The use of visual reasoning by successful mathematics teachers : a case study.

Abstract

Visualization has become increasingly important in view of the advent of technology which allows us to understand an idea at a single glance. Globally, educationists have been searching for ways to improve learners‘ understanding of mathematics. This has led them to believe that perhaps the focus on the teaching of mathematics needs to change. Contrary to the view that mathematics can only be presented sequentially, another view exists that mathematics is a multimodal discourse where different modes of representation are necessary. Whilst many of our learners experience serious difficulties in mathematics, as testified by the education authorities, there are groups of teachers that attain outstanding results in this subject. In this study I chose to explore how this group of people attain success, whilst engaging with the phenomenon of visual reasoning. The intention of this research was to interpret the kind of meanings that these successful teachers offered in their use of visual reasoning in their practice. Therefore in order to explore the personal, social and learning experiences of these successful mathematics teachers, a case study form of enquiry was employed, with the use of a social constructivist research paradigm, following a qualitative research tradition. A purposeful maximal sampling technique was used to identify five participants. Knowledge is not merely received but constructed by individuals or groups of people who try to make sense of their experiential worlds. This study sought to explore the ways in which these successful teachers constructed and interpreted the knowledge that they passed onto their learners, using the phenomenon of visual reasoning. Furthermore, constructivism as a research paradigm is characterised by plurality and multiple perspectives. Taking this into account, Attribution Theory, Gardner‘s Multiple Intelligences Theory and Situated Cognition Theory were used as a lens to explain the complex phenomena of visual reasoning and successful teaching. The results of the study showed that all the participants were actively engaged in using visual reasoning as a pedagogic practice in their mathematics classrooms. Explanations for their actions in terms of using visual reasoning resonated with the literature and the theoretical frameworks that were used.