On the Introduction of Fractions through the Measurement of Quantity

Abstract

One of the aims of didactical study is to construct a general theory for creating the educational contents and methods which enable all children to learn fundamental parts (laws and concepts) of sciences, technics and arts with pleasure. From this viewpoint, the study on mathematics education is aimed at the creation of the educational contents and methods which enable all children to learn mathematics with pleasure. In this paper, we propose a plan for introduction of fractions through the measurement of quantity to elementary school children. And we examine the process and the result of the experimental lessons based on the plan. The fundamental viewpoints of our plan are as follows: (1) When we measure a continuous quantity, we sometimes get fragments. We introduce fractions as one way of expressing the fragments. (2) To express the fragments, we adopt the principle of Euclid's algorithm as a fundamental method. (3) We evaluate the role that the ratio aspect of fractions plays in the teaching and later unify it with the division aspect of fractions. The experimental lessons are carried out in a third grade class in Tagajou-higashi elementary school by Mr. Takayuki Sato in December 1997.