• Journal of the Korean School Mathematics Society
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• v.19 no.4
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• pp.357-371
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• 2016

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 Course 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.