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<p>Analogies are commonly used in mathematics teaching as a means to promote understanding of new potentially abstract concepts, by linking them to well-understood contexts. Despite strong intuition that analogies are helpful in supporting students’ learning of mathematics, there is a lack of agreement on how to objectively judge the utility or conceptual affordances of these analogies. In this paper, we aim to conceptualise how to assess the effectiveness of an analogy by employing Gentner’s structure-mapping theory to analogies and explore two teacher-made analogies (the ‘child-mother’ and the ‘machine’) for learning the formal definition of a function as illustrative examples. By applying the criteria for effective analogies, we are able to evaluate the effectiveness of the analogies in terms of both their affordances and constraints, thereby providing a structured approach to articulate the source specificity, clarity, scope, and appropriateness of an analogy.</p>

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What Makes an Analogy Effective for Students’ Learning of Mathematics? Conceptualising Analogy Effectiveness for Teaching Mathematics

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  • 发表日期：

    2026年7月1日

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  • Vesife Hatisaru,
  • Steven Richardson

摘要

Analogies are commonly used in mathematics teaching as a means to promote understanding of new potentially abstract concepts, by linking them to well-understood contexts. Despite strong intuition that analogies are helpful in supporting students’ learning of mathematics, there is a lack of agreement on how to objectively judge the utility or conceptual affordances of these analogies. In this paper, we aim to conceptualise how to assess the effectiveness of an analogy by employing Gentner’s structure-mapping theory to analogies and explore two teacher-made analogies (the ‘child-mother’ and the ‘machine’) for learning the formal definition of a function as illustrative examples. By applying the criteria for effective analogies, we are able to evaluate the effectiveness of the analogies in terms of both their affordances and constraints, thereby providing a structured approach to articulate the source specificity, clarity, scope, and appropriateness of an analogy.