I am sure it will be necessary to take a few days to work on factoring before we start rationals. I need to review quadratics, teach cubes and grouping, and put them all together. I am working on how to structure that.
I have been doing some reading and searching for ideas. It seems that almost every method out there requires students to memorize some sort of process. (Except for this, and I am not sure my students are ready for that). As far as algorithms go, I am happy with what I've been using.
There are two issues that I want to address:
1. Helping students make a connection between what they SEE (trinomial, difference of squares, four terms, cubes, etc.) and what they DO (write two binomials using your preferred method, grouping, use a formula, or whatever).
2. Helping students get through problems where more than one method is required. (Like factoring out a GCF and then factoring the trinomial, or using grouping and then recognizing that one of the binomials is a difference of squares).
Here is a flow-chart I sketched out this morning:
I am picturing this on the white board, with an answer box next to it. You could 'drop' a polynomial into the top box and it comes out factored. If there was a GCF, you could put it in the answer box and then examine the remaining part and possibly drop it into another box. You could then take the pieces that come out of the second box and either add them to the answer box or drop them into another box. This all seems a little elementary, but I want it to be very obvious and very clear . . .
I am still refining this and hope to use it for the beginning of second semester. I will write about the final product. In the mean time, suggestions welcome. :)