Saturday, February 05, 2011

Improving Learning in Mathematics

Over a dy/dan, a recent post recommended a document on improving math education. I looked over it and there's several ideas I think are pretty good in it.

The first is the use of mini-whiteboards which allow students to write largely and display their thinking easily and quickly to a teacher as well as the rest of the class. I think I may have to get a collection of these as I think the idea is very good. The disadvantage I see in this (which as usual, goes completely undiscussed) is that the record of their work either doesn't get preserved, or requires extra time to retransmit to their notes which would be a subject of much complaining. Part of my teaching method is to make students fully aware of all the resources available to them to learn the material such as, my lecturing, their book, their notes, their homework, review sheets, one another, and even the internet. I frequently remind them that with so many resources I ensure they have that this really puts the responsibility to use them and learn on them. Thus, losing any is something I'm somewhat reluctant to do.

Not directly from the document, but spawned directly from it is a way I'm considering to get students to pay more attention in classes. The challenge I've noticed at small private schools is that all of the students are friends and controlling talking is near impossible. In one of my classes this year, I have the unfortunate case of having one student that doesn't need me to explain anything before seeing how to solve the problems. She tends to get bored and then start side conversations, disrupting half of the class. Yet on the other hand, I have another student that doesn't understand (or doesn't try to understand) no matter how much I break it down and how many examples I give. If I don't slow down for her, she disengages and disrupts half the class. It's a horrible catch 22.

Thus I'm considering ways to force idle hands and minds into motion and add a little more peer pressure to the situation since I've had a few students actually complain about their classmates descriptiveness. Students that want to learn! What a concept!

One of the ways I'm thinking of doing this is by taking a small inflatable ball to class. Instead of calling on someone, I'd toss them the ball, literally putting it in their hands, and asking for the next step. Then they're free to pass it on to another student for the next step and students would (conceivably) not engage is as many side discussions since they would (hopefully) not want to turn around for fear of getting smacked in the back of the head by a ball.

The document also offers some ideas on how to manage my catch 22. It suggests allowing more individual (or small group) work, which is differentiated in one of several ways.
1) Giving advanced students extra problems that allow them to explore concepts deeper.
2) Differentiating by problem sets: While they note that this may encourage some teachers to remove material that is "too difficult" for lower achieving students, they recommend instead, that they allow students to pick from easy, medium, or hard level of difficulty problems and that most students would be able to better judge the difficulty of their learning.
3) Different levels of support in which students are all given the same problem, but more support material is provided to some than others.
4) Letting students create problems on their own level. An example is asking students to create problems they feel are "difficult" but know that they could solve correctly. These could then be passed to students on similar levels of achievement to solve and then passed back to have the original creator correct.

There's also a section on how to deal with technology on the classroom. So far, this is something I haven't been able to deal with much due to the lack of projectors in my schools. When I eventually have access to one, however, I'm not entirely sure how much I want to use them. One of the greatest pitfalls I frequently notice (that, again, is never discussed) is that using programs that aren't entirely intended for the purpose, and are co-opted and not entirely intuitive, students can often get distracted by how to use the program and not concentrate on what the mathematics or science is that's driving the entire experience. It's a double edged sword.

Still, there's several ideas that I think I may institute into some of my more challenging classes and see how it goes.

1 comment:

Stephen said...

Could work.

My best idea for teaching math is the Japanese abacus. Like white boards, there's no record of work. The Japanese abacus is optimized for decimal (unlike the Chinese abacus, which is optimized for hexadecimal). The techniques lead to highly reliable arithmetic. It achieves this by taking care of carries and borrows without having to remember them for later. The procedures become rote, almost mindless, with practice. Addition and subtraction can be started with fingers. The thumb is worth five, so one hand can represent zero through nine. So two digit arithmetic can be done by any student with two hands. And, the technique can lead to mental arithmetic. But anyway, having reliable arithmetic should considerably reduce fear of math. This is a psychological barrier, but more than a little significant. If the abacuses are expensive to buy, they make a great (and cheap) middle school or Jr. high shop project. I started a writeup some years ago.