EDUC4105

This second article by Gough dicusses the artificial symbolic nature of mathematics, with its reliance on many non verbal ways of representing information. He makes an interesting point when he suggests that we need to be able to describe what we are doing in non-mathematical language as well as mathematical language. This use of students’ own understanding and explanations when dealing with new ideas is important as it connects the new knowledge with established structures that can later be refined to be more in line with conventional definitions. This, Gough asserts, is social constructivism (remember Piaget ?). I also liked the idea for imagining a square root as thinking of a number as a square and a square root as a side of that square, which makes you think geometrically and calls on previous knowledge of squaring something. Finally, though we should encourage students to talk in mathematical English, at times it is appropriate (and neccessary) to talk about examples in normal English to aid discussion and the deeper understanding that comes from such a free flowing discussion.

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