Tag: surprise

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Mathematical Surprise

I gave a talk at the Wisconsin state math conference earlier this month and this woman was the best part.

I don’t know her name. I’ll call her Jan. Jan is about to testify to the power of surprise.

I asked the crowd to give me three numbers between 1 and 6, numbers you might get from a roll of the dice. They said 2, 3, and 5. Then I asked all of them to evaluate those numbers in this expression.

Most of the crowd started working on that task, but Jan didn’t. She laughed and said, “I teach second grade,” excusing herself.

I encouraged her to show off whatever she remembered from the last time she worked with expressions like this. She scribbled on the notebook in her lap and we managed to evaluate x = 2 in the time we had, but not 3 or 5.

I asked the crowd to call out the result for 2, 3, and 5. They called out 2, 6, and 20, one after the other.

Then I asked the crowd to evaluate those same three numbers in this expression.

Jan tossed her notepad on the desk, a reaction of “no way, no thank you” to the length of that expression. I decided not to press her at that exact moment, because I had a secret everyone in the crowd would come to understand at different times, Jan last of all and perhaps best of all.

I asked for their result for 2.

“0.”

“Okay, what about 3?”

“0.”

“Okay, that’s weird. What about 5?”

“0.”

I played up my surprise, acting like I didn’t know all of those terms would simplify to 0.

That’s when I noticed Jan. Out of the corner of my eye, Jan straighted up in her chair and then picked up her notebook to sort out what just happened.

I wish I had a sharper vocabulary to describe this transformation, as well as more strategies for provoking it. By showing Jan a situation where order arose from apparent disorder, she felt something in the neighborhood of … cognitive conflict? Intellectual need? “Surprise” feels closest.

I don’t know all the words and I don’t know all the strategies, but I know there are few gifts a teacher can give a student more satisfying than helping her transform from “no way, no thank you” to “okay, let’s sort this out.”

Discuss:

  • I don’t think this experience has much to do with Jan’s growth mindset about herself, or mine about her, but I’m willing to be proven wrong. How was this experience distinct (or similar) to a mindset experience?
  • Think about the design of this activity, all of its different permutations, and how each one might have affected Jan. What if, for instance, I had given given the class those three numbers instead of soliciting them from the class? What if I had only solicited one number? What if all three numbers didn’t evaluate to the same number? How would these permutations have affected Jan’s interest in picking up her notebook?