Friday, May 04, 2012

A Broken Record

My Advanced Algebra 2 students had their quiz today. It had some rational expressions and some radical expressions on it. My Algebra 2 students are working on radical expressions. It continues to boggle me why these students cannot retain material. We did multiplying binomials - and a few still struggle with this - but when it comes to multiplying two radical expressions like (2 + sqrt 3)(4 - sqrt 3) - a majority of them forget to distribute both terms in the first parentheses to both terms in the second parentheses. I just don't get why they had it at one point (or close to had it) and now they can't remember to distribute. Does it have to do with the fact that they weren't taught it until May of the Algebra 1 year? Does it have to do with how it was taught to them at that point in time? I don't think I did anything majorly different in how I taught it back in December and January, in fact I had given them some additional practice in a different way that I described here. And don't even get me started on perfect squares. When simplifying radicals, they are sometimes choosing numbers that are not perfect squares (like 8). I'm sitting here trying to figure out why it still isn't sticking with them. Is it me? Is it them? Is it a combination of both? Or does it have to do with that it's May 4th and they don't want to work very hard at this point? Or all of the above?

If it's me - I am trying to figure out what to do differently next year. Although I still don't know what I am teaching, I am hoping that I am still teaching Algebra 2. Next year's group will have been exposed to more material and in (hopefully) a better manner, so maybe that will help. But if I'm the one making the mistakes - I need to figure out what they are and make serious improvements. I have taught 20 years and I have never seen so many students not be able to retain and/or transfer concepts like this. I know I have made some changes in how I do things but I thought they were for the better. When I do some of the different things I have done this year, students are more involved in class. They seem to be working through the problems (although they are still asking a bunch of questions). So why does it seem worse and not better?

I have blogged about this before (see here, here, here, here, and here). I know I sound like a broken record, but it is really bothering me. How do you get past this? I am also concerned because my last unit with them will be exponentials and logarithms and I am counting on them to remember the exponent rules we talked about earlier in the year as well as some of the powers (like 5^2) without going to their calculators all of the time. I am already sensing I am going to be fighting an uphill battle with them during the last few weeks of school. I know that I am more frustrated about it because it's a Friday in May and it is Prom today on top of that, so I have spent most of today dealing with students who don't want to do anything. But regardless of when it is, it is still an issue and I need to figure out what to do about it. I've got nothing right now.

2 comments:

Lsquared said...

I don't have anything like an answer for you, but this is just such an interesting question I have to post some thoughts anyway...

(I just went back and read all of the previous posts you linked to, and I notice that in 3 of the posts it's specifically expanding and factoring that students aren't retaining. So, I have a couple of thoughts about factoring (maybe useful, maybe not)...
First, I think about learning multidigit multiplication in elementary school: I think we did that for several weeks for 3 years in a row--maybe people just need longer to really learn something multi-step like that. Second, my own kids are at the top end of math ability, but I found that they forgot factoring (though not expanding) from one year to the next for the first several times they encountered it--maybe factoring takes longer to learn than I/we remember it taking. I get the students when they come to college. For what it's worth, most of them (at least the ones who don't get tracked into remedial math) have got factoring down by then (though not always expanding squares, and not necessarily exponents).

It seems like the things you've been doing to try to get the students to do more practice and do more learning work look very promising (you have done some seriously cool things in the last few months). I also get the feeling, thought, that you are wrestling with one of those really difficult problems in teaching. OK--I'm getting down to waffling about nothing, except--1. wow, that's an interesting problem, and 2. keep it up, you're doing good, important work!

confidentlylimited said...

Since it is happening not only with your kids, but also with my kids and X's kids and Y's kids, etc. may be it's not how we are teaching, but (a) their study habits (b) the way they were taught math in middle school. If all the contortions we go through as teachers do not help, may be the answer is at the other end.
No practical help, but worth investigating...