Gary Rubinstein teaches mathematics at Stuyvesant High School in New York City, a highly selective school where admissions are based on one test. He has written a series about what’s wrong with the math curriculum taught today and how to improve it. This is Part 5.
Gary writes:
If you’ve read parts 1 to 4 of this series, you may be confused. I the first part I said that not much of the school math is useful. In the second part I listed a few of those useful topics. In the third part I listed some topics that I don’t consider so useful. If I ended it there, it would seem like the best course of action would be to cut the amount of math we teach by at least half. But in the fourth part I wrote about something that seems to negate the point of the first three posts. I said that some of that ‘useless’ math was just as important as the useful math because it is engaging in the way that art or music can be useless but engaging. So this fourth part could be used to defend the position that no math topics should be put on the chopping block and we should just leave the math curriculum exactly how it is, maybe cutting the topics that are deemed ‘useless’ and not thought provoking but maybe expanding the remaining topics so those can be learned to more depth.
If you’re worried that that’s where I am going with this series, you can relax because in this post I will suggest a radical change to the K-12 math curriculum. But before I can do that, there are three really important questions that have to be answered: 1) What is the current K-12 math curriculum? 2) What is the current K-12 math curriculum trying to achieve? and 3) What is the current K-12 math curriculum actually achieving?
I think I should answer question 3 first. What the current K-12 math curriculum is actually achieving is traumatizing the vast majority of students. We know this because the moment that math becomes optional for the vast majority of students, they never take it again. And they forget most of the math they learned and are left with a vague memory of how much they hated math.
Diane Ravitch's blog 
One of the books I used with elementary ELLs that often had little to no background in math was “Mathematics Their Way.” It was written by a non math wizard for others that may find math a challenge. It explained most of the basic math operations by starting out using manipulatives that helped students understand the concepts in concrete ways. As students progressed, the manipulatives were eliminated. I found this approach worked well with this population.
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The great classic here, IMHO, is Morris Klein’s Mathematics for the Nonmathematician.
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I as grew that younger children should be taking it easy through the math curriculum. Most elementary teachers are not comfortable teaching math. Many are familiar, but, mostly on account of testing, teach shortcuts that undermine real understanding of the concepts.
That said, there are so many people who practice what I call feather in the cap curriculum. This is best illustrated by a controversy at a middle school near a science research facility in which parents were genuinely anxious that their middle schoolers were not being trained to do equations concerning thermodynamics. This occurs on a more subdued scale elsewhere. Our kids are taught to add vectors (puff, huff, etc). Our kids can graph coordinates. Our kids can graph on the imaginary plane. Them everybody else has to do that because the teachers who have time to go to the curriculum conference where state guidelines are drawn up teach where everyone lives in a stable household. Reason will not prevail.
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Thanks for sharing Mr. Rubinstein’s series, Diane!
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It’s always worth reading whatever Gary writes.
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Agreed!
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I bought and read his collection of essays, My Unusual Life. Delightful!
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Rubinstein’s series on VAM was brilliant and devastating to the claims of the VAMbots like the Chettypicker and the Handfistedsheck
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I have not read part five yet and I enjoyed the first four. However, I profoundly disagree that any art or music is useless. The arts are aspirational risky undertakings that provide no answers. This does not mean that there is no bad art. This posits that no effort in the arts is bad, or useless. It dawned on me watching Oppenheimer that the subliminal aspects of quantum theoretical physics is, in fact, Art. E=MC2 was as much the product of a wandering mind as mathematical. Although I have come to the conclusion that math and art have profound commonalities, giving art a value actually lessens its potential epiphany. I was first a studio art major and art teacher. I learned not to judge student work as a failure but simply as a spring board to keep expressing. As an educator, I struggled a great deal with the oversimplification of academic progress in our profession. Our collective dismissal of the arts as trivial in education misses the importance of aspirational expression as a critical feature in our sentient experience. From what I can tell in Rubinstein’s writing, there seems to be an admission that discrete mathematical formulation can be a waste of time for those who are interested or driven by something else. Our ongoing inquiry into who we are means that our artistic exploration is not only important, but required.
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This has been a very interesting series!
I’m kind of surprised at Part 5. I’m a person who struggled in math, and don’t think it was taught well for the many like me. For me, 8th grade math (Alg I) was a disaster. It felt like a jumble of stuff that wasn’t connected, and for several (e.g.,set theory—even plotting x/y graphs) I never understood the purpose, so it was meaningless memorization of how-to’s that I didn’t grasp. We always rushed on to the next before I’d understood much of anything.
Therefore: without a full year of Alg [II] in hischool, + an excellent teacher, I’d never have gotten even my basic grasp of algebra. And I’d certainly never give up my full year of geometry, which I loved—especially the proofs!
A mish-mash of fun math topics in 9th grade? That would have been torture. More running on to the next thing before really “getting” anything. Hardly an incentive to take more math if not required.
Most likely I had a poor foundation. I would like to see a lot more on what should happen in grades K-7– especially K-5. It’s not enough to shrug it off because “most elemschool teachers are uncomfortable teaching math.” There are ways to address that. My youngest’s best math instruction in any grade was by his 5th grade teacher. That guy should have been teaching all the math in K-5. These things can be arranged!
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