PROSPECTIVE TEACHERS ’ UNDERSTANDING AND REPRESENTATIONS OF MULTIPLICATION OF FRACTIONS

There is a growing consensus that teachers ’ knowledge is an important element in student learning. Since Shulman (1987) classifies pedagogical content knowledge as typical knowledge teachers should have, there is a lot of research which is interested in what a teacher should know and be able to do. However, many studies show that teachers possess a limited knowledge of mathematics, including the mathematics they teach (Ma, 1999; Ball, 1990;Behr, and Lesh, 1991; Simon, 1993). A majority of teachers are good at performing computation, but few are able to explain the conceptual basis of the procedures in performing computation. The purpose of this paper is to explore how prospective teachers understand multiplication of fractions with word problems and how they explain and justify the meaning behind their coumputation steps with multiple ways of representations. Sixty prospective teachers were participated. All participants were majoring in elementary mathematics but have different grade level. The task was written task. It consisted of three problems and took about 10-20 minutes