Earticle

The purpose of this study is to set up a hypothetical learning trajectory (HLT) in graph drawing among trigonometric functions, to check at what level of HLT students make misunderstanding, and to find the reason. In addition, it is to study what kind of tasks are set and how to solve these misunderstanding. For HLT setting, various misunderstanding or error data were collected through literature study, and the HLT level of graph drawing was set by analyzing it. Based on this level, a diagnostic test was performed on 11 students and the developmental level of the students was categorized. Two of them were selected to execute a task for solving misunderstanding and the results were observed. Find of misunderstanding based on HLT level and tasks for solving them were effective.

In this study, we investigated how to infer the perception of quantity and the relationship between them. In addition, existing tasks using technical instrument were investigated. The purpose of this study is to propose a task using an technical instrument that can be used to identify the limitations of existing tasks and to understand the perception and inference method of quantity. The results of this study are as follows. First, it is expected that the use of technical instrument will provide dynamic representations that were not in the existing tasks and more efficiently grasp students' reasoning methods. Second, teachers' competence in engineering tools should be enhanced for efficient use of tasks.

The purpose of this study is to develop a task that can explore the translation learning trajectory between representations included in the contents of the coordinate plane and graph of the middle school's regularity and function area and determine the level of development of students based on the explored learning trajectory. As a result of the study, the translation learning trajectory between representations included in the contents of the coordinate plane and graph could be divided into nine developmental levels. Considering the results of the study, By suggesting the optimal learning trajectory related to students' representative translation development in coordinate plane and graph content and developing and providing tasks for teachers to determine students' level of representative translation development in coordinate plane and graph content in the future.