Mar 30 2008

Week 7 Conceptual Complexity and apparent contradictions-John Gough

Published by Geoff at 3:42 am under Uncategorized




In this article, Gough discusses the nature of the technical language of mathematics and how the use of normal English in our instruction can lead to difficulties for students. He makes a good point when he describes how we all feel a sensory version of words, for example, to talk about increasing at a decreasing rate can make us feel a bit whoozy, but to decrease at an increasing rate can have us (and our students) feeling confused or maybe slightly nauseas. Our spatial interpretation of terms can often be at odds with the numerical meaning, making it neccessary for the teacher to be aware that the language they are using may be misinterpreted by their pupils due to the student’s strong intuitive meaning they have of some terms. The real difficulty of teaching maths in terms of language is that we do use everyday language interspersed with mathematical language that has usage of common terms with different meanings. This has further implications for students whose first language isn’t English. Tho only way to know what your students are thinking is to ask them often and encourage them to talk to you and each other about the contradictions between the language they use and the language they are trying to learn. As Gough points out it is easy to forget the confusion of technical terms once they have been learnt and even easier to blame the students for having trouble when they have been subjected to ambiguity and ’slippery words’ from teachers. The recommendations at the end of the article are an excellent checklist to help teachers avoid confusing students and increase students’ understanding of new concepts and terms, while remaining aware of the student who struggles with vague explanations.

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