10/18/12

 I’ve never used algebra tiles, and when I came to the school that I’m working at now I was actually given some to use. However, when I asked how they were used I was only given an old book of transparencies. I looked at it briefly and then it went into a stack in my cupboard where I keep all the stuff that will most likely never get around to using. Now having read the Leitze article I see how they may have helped when I taught my students factoring. Other than that they would probably be most useful in Algebra 1. Reading the article also made me wish that I had algebra tiles when I was working at a Montessori middle school last year. It would have fit with the curriculum well.

Reading Rubenstein reminded me of what a technical language mathematics is. I usually tell students that learning math is like learning a foreign language, only harder because there are calculations involved. Students have to acquire this language in order to participate and become part of the discourse community in the classroom. I just finished teaching a chapter about polynomials and one piece of working with polynomials includes naming them by their degree and number of terms. I focused on this the first day and continued to use the specific language (i.e. cubic trinomial) and asked the students to use it also. It was difficult at first, but I see some improvements. By explicitly making connections to the roots of the words I hoped to help the students remember. However sometimes I think that the specific language can also turn off students, especially when they are behind because they have less comprehension of what is going on in the classroom when the technical language is used without explanation.

I liked the fact that the Coburn article had some alternative approaches to working with polynomials. I never remember factoring quadratics the way the author proposes, and I like that the fraction methods makes the zeros more apparent, but my students freak out any time they see a fraction in a problem. Fractions combined with factoring would cause me students to use other F words. On the other hand, I liked the “push principle” used to find the sign of an interval. The last method presented to solve quadratics seemed a bit complicated. I suppose it’s convenient for finding the zeros, maybe, but I’m just not sold on it. I had to read through it three times before I could figure out what he was doing and why.