Thinking About Math

I’ve been listening to some Ted Talks this week about education, and they’ve inspired me. One Ted Talk was on how students can make their own connections without the help of a teacher–only a computer. Another one about mathematical numeracy and how calculators and computers can do that all for us. What we really need to learn in Math is how to think and problem solve. I knew this before, but hearing it repeated always helps.

And I realized what I love about teaching and what most energizes me is…to hear kids think.

This doesn’t make for a quiet classroom. Sometimes, it can be too energetic and verges on being out of control…but I love it when students believe they can express the ideas they want and can inquire into their own learning.

Take today, for example. We are studying probability in Math, and this week, we’ve done several experiments with probability. Here is a condensed transcript of what happened.

Me: Yesterday, we explored probability, and we spun some spinners.  You predicted that with ½ of a circle colored, the spinner would land on the spinner 50% of the time.  Then we spun the spinner 50 times. What were our results?
Everyone: Different. I got 15! I got 17! I got 32!
Me: Why was it different? I want you to think about that a minute and then talk with someone behind you. Why was your prediction of probability different than the actual results?
(Time to chat)
Joseph: It was different because it’s not a magnet. Only if it was a magnet would we get the pointers to point toward the correct area.
Ayana: It was chance.
Nyah: I think it depends on how hard you spin it. If you just spin it a little, then it’s different.
Deven: Well, it’s just chance. It’s different than probability.
Joseph: Hey, probably. Probability. Probability must mean probably, like maybe likely.
Me: What does probably mean? How is it different than probability?
(Everyone thinking)
Kanna: Sounds the same.
(Everyone not sure how to respond but thinking)
Me: So, why did we get different results? Does probability have anything to do with it?
Susanna: It just depends on how hard you spin it.
Valdemar: Yeah, it depends.
Joseph: It’s luck.
Me: What is luck?
Joseph: It’s a good thing.
Kanna: (thinking) Hey, but you could wish someone good luck or bad luck, so that means it’s not necessarily good.
Me: Interesting thinking, Kanna. What does everyone think? So, our experiment was this just luck? When people predict probability, does it mean anything?
(Everyone thinking and nodding)
Brandon: Like the weather. People always predict the weather.
Totah: They predicted snow the other night.
Me: And, did it snow?
Everyone: No!
Me: So, is there any point to predicting?

(Everyone thinking)

I loved how Joseph started making connections with words. It was as if you could see his brain making connections. And then there was the look on their faces when they looked at their data from their experiment and tried to connect it with their prediction. Confused. Befuddled. Definitely not bored. They were relaxed, questioning and stumped a bit by the last question.

We took it another step and analyzed our data. We  looked at the line plot and the shape of the data. We discussed median, mode and mean in the context of it and looked at the range of data. Students drew in the air the shape they saw. After a bit, we realized both sets of data looked like hills. Students talked with each other again about this question: Is there any point to predicting? After closer examination, again the question…

Me: So, after looking at the data and the range of results and the median and the shape, now how does that fit with our guess of probability?
Joseph: Well, it centers right around what we guessed.
Deven: It’s all clustered right around where we guessed, so most of the results are close to what we guessed.

Hmm..The looks on their faces again. We said we would continue on again the next time we meet. My students are best when they’ve not just computing numbers without thinking or throwing out formulas for the sake of it. It’s taken some of them a while to relax and discuss Math. For some of them, thinking about concepts makes them nervous. Many of our students attend Kumon, which gives them great rote skills and a lot of confidence with speedy calculations, but it doesn’t give them the opportunity to make their own connections.

As much as I can, I’ll continue to push kids to think and to listen to them make connections, even when their connections might not sound the most sophisticated. They’re thinking. They’re making their own connections. That’s going to move them forward.

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