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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1. October 22, 2010 am31 8:30 am 8:30 am

My favorite classroom lie is a line from Monty Python: “And now for something completely different.” Whenever I say that, my students know (at least the conscious students know) that I am about to present something strongly connected with whatever we just did. It’s time to watch for whatever parallel/analogy/similarity lies hidden below the surface and call out the teacher on it. And they do.

• October 22, 2010 pm31 7:56 pm 7:56 pm

Clever. I can’t imagine that I won’t steal this, since it often fits how I structure a lesson or a unit.

2. October 22, 2010 am31 11:47 am 11:47 am

If we ever meet in real life, JD, maybe we can play 2 truths and a lie.

Maybe I could start with telling my students I’m going to include one lie in each lecture. They already try to catch my mistakes (for donut points). This would give them a bit more incentive to try to catch me out.

I’d have to remember to plan one for each day…

• October 22, 2010 pm31 8:03 pm 8:03 pm

I would want to make sure that each lie had been corrected before a kid leaves class that day. What if they never come back, right? What if the incorrect knowledge cements overnight?

3. October 22, 2010 pm31 8:04 pm 8:04 pm

I also play “correct my mistake” – usually with a warning right before or right after the error. The error is usually a sign, or division by zero, or a missing ±.