영재아들의 세 유형의 유추 과제 해결 = Solving Three Types of Analogy Tasks by the Mathematically Gifted

다국어 초록 (Multilingual Abstract)

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.

국문 초록 (Abstract)

유추적 사고는 수학적 발견의 주요 도구로 강조되어 왔다. 그러나 영재아들을 대상으로 한 교육 자료에서 유추적 사고를 활용한 예는 현재까지 많지 않은 편이다. 이 연구에서는 영재아들을 대상으로 한 수업에서 유추적 사고를 적극적으로 강조하였을 때, 학생들이 어떤 반응을 보이며, 실제로 유추적 사고가 이들의 수학적 발견을 어떤 방식으로 돕는지 알아보았다. 고전적인 유추 문제는 유사한 두 대상과 각각의 대상에 대해 성립하는 성질을 비례식과 같은 형태로 제시하고, 네 항목 중 주어진 세 항목을 토대로 한 항목을 찾아내는 것이었다. 이 연구에서는 이를 변형하여, 세 가지 형태의 유추 과제를 제시하였으며, 각각의 유형에 대한 학생들의 반응을 분석하였다. 학생들은 비교적 유연하고 유창하게 유추적 사고를 사용하였으며, 유추적 사고 능력에 따라 수학적 발견에 차이를 보였다. 유추적 사고는 이미 알고 있던 개념을 재해석하고, 새로운 관점으로 변형하게 하는 역할을 하였으며, 새로운 지식의 발견에 도움을 주는 것으로 나타났다.

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