算数教育におけるパフォーマンス・アセスメントに 関する基礎的研究 ─ 算数教育におけるパフォーマンスの核心としての数学化に着目して ─

抄録

　　The purpose of this paper is to reveal the tasks to structure the performance in the arithmetic education. For the purpose, the first described an idea of PA, considered some concrete instances in Pedagogy and Mathematics education. These view pointed out that there was the need to pay its attention to the original performance in arithmetic education. It was clarified that Mathematization had included position as a core of performance from immutability and trendy point of view.

　　Therefore, the second considered the historic flow in Mathematization of Freudenthal, Treffers, Lange. By these considerations and from the perspective of “mathematical method”, it was pointed out that Mathematization of Lange was required by arithmetic education in the future. Furthermore, based on them, it was clarified that a performance in the arithmetic education was globally structured as a cycle of Mathematization described by OECD / PISA.

　　It is difficult to push forward learning instruction, however, without a viewpoint to catch the performance in a cycle of Mathematization.　As a policy of that purpose, it is thought that a performance is caught as a model.　Furthermore, it is necessary to pay its attention to the transformation of the model. As a solution for the task, some researches of Gravemeijer to be focused on the model-of / model-for transition are very suggestive. According to this activity, there were four levels activity “activity in the task setting”, “referential activity”, “general activity”, “formal activity” in the process of constructing models.　These four levels of activity illustrate that models are initially tied to activity in specific settings and involve situation-specific imagery. These illustrated the transition of from “model-of” to “model-for” in Mthematization.

　　As a result, it was clarified that a rise of the mathematical recognition was appropriate to assess as the formation of the model and the model-of / model-for transition in learning instruction by PA in the arithmetic education.