Approaches to learning mathematics through reading : Reading-to-learn
In terms of the mathematical English, the language used in texts varies in terms of the level of technicality employed. For example, the style, technicality and 'density' of the English used in statistics textbooks is quite different to that used in linear algebra or real analysis books. Consequently, students need to be able to make sense of the text they are reading (if they are to better learn from their reading) whatever style of mathematical English is being used. As such, I have developed and implemented techniques and strategies for supporting students' learning when reading the various types of mathematical English language used in mathematics textbooks.

In terms of the formal mathematical symbolism (expressed via, theorems, proofs, examples, etc...), it might (can ?) be said that 'the mathematics is the mathematics' and that we do not have the problem of style which accompanies the use of natural language, even if that natural language happens to be technical. This is indeed the case, but we are still faced with the the problem of learning from what might be considered to be the ultimately technical language : mathematical symbolisation and the expressions, theorems, proofs, examples, etc... which form part of the discourse of that mode of language. As such I have developed an approach to 'viewing' the language of mathematics so that students may read such a formal mode of language with meaning and understanding.

Finally, there is the issue of being able to read-to-learn from mathematical diagrams. By mathematical diagrams I mean those diagrams, sketches, and other visual forms of representation which are used in texts in order to support the description and explanation of mathematical concepts and processes. Consequently, it is just as important to be able to fully and clearly understand diagrams which are so presented if a student is to be able to use them in support of learning from the mathematics or technical English. A picture may speak a thousand words but only if you know how to read the picture with meaning. In this case I do not assume (which so many teachers seems to do tacitly) that diagrams are the literacy panacea which may solve all the problems encountered by students when trying to make sense of mathematics to which the diagrams refer.

From the above I am then led to the perspective of reading-to-learn mathematics as a whole, namely the ability to read with purpose and personally significant meaning a whole page of mathematics containing all three modes of language : mathematical English, mathematical symbolism, and mathematical diagrams, and to do so with control and fluency.

This 'whole' can then be seen in the diagram below as the central feature which makes up the concept of reading-to-learn. This 'whole' can also be seen to be fed by the three separate perspectives on reading given by the reading-to-learn of mathematical English, the reading-to-learn of mathematical symbolism, and the reading-to-learn of mathematical diagrams, which when used together in an integrated and systemic manner leads to a coherent approach to reading-to-learn from mathematics texts.

	Choose from the essays below _____________________________________________________
	The above text in PDF format
	Introductory comments on learning from the reading of mathematics texts
	Reading-to-learn mathematical English
	Reading-to-learn mathematical symbolism
	Reading-to-learn mathematical diagrams (to come)
	Whole page reading-to-learn (to come)

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