Hidden math masterpieces

We’re hiding math’s masterpieces from students, writes Edward Frenkel, a Berkeley math professor in the Los Angeles Times.

Imagine you had to take an art class in which you were taught how to paint a fence or a wall, but you were never shown the paintings of the great masters, and you weren’t even told that such paintings existed. Pretty soon you’d be asking, why study art?

That’s absurd, of course, but it’s surprisingly close to the way we teach children mathematics.

Math is the “language of abstraction,” writes Frenkel. To “gain proficiency with abstraction,” students need “mathematical knowledge plus conceptual thinking times logical reasoning.”

Rubik's CubeFrenkel talked about math ideas with students in fourth, fifth and sixth grades at a New York school. They were too young to be scared by math.

Using a Rubik’s Cube, he explained that 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,” writes Frenkel.

We next studied the majestic harmony of Platonic solids using dice. And I told the kids about the curved shapes (such as Riemann surfaces) and the three-dimensional sphere that give us glimpses into the fabric of our universe.

The professor dreams of spending 20 percent of class time “opening students’ eyes to the power and exquisite harmony” of math.  The rest of the time they’d learn the multiplication tables, etc.

Would they be inspired? What percentage of math teachers are capable of doing this?

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  1. I felt pretty awe=struck when I grasped that having a true feeling for ratios would let me see the proportionality (or lack thereof) in everything from how to grow crops to how well a politician was doing in her/his run for office, according to the polls. In other words, even pedestrian mathematical ideas (or pedestrian to PhD mathematicians) are pretty beautiful and powerful to those of us with more average talents. But only if we are taught well enough, and practice well enough, to own those ideas and use them as tools.

  2. I’m one of the unfortunates who suffered from the first dose of the New Math, in HS, such that I could never get full credit for any problem because I didn’t do them the “right way.” Given my experience, I’d say that the number of kids who might understand and benefit from this is both vanishingly small and confined to very bright and mathy kids who have teachers who really understand it all.

    For most, forget “the beauty” and concentrate on practicality. I’d like to see the focus in k-8 math on making sure that all close-to-average kids master basic arithmetic and the top 25-30% are accelerated to finish algebra I, with geometry for some. We’re a long way from achieving that.

  3. If we had teachers who could teach it, it’d be both interesting and inspiring. But in order to really understand the Rubik’s cube example, you’d have had to have taken AND UNDERSTOOD group theory, which is an upper-division course for math majors. In effect, you’d require math to be taught at all levels by only math majors, and not just that, but math majors who passed with flying colors, really understand their subject matter at ALL levels, and are enthusiastic about it.

    I don’t think we can find the staff. And I think that it being taught by someone who doesn’t understand it and is reading from a script is going to be worse than not teaching it.

  4. cranberry says:

    We can spare 20% of math class time for this? Students are learning “multiplication tables, etc.” in only 80% of class time now?

    Some students are ready to think abstractly very early. I would expect anyone making a living as a mathematician would fall in that very small group of people.

    It would be wonderful if we could supply elementary classrooms with teachers who like math. Even better, if they could present multiple approaches to understand problems.

    • Plenty of us do this and still get through the current material. Why not have kids learn the beauty of mathematics? Although how about paying us more, it is a highly sought after skill. 🙂