I haven't figured out how to break these bad habits. But I'm working on it.
Needless to say, the thought of teaching factoring was a bit daunting. How can I teach them to un-distribute, if they can't distribute correctly in the first place?
And then a couple colleagues of mine introduced me to the x-method, or what I call the teepee method. This may be old news to many, but I had never seen it before, and I found that it was just the bit of organization some of my students needed in order to factor trinomials.
So, let's say we want to factor x^2-9x+20. We create the following teepee:
This by no means solves all my problems. How can we find those numbers in the first place if we don't know how to multiply? However, it is a nice little organizer for those students who are visual learners.
I can't take any of the credit for this visual organizer. I'm just passing along what I learned from my wonderful department. But, in the words of LeVar Burton, "Don't take my word for it." Here's what some of my students wrote when I asked them to choose their favorite form of factoring from the ones we had discussed so far (GCF, difference of squares, and trinomial factorization) and tell me why...
“Trinomials are my favorite because I like to make lil x’s and then put the numbers inside that would make the others true.”
“My favorite factoring exercise is trinomial factoring because it really makes you think. The x’s really help too.”