• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.45-61
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• 2009

The powerful role of analogical reasoning in discovering mathematics is well substantiated in the history of mathematics. Mathematically gifted students, thus, are encouraged to learn via in-depth exploration on their own based on analogical reasoning. In this study, 57 gifted students (31in the 7th and 26 8th grade) were asked to formulate or clarify analogy. Students produced fruitful constructs led by analogical reasoning. Participants in this study appeared to experience the deep thinking that is necessary to solve problems made with analogies, a process equivalent to the one that mathematicians undertake. The subjects had to reflect on prior knowledge and develop new concepts such as an orthogonal projection and a point of intersection of perpendicular lines based on analogical reasoning. All subjects were found adept at making meaningful analogues of a triangle since they all made use of meta-cognition when searching relations for analogies. In the future, methodologies including the development of tasks and teaching settings, measures to evaluate the depth of mathematic exploration through analogy, and research on how to promote education related to analogy for gifted students will enhance gifted student mathematics education.