Traces of Mathematical Facts and Students’ Understanding of the Concept `Quadrilateral´ : An enquiry into young students’ communication

Abstract: Mathematics could be described as a special kind of language, a discourse in which participants communicate abstract concepts. Communication and language are known to be important factors in teaching and learning but little is known about neither communication between students in relation to geometrical concepts, nor what traces of mathematical facts and understanding is incorporated into their communication. Such knowledge would contribute to teachers´ understanding of students’ knowledge of this aspect of mathematical thinking. The purpose of this study is to investigate young students’ communication in the Discourse of geometry. To accomplish this, Swedish students aged between ten and eleven were video-recorded while working with two assignments, one involving describing quadrilaterals to each other and the other sorting quadrilaterals. An analysis of the students’ communication has identified a number of issues that teachers could benefit from being aware of in their teaching of the concept of `geometrical figure´. Examples of issues identified being that conceptual characteristic remain too much in the background of what in the study has been called the visual shape. For example, a long and narrow shape of a geometrical figure seems to draw students’ attention. Students also seem to be having difficulty in understanding that naming a figure is a way of merging the figures´ definitions into one word, and there were problems with words that anchor in daily life.