현실적 맥락을 활용한 수학화 학습이 수학적 사고에 미치는 효과

Abstract

The purpose of this study was to look into whether this mathematising learning utilizing realistic coherence has an effect on the mathematical thinking. To solve the above problem, two 5th grade classes of D Elementary School in Seoul were selected for performing necessary experiments with one class designated as an experimental group and the other class as a comparative group. Throughout 17 times for six weeks, the comparative group was educated with general mathematics learning by mathematics and "mathematics practices," while the experimental group was taught mainly with mathematising learning using realistic coherence. As a result, to start with, in case of the experimental group that conducted the mathematising learning utilizing realistic coherence, in the analogical and developmental thoughts which are mathematical thoughts related to the methods of mathematics, in the thinking of expression and the one of basic character which are mathematical thoughts related to the contents of mathematics, and in the thinking of operation, the average points were improved more than the comparative group, also having statistically significant differences. Besides, in the mathematics group that performed the mathematising learning utilizing realistic coherence, I could see that the students of the upper and the lower groups had more active mathematising of each process as the teaching progressed to the former period, the middle one and the latter one, in each process of four steps for mathematising processes─intuitive study, conceptual mathematising, formalizing and abstracting step, and application in reality. The study suggested that it is necessary to conduct subsequent studies that can verify by expanding to each grade, sex and region, develop teaching methods suitably to the other content domains and purposes of figures, and demonstrate the effects. In addition to those, evaluation tools which can evaluate the mathematical thinking processes of children appropriately and in more diversified methods will have to be developed. Furthermore, in order to maximize mathematising for each group in each mathematising process, it would be necessary to make efforts for further developing realistic problem situations, works and work sheets, which are adequate to the characteristics of the upper and lower groups.;본 연구의 목적은 현실적 맥락을 활용한 수학화 학습을 실제 현장에 적용하여 이러한 학습이 아동의 수학적 사고에 어떠한 효과를 나타내는지 알아보는 데에 있다. 이러한 연구 목적을 위해 서울시 D초등학교 5학년 2개 학급을 연구 대상으로 6주간 17차시에 걸쳐 실험이 이루어졌고, 실험 설계는 전후 검사 통제집단 설계를 하였다. 또한 1학기말 수학 학업 성취도 평가 결과를 기준으로 선정된 실험 집단의 상(30%), 하(30%) 집단 학생들을 대상으로 하여 시기별(전기-중기-후기)로 관찰, 질문지, 녹음, 활동지와 형성평가지 분석의 방법을 사용하여 현실적 맥락을 활용한 수학화 학습을 통해 나타난 아동의 수학화 과정이 어떠한지를 각 과정별로 분석하여 살펴보았다. 그 결과 현실적 맥락을 활용한 수학화 학습을 실시한 실험 집단의 경우 수학의 방법 및 내용적 측면에서 나타난 수학적 사고에서 평균 점수가 비교 집단보다 향상되었고 통계적으로도 유의미한 차이가 나타났다. 또한 현실적 맥락을 활용한 수학화 학습을 실시한 수학 집단에서 수학화 과정의 4단계인 직관적 탐구, 수평적 수학화, 수직적 수학화, 응용적 수학화 각각의 과정에서 상․하위 집단별 학생들은 수업이 전기-중기-후기로 진행되어 갈수록 각 과정의 수학화가 더욱 활발히 일어났음을 알 수 있었다.