Abstract:

While teachers use manipulatives frequently and extensively to teach math at the elementary level, teachers’ use of manipulatives in teaching math at the upper grade levels gradually and dramatically decreases. The current research explores middle school teachers’ beliefs about the use of manipulatives in teaching math. In this study, we considered two types of manipulatives–physical and virtual manipulatives–to explore teachers’ beliefs in their classrooms. A case study was used to explore teachers’ beliefs about manipulatives in middle school mathematics classrooms. We conducted semi-structured interviews with each teacher in order to explore his or her beliefs about teaching mathematics using manipulatives. This study found teachers’ beliefs about the hindrances of using manipulatives in general class management. For example, some of them considered particular hindrances of using physical manipulatives, such as:
(a) excessive learning time or
(b) management difficulty.

These issues seemed to make the teachers hesitate to use physical manipulatives in the classrooms. However, we also found more teachers’ beliefs of the helpfulness of using manipulatives in teaching middle grades math. For example, the teachers believed that using manipulatives helped students
(a) build deeper understanding;
(b) visualize mathematics concepts;
(c) create active learning;
(d) be more motivated to learn mathematics; and
(e) understand mathematics more effectively, particularly those who are lower achieving.

The teachers also believed that virtual manipulatives were more effective to use in a large classroom than physical ones. As some of the teachers believed the development and use of virtual manipulatives could be a way to improve the use of manipulatives in teaching math at the middle grades level and ultimately to support more conceptual understanding of middle grades math. In spite of these teachers’ beliefs about the helpfulness of using manipulatives, the use of manipulatives in teaching middle grades math seemed to be more strongly influenced by their beliefs about the hindrances of using manipulatives. It seemed that the teachers needed to have a better understanding or more opportunities of using physical or virtual manipulatives in their classrooms so that they could be familiar with the use and thus efficiently manage class time and students’ engagement. The results will help educators develop manipulatives for the upper grade levels while reducing the hindrances indicated in this study.

Keywords:

Manipulatives, teachers’ beliefs.