I hit the students heavy with direct instruction on factoring today.
As I am sitting here writing this, I’m considering whether I should have taught it differently or tried some open-ended approach, but my gut is no. I could have given them rectangles with areas filled in and asked them to find the dimensions, but I can still do that tomorrow or later this week and it will come easier to them now that we have talked about and tried factoring by GCF and by grouping.
I was able to make a connection in lecture about prime factorization of numbers using factors trees and prime factors of polynomials. I even expressed the factorization of a few polynomials using factor trees. I spoke briefly about the idea of irreducible versus prime and I had several students respond positively to that.
I think one of the difficult things about teaching math is sorting which concepts and strategies students will come up with on their own, and which will need to be introduced and practiced. I am convinced that a curriculum is never entirely one or the other, and which topics belong in which category can change from class to class and within classes from student to student. Maybe that sounds obvious but it doesn’t feel obvious to me every time I sit down to plan a lesson. I think our default response as teachers to lecture, but I am not convinced a default response of discovery is always the best practice either.
In any case, all of my classes went pretty well today, and my final block especially seemed to respond well. I will continue factoring tomorrow with a mix of both notes and some practice with area models to see how they do. Now that the idea of factoring has been introduced I could probably throw some polynomials at them that they don’t quite have techniques for yet simply because they have already been prepped with the idea and some underlying strategies.
We are hurting for time because we have school wide testing on Wednesday so I will not see one of my blocks at all and the other two will be shortened. Add on to this the fact that I am behind the other algebra teachers in the building and I am pushing my students a little faster this week than I would feel comfortable with normally. But I explained to them about the testing and told them we need to push a little harder this week to make sure we get where we need to be and they responded well to that.
This semester has had its bumps but it is certainly much smoother than last semester. I am just hoping this is a strictly monotonic trend as I transition to Year 2 and behind.
I doubt it.
Thanks for reading.