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.
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.
This is an approach with a simple goal: Make Math Useful. Continue reading
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…
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.”
A lot of things startled me when I started teaching in the UK. The accents. The ubiquity of tea. (As I like to say: “ubiquitea.”) The adorable and inexplicable pluralization of “math.” But what stunned me most was that the Brits don’t follow a sequence of math courses anything like ours.
You know the traditional American chain—Algebra, Geometry, Trigonometry, and so on?
In Britain, they make no such distinctions. It’s all “maths.”
Now, we teachers know that we inhabit imperfect systems. (Some days, we feel like we know it all too well.) I don’t think you’d say we’re unduly attached to them. If you ask most British or American math teachers, “Does your country have a well-functioning educational system?” you’ll get anything from a cynical scowl to a bout of weeping.
But ask us, “Isn’t the other country’s structure better?” and you’ll witness a sudden and righteous swell of patriotism.