**really**well, here.

## Wednesday, January 13, 2016

## Monday, December 28, 2015

### Math excellence for girls

From MIT and NBER, this just in:

*"...almost all girls with the ability to reach high math achievement levels are not doing so."*

(Here's the paper.)

The basic premise, which I believe in my bones to be correct, is that half of the very best math students in this country -- the female half, by and large -- do not participate in the ranking systems that serve to identify them.

The end result is a mess all around:

* These students lose a crucial opportunity for self-actualization

* Because they are not identified early, these students experience the stress of the mainstream ranking system, which by and large does not rank them accurately.

Good news, though: fixing the problem is as simple as raising awareness. Any girl who has yet to finish 12th grade can participate in these competitions. If you know a good candidate, send her to maa.org/amc, to dtmath.com/amc, or to this short video series on YouTube.

## Wednesday, April 11, 2012

### An interesting discussion on SAT prep

A 35-year-old recently took the SAT and wrote an article about his experience... and in so doing, revealed a number of widely held misconceptions that I skewer, debunk, and clarify in this animated discussion. Enjoy.

## Wednesday, February 22, 2012

### The most underserved students

What if the 32nd individual on the planet to achieve a nuclear-fusion reaction was only 14 years old? It's not science fiction. And the article about it makes the insightful point that the most underserved students in the country are those at the top.

Labels:
brilliance,
gifted

## Friday, December 2, 2011

### Cheating on the SAT

The thing I can't get out of my head when I read this NYT article on kids paying other kids to take the SAT for them is simply this:

Don't get me wrong: you shouldn't cheat, both because it's wrong (which should be enough reason) and tactically too risky (in case the first argument wasn't enough).

But I mean, come

For those of you who are fans of the Drake equation, which uses best-guesses to try to figure out whether there's intelligent life out there, I challenge you to apply this reasoning to SAT prep.

In fact, you might even try to create an analogous equation governing this stuff, like I just did. (I hope you have more luck than I did; if so, please let me know.) But, equations aside, it's not really that hard to think about.

To figure out what a higher SAT score is worth, just do the following steps:

First, get a lifetime earnings calculator. (Google it; there are many.)

Then, use it to estimate the student's lifetime earnings, given that he or she attends the best school to which he or she can gain admission given the initial SAT scores.

Then, take the average (expected) gain in SAT scores given a particular preparation method.

Then, use the calculator to estimate the student's lifetime earnings, given that he or she attends the best school to which he or she can gain admission given the

The difference between the two lifetime earnings is the value of the higher SAT score.

And now that I've said all that out loud, I'm starting to realize that four-digit prices for SAT prep only make sense for providers who can offer only single-percentage-point gains with a high variance, as delineated in this article in the Wall Street Journal regarding the average benefit of SAT prep.

And you know what that means. Yep: I'm doing it wrong.

Ah, well, yet another learning and growth opportunity. Never a bad thing.

*All they charged was $3600?*Cripes, that's a bargain at ten times the price.Don't get me wrong: you shouldn't cheat, both because it's wrong (which should be enough reason) and tactically too risky (in case the first argument wasn't enough).

But I mean, come

*on*, people, do the math: a one-percent increase in salary over your life is easily a five-digit number even if you're kind of a slacker. Two significantly different SAT scores mean admission to schools of two significantly different calibers. And I doubt the salary increase we're talking about here is just 1%.For those of you who are fans of the Drake equation, which uses best-guesses to try to figure out whether there's intelligent life out there, I challenge you to apply this reasoning to SAT prep.

In fact, you might even try to create an analogous equation governing this stuff, like I just did. (I hope you have more luck than I did; if so, please let me know.) But, equations aside, it's not really that hard to think about.

To figure out what a higher SAT score is worth, just do the following steps:

First, get a lifetime earnings calculator. (Google it; there are many.)

Then, use it to estimate the student's lifetime earnings, given that he or she attends the best school to which he or she can gain admission given the initial SAT scores.

Then, take the average (expected) gain in SAT scores given a particular preparation method.

Then, use the calculator to estimate the student's lifetime earnings, given that he or she attends the best school to which he or she can gain admission given the

*final (expected)*SAT scores.The difference between the two lifetime earnings is the value of the higher SAT score.

And now that I've said all that out loud, I'm starting to realize that four-digit prices for SAT prep only make sense for providers who can offer only single-percentage-point gains with a high variance, as delineated in this article in the Wall Street Journal regarding the average benefit of SAT prep.

And you know what that means. Yep: I'm doing it wrong.

Ah, well, yet another learning and growth opportunity. Never a bad thing.

## Wednesday, December 15, 2010

### TED meets math

## Monday, November 15, 2010

### What's wrong with math education

If I could say it better than Tom Henderson, I would. But I can't. So here he is:

In a nutshell, what is the problem with math education in the US?

I have no idea. Let me instead describe the attitude that students have that is problematic, and you can reconstruct what must be wrong with it from that angle.

“Show me the steps.”

Many students want teachers to “show me the steps.”

They want a sequence of steps that they can perform that will give them an answer. This is not unreasonable; they know that their performance on exams, and therefore their performance on the All-Seeing Grade Point Average, is largely determined by being able to Do The Steps.

But “The Steps” are cargo cult mathematics.

The Steps are seeing the sorts of symbols that count as “right”, and trying to replicate that dance of steps. It turns out that the easiest thing in the world is to look at a student’s work, and tell the difference between “Knows what’s going on, made mistakes and dozed off” vs. “Can memorize steps, has no idea what’s going on.”

Now, the way that I explain mathematics, it sort of looks like I’m torturing the poor bastards. I handwave. I refer to certain groupings of symbols as “Alphabet soup” and write it down as a wild scribble with one or two symbols around it.

Because I’m trying to avoid showing The Steps and instead show them enough of The Idea that they can reconstruct what the steps MUST be.

Many students want to know the formulas, so that they can float them on top of their short-term memory, ace the exam, and then skim them off. Why do they want to know that?

Probably because, for their entire mathematical careers, math has been a sequence of Steps, and if they get them wrong, they get red pen, bad grades, No No No Look What You Did. Plus, bonus, there is no apparent relevance of these algorithms other than To Get The Answer.

What’s wrong with math education in the US? What’s wrong is, Whatever it is that makes my students uninterested in learning any more math than is required to minimize feeling stupid.

So that we’re clear, lots of my students are totally awakened to the interesting weirdnesses of mathematics. But, it takes some doing, and I can’t do it by myself. Hence the podcasts and the lunatic twitter stream and the plans for TV shows and online games and godknowswhat else.

I’m trying to get across that if you are highly motivating, if you have a high degree of fire and “**** yeah!” and “What, that’s impossible, but true!”, you can get students to express interest in theorems named after dead Hungarians.

In a nutshell, what is the problem with math education in the US?

I have no idea. Let me instead describe the attitude that students have that is problematic, and you can reconstruct what must be wrong with it from that angle.

“Show me the steps.”

Many students want teachers to “show me the steps.”

They want a sequence of steps that they can perform that will give them an answer. This is not unreasonable; they know that their performance on exams, and therefore their performance on the All-Seeing Grade Point Average, is largely determined by being able to Do The Steps.

But “The Steps” are cargo cult mathematics.

The Steps are seeing the sorts of symbols that count as “right”, and trying to replicate that dance of steps. It turns out that the easiest thing in the world is to look at a student’s work, and tell the difference between “Knows what’s going on, made mistakes and dozed off” vs. “Can memorize steps, has no idea what’s going on.”

Now, the way that I explain mathematics, it sort of looks like I’m torturing the poor bastards. I handwave. I refer to certain groupings of symbols as “Alphabet soup” and write it down as a wild scribble with one or two symbols around it.

Because I’m trying to avoid showing The Steps and instead show them enough of The Idea that they can reconstruct what the steps MUST be.

Many students want to know the formulas, so that they can float them on top of their short-term memory, ace the exam, and then skim them off. Why do they want to know that?

Probably because, for their entire mathematical careers, math has been a sequence of Steps, and if they get them wrong, they get red pen, bad grades, No No No Look What You Did. Plus, bonus, there is no apparent relevance of these algorithms other than To Get The Answer.

What’s wrong with math education in the US? What’s wrong is, Whatever it is that makes my students uninterested in learning any more math than is required to minimize feeling stupid.

So that we’re clear, lots of my students are totally awakened to the interesting weirdnesses of mathematics. But, it takes some doing, and I can’t do it by myself. Hence the podcasts and the lunatic twitter stream and the plans for TV shows and online games and godknowswhat else.

I’m trying to get across that if you are highly motivating, if you have a high degree of fire and “**** yeah!” and “What, that’s impossible, but true!”, you can get students to express interest in theorems named after dead Hungarians.

Labels:
show me the steps

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