A Research on Mathematical Activities as Purpose: Focus on Function

Abstract

　　The purpose of this paper is to clarify the mathematical activities as purpose.　For attaining this purpose, firstly it is described the mathematical activities by two points of view of mathematical modelling as process and thought of function as product of learning.　In addition, it is described finally the ideal of the mathematical activities from as purpose these two points of view focusing on proportion.　In the end, it is described future problems to materialize the activities.

　　Focusing on the purpose of learning and teaching, the mathematical activities are divided into two parts: “purpose model” and “method model”.　And for the nature of mathematics activities and in the current discussion, it is necessary to learn mathematical methods.　However, the status of learning and teaching is focused on mathematical contents, so not method so much.　Consequently the problem is that find out the method of learning and teaching for mathematical activities as purpose.

　　Then in the activities of proportion, it is necessary to find two depending quantities.　In such a case of using mathematical model as a solution, it is necessary to make and remake mathematical model.

　　And to materialize the activities, there are four problems: (1) To design lesson and practice; (2) To study another products of learning; (3) To develop teaching methods; and (4) To develop a curriculum centered on methods.