Checking Education Week: How Wealthy are Calculus-Taking Kids?

I.

Last spring, Education Week published an article about calculus. It said:

More than half of students who take calculus in high school come from families with a household income above $100,000 a year, according to a study this month in the Journal for Research in Mathematics Education. By contrast, only 15 percent of middle-income students and 7 percent of those in the poorest 25 percent of families take the course.

But this is a mistake, because the linked-to article says absolutely nothing about this. The JRME piece was a big survey of college freshman in calculus classes. The professors handed out surveys asking about their background and previous courses, and then at the end of the semester attached grades to the surveys and sent them back to the researchers. Then the researchers looked for connections between high school background and the final semester grade.

Here’s the thing though: the survey didn’t even ask about income. And as far as I can tell (correct me if I’m wrong!) the article mentions absolutely nothing resembling the EdWeek stat.

That’s fine. People make mistakes. People should correct mistakes when they find them, and it’s sad that the corrections never get as much attention as the original. Hopefully EdWeek will fix the link, or the writer will issue a correction, and then redesign their website because it’s quite clunky and I can never find my password.

II.

Yes yes yes, mistakes were made, but that’s boring. Interesting: what’s the actual percentage of high school calculus students whose parents make such and such amount?

I couldn’t find a source for the Education Week quote, but I did find a lovely table that answer the exact opposite of our question. It doesn’t tell us what percentage of calculus students are rich, it tells us what percentage of rich students take calculus.

It’s from a report from the NSF that is built on NCES’ High School Longtitudinal Study of 2009, aka not some rando. And no surprises here:

Students in the highest SES quintile were more likely to take advanced mathematics courses than their peers in the middle and lowest SES quintiles …For example, the percentage of students in the highest SES quintile taking calculus or higher was four times higher than the percentage of students in the lowest SES quintile (37% versus 9%) and two times higher than the percentage of students in the middle SES quintiles (37% versus 16%).

Here’s the full table:

Just a quick note that the denominator here isn’t high school students, it’s high school completers. So this is the wealthiest 20% of people who finish high school. Out of that 20%, 36.7% take calculus (or a higher level class).

It took me a while of staring at these numbers to make sense of them, as there are a bunch of units involved. Here is the diagram that helped me visualize what’s going on:

But if we want to know what percentage of calculus takers are wealthy, we need to switch units from HS completers to calculus takers. Meaning, this is our new “whole”:

The blue region in the above diagram is 36 out of 36 + 9 + (16 x 3), or 38.7% of people who take (at least) calculus in high school. Repeating those calculations (correct me if I’m wrong!) gives me this:

Wealthiest 20%: 38.7% of calculus (or higher) takers

Middle 60%: 51% of calculus (or higher) takers

Poorest 20%: 9% of calculus (or higher) takers

But this isn’t just the wealthiest 20% of US households — this is the wealthiest 20% of US households of high school completers. So to really answer the question that Education Week raises, we have to connect this with some numbers about income and high school completion…

But I think this is actually OK, because the sample was nationally representative and by 2016 when this table was created, the vast majority of the study group had completed high school.

PDF: https://nces.ed.gov/pubs2018/2018139.pdf

It’s 96% completers of any kind of high school credential, and I’m sure that the last 4% is skewed towards poorer students, but look it’s 96% and we’re not trying to land on the moon here.

(There’s info about the socioeconomic breakdown of high school dropouts for this cohort in the 2012 follow-up, but I couldn’t find a similar table from the 2016 follow-up.)

I’m not sure how to translate socioeconomic status into parental income — I’m pretty sure you can only do this heuristically — but using this table from BLS, what the heck, I’ll give it a shot.

Household income is $108,040 or higher: 38.7% of calculus (or higher) takers

Household income is between $19,868 and $108,040: 51% of calculus (or higher) takers

Household income is less than $19,868: 9% of calculus (or higher) takers

I hope I’ve failed to convince you that this analysis is correct, as I am clearly playing around with things that I don’t totally know how to handle.

But my calculations lead me to believe that it’s not super-duper plausible that 50% of students taking calculus live in households that make more than $100,000 a year. More like 40%ish.

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