수학 문제해결 역량 평가도구 개발

Abstract

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.