A "Clinical Trial" of Modes of Teaching Calculus.

[NNadir]

Do not worry about your difficulties in Mathematics. I can assure you mine are still greater. - Attributed to Albert Einstein.

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.

Calculus instruction needs substantial transformation because it is often a barrier to STEM degree attainment, especially for traditionally underrepresented groups (1–3), depriving both individuals and society of the potential benefits of their inclusion. National calls for calculus transformation are numerous (4, 5), because failing calculus can contribute to a student’s departure from STEM degree programs. Only ~40% of students entering universities with STEM degree intentions actually graduate with a STEM degree (6). More concerning is that the odds of female students switching out of a STEM program after a calculus course is ~1.5 times higher than that of comparable male students (3). Furthermore, Hispanic and Black/African American students had >50% higher failure rates than white students in calculus (7, 8).

Evidence-based instruction, which is implemented in many STEM disciplines, has reliably led to profound improvement in student success (9–11). However, common approaches to calculus instruction continue to rely on traditional, lecture-based practices in which students are passive learners in the classroom and are expected to construct their knowledge mostly outside of the classroom by doing homework or in recitation sessions (12). Mathematics as a discipline thus needs to embrace its role in enabling STEM careers that will lead to prosperity for both individuals and society at large. “Calculus … must become a pump and not a filter” for the STEM pipeline, as noted in 1988 by Robert White, president of the National Academy of Engineering (13)...

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.

[hunter]

1. I have nothing nice to say about the way I was taught calculus...

... except for the year I spent in overseas where it was simply considered basic "maths" and fully integrated with the science curriculum.

I quit high school for college. I don't believe my "gifted" high school classmates were served well by their senior year high school calculus experience. It was largely a waste of time, a "droning exercise in abstractions." In college I saw calculus had practical applications in other classes, which is the only reason it mattered to me. That wouldn't have been the case in high school.

My wife, who is a very practical person, saw that she could skip high school calculus by taking both calculus and statistics in college while finishing high school, and do it in half the time. As a college student she later tutored others in both subjects and has occasionally taught medical statistics since then.

I have a niece, my brother's daughter, who is similarly comfortable with math. She skipped the typical U.S.A. high school calculus experience too.

Algebra, calculus, and statistics are all subjects our schools could be laying a solid foundation for as early as the third grade, and explicitly so. There's no reason every kid coming out of elementary school shouldn't know at least what they are.

Innumeracy and scientific illiteracy are serious problems in the U.S.A..

[Tetrachloride]

2. +++ to 3rd grade

[PoindexterOglethorpe]

4. Worse yet, people are openly proud to declare they are bad at math.

I really don't get that.

[PoindexterOglethorpe]

3. I started high school in 1962. I had a choice between traditional math

or something called UICSM (University of Illinois Committee on School Mathematics). I chose UICSM.

It was AMAZING!! We discovered everything. In the geometry part, (which lasted a semester because that's really all the geometry you get the first time around) we were given (if I recall correctly) four postulates, and derived everything else, meaning all the theorems, from them.

I took 3 years, at the end of which we were well into calculus, which I quite frankly was having a very difficult time with.

Fast forward some 30 years. I'm trying to get into a degree program at the University of Kansas that required math through college algebra. So I went to the math department at my junior college and promptly tested into algebra 2. After 30 years of no math classes. I did well in algebra 2, even better in college algebra. I decided to take statistics as I knew it could be useful for the degree I was planning. That was so much fun that I decided to take calculus. I'm probably the only woman who ever took calculus for fun at age 43.

All during those courses, I'd sit in class and specifics from high school UICSM would bubble up in my head. Things, such as something is only true "if and only if" something else is true. I asked one of the math teachers at my community college about that phrasing and was told that kind of language is typically used in much more advanced classes.

In all of the decades I've been telling people about UICSM I'm yet to meet someone who has even heard of it, let alone taken or taught it. I suspect the reason it went away is that it would have been a much more rigorous and difficult class to teach, compared to traditional math. But oh, dear lord, I learned a lot. Thanks to the amazing and wonderful Clifford Haugh who I had for years 2 and 3 of that program.