## Wednesday, January 9, 2013

### Followup on exponential activity

So happy to be writing about math for a change! If only so that next year I have something to start with that is a little further along the effective-f2f-time continuum than this year.

So here's what happened:

I showed the first slide to all, had random volunteers find a few simple equivalent rules, to warm up before putting them in pairs to do the rest. After about 10 minutes, we talked.

Here are the screen shots of the different groups' sorting of the "exponential things":
 amje

 dafr
 jali

 mibo

 pama

 saca

 tyelel

Observations during their work time:
• almost no team was able to finish this first slide, and most started with the algebraic rules.
• some gravitated to the graphs and sentences later. I think that for a lot of them it is a revelation that a graph represents the same thing as an equation. Or a sentence.
• lots used geogebra to see if rules were equivalent, instead of working through the algebra
• only two groups looked at the rule with e in it, and only one found its correct equivalent (at the left)
• saw lots of discussing and questioning of each other, just a little of "miss, we're totally lost"
What I did:
• I brought everyone back and went through the answers, pausing to let them either high-five or ask questions. They are really weak overall on evaluating things like $27^{-\frac{1}{3}}$.
• Since we ran out of time, I decided to put the whole set of slides, answers and all, on this voicethread: and told them to look at it and leave their questions there, or answer other peoples' questions. Another opportunity to get their reflections, so that makes 3 ways.
• In only one class were we able to get to the next activity, which was all english situations. I gave the hint that 3 of the 5 were equivalent, and immediately regretted it. Won't do that next time.
Next time: start with a slide that has only rules, then the next has rules and english, then the next has all three types of representation. Actually, it might be better to leave out graphs, not sure they helped at all.

It's only after doing this type of thing that I realize what I was trying to do. I made this activity up on a hunch, it seems, and now I what it could have done if I had done it better:
• I want them to not only know THAT two things are equivalent but WHY they are - why they are algebraically and why they are realistically. It's not enough to get the algebra behind
• $2^{3x} = 8^{x}$, I want them to see that if something octuples every hour, it also doubles every third of an hour. I want them to be able to read that kind of info off the rule, like if the nbr of bacteria after x hours is $y = 3^{2x}$, then they're tripling every half hour.
• I pushed geogebra so much that now they rely on it too much. I have to find a way to balance things. Maybe I need to model using it more, as a way to verify their algebra, rather than to guess and check.
• The idea that the base can be ANYTHING as long as you make the necessary adjustment to the coefficient of the exponent - is that too much for them at this age? Or will this help them out when we get to logs?
• I think they need to sleep on things sometimes, so it will be interesting to see if anyone gains any insight tomorrow. Including me.
But the point is, I never even tried getting this idea across before, so even if it doesn't work, it has to have stretched some minds a bit. I haven't received any of their reflections yet. So looking forward to that, almost more than the math!