수학 문제해결 역량 평가도구 개발

A Study on the Development of the Assessment Tool for Mathematical Problem Solving Competency

본 연구의 목적은 수학 문제해결 역량을 측정할 수 있는 평가도구를 개발하는 것이다. 이를 위해 첫째, 문헌 연구를 통해 수학 문제해결 역량의 하위요소를 설정하고 둘째, 수학 문제해결 역량이 우수한 학생을 대상으로 설문 조사를 실시하여 예비문항을 추출하였다. 셋째, 내용타당도 및 안면타당도 검증을 실시하였으며 마지막으로, 예비조사와 본조사를 거쳐 문항분석과 탐색적 요인분석을 실시한 후, 도출된 모형에 대한 확인적 요인분석을 통해 적합성을 확인하였다. 연구 결과, 수학 문제해결 역량의 하위요소로 문제 이해, 계획 수립, 전략 탐색, 계획 실행 및 반성, 협력적 문제해결, 수학적 모델링, 문제 만들기의 7가지 요인이 추출되었으며, 이를 측정할 수 있는 총 40개의 측정 문항이 개발되었다. 이는 향후 수학 문제해결 역량 측정을 위한 평가도구로 활용할 수 있으며, 이를 토대로 수학 문제해결 역량 성취를 위한 교육 목표 및 방향을 설정하는데 지표가 될 수 있을 것이다.

The aim of this study was to develop an assessment tool that can be used to evaluate the mathematical problem solving competency. First, a literature research was conducted to document the concepts of the competency, the problem solving competency, the mathematical problem solving competency and the relevant sub-elements. Second, a survey was conducted targeting the students having excellent mathematical problem solving competency to examine the behavioral examples of mathematical problem solving competency, and provisional preparatory questions were deducted. Third, content validity verification was performed twice by the mathematics education experts and teachers to verify the derived preparatory questions. The face validity verification was conducted targeting the first-grade students of high schools located in Seoul. Finally, preliminary survey and the main survey was conducted. The descriptive statistical analysis(average, standard deviation, skewness, and kurtosis), correlation analysis between the questions and total scores, reliability analysis, and exploratory factor analysis were performed to analyze the preliminary survey. And for the main survey analysis, the confirmatory factor analysis, which was about the verification of reliability and validity of the latent variables and measured variables, was performed to evaluate the suitability of measurement model. The construct validity was derived by reviewing the convergent validity and discriminant validity. In conclusion, the seven subordinate factors of mathematical problem solving competency, including the problem understanding, planning, strategy seeking, plan execution and self-questioning, cooperative problem solving, mathematical modeling, and problem making, were extracted. Also, a total of 40 questions were developed to be able to evaluate the factors. Hence, the mathematical problem solving competency assessment tool developed in this study could provide a practical basis for further studies and education fields.