A "Clinical Trial" of Modes of Teaching Calculus.

After "people like me" moved into the town in which I grew up, from the age of 2, they changed the zoning so that only relatively wealthy people could afford homes, largely excluding more "people like me."

By "people like me," I meant the children of union laborers, the white uneducated lower class, of which my father and mother were members, neither of them having finished high school; in my father's case he never started high school. He was a drop out after the eighth grade, whereupon he went to work, self employed as a shoe shine boy. My mother completed 9th grade and nothing more.

Still it was a very different time; a laborer could afford a house in a good school district.

As a result of the zoning change, most of the kids with whom I went to elementary school, junior high school and high school were the children of college educated professionals, heavily weighted for engineers who worked for Grumman, with a smattering of high end lawyers, research scientists, airline pilots, those sort of people.

At a certain point, I'd guess around 7th grade, my math classes were well beyond anything my parents could discuss. I recall, as a result, a feeling of mathematic inadequacy even though I was in the "math honors" classes and skipped a grade (as many of my friends did.) I recall taking my first calculus course in the 12th grade, and never escaping the feeling - a feeling that was completely wrong and naïve - that it was nothing more than an abstraction.

I had a lot of math anxiety growing up, and taking high school level calculus intimidated me. I did OK; but I recall it has a painful exercise and frankly the same anxiety followed me into college. I always felt like the dumbest guy in the room, which I may not have been. (Later on I made a point of being the dumbest guy in the room deliberately.)

One of the happiest things for me was that my youngest son ripped through 4 calculus courses in high school without breaking a sweat; he grew up with math, like my elementary school, junior high school and high school peers did.

I think for me the issue was heuristic more than anything, taught as droning exercise in abstractions rather than a key to real life. I got through of course, and eventually came to understanding the implicit aesthetic beauty of mathematics, but it was unnecessarily, I think, painful.

Thus it is with interest that I came across this paper in the current issue of Science: Laird Kramer, EdgarFuller, Charity Watson, Adam Castillo, Pablo Duran Oliva, and Geoff Potvin Establishing a new standard of care for calculus using trials with randomized student allocation. Science 381,995-998(2023)

The paper is open sourced, and there isn't much call for too many excerpts, but a few are worthwhile for the point.



I really like that locution, "Calculus must become a pump and not a filter."

The study used a "clinical trial" type motif, with randomized subjects and controls for math classes in a University; I'm not sure I understand if there was consent forms provided as there might be for medical trials, but no matter.

The study showed significant improvements to students with the highest "major change" rates, women, African Americans, Hispanics, and interestingly, among majors, biology majors.

It's interesting. It's sad that the study took place in Florida, which now has officially abandoned education in order to indoctrinate people with "Fox News" fascist, racist values, but I'm sure the study took place before Florida's educational system switched from being a teaching exercise to producing ignorance factories.