Friday, March 12, 2010

Student centered learning using WolframAlpha

Recently I had a really successful lesson on exponent rules.  Every year I go through exponent rules with my algebra 1 class, and though it's likely they've seen much of them before, their retention is such that it feels like they are seeing everything for the first time.  This year I tried to change it up a bit in order to do two things that I've been trying to get right this year:  Increasing my student centered learning and using wolfram alpha as an effective learning tool in class.

At the beginning of class, students were given what was last year's quiz I gave after teaching and practicing some exponent rules.  The instructions:

1)       Answer every question with your best guess.  We haven't learned this stuff yet, so I don't expect you to get many of the questions right, but I do want you to try to make some sort of guess for each.

2)      Use your laptop to go to wolfram alpha to check each of your answers.  Write the correct answer separate from your original answer and try to figure out what each exponent rule is.

3)     For each answer you got wrong originally, make up 3 similar problems that use the same rule(s), answer them and check them using Wolfram Alpha.

4)    Once you are confident that you could get every problem right without help, I will give you your quiz.

The result?  Students did better on the quiz than in previous years where I taught the material.  Granted, there are some other variables involved in that, but it was clear from moving around and talking to them that figuring out the rules themselves gave them a better understanding of what was going on. The whole thing took two 45 minute periods, part of which was getting them used to typing the expressions and a discussion about why they shouldn't use wolfram alpha to do all of their homework for them.

You may be saying to yourself "Hey wait a minute, you could've just given them an answer sheet and done the same thing."  Well yes, and no.  Answer sheets would take away the flexibility of being able to check answers to the problems that they make up.  The making up step also helps them to understand what they are really looking for and is a good strategy they can use to help study for tests.  Also, part of the point(which I discussed with them) was to get them used to using Wolfram alpha to check their work any time, like for homework or studying for instant feedback.

Now as pleased as I am with how this went I'm certainly not ready to give up explaining things at the board ever.  Exponent rules lend themselves well to this sort of activity as they are reasonable to figure out with the answers and I'm definitely going to look for more topics that would work well with this kind of activity in the future.  Can you think of any?


  1. Off the top of my head, good topics might be:
    Power Rule (calculus)
    Translations/reflections of graphs

  2. Nice idea. Gonna be stealing, er, borrowing this one. Nice to see you back in the saddle.

  3. Yep, us teachers are such good borrowers. I'll take one too, please. :^)

    I'd also ask them to determine why the properties of exponents work the way they do. I wonder if they'd be able to get a good reason for negative exponents on their own.

  4. Probably things they've "done before" lend themselves best? Or pretty easy to figure out through seeing a bunch of examples. But also you have to consider how tortured WA's method and format of an answer is. For example, it seems to solve every quadratic by completing the square, even if factorable. However, if you command it to factor a quadratic, it gives you the answer you'd expect.

  5. I'm intrigued!
    I'm basically teaching all geometry right now (with some trig scattered in), but I'm trying to figure out a way to use this. Thanx for posting this!

  6. So is the real quiz the same quiz that you gave them at the beginning of class or a similar version?

  7. It's a similar version. I changed the order of everything and switched up exactly how some of the rules were used to make sure they really understood it instead of just memorizing.

  8. Very cool. Would you share your worksheet?

  9. First worksheet

    Second worksheet(quiz)

  10. Great idea! I think this would be great when teaching logs. I think the kids would really "get it" and not "forget it" if learned in this way. Also, kids are so scared of logs. If they realized via this lesson that they could figure it all out by themselves then how hard could it be?

    1. I use grapher, an application on my mac to do the same thing with translations. It helps all our students have macs.