On intuition and the quadratic equation

“Dr. Po-Shen Loh has discovered a new way to solve quadratics.”

Well, yes and no. Dr. Loh is a great coach, educator, and evangelist, and I admire and respect him. If he says he was “dumbfounded,” then there’s something there.

The thing is, though, that the press is making a big thing about the “new formula he’s discovered”.  That’s just plain incorrect: the interesting part here isn’t the formula. That formula is just shoehorning a simple idea into the language of math, and in this instance the language is almost as cumbersome as with the original, better-known formula. So, not an improvement.

No, the key idea here is in putting together two facts:

  • that the roots of a quadratic are equidistant from the centerline of its graph
  • that that allows one to systematically work out the roots of a quadratic without either guessing or an explicit formula

Taught well, this new method will relieve students of the need to memorize any formula per se.  Instead, students who understand this will follow the method intuitively, and will wonder why quadratics get so much careful attention in math texts: instead, they’ll just be obvious.

(Now that is a development worth writing about.)

Zeke and TEP hits it on the head

Of course we’ve all thought it at one time or another. I’ve been thinking it aggressively for five years now. It’s why I’ve set up my tutoring business the way I have. But Zeke Vanderhoek is actually getting it done, and my hat’s off to him.

I quote: “The money, as funny as this may sound, is not about the money. The money is a signifier. Because money, in our culture, is a signifier of how jobs are valued, and right now schools are telling teachers that they are not valued. The great and talented people who go into teaching are incentive-ized in every possible way to leave the classroom for jobs in administration or jobs outside of schools altogether. What we are trying to do is reverse those incentives. We want the best teachers to keep on teaching, to be challenged and valued.”

I just wish I’d had what it took to do it myself.