A Case Study on Instruction for Mathematically Gifted Children through The Application of Open-ended Problem Solving Tasks

개방형 과제를 활용한 수학 영재아 수업 사례 분석

Mathematically gifted children have creative curiosity about novel tasks deriving from their natural mathematical talents, aptitudes, intellectual abilities and creativities. More effect in nurturing the creative thinking found in brilliant children, letting them approach problem solving in various ways and make strategic attempts is needed. Given this perspective, it is desirable to select open-ended and atypical problems as a task for educational program for gifted children. In this paper, various types of open-ended problems were framed and based on these, teaming activities were adapted into gifted children's class. Then in the problem solving process, the characteristic of bright children's mathematical thinking ability and examples of problem solving strategies were analyzed so that suggestions about classes for bright children utilizing open-ended tasks at elementary schools could be achieved. For this, an open-ended task made of 24 inquiries was structured, the teaching procedure was made of three steps properly transforming Renzulli's Enrichment Triad Model, and 24 periods of classes were progressed according to the teaching plan. One period of class for each subcategories of mathematical thinking ability; ability of intuitional insight, systematizing information, space formation/visualization, mathematical abstraction, mathematical reasoning, and reflective thinking were chosen and analyzed regarding teaching, teaming process and products. Problem solving examples that could be anticipated through teaching and teaming process and products analysis, and creative problem solving examples were suggested, and suggestions about teaching bright children using open-ended tasks were deduced based on the analysis of the characteristic of tasks, role of the teacher, impartiality and probability of approaching through reflecting the classes. Through the case study of a mathematics class for bright children making use of open-ended tasks proved to satisfy the curiosity of the students, and was proved to be effective for providing and forming a habit of various mathematical thinking experiences by establishing atypical mathematical problem solving strategies. This study is meaningful in that it provided mathematically gifted children's problem solving procedures about open-ended problems and it made an attempt at concrete and practical case study about classes fur gifted children while most of studies on education for gifted children in this country focus on the studies on basic theories or quantitative studies.

수학 영재들은 타고난 수학적 소질과 적성, 지적인 능력과 창의성을 바탕으로 참신한 과제에 대한 도전적이고 창조적인 호기심을 가지고 있다. 영재아들의 창의적인 사고력을 길러주기 위해서는 다양한 방법으로 문제 해결에 접근하게 하고 전략적 시도를 할 수 있도록 만들어주어야 한다. 이런 관점에서 볼 때 개방적이고 비정형적인 문제를 영재 교육프로그램의 과제로 선정하는 것은 바람직하다 할 수 있다. 본 논문에서는 다양한 유형의 개방형 문제를 구안하고, 이를 토대로 영재 학급에서 학습 활동을 전개한 후, 문제해결 과정에서 영재아들의 수학적 사고 능력의 특성과 문제 해결 전략 사례를 분석하여, 개방형 과제를 활용한 초등학교 영재 수업에 관한 시사점을 얻고자 하였다.