Development of Concepts of Mathematical Functions: A Quasi-experimental Study of Fourth- and Fifth-Grade Learners in Japan

According to the Programme for International Student Assessment, functions constitute an important part of mathatical literacy. In Japan, students start learning about bivariate relationships in the fourth grade (at the age of 9). However, reports suggest that elementary school students and lower-level secondary school (junior high) students have an inadequate grasp of the concept; therefore, an educational intervention that facilitates elementary school students’ comprehension of functions is necessary. For this purpose, this paper reports a pilot study that applied an action- learning approach to two fourth graders and two fifth graders. The intervention avoided using numerical concepts so that the learners could form a qualitative understanding of bivariate relationships, which is a prerequisite for being able to solve quantitative problems. The results indicated that the intervention was effective and could facilitate the formation of bivariate qualitative relational concepts. These findings imply that the intervention could be effectively applied to elementary school classes through an action-learning approach.