TY - JOUR

T1 - Do mathematicians and undergraduates agree about explanation quality?

AU - Evans, Tanya

AU - Mejía-Ramos, Juan Pablo

AU - Inglis, Matthew

N1 - Funding Information: This work was supported by the University of Auckland Faculty of Science Research and Development Grant (Project code: 3720159). Publisher Copyright: © 2022, The Author(s).

PY - 2022/11

Y1 - 2022/11

N2 - Offering explanations is a central part of teaching mathematics, and understanding those explanations is a vital activity for learners. Given this, it is natural to ask what makes a good mathematical explanation. This question has received surprisingly little attention in the mathematics education literature, perhaps because the field has no agreed method by which explanation quality can be reliably assessed. In this paper, we explore this issue by asking whether mathematicians and undergraduates agree with each other about explanation quality. A corpus of 10 explanations produced by 10 mathematicians was used. Using a comparative judgement method, we analysed 320 paired comparisons from 16 mathematicians and 320 from 32 undergraduate students. We found that both mathematicians and undergraduates were able to reliably assess the quality of a set of mathematical explanations. Furthermore, the assessments were largely consistent across the two groups. Implications for theories of mathematical explanation are discussed. We conclude by arguing that comparative judgement is a promising technique for exploring explanation quality.

AB - Offering explanations is a central part of teaching mathematics, and understanding those explanations is a vital activity for learners. Given this, it is natural to ask what makes a good mathematical explanation. This question has received surprisingly little attention in the mathematics education literature, perhaps because the field has no agreed method by which explanation quality can be reliably assessed. In this paper, we explore this issue by asking whether mathematicians and undergraduates agree with each other about explanation quality. A corpus of 10 explanations produced by 10 mathematicians was used. Using a comparative judgement method, we analysed 320 paired comparisons from 16 mathematicians and 320 from 32 undergraduate students. We found that both mathematicians and undergraduates were able to reliably assess the quality of a set of mathematical explanations. Furthermore, the assessments were largely consistent across the two groups. Implications for theories of mathematical explanation are discussed. We conclude by arguing that comparative judgement is a promising technique for exploring explanation quality.

KW - Comparative judgement

KW - Explanation quality

KW - Mathematical explanation

KW - Mathematical practices

KW - Undergraduate mathematics

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U2 - https://doi.org/10.1007/s10649-022-10164-2

DO - https://doi.org/10.1007/s10649-022-10164-2

M3 - Article

SN - 0013-1954

VL - 111

SP - 445

EP - 467

JO - Educational Studies in Mathematics

JF - Educational Studies in Mathematics

IS - 3

ER -