수학적 모델링의 과제공간과 과제복잡성의 평가척도(rating scheme)설정

A Study on Setting of Mathematical Modelling Task Space and Rating Scheme in its Compexity

본 연구는 수학적 모델링의 과제공간을 설정하고 이를 기반으로 모델링 과제의 복잡성을 나타내는 평가척도(rating scheme)를 설계하여 그것의 타당도를 확인하였다. 예비 수학교사를 대상으로 두 단계의 과정을 거쳐 실험을 진행하였고 다음과 같은 결과를 얻을 수 있었다. 첫째는 종전의 문제구조를 표현한 문제공간을 발전시켜 모델링 과제에 맞는 과제공간을 설정하고, 모델링 과제의 복잡성을 수치로 나타내는 계량적인 평가척도를 설계하여 의미 있는 타당도를 확인하였다. 둘째로는 모델링 과제 복잡성의 평가척도, 학생 성취수준, 과제 특수 발견 전략의 개수 사이에는 일관된 패턴이 있음을 발견하였다.

The purpose of this study was to decide the task space and Rating Scheme of task difficulty in complicated mathematical modelling situations. One of main objective was also to conform the validation of Rating Scheme to determine the degree of difficulty by comparing the student performance with the statement of the theoretical model. In spring 2014, the experimental setting was in Modelling Cource for 38 in-service teachers in mathematics education. In conclusions, we developed the Model of Task Space based on their solution paths in mathematical modelling tasks and Rating Scheme for task difficulty. The Validity of Rating Scheme to determine the degree of task difficulty based on comparing the student performance gave us the meaningful results. Within a modelling task the student performance verifies the degree of difficulty in terms of scoring higher using solution approaches determined as easier and vice versa. Another finding was some relations among three research topics, that is, degree of task difficulty on rating scheme, levels of students performance and numbers of specific heuristic. Those three topics showed the impressive consistence pattern.