Abstract
This paper describes how the visual aspects of mathematics influence the understanding of mathematical concepts. It attempts to contribute to the discussion that surrounds the ideas of visualisation, more specifically in mathematics classrooms. Two teaching interventions are described that may indicate how visual strategies can contribute to teaching in the classroom. An important finding of the research reported here is the ease with which dynamic geometry software can be used as a visual tool to develop analogical reasoning skills.
Highlights
Mathematics teaching is generally conducted in a verbal way, where the teacher orally engages his or her learners with new or old concepts
“mental images arise from perceptual representations that are created from stored information not from information currently being registered by the senses” (Borst & Kosslyn, 2008, p. 849)
English (1997) reinforces this idea when she states that “one of the major goals of mathematics education is that children see the connections and relationships between mathematical ideas and apply this understanding to the solution of new problems” (p. 191)
Summary
This paper describes how the visual aspects of mathematics influence the understanding of mathematical concepts. Thinking with diagrams whilst writing with words illusion (see Figure 1), we see a whiter-than-white triangle, when no such triangle really exists In this example, the mental cue directs our mind to some old information that we already know and an association is formed. This paper further alludes to the fact that children are quite capable of solving difficult mathematical problems if their analogical reasoning skills are developed in a dynamic geometry environment. It is perhaps at this point necessary to draw a distinction between that which is visualised and visual literacy. The spiral nature of the model implies that the solution to a problem should begin with visualisation and followed by an analysis process
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