Last week I wondered about why students scoring poorly on the NECAP math did *especially* poorly on this question:

A real-estate agent received a 3.5% commission on the sale of a house that costs $200,000. What is the amount, in dollars, of the commission? [commission = sale price x rate]

I very obliquely followed that up with a suggestion that maybe it is really a vocabulary/general knowledge problem *a la* E.D. Hirsch. If you aren't really sure what a commission or real estate agent is, or what the "rate" refers to in the question, you're going to have problems. And that is probably the case for some kids (especially recent immigrants, etc.).

The problem with this interpretation is that the reading scores have proven both higher in general and much easier to improve than the math scores, so it seems unlikely that the difficulty of the math NECAP is due to reading issues.

I was also wondering if for some kids the answer -- a real estate agent would get $7,000 for selling a house -- would not seem plausible, since $7,000 could easily be two or three months income for the student's family (or more) for what might seem like a day or two of work by the agent. How long does it take to sell a house and how many does an agent sell a year? Do you even know?

Regardless, actual math teacher Jonathan jd2718 commented:

Percents. Percents are killers. Ratios are worse. Stick to the algebra, you'll get better results, at least in this country.

OK, I can certainly buy that explanation too. It does illustrate that math is less orderly and sequential than we like to think of it.

## 2 comments:

I taught a course in teaching problem solving. One lesson was on raising the level of difficulty of a problem (we have a neat problem, good for 4th graders, but we have 7th graders). Among the options: take away the diagram, use fractions instead of natural numbers, add a variable instead of a number, ask for a ratio...

Just this fall, in the middle of some challenging algebra that my freshmen were handling strongly, I threw in a problem with an extra fraction and an extra negative, and I crashed the class - a 7 minute question took over half an hour.

These things - no picture, fractions, ratios, variables - really ramp up the level of difficulty and the number of mistakes. And in combination the effect (multiplies???) gets very very large.

So:

In James K Polk HS there are 220 boys and 385 students. Find the number of girls.

and

In James K Polk HS there are 220 boys and 385 students. Find the ratio of boys to girls.

are not even close in level of difficulty.

Really.

Someone probably has studied this. And if they haven't, they should.

Jonathan

When I took the mock NECAP, they definitely cranked up the combination effect a lot.

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