Defenestrating Thoughts from the Bivouac

Everyone has been abuzz about the latest research which shows that boys and girls in the US are as good as each other in math. After decades of “girls can’t do math”, it really nice that we’re dispelling this horrible myth.

This news got tons of coverage from the news media. And rightly so. But in their haste to cover the story, almost all the outlets omitted something rather important, which the ScienceNow did pick up on:

Neither boys nor girls get many tough math questions on state tests now required to measure a school district’s progress under the 2002 federal No Child Left Behind law. Using a four-level rating scale, with level one being easiest, the authors said that they found no challenging level-three or -four questions on most state tests. The authors worry that means that teachers may start dropping harder math from their curriculums, because “more teachers are gearing their instruction to the test.”

There are two very important points here:

1. Today’s tests are mostly easy questions.
2. Students aren’t being taught to answer average or above average difficult questions.

Keeping this in mind, let’s revisit the conclusion that boys and girls are getting the same test results. It’s possible there’s a big, important point missing from the study.

Let’s invent a scale of 1 to 10 with which to measure mathematical ability. And for sake of argument, let’s say that the scores used to be as follows, with the boys scoring better than the girls:

• Boys - 8 out of 10
• Girls - 6 out of 10

Now, what if these are the new scores?

• Boys - 3 out of 10
• Girls - 3 out of 10

In this case, boys and girls are equal. Unfortunately, they are equally stupid. :-(

Now re-read the two important points above about students not being tested with hard questions and not be even being taught hard math. Whoa.

So, could this be what happened? Did boys and girls just score worse?

The problem here is that the reporting is relative, not absolute. We were asking, “how good are girls at math compared to boys?”; instead we should be ask “how good are girls at math?”. It’s not like K-12 math has changed that much in the past 100 years. You’d think we could figure out a way to do this objectively.

This reminds me of how SAT scores were re-balanced. The SAT is designed to have a mean score of 500 with a standard deviation of 100. Over time the median started to drop and the SAT was re-centered in 1995.

My older sister took the SAT before the rebalancing and I took it afterward. As a result, my scores are “higher” than hers; though if you convert them to the same base, we scored roughly the same. Yeah for grade inflation! :-)

Speaking of grade inflation, did you know that for a while at Princeton 46% of the grades given were A’s? Now the policy has changed so that “35% of grades in classroom work, and 55% of grades in independent work” are A’s. Yes, this seems more reasonable. :-P