“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.)
My sister-in-law recently wrote this piece on modern work and its relationship to family and community. So I’m taking this opportunity to thank Adam, Aidan, Amy, Audrey, Debbie, James, John, Michael, Michael, Owen, Ollin, Rora, and Stephanie: you past-or-present teammates have all contributed materially to our shared success, and every single one of you has done it on hours that corporate America would consider unworkable.
(Goes to show you what real A-players can do.)
Thank you all for making work fit into your lives instead of the other way around, without ever compromising the quality of your work.
I didn’t expect Farnam Street to relate so directly to college admissions, but it does, and in a way that is as important as it is deep.
According to the post linked above, the outcome of a “winner’s game” is determined mostly by the actions of the winner; the outcome of a “loser’s game” is determined mostly by the actions of the loser.
So, in a winner’s game, superior skill matters, whereas in a loser’s game, it’s consistency that matters.
Everyone acts as though the SAT and ACT are winners’ games. And, for middle-tier scorers, they probably are. But for high scorers, these tests are loser’s games, 100%.
In other words, you don’t get from 1400 to 1550 by becoming smarter or more knowledgeable. You get there by consistently avoiding mistakes.
You show me a 1400 scorer, and I’ll show you someone who already has the necessary knowledge, but who also experiences some combination of anxiety, hubris, wandering attention, and/or magical thinking when it comes to answering the hard questions.
Getting rid of such bad habits is really hard. That’s why so few people get perfect scores.
That’s also why high scores are so prized.
Students suffering from test anxiety often make things worse by misunderstanding the nature of successful preparation work.
They think: “my goal is to have new knowledge and new techniques.”
But that’s wrong. The right goal is to have new habits.
Under pressure, all people follow their habits. So if you don’t have new, well-established, constructive and functional habits by Test Day, you’ll just automatically revert to what you did before.
And of course, when you do what you used to do, you’ll get the score you used to get.
The alternative is to painstakingly train new and better habits in the weeks (months?) leading up to Test Day. Then, under pressure, you’ll thrive.
(Also check out my book, specifically Chapter 9, Stress.)
“Test day jitters” manifests as “the problems were hard!” when what’s really going on is “I’m not quite as capable when I’m nervous / amped up / in the spotlight.”
The biggest barrier to addressing this issue is misunderstanding what’s really going on.