Invasion of the Math Snatchers

The Independence Institute ^ | Barry Fagin

[hsmomx3]

"Math is hard, let's go shopping!"

When Mattel released a talking Barbie who offered that bit of teenage wisdom, public reaction was so furious they pulled her off the shelves. Mattel is still trying to recover from the PR disaster.

I assume they fired the guy who came up with that little gem. Not that it mattered much.

I have every confidence he's enjoying a new career, designing math programs for American public schools.

What else can I think about programs that encourage children to "shop" for the correct way to multiply? That ask kids what "color" they think math is, like it's some sort of lip gloss? It'd be funny, if it weren't so tragic.

It's tragic because, in a modern global economy, mathematical literacy is essential. The most important product humanity produces in the 21st century is information. Working with information requires intellectual discipline and the ability to think abstractly. That's what math is all about.

Unfortunately, other countries do a much better job of teaching math than we do, with potentially serious consequences. Why shouldn't American firms contract out high-tech jobs to engineers from overseas, if that makes them more competitive?

Do you know any immigrants at your school? Ask Asian or European families what they think about math classes. Chances are their children placed into the most advanced math the district has to offer, yet are still having a very easy time.

My own experience as a teacher bears this out. I am proud to be on the faculty at one of the most selective colleges in America. My students are America's best and brightest.

And yet, when I went to Russia on sabbatical, I couldn't believe how good my students were at math. After two weeks of class, I had to redo all my lesson plans. I wound up covering more material in more detail than I had thought possible. It was a great experience, but a sobering indictment of American education.

Fortunately, what American students lack in fundamentals they make up in initiative and creativity. It's a constant struggle to get Russian students to 'think outside the box," while my American classes are always abuzz with interesting ideas. Fix the math problems, and American students will do great things.

So how do we do that?

First we have to undo two decades' worth of damage done by faddish mathematical programs. Here's how you can tell if your school has one:

Your school emphasizes children "discovering" or "constructing" their own techniques for arithmetic. This is nice in theory, but most children lack the intellectual curiosity and focus to discover even basic arithmetic rules. Besides, it took humanity a couple of millennia to develop the math we have now. Asking a roomful of 4th graders to start from scratch is an idea only an education professor could've come up with.

Your school de-emphasizes drills. "Boring" facts like multiplication tables and algebra formulas are no fun to teach, but they're an essential part of developing mathematical fluency. If your child's teacher doesn't pay much attention to drills or thinks math facts aren't important, be on the alert.

Your school encourages extensive, early calculator use. Calculators are appropriate once mathematical fluency has been gained. But they're crippling if introduced too soon, particularly in the early grades. There is a big difference between a child who knows *why* six times seven is forty-two, and a child who merely pushes "6 X 7 =" on a calculator.

Fortunately, all is not lost. There are some terrific mathematics programs out there, ones that are both rigorous and fun. They're ready and available to replace the silliness we have now, if only parents will demand them.

But it won't be easy. We'll have to do our part. We must support teachers who set high standards. We must support schools that hold students accountable. We must understand that self-esteem in mathematics is earned, not given. It comes from getting the right answer.

These and other "back to basics" ideas fly in the face of the modern educational establishment. They are in direct contradiction to incentives parents, teachers, and administrators face on a daily basis. Trying to solve this problem will be very, very hard.

But so what? Math is hard. Let's go to work.

(c)2004 The Independence Institute

[Carry_Okie]

Is your 11 year old using the definition of the limit (epsilon-delta)?

Yes. The text is Thomas' Calculus and Analytic Geometry. I actually have to limit her on it or she'd do math most of the day. She's enjoying this course more than any math she's done to date.

I made a big deal of rigor in her proofs when she went through intermediate Algebra (a ten year old Dolciani) and made sure she was doing proper diagrams and graphs for each word problem (she already understands an area under a curve as an output variable). In that text, there were perhaps three problems that had us stumped, one of which I know for a fact was an error in the text. As far as units go, well, I'm totally uncompromising there. she's been using dimensional analysis and identities since first grade.

Freeper NattieShea is virtually self-teaching in math at this point. I get to show her how rusty and sloppy I am every once in a while when she gets stuck, but it's a wonderful thing when the ol' man sits down, asks a few questions, and gets her through that, "Oh, duh," moment. I still need to guide her in her writing (she has a "forest for the trees" problem).

Her sister isn't quite as far along. She is nine and has completed one year of high school algebra with an additional course in extreme arithmetic. PowerBaby is probably a better abstract thinker than her older sister, but her sloppy habits will kill her at a higher level. We're working to fix that.

[luckystarmom]

How did you teach your kids this? Obviously, it wasn't in school.

My son is gifted in math, and he is bored. I just don't know what to start teaching him. There's basics he has never been taught, and I don't know when/what to teach him.

His teacher took off points for him not showing his work on long division. He does it in his head. (Just irked me.)

[AmishDude]

That is impressive. One of my worries is that young people, no matter how advanced or brilliant, just have trouble with the concepts of things like limits.

You'll find that the geniuses in places like Budapest spent their youth thinking about number theory and discrete math problems. Calculus is something that takes a bit of a leap.

Nonetheless, you should be very proud, she is quite talented, as the link demonstrates. Have you considered something more traditional, like number theory or something more fun, like graph theory?

[Carry_Okie]

Have you considered something more traditional, like number theory or something more fun, like graph theory?

Actually, I think we're headed toward symbolic logic and Boolean Algebra. I'm trying to impart the lower division of a double major in two technical disciplines before she's 18. Other than using a word processor, she has yet to use a computer, so we have work to do there too. Basic electronics first. From there to gates (Boole there), assembly language, then programming. Frankly I think her talent would be law or accounting, but to be technically illiterate in this century is a grave mistake for any person wishing to consider themselves educated.

[Carry_Okie]

How did you teach your kids this? Obviously, it wasn't in school.

At home.

IMO, you need to get him out of school.

Gotta go, we're headed out to see the Globe Trotters tonight.

[luckystarmom]

Why would you do assembly before a language like "C"? To me, it's easier to learn the higher order languages than work down to assembly language.

Has she done any of the lego robotics? It teaches some computer programming, and my son loved it in his gate program in 3rd grade.

[AmishDude]

Actually, I think we're headed toward symbolic logic and Boolean Algebra.

That's kind of boring. It's formalized pedagogy and not real mathematics. If she has talent in mathematics, I'd encourage her to pursue it until she's had enough to decide it's not for her.

Here's a problem

Let there be six people in a room. Every pair of them either has met before or has not. Prove that there is either (1) a subset of three of them such that each one has met the other two or (2) a subset of three of them such that each one has not met either of the other two.

Prove that this is not necessarily true for a room with a total of 5 people.

Now the hard one: How many people need to be in the room for the conclusion of the first problem to hold where "three" is replaced by "four"?

Just for fun.

[BJungNan]

My math teacher in 7th grade used to get so frustrated with me that he would start yelling, "why don't you get it?"

New math, old math, it's all a calculator to me now.

[FreedomFlynnie]

I'm by no means a parent, but I did have to read that in 8th grade or so. Of course, by then, I'd already read 1984, Brave New World, Animal Farm, etc. I considered The Giver a very juvenile version of the above type of dystopian fiction.

IMO, if a child is old enough to read The Giver, probably around 5th grade or so, he's old enough to read Animal Farm, and would be better served by the latter. I actually remember feeling somewhat bitter about having to read a book I thought was a good bit beneath me at the time.

[Carry_Okie]

I'll give her the problem and see what she does with it.

The symbolic logic has an insidious goal (along the lines of what Carnap did with philosophical problems): develop a computer program to analyze law for constitutionality. It's a worthy project.

[RightField]

#30
I took a year off of regular math (I used ABeka) to make sure my son was totally fluent in basic arithmetic, especially fractions and decimals. In the 6th grade, we went through most of threee "Key To" series: fractions, decimals and percents. Upon completion of that year, he proudly labeled himself "The Percent King!"

Only then, when he could do fractions, decimals, and the four basic operations, was he allowed to use a calculator (and for "word problems" only, at first). And through 8th grade, he was not allowed to use a calculator ever, for the problems that were just straight practice problems. Call me a cruel, drill & kill taskmaster!

And ... for each of my kids ... I taped a huge multiplication table on their closet door at the beginning of 3rd grade. It was just there for them to look at, ponder over, and to see relationships in the numbers. It worked, too ... both of my kids said that they studied that chart even when they didn't mean to!

[Land of the Free 04]

we know that 6X6=36 and since 6X7 is one multiple of 6 more than 36 it must be 42

So why is 6 times 6 36?

[hripka]

#2 Core Problem: POOR EDUCATION QUALITY PERFORMANCE
Math & Science Literacy
from Grandfather Economic Report series
http://mwhodges.home.att.net/summary.htm