Praise for a good lie

I caught some compliments over at Research in Practice.  Seems the owner, Ben, can’t lie to students the way I can… And neither can commenter Sue (from Math Mama Writes).

I lie to help kids learn.

I teach kids to trust the math, and to trust my math…. but…  Along the way I make things up. Always correct them before they leave. But in the moment, they need to evaluate what I am saying, not just trust it. Trust the math.

A few examples:

Even numbers such as 10 have an even number of factors (1, 2, 5, 10), and odd numbers like 9 have an odd number of factors (1, 3, 9). In my universe, students think, and argue. If they don’t, then I direct them to the point where they want to challenge this false statement.

Did you know that numbers greater than one are perfect squares or perfect cubes, or neither, but never both? (Of course you didn’t – it’s not true.) But it makes good play for exponents, and a beautifully simple example of why a ton of specific cases don’t prove a rule, but how a single counterexample can destroy one.

The alternating harmonic sequence converges to 7/10, right?

A kid who’s fought this, even if he only played the lead role once, has some appreciation beyond what his peers would have.

Yesterday, with this draft playing in my head, I wheeled a blackboard over to my elective students. Earlier this week they engaged briefly with the question: “How many factors does 360,000 have?”  (I’ve blogged that question before, here and here). So I had given them time to look round the edges, but not dive in, and now I was taking over.

“How many factors does 10 have?”  – 4  “and 21?”  – 4  “and 6?” – 4 “and 22?” – 4 – and so we continued for 2 or 3 minutes and a bunch more numbers.

“Somewhat surprisingly, all numbers have four factors, and the question I gave you the other day, about something million, turns out to be uninteresting”

Can you imagine what happened next?

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