Alyson:

This post is dedicated to Sarah P, Pru, Marjorie, Chris, Geoff, Dave, Nick and Ben. Love your work guys!

All of the articles in the course to date are starting to show similar ideas. Teachers need to discuss mathematical applications and use of mathematical language. Students need to see where problems can occur in the use and talk of mathematics and find ways to conquer these problems. Mathematics is a language in itself, and yet we try to explain it using another language. Problems arise when we use words that have relatively straightforward meanings in colloquial use, yet we use these same words to describe quite complex concepts. Conceptual complexity and apparent contradictions in mathematics language, and the artificial symbolic nature of mathematics, with its reliance on many non verbal ways of representing information, often acts to disturb students. Using background knowledge, using multiple teaching methods (for students from different learning styles) is helpful.

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. 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.

This week’s readings have a similar message to previous weeks; the language of maths conflicts with everyday use of the English language. They also offered similar suggestions for handling the difficulties that can arise for students. Mathematics “borrows words that already exist with everyday meaning” and in doing so changes the context of the word and therefore changes the meaning. cause a lot of difficultly and impatience for the untrained mathematical mind.

For example starting with a number and imagining that it is the area of a square, the square root gives the side length of that square, which is something that gives students a real example of how to view the square root. Teachers need to foster the use of correct mathematical language in the mathematics classroom at all times. Correct mathematical language should be prevelant in any mathmatical discussion. I also disagree that zero should be used as a number. For example, “zero years old” is not a useful description and would be taking things to extremes.

Students need to participate with the language, that is they need to be using it both orally and in its written form. It is usually agreed that mathematics cannot be learnt by watching, therefore it makes sense that using correct mathematical language cannot be learnt by simply reading and listening.