Mathematical Elaboration Process of the Elementary Gifted Children's Board Game Re-creation in Group Project

모둠별 게임 변형을 통한 초등수학영재들의 수학적 정교화 과정 분석

  • Received : 2013.08.08
  • Accepted : 2013.09.16
  • Published : 2013.09.30

Abstract

One area where research is especially needed is their elaboration process and how they elaborate their idea as a group in a mathematical board game re-creation project. In this research, this process was named 'Mathematical Elaboration Process'. The purpose of this research is to understand how the gifted children elaborate their idea in a small group, and which idea can be chosen for a new board game when they are exposed to a project for making new mathematical board games using the what-if-not strategy. One of the gifted children's classes was chosen in which there were twenty students, and the class was composed of four groups in an elementary school in Korea. The researcher presented a series of re-creation game projects to them during the course of five weeks. To interpret their process of elaborating, the communication of the gifted students was recorded and transcribed. Students' elaboration processes were constructed through the interaction of both the mathematical route and the non-mathematical route. In the mathematical route, there were three routes; favorable thoughts, unfavorable thoughts and a neutral route. Favorable thoughts was concluded as 'Accepting', unfavorable thoughts resulted in 'Rejecting', and finally, the neutral route lead to a 'non-mathematical route'. Mainly, in a mathematical route, the reason of accepting the rule was mathematical thinking and logical reasons. The gifted children also show four categorized non-mathematical reactions when they re-created a mathematical board game; Inconsistency, Liking, Social Proof and Authority.

본 연구는 초등수학영재들이 수학적 소재의 기존 게임을 변형하여 새로운 게임을 만들어가는 동안 모둠내 토론 과정에서 드러나는 수학적 정교화 과정을 분석하고 이를 모델화한 것이다. 이를 위해 한 개의 지역공동영재학급에서 5주간의 수업을 진행하였으며, 특히 게임의 변형의 아이디어를 모둠별로 모아가는 수학적 정교화 과정을 모델로 구안하고자 하였다. 정교화 과정에서 수학적 경로와 수학외 경로가 상호작용을 하는 이중 경로의 모습을 띄었으며, 수학적(논리적) 근거에 따라 3가지의 수학적 경로(호의, 비호의, 중립)와 4 가지의 수학외 경로(비일관성, 사회적 증거, 호감, 권위)으로 분석할 수 있었다. 이 과정에서 수시로 통찰이 일어났으며, 이 과정을 거쳐 수학적 규칙이 모둠에서 수렴되는 정교화의 모습을 볼 수 있었다. 이를 바탕으로 초등수학영재들이 모둠별로 게임을 변형하는 과정에서 보이는 수학적 정교화 과정을 분석하고 수학적 정교화 모델을 제안하였다.

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