ColbyCosh.com

Anecdote: like many grad students, I used to teach undergraduate math and physics tutorials for the dep't to pay the bills. One common problem was that well-intentioned people taught (allegedly) simple tricks for simple problems which didn't scale up to more complex ones.

Every year you'd see the "concrete" thinkers hit the wall pretty early -- usually in the first month as soon as the problems became nontrivial -- and then you'd have to try to convince them that the more general way of looking at things was actually easier. E.g. the students would often try to solve collision problems not by writing down equations for the object positions and equating them, but by playing high-school games with the displacements (confusing them with the distance along the path, natch) which don't generalize as well.

Sometimes I'd be very impressed at how clever they were, pushing their techniques far past the point where I'd have thrown in the towel, but in introductory physics cleverness isn't a feature-- it's a bug. To my mind, teaching students in less abstract ways is downright perverse, as it rewards patterns of thought which will have to be unlearned eventually.

Daniel T Willingham Why Students Don't Like School is an inexpensive book by a cognitive psychologist that should be required reading for any teacher, yet isn't.

Read the entire article and am dumbfounded about all the concern about kids left behind because the subject is too hard. Holy lowest common denominator Batman! I mean, holy half pizza Batman!

Somehow the education system has never figured out how to teach math. When I was in school, I performed acceptably in math because I "got it" to a certain extent, but university-level courses were more challenging for me than they needed to be because my knowledge base wasn't that solid. Still, I managed to get through grad studies and finally had the good fortune to encounter a superb mathematics instructor in my final year. Everything clicked when he started teaching a solid problem-solving approach to math, and it became EASY after that. That's when I got to start doing real mathematics, modeling problems with partial differential equations and using tensor notation. Math is a powerful and fundamental way of looking at the world, and I think our future success as a society depends on improving our ability to analyze the world instead of relying on wooly intuition.

But then I'm not sending any kids to St. Albert public schools.

Considering that the "public" option is St. Albert Catholic and the only other option is St. Albert Protestant, I would guess that the math curriculum isn't the only reason you're thankful that you are not sending any kids to St. Albert schools.

The telling part of the NYT article linked is:

"Dr. Kaminski and her colleagues Vladimir M. Sloutsky and Andrew F. Heckler did something relatively rare in education research: they performed a randomized, controlled experiment."

I'm sure the new curriculum is terrible, but...

Re: "if you are not working with abstractions, by definition you are not teaching math"

Including concretes doesn't mean they aren't working with abstractions. _Doing_ the actual math obviously needs to be completely abstract, since the whole need for the field arises from the fact that we can't do the operations practically with real things, but learning and doing are different things.

Using concretes to teach abstract principles and concepts is a pretty widespread device. Since abstractions are drawn from concretes, this makes a lot of sense, no? I think so, and one study isn't going to change my mind.

http://www.cut-the-knot.org/books/Reviews/KiselevsGeometry.shtml

Russian Geometry text anyone?

As a St. Albert ex-patriate, I'm frankly just surprised the Gazette is still publishing its particular brand of overadvertised, underread fishwrap.

Oh the Gazette is every bit as horrid as it ever was. In the future, there will be only two newspapers: the New York Times and the St. Albert Gazette.

I can fully understand how concrete examples can mess up math. It doesn't take too long to hit a point where concrete thinking is impossible. http://en.wikipedia.org/wiki/Complex_number

I'd hate to handicap a future electrical engineer for the sake of making some snowflakes happy.

By what standard do you figure the New York Times is guaranteed to survive any future farther away from this moment than "Thanksgiving"?

The New York Times will survive because there is a healthy market, with parameters known to some degree, for the privilege of being the owner of the New York Times.

The St. Albert Gazette is still being published due to the amount of advertizing of real estate. That, and the city helps fund it. Which makes one understand why it supports everything the City of St. Albert's council wants to push through. Thus, the stupidity of this particular article, and many many others.
Just saying.

Canadian mathematicion, John Mighton, wrote a great book on math education called the "End of Ignorance". Colby, do yourself a favour and read this book (if you haven't already). Mighton should be much more well-known than he already is. Truly inspiring.

In his book, among many other great debunks this obsession with the "concrete" in math classes. He also points out the inherent problems with having lots of blocks, etc in a class with 20 kids.

He has, with his non-profit group, created a whole program called JUMP math. If any of you are interested you can buy the whole set of books from the U of T at cost and teach your kids and/or volunteer your time to start a JUMP program at a local school (St. Albert?)