A delusion of rigor in math

U.S. high school students are taking more advanced math classes and earning higher grades, but math achievement hasn’t improved, writes Mark Schneider, a visiting scholar at AEI and a vice president at American Institutes for Research.

More of our high school students are getting through Algebra II and calculus, while fewer and fewer of them are stopping at general math and Algebra I. And transcript data show that even as they take more difficult courses, they are earning higher grades.

. . . while the math skills of elementary and middle school students entering high schools have improved, what American high school students know and what they can do in math have barely changed over the course of thirty years and not at all over the last fifteen. And when we step outside the United States to compare our high school students to students in other advanced industrial countries that are our peers and our competitors, the picture is also grim.

The new NAEP scores for math achievement will be out next week.

In the second year of the American Diploma Project‘s multi-state end-of-course exams for Algebra II, 80 percent of students were judged not prepared for entry-level college math.

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  1. Carol Bartz, the new CEO of Yahoo, was ticked off when attending a college recruiting event with her daughter—the guy said “we do have a math requirement, but girls don’t need to worry, because it can be satisfied by taking ‘History of Math’.”

    Of course, it *would* be possible to teach a rigorous math class via a historical approach, but I seriously doubt this was what was going down.

  2. I remember teaching freshman calc…. and having to re-teach the equation for a line, and then the claim, after a huge portion bombed out on a related rates quiz, that they didn’t know the formula for the area of a circle.

    First thing to do: remove all calculus classes from high school. [About half my students claimed to have done well in calculus in high school… but their AP scores/achievement test scores weren’t high enough to place out. I soon saw why]. It gives schools impetus to push students through math without really checking if they’re ready to go on to the next level.

    If they want to replace calc with something, I recommend probability and statistics.

  3. I’d have to agree with meep’s comment, I took a course in informatics a year ago, and some of the coursework covered basic statistics (mean, mode, variance, std deviation, and some probability). The average class grade on the exam was 69 (I scored 93), the bulk of the class were freshmen students, most of which didn’t know how do basic statistics (and everything on the exam was in the professor’s online notes). I graduated in 1981, long before electronic calculators were commonplace like today (back then, you actually had to do the math with pencil and paper).

    IMO, it’s time schools stopped placing students into math that they aren’t ready for, and to give the students a hard dose of reality (IMO, if you don’t know the formula for the area of a circle, you have no business in calculus in the first place).

  4. I read the AEI paper linked. At the very end it mentions the changing demographics of the US and how the racial performance gap explains the lack of progress. White and Asian kids perform better, the percent of white students has dropped from over 70% of the population to around 57%, while the hispanic percent has increased by about 20%. The lack of progress is explained by demographics. Now, can someone explain the racial performance gap? Why are African Ameican and Hispanic kids persistently performing below white and Asian kids? I guess the question makes me a racists, but until we can ask and answer it with any accuracy, how can we improve the situation and improve the prospects of these lower performing kids?

  5. Lisa Brown says:

    I teach 5 different high school math classes. My kids may be lower than average, but they can learn. I’m angry with the previous teachers that allowed calculator use since the 4th grade. Almost every day some student asks me when I will let them use calculators. My answer: When you don’t NEED one.

  6. The use of calculators from 4th grade…geez, this is a sad situation indeed…The concept that all kids can learn is correct, the question is “does the student want to learn, and how is the best way to instruct this student”.

  7. Former PhysicsTeacher says:

    Yet teachers get brownie points for using “technology”, with calculators as an example. One of the few things good things my former boss ever had to say during my evaluations was the fact the my students were using GRAPHING (Whooooo!) calculators in class.

    Even more stupid: students who are having in problems in math get to use more advanced calculators as one of their accommodations.

  8. Nothing about the math we’re teaching in high school has changed for more than 200 years. Up until 40-50 years ago calculus (at least differential calculus) was a common requirement in high school. My father took it (everyone had to take it in his Catholic school of the 1940’s). I took it (but was in a minority at my high school in 1970’s) and was able to test out of first year calculus in college. If you read Homer Hickam’s book _Rocket Boys_ about going to high school in the 1950’s, you see that calculus was commonplace then. Now, we can’t get there.

    What changed?

    That was a rhetorical question, of course…


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