Saturday, June 04, 2011

Correlation does not imply causality: the algebra version

We've come a long way since the controversial "Math class is tough!" Barbie.

I have repeatedly mentioned that our school district places ~20% of the 6th graders in a math class that compacts the CA 6th grade and 7th grade math curriculum into one year. Those kids are then able to take algebra in the 7th grade, putting them on track to complete calculus by 11th grade. That's the de facto honors math track.

Nationally, it is quite rare. Even within California, only 6.7% of all 7th graders do so--mainly in well-to-do and high-tech areas. That 18.5% of the kids at my daughter's Title 1 school (40% of the kids are poor and/or have parents who did not complete high school) did so last year is a source of pride for our community. (Even though kids of highly educated parents are more likely to be on that track, a significant number of at-risk kids take the class alongside them and do fine.)

I was chatting with my daughter's pre-algebra teacher at open house, when I lamented that the 7th graders wouldn't be segregated from the 8th graders in algebra. I had hoped my daughter could continue in a fast-paced math class. She has often told me how much she liked that class and the teacher. I was worried that the 8th graders would slow the 7th graders down.

If you look at the CST Algebra 1 test scores for the entire state of California (below), you will see that 7th grade algebra students score much, much higher (430 vs 350 ) than 8th graders. 9th graders fare worse and 10th and 11th graders do even more poorly.

Then the teacher said what appeared to be a non-sequitur. She said that we could sign her up for gender-based algebra.

When my daughter asked us to fill out a gender-based algebra form, stating our preference that she be placed in an algebra class of all girls, we reluctantly signed it. It was her preference, not ours. My husband and I had assumed that the class would be filled with girls who were NOT math-confident.

The teacher elaborated that the school district superintendent was a big proponent of gender-based algebra and that education scholars were following the results in our district with great interest. I said the results are not statistically valid because of selection bias. At this point, I was still clueless, assuming that the girls' scores would be lower than the boys'. But I couldn't understand why the superintendent would so strongly support this program because he struck me as a data-driven guy.

Then the teacher said that the parents of the boys complained because the girls' algebra class had become the de facto honors math class because only the girls very serious about math signed up for it. The boys were relegated to algebra classes with a higher percentage of kids who had difficulty with math. To be fair to the boys, she would also teach a boys only algebra class next year.

Her point was that gender-based algebra test scores look really good because of selection bias.

I would like to point out that 7th graders test higher than 8th graders in the same math class because of selection bias, too. In a perfect world, kids take algebra when they are prepared for it. The kids that are ready at a younger age are more likely to excel than the kids that take it at a later time. But, you can't take the same kid and throw them in a higher level class and expect them to do better. (With the exception of bored and under-achieving kids.) Sorry, putting Kindergardeners in algebra is not going to make CA stack up against Singapore. ;-)

Correlation does not imply causality is my statistical pet peeve.

Just the same, I went to the assistant principal in charge of curriculum to explain that my daughter really, really wants to take gender-based algebra next year and could he check to make sure it doesn't conflict with her preferred electives?
We've come a long way, baby. Even MIT has matriculated more girls than boys in recent years.

CST Algebra I (California overall)
Result Type 7 8 9 10 11 EOC
Students Tested 31,492 274,508 269,800 118,412 56,830 751,042
% of Enrollment 6.7 % 57.3 % 52.3 % 23.8 % 12.1 %
Students with Scores 31,480 274,182 268,975 117,798 56,451 748,886
Mean Scale Score 430.9 350.3 307.9 290.1 282.3 323.9
% Advanced 50 % 16 % 3 % 1 % 1 % 9 %
% Proficient 35 % 30 % 19 % 11 % 8 % 22 %
% Basic 11 % 24 % 26 % 23 % 19 % 24 %
% Below Basic 4 % 22 % 36 % 42 % 45 % 31 %
% Far Below Basic 1 % 7 % 16 % 23 % 27 % 14 %


  1. Very interesting!

    I wonder how Caltech's gender balance is coming? Back when I was looking at schools is was 75% male. They were trying hard to fix that, but I'll admit that it sort of scared me off. I went somewhere that was just 60% male instead!

  2. Thanks so much for visiting my blog. My record keeping is rather haphazard in comparison to your long standing documentation. But "meme"'ve just gotten way ahead of me technologically speaking. Not quite sure how that works.

  3. Anonymous04:57

    I was in a high school that experimented with girls only physics.

    Problem (besides not having an actual treatment/control set-up): The physics teacher teaching that class was a sexist asshat. Also creepy (liked to touch, a LOT). The girls who took the class would complain that he would do things like bring in a wrench and carefully explain to the delicate females what a wrench was. Not so for the other class (all boys by default).

    I took one semester coed from him after the experiment "failed" and did poorly. Next semester I took from the female teacher and not only passed with flying colors but LEARNED a lot. Even the right hand rule was less sexist when she taught it.

    Selection bias is definitely an issue, but not just on the student-side.


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