Investigating prospective science and mathematics teachers’ meanings for and representations of functions: an international study

Abstract

The concept of a function is crucial in both mathematics and science education. Appropriate teaching of the concept is therefore very important, and an understanding of the knowledge of functions possessed by prospective teachers of science and mathematics is highly desirable. The present study was instigated by the Association for Teacher Education in Europe's Research and Development Community (RDC) on Science and Mathematics Education in order to explore this knowledge across different countries. Using theoretical frameworks provided by research on teacher knowledge and representations in mathematics and science education, the study is investigating meanings that prospective teachers give for the term "function" and representations that they associate with it. An instrument was adapted from a previous RDC study (on ratio). For the initial phase, reported here, research team members in Portugal, Ireland and the Netherlands collected data from opportunity samples at their own institutions, focusing on prospective mathematics teachers. Analysis of the responses (N=145) started with team members examining their own data; they listed themes, guided by curricular traditions in their own countries as well as by research on knowledge of functions. Lists were then shared in order to identify commonalities and contrasts. The data reflected meanings and representations involving correspondence/dependence relationships and also those based the idea of a "machine"/formula/rule; the former were most prominent in the Portuguese data and least in the Dutch, in line with national curricula. The findings suggest that, in the ongoing study, the instrument will provide useful information for teacher educators.