Comments on: College students stumped by X + 2 = 4

By: Darren

Darren — Tue, 13 May 2008 21:26:53 +0000

I encountered another explanation today, as my pre-calculus students were working on inductive proofs.

I teach them to SHOW the formula you’re proving works for n=1, ASSUME it works for n=k, and PROVE it works for n=k+1. When students get down to the proving part, there can be lots of algebra to work through. Here I have this class of very bright pre-calculus (trig and math analysis) students, and I can’t tell you how many were asking questions about what to do next. They didn’t see the algebra right in front of them. I could tell them and *then* they’d see and know how to do it, but they couldn’t see what to do without my initial nudge.

It’s almost like they’ve compartmentalized their knowledge. “Oh, we’re not working on getting a common denominator, so I didn’t think to get a common denominator when adding these two rational expressions.” As soon as I said “common denominator”, though, they knew right what to do.

It’s very frustrating.

By: SuperSub

SuperSub — Mon, 12 May 2008 21:46:18 +0000

Darren -
You do make a good point regarding taking tests seriously. One of the biggest challenges that I have had this year is to get my students to treat tests, well, as tests and not simply as a nuisance.
I have literally forced students to answer a question in front of me and then asked them to explain their reasoning to ensure that they understood the material. Later, on the test, I’ve given them the same exact question (word-for-word) and gotten wrong answers. When I’ve asked them afterwards why they would mark an incorrect answer when they did know the correct answer, they’ve responded that they didn’t care or were in a hurry. Of course, they then act surprised that I didn’t offer them a test retake, corrections to raise their score, or the opportunity to drop their lowest test grade.
Some students care so little for educational success that they won’t even bother to use the material that they DO know.

By: Darren

Darren — Mon, 12 May 2008 20:21:29 +0000

There are a couple factors at work here.

Yes, some teachers water down the material so their students don’t fail. And some high schools won’t teach any math lower than Algebra 1, even if that’s what the students need, under the guise of “higher standards”.

And some students don’t take the Entry Level Math test seriously. Many haven’t really been held to any standard before; why should they expect any different when the go to a university?

By: Cal

Cal — Mon, 12 May 2008 17:51:47 +0000

Why would you link high school requirements to college performance? Where is it written that a high school diploma is proof of college readiness?

The solution, obviously, is to raise college standards rather than allow all high school graduates to go to college.

Regardless, your title is misleading. It’s not that “college students are stumped” by that simple algebra problem, but that colleges, either by choice or legal requirement, accept students who don’t know algebra.

But it’s much more dramatic, I suppose, to imply that college students routinely profess ignorance of algebra.