Norwegian Mathematics Teacher Educators’ and Research Mathematicians’ Views on Different Aspects of Mathematical Definitions: a Comparative Judgement Study

Abstract In this article we investigate the extent to which characteristics used to describe mathematical definitions in mathematics education research literature reflect what is important to research mathematicians and mathematics teacher educators. We report results from a comparative judgement survey of 57 research mathematicians and 62 mathematics teacher educators. Our results indicate that the two groups are mostly in agreement about the rankings, however, there are some differences. Research mathematicians rank most highly characteristics related to non-ambiguity and non-contradiction, while mathematics teacher educators rank characteristics related to comprehension and referential clarity as highly as characteristics related to non-ambiguity and non-contradiction. Neither group ranked minimality highly, even though this is the characteristic most often listed in the mathematics education research literature. Our study contributes towards a more consistent characterization of mathematical definitions in mathematics education research.