수학 문제해결 신념의 측정도구 개발 = Instrument Development for Mathematical Problem-Solving Belief

국문 초록 (Abstract)

본 연구에서는 우리나라 학생들이 가지는 수학 문제해결 신념 측정도구를 문헌연구와 심리측정학적 분석을 바탕으로 중학교와 고등학교 모두에서 간편하게 활용할 수 있는 표준화된 도구를 개발하였다. 구체적으로, 문헌 연구를 바탕으로 1차 도구를 개발한 뒤 대단위 표집 검사로 측정한 우리나라 중학생과 고등학생의 수학 문제해결 신념을 탐색적 요인분석과 문항간 상관분석을 실시한 결과, ‘과정’, ‘도전성’, ‘끈기’라는 세 가지 하위 요인을 도출하였다. 그런 다음, 확인적 요인분석을 실시하여 최종적으로 ‘과정’ 요인에서 4문항, ‘끈기’는 3문항, ‘도전성’은 2문항을 개발하였다. 또한 일원분산분석과 다집단 분석을 실시하여 중학교와 고등학교 모두에서 성별, 성취 수준의 영향을 가능한 적게 받으면서 학교급과 상관없이 동일한 문항으로 간편하게 측정할 수 있는 표준화된 측정도구를 개발하였다. 우리나라 중고등학생의 수학 문제해결 신념에서의 특성을 살펴본 결과, 중학교와 고등학교 모두 남학생이 낯선 문제에 도전적이고, 금방 답이 나오지 않는 문제를 해결하는 것을 더 좋아하는 경향성이 나타났다. 그리고 수학 성취 수준을 우수, 보통, 기초이하 집단으로 나누었을 때 우수 집단은 ‘과정’ 범주가 가장 높고 ‘끈기’가 가장 낮았으며, 보통집단은 ‘과정’이 가장 높고 ‘도전성’이 가장 낮았고, 기초이하 집단은 특히 ‘도전성’ 범주가 매우 낮았다.

다국어 초록 (Multilingual Abstract)

The purpose of the present study is to develop an instrument for mathematical problem-solving belief and to analyze the results of the instrument. The instrument was developed to investigate mathematical problem-solving belief by reflecting Korean middle school and high school students' psychological characters. To develop the appropriate items for the mathematical problem-solving belief, after reviewing literature thoroughly, first version of the instrument was developed and exploratory factor analysis and confirmatory factor analysis were conducted. Then, to reduce the effect of the gender difference and achievement level difference, Correlation Analysis and 1-way ANOVA was performed. Also, using multiple group confirmatory factor analysis, this instrument was investigated to see whether this can be used for both middle school and high school. The final items for mathematical problem-solving belief are 4 items for process, 3 items for challenge, 2 items for persistence. Students of higher achievement level showed that the degree of process was the highest and the degree of persistence was the lowest. Students of middle achievement level showed that the degree of process was the highest and the degree of challenge was the lowest. Students of lowest achievement level showed that the degree of challenge was the most lowest. Also, Male students preferred more challenging in mathematics learning than female students. The instrument was developed by using large samples and psychometric analysis. Therefore, mathematic teachers can use this instrument efficiently to make a foundation for better learning environment so students' cognitive area and affective area can be harmonized.

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