중학교 삼각비 교과서 과제 및 교사 설계 과제 비교⋅분석

Abstract

Objectives In this study, the triangulation task actually used in the middle school class is analyzed from the perspective of the mathematical modelling tasks.
 Methods Various triangulation tasks were collected from middle school trigonometry textbooks and activity sheets produced and used by teachers, and classified based on whether connectivity and openness, which are the core characteristics of mathematical modelling tasks, were met, and cognitive activities required. Then, mathematical modelling tasks is selected from among the teacher-designed tasks, and the activities of the tasks and the interviews of the teachers in each mathematical modelling tasks are interpreted according to the mathematical modelling cycle.
 Results Teacher-designed tasks were found to have higher connectivity and openness than textbook tasks, including familiar material, offering practical and specific data, or insufficient data to solve the task. On the other hand, all tasks selected as mathematical modelling tasks among teacher-designed tasks emphasized simplifying, mathematising, and working mathematically, but relatively put less emphasis on understanding, interpretation, and validation. In particular, the process after working mathematically turned out to be limited to the extent of attaching units to the mathematical results, rounding it, or reviewing whether the calculation of the result were correct. In addition, all tasks used only the concept of tangent and did not require other concepts of trigonometric ratio.
 Conclusions Several examples of triangulation tasks can be found in Korean and foreign mathematical modelling studies. As such, mathematical modelling teaching/learning method is useful to teach trigonometry due to its usefulness in real life. According to the results of this paper, teachers want to design assignments rich in connectivity and openness so that students can recognize the usefulness of the concept of trigonometric ratio. Furthermore, if the various cognitive activities in the mathematical modelling cycle are evenly included, and various trigonometry tasks including various models are designed, it would lead more meaningful teaching and learning of mathematical modelling as well as trigonometry and ultimately it would help students improve problem-solving skills.