Reading in Mathematics - response

The article mentions four main aspects as to why students may struggle with mathematics text reading:

1) Density
2) Mixed translation
3) Changing variables, symbols, and graphics
4) Concepts are interconnected

 1) In LLED 361, we explored the idea of literacy and multiple modes of expression. One activity which was suggested for "translating" mathematical language is to create two columns, where one contains mathematical text, and the other contains the "translation" of that text. It's a little bit funny, because both are a form of English, but mathematical text is used very infrequently. This sort of activity, I would argue, is only to be used with students who have not gotten into the habit of translating mathematical text or asking themselves questions about the content or question being asked. Much like students may need to be taught how to complete a multiple choice exam efficiently, so to do they need to be taught how to "translate" mathematical language, hopefully without writing down the interpretation in the interest of time.

2) "Or", or "or". Oh, how I've missed you. "The mathematical 'or' is different from the categorical 'or'," my proofs professor used to say. For context, in the "every day world", one would say "please bring me coffee or tea", and this would be the exclusive use of "or", since you would not wish to drink a concoction of coffee and tea, call it cofftea. However, in mathematics, this would be exactly the case; asking a mathematician to bring you coffee or tea would mean that the mathematician would bring coffee, tea, or both.

3) I find that students struggle a lot of greater than and less than signs. I know in school, we were always told that the "sign has teeth on it, and the teeth eat the bigger number". But when it comes to reading an inequality, it actually takes a second to recognize which number is bigger, and whether you need to say "greater than" or "less than" as you read from left to right. I would like to suggest that the reason for the discrepancy is because as language users, we are used to reading from a certain point on a page to another point on a page, and in many languages, symbols do not have individual meeting, but must be connected before a meaning is derived. Mathematics symbols all have individual meanings, such as + <=, =/=, etc. Knowing both the meaning of the symbol as well as its collective meaning in a statement means that mathematics reading can be especially challenging.

4)  I can't get over the fact that I find myself teaching high school students about fractions more and more often. I don't mind doing so, but to me, it's appalling that they have managed without it. I imagine a calculator has something to do with it. What was the reasoning to change the math curriculum in BC from linear, compounding concepts to more scattered ones? I remember there was an issue with too much repetition; was there any other reason as to why the math curriculum changed so drastically in the last few years?

I will say, however, that I disagree with Marzano et al. in using direct instruction on words. I discussed with my inquiry class, that an inquiry science classroom may have students determine a definition together. I like this idea for mathematics; although mathematics is less fluid than science is; I would say that defining a mathematical concept in a way previously unbeknownst to a student means that the student can learn a great deal from their peers about how to express an idea that they all share but are unable to get across to other students or to the teacher.  All they would need at that time would be a label to have a definition.