VARIATION WITHIN, AND CO VARIATION BETWEEN, REPRESENTATIONS

This is a theoretical paper in which we conjecture that some difficulties in learning mathematics may be due to the need to coordinate covariation between different representations, not merely to 'match individual states. We use research within variation theory on learners' understanding of the infinity of numbers in an interval to draw attention to the need to coordinate variation of decimal representation with position on a numberline. We problematise this relationship and use a small empirical study to hypothesise how learners might relate these implicitly and explicitly. This covariation lens augments the usefulness of variation theory in thinking about mathematics pedagogy and learning.