide a major methodological contribution to transform how educational interventions are evaluated. It also hopes to provide robust evidence to inform the abstract vs. concrete debate, and influence how mathematics lessons are designed and taught.