Musk's Musky Math Ideas

Elon Musk doesn't think math teachers are teaching correctly:

Speaking at the ISSR&D Conference in Washington D.C. Wednesday, the CEO of SpaceX and Tesla (TSLA) was asked about the education system. Musk explained that he believes schools aren't doing enough to help children grasp why they're learning each subject. 

"You just sort of get dumped into math. Why are you learning that? It seems like, 'Why am I being asked to do these strange problems?'" Musk said. "Our brain has evolved to discard information that it thinks has irrelevance." 

Musk suggested learning be focused around solving a specific problem, such as building a satellite or taking apart an engine. Then students will encounter and master subjects such as math and physics on the path to solving their problem. Understanding how to use a wrench or screwdriver will have a clear purpose. 

It would be easy to trash Musk's argument--by, for example, pointing out that there isn't a lot of K-12 math in building (or launching, or tracking, or maneuvering) a satellite--but instead I'll be a little more respectful.

Musk's idea isn't new.  What he's suggesting is called "problem-based learning", an old (Dewey promoted it a hundred years ago) pedagogical style which I describe as "inefficient at best".  Barry Garelick of the Traditional Math blog wrote a brief post about Musk's PBL suggestion, and then wrote a follow-up post highlighting some of the comments from that post.  One of those comments hit the nail on the head--in problem-based learning, so much of the time is spent on the "problem" that the kernel of math that's supposed to be gleaned from the "problem" is lost in the shuffle.  Very little math gets learning in a class period, and that which does get learned is mostly a by-product.  "Exactly!" scream the proponents of problem-based learning.  But no.

Remember when manipulatives were the big thing in math?  Many (many!) moons ago I found one that I really liked--Hands-On Equations.  Used to teach students how to solve algebraic equations, it involved dice, pawns, and the idea of "legal moves" (e.g., it's "legal" to add a pawn to both sides) to provide a physical representation of algebraic operations.  Gradually, through 26 lessons, the program transitions students from solving problems with the manipulatives to solving them using standard algebra.  Sounds great!  My students loved it, I loved it, everyone had fun, the kids were engaged--anyone walking in to my class would think that this, this was a place where learning was taking place.  You could have checked every box on an evaluator's clipboard.

Cut to the end of those 26 lessons, though, and students did no better on a test than had previous classes who did not use Hands-on Equations.  No better at all.  Despite the program's built-in transition from manipulative to algebra.  Students saw that transition as just part of the program, part of the game.  They didn't make the leap from the "game" to the math.  They learned the game well, they didn't learn the math.  They spent a lot of time learning a little math.

And that is what's wrong with Musk's idea.  He made the classic rookie mistake; I won't be hard on him because it's such a common mistake.  But people who are really smart, or very talented in a certain area, can see "connections" between the many things they know.  That excites them, it's so cool!  If they can share those connections, everyone else will be excited about the topic, too, and will learn!  In the post-Sputnik days of "new math", the smart people got together and decided that if everyone learned basic set theory and different bases, our country's "math deficit" would be instantly erased!  Today the silver bullet is matrices.

What they get wrong, though, is the confusion between cause and effect.  Being excited and understanding the material and seeing connections doesn't cause learning, it's the result of learning.  There is no way set theory and bases are going to help someone who doesn't already understand math, and the same goes for matrices.  You have to teach fundamentals.  No one starts playing piano with a Bach concerto; they start with notes, and chords, and Chopsticks.  So it is with math.

Now I hope that some won't (intentionally) misunderstand what I'm saying.  I'm not saying that math should be taught as an abstraction; on the contrary, it's the language of science and the universe, and that's part of the reason we learn it at all.  There's no way I would advocate divorcing math from the sciences, from engineering, from games.  Math is learned best when it is taught with applications and examples.  But the examples are there to highlight the math, not to subsume it.

Additionally, high school math takes us up to what was learned and developed in the 1600's (calculus).  That's why "Train A" and "Train B" problems exist; there's no real-world need to solve such problems, they just subtract a little abstraction to make the problem easier to understand.  Seriously, outside of some statistics (i.e., social science problems), what real-world problems are ordinary K-12 students going to solve using the math we teach them?  Darned few!  But we can help them understand real-world things, often with the help of physics, especially where driving, a real-world activity if ever there was one, is involved--doubling speed quadruples energy, speed going around a curve, how long it takes to stop if you lock up the brakes, how police determine your speed from the skid mark your car left on the road, etc.

So to close, I give Musk credit for having his heart in the right place.  He's just a little off in the time scale--problem-based learning can only occur after the elementary learning has already taken place.