1. Ambiguity
In the abstract it’s a fair question. Does this mathematical notation
(2,7)
represent a point in the x-y plane with coordinates x=2 and y=7? Or does it represent an interval on the number line extending from x=2 to x=7?
The notation by itself really is ambiguous.
2. Clarification
When he called me over, he pointed to his laptop screen.
“I’m not sure about this question,” he said. “Are these points or intervals?”
“Well,” I said. “Read the question carefully.” And I pointed to the sentence:
Consider the two points, (2,7) and (5,10), ...
“Oh,” he said.
No ambiguity!
3. Close Reading
Of all the challenges in teaching AP Precalculus, I find this the greatest: The kids do not “read” the questions. Their attention snaps to the math-y stuff, and they immediately begin answering, often before they know what the question is.
This is a recipe for disaster on the AP Precalculus test, and they’re not used to it. The AP test is loaded with questions where it is absolutely crucial that they slow down (and maybe set down their pencils?) and read every single word as if their success depended on it.
And so my mission in this class is to teach the kids to read closely, just as much as teaching them them the (challenging) mathematics.
Because on this test, words matter.