The Catchy Nonsense of “Two Negatives Make a Positive”

My 6th- and 7th-grade students are pretty effective at calculating with negative numbers. They all know, for example, that 5 – (-2) = 7. Ask them why, and you’ll hear this:

“Because two negatives make a positive!”

Then, if you listen carefully, you will hear something else: the low rumble of my teeth grinding together with tectonic force.

“Two negatives make a positive” is one of those math slogans that drives me crazy, because it is so pithy, so memorable, so easy to apply… while also being so vague and non-mathematical that I’m amazed students find it useful at all.

20161205084636_00005 Continue reading

Other Ways to Carve Up the Math Curriculum

If the Food Network has taught me one thing, it’s that how you plate a meal matters almost as much as what you’re serving.


So here are some ideas of other ways to slice, dice, and rearrange the mathematics currently taught in high schools. (And hey, maybe we’ll want to switch out an ingredient here or there, too.)

I’ll lay out four proposals.

First up…


This is an approach with a simple goal: Make Math Useful. Continue reading

The Student-to-Teacher Dictionary

Sometimes students say precisely what they meant. “I don’t understand the question” means they don’t understand the question. “This is too hard” means it’s really too hard.

But sometimes, it takes a little translating…20161024085458_00043

Half of my classroom conversations go like this.

Student: “I don’t get the question.”
Me: [longwinded, exhaustive explanation of what the question is asking]
Student: “Yeah, I knew that. But I don’t get the question.
Me: “Oh. This is one of those conversations.”

Continue reading