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I have been fascinated by math education for decades--mainly because math was a struggle for me in middle and high school as well as college. I was taught arithmetic the old-fashioned way--multiplication tables, lots of rote memorization, long division--I got very good at it--still am----but then we were confronted with "New Math" in the mid-1960s--I was in 8th grade in a Department of Defense school in England--and I understood very little of it. Then came traditional algebra and geometry in high school--then three trips through calculus in college. The concepts behind much of the math intrigued me--still do--but the kinds of approaches used to teach math beyond arithmetic did not work (or maybe I decided they did not work).

After 30 or so years teaching English in a variety of colleges, I've been thinking that one of math's problems is that it is like learning a foreign language in college--unless you're in an immersion program of some kind, it's tough to learn. Math is not reinforced outside the classroom in the same way English composition or literature is--even students who struggle to write an essay in freshman composition are competent users of the language in texting and social media. But few folks have to perform differential equations or determine a derivative in their daily lives--just as most Americans can go for years without speaking a word of another language day to day.

I think the "problem" with math beyond arithmetic is that math teachers teach it--the folks who can master complex calculation in such a limited environment as a college classroom are the ones who then frequently become teachers themselves--they are very good at working with decontextualized information, which is really quite a skill. But it's not one that many others have--and thus they get frustrated with students who do not respond to their subject in the same way that they do.

We have similar problems with college English teachers, in that there are many who are really good at grammar, but may not be so good at showing students why one version of an essay is better at reaching its audience than another. It's similar to the math teacher problem--they may be good at computation, but not at illustrating the underlying values that make such computation vital. But most English faculty have not spent much time outside the world of English studies, so it's sometimes tough for them to connect student writing to the professional world. The fields share some similar frustrations.

We in English have developed a variety of pedagogical approaches to teaching composition, but math does not seem to have done so as much, at least at the college level. Some of our approaches may have good intentions, but are difficult to execute successfully (the recent rise in anti-racism pedagogy, for example; another is the notion that instructors should not teach grammar--that is a misunderstanding of the research).

I think the two approaches the article you included reflect the same kind of dichotomy. And it's not very helpful to students or to the future of math as a subject. Some melding of the two approaches is more likely to be the solution. But it's hard to get to because both sides are fighting decades-old battles (as they are in English).

One of the newer ideas to come along is developing different college math pathways for different majors--maybe English majors don't need calculus, and maybe citizens need to be better consumers of statistics so that they can more fully participate in our society. Complete College America has been very influential in pressuring state legislatures to adopt such pathways (https://completecollege.org/strategy/math-pathways/) but acceptance of this is resisted by some in the math education world.

All that being said, I return to my original point, that the lack of reinforcement outside the classroom is math's biggest problem, and it's one they really can't solve on their own. I hope the fight among the various factions discussed in the Hechinger article leads to some solution.

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