This is the graphic organizer I ended up using this year:
Students find it helpful, which is a good thing. I like/hate it.
I want them to be able to factor without it.
Students find it helpful, which is a good thing. I like/hate it.
I want them to be able to factor without it.
Here are some things I am thinking of changing for next year:
1. Fewer methods: Reduce the number of factoring strategies, so students have less to sort through. I am thinking I could teach trinomials with ax^2 first, and then apply that method to trinomials where a=1. Students should be able to adapt to the simpler situation, and they'll have one less method to remember.
2. Figure out how to connect the type of polynomial with the name of the method and how that method is completed: I am currently expecting students to see a trinomial, then identify that it has a leading coefficient, then recognize that they should use the "airplane" method, and then remember how to do the airplane method. So complicated! It is kind of amazing that any of them can do this at all.
One of my students pointed out that the arrows I am drawing for the "airplane" method resemble a trident. What if I renamed the "airplane" method the "trident" method? That seems like a better connection between the original expression and what you do with it. (Trinomial = Trident method?).
3. School-wide consistency: There are only three math teachers in our school. Why haven't we done this already? No idea. We definitely need to get together and agree on an approach to factoring so that students aren't seeing a completely new process from year to year.
4. Find a hook: I haven't figured out how to motivate factoring beyond, "You are going to need to use this all kinds of ways later this year and next year".
All things to keep in mind for next time . . .
Unless . . . Is there a magic factoring wand that I don't know about?
I only teach quadratics one way because the a=1 is just a generalization of the a=/=1. Also, I've gotten to the point of not really teaching difference of squares either. I love it if the kids see the pattern, but I'm okay if they don't and they use the general quadratic method. I love your organizer though - totally stealing this if/when I teach alg2 again! :)
ReplyDeleteIn regards to reducing the number of methods: I teach factoring ax^2 and then have a=1 just show up as we're practicing, that definitely helps!! I also don't teach the difference of two squares as a separate method. I have them write it as a trinomial with the middle term equal to zero, then factor using the same method we've been using. I just taught diff of two squares today - students saw the pattern as we factored, but they did not have to learn a new method of how to do the problems. I am hoping I will be able to increase the difficulty of the problems without them struggling too much...we'll see!
ReplyDeleteI had the same thought about throwing difference of squares in there with other trinomial/quadratics. I am guessing most of them would figure out the shortcut on their own. Then I would be down to three methods, and that would have to be easier for students. Thank you both for the input! I love blogging!
ReplyDeleteHi Amy, found your site through Math Teacher Mambo, she has so many on her blogroll, and I'm committed to checking them all out today (and tomorrow).
ReplyDeleteI just wrote a post on my frustration with this chapter, but not so much on the factoring itself, more on how much they struggled with the word problems involving quadratics. Most of my kids actually have the algorithm down for factoring when a is not 1. (They even like it!) Yesterday I actually didn't recognize a perfect square trinomial when my kids did! :) Thanks!
3 Methods of Factoring
ReplyDelete1. Common Factor
2. Difference of Squares
3. Guess
I teach my students to look for a common factor 1st, then look for a difference of squares, and finally take an educated guess using the factors or c, then a.
This method I learned from Dr. Khan at Wayne State University, Detroit Michigan. My students rock factoring with this simple method.
Have you heard of diamond problems and generic rectangles. It takes out the guess work and makes it more concrete
ReplyDeleteHave you heard of diamond problems and generic rectangles?
ReplyDeleteIt makes factoring more concrete with very little guessing.
Thank you all for the suggestions. I definitely see that I need to simplify with fewer rules for next time.
ReplyDeleteI noticed that no one mentioned sum/difference of cubes. Do you teach those in Algebra 2? If so, do you keep them separate from quadratic methods?
HEre at the community college, I stress the difference of squares. It seems once it's introduced, it keeps showing up, again and again, in subsequent chapters and courses and just about any math assessment a person ever takes that includes algebra.
ReplyDeleteYes, I take the time to make 'em understand *why* that middle term drops out -- especially since it reminds them what factors are. Still, I tell 'em I should be able to call them up at 3 a.m. and say "a squared minus b squared" and they should be able to grumble "a + b times a - b" before they hang up and report me to the police.