How our 1,000-year-old math curriculum cheats America's kids

Teachers only need minimal knowledge of their subject, and if someone discovers that they don't actually like teaching then they just keep doing it anyway because they got a teaching degree, and can't do much else with it.

Some possible ways to help: give teachers less class time and more time to prepare interesting lessons, pay teachers more, raise the standards of training and hiring.

When reading an advanced math book for the fist time, I can spend 1 hour per page, because I must copy the proof, try a few "improvements" that are dead ends, do some exercise, and understand what is the main idea of that part.

It's very difficult to mixing some modern subjects without calculation. Most of the time, the idea is to just hide the technical details so now it's totally unintelligible and the only possible way to learn it is by memorization. It's possible to teach magic and religion in the same way.

I like to add some comments about applications in my classes, but they are marked as off topic, and they are short because usually there is no time to spare.

Some of the proposed subjects are plausible to teach, for example module arithmetic. I'd like to see a discussion in school about the module 2, 9 and 10 arithmetic. (2 is almost intuitive, 10 is easy to see, and 9 is the base for the "rule of nines" test, that is usually teached without proof)

But, for example, Riemannian geometry is difficult. It's possible to pick a sphere surface and show that the geodesic intersects in two points. Explain the sum of the angles in a triangle? And then what? I don't have any intuition about hyperbolic geometry. It's difficult to students to see what is happening with the geometry in a plane in spite it's easy to draw, and we have paper everywhere to tray.

> I recently visited students in fourth, fifth and sixth grades at a school in New York to talk about the ideas of modern math, ideas they had never heard of before. [...] I used a Rubik's Cube to explain symmetry groups: Every rotation of the cube is a "symmetry," and these combine into what mathematicians call a group. I saw students' eyes light up when they realized that when they were solving the puzzle, they were simply discerning the structure of this group.

It's an interesting topic, but the problem is not how much you can explain but how much the students understand. Did he make any test to measure it? Can the students solve the Rubik's Cube?

I'd like to see a test for this idea. Pick 10 classes and divide them in two groups. Give 5 of them the traditional education and 5 of them the "modern topics" proposal. Pick the classes at random. Pick the teachers at random!!! Don't compare one class with a standard underpaid "traditional" teacher with 30 students and a class with a specially selected for the experiment teacher with 10 students. And compare them with multiple choice exercise, not teacher opinion or self report interest.

An occasional lecture on a 'fun' topic (or even better, an assigned reading and short essay -- expository writing should be practiced in every subject starting in middle school or earlier) could be motivational. But the author wants to spend "20% of class time opening students' eyes to the power and exquisite harmony of modern math," which he expects would "feed their natural curiosity, motivate them to study more and inspire them to engage math beyond the basic requirements." That's fantasy land. The author sounds like what he is, a UC Berkeley mathematics professor. If students are going to succeed in his college-level courses then they need the basics down cold, which means memorization, repetition, and application to concrete problems. That is, the "stale and boring" stuff.