results of our country's education system. This has been extremely

informative.

One guy who came in for tutoring was incapable of dividing 800 by 400

in his head. He had come in to my office for help with a problem, and

our problems are usually designed so that you can do it without the

aid of a calculator. That's the theory, anyway. The problem required

finding the percentage change of something, which meant doing the

aforementioned calculation. I was guiding him through the problem,

and when we got to that part, he said, "I can't do it; I don't have my

calculator with me." I said, "You've got scrap paper; do it by hand."

The words did not seem to register. He looked at me like I had asked

him to calculate a cube root by hand.

Now, this guy admits that he is not good at math. But he got acecpted

to a big-name university, one of the top 30 in the nation. This year,

we accepted about 3,000 incoming freshmen out of over 15,000 freshman

applications. Half of the incoming freshmen were in the top 10

percent of their high school graduating class, and they have an

average SAT of 1226.

My aunt is an elementary school teacher with a couple of master's

degrees in education. I asked her at what grade students would be

expected to divide 800 by 400. Her answer: second grade.

So we have a guy who got into a high-quality, selective university,

and he can't do second-grade math reliably. I'll give him the benefit

of the doubt; maybe he could have done it if he really had to. But

this learned helplessness, this dependence on machines to do math, is

endemic among the freshmen I am teaching.

I toyed with the idea of giving a five-minute math quiz in class one

day. I'd hand out a paper with 100 simple arithmetic problems, give

them five minutes, prohibit calculators, and see what the results are.

When I mentioned this to my aunt, she pointed me to some websites

that have math testing materials for elementary school tachers. None

of the tests fit what I wanted to do, but I say something that

literally stunned me: a test on imaginary numbers meant to be given to

fifth graders. My aunt confirmed that the standardized tests do

indeed include imaginary numbers.

This is ridiculous. Nobody except mathematicians and electrical

engineers, and maybe computer programmers, needs to know anything

about imaginary numbers. I was first introduced to imaginary numbers

in an elective class in my senior year of high school, at a

math-oriented magnet school. I am studying a math-intensive research

field, and I will never, in my professional career, ever use imaginary

numbers. There is no possible justification for trying to test

elementary school students on this stuff.

Clearly this is a symptom that the people who make these tests are

losing contact with reality. What were they thinking? Maybe it was

along the lines of "Advanced mathematicians use this stuff, and it is

technically possible to make the kids memorize it, so if we teach it

we are teaching high-quality math." This is of course rubbish.

Making kids memorize the rules for manipulating complex numbers does

nothing to teach the fundamental concepts. The brains of little kids

are simply not equipped to grasp the concept of 'The square root of

negative 1'. I can barely understand the meaning of the concept. I

would be pleasantly surprised if a fifth grader even understood the

concept of the square root, and knew how to use it.

Is it any wonder that kids ignore or forget basic math lessons? If

the imaginary numbers are any indication, they have been subjected to

cargo-cult math lessons their entire life. They may be able to

memorize a routine and pass a test, but the system has clearly put

very little effort into teaching them how to actually use math. Math

is a set of tools that you use to understand reality. If you don't

understand that, then you will always be hopeless at it. If you don't

know how to connect math to reality, than the math is useless.

I have opten complained about how algebra is a requirement for getting

a high school diploma, even as there is almost no effort to teach

basic financial literacy. I would guess that only about 10% of the

people on the planet actually need to use algebra in their jobs. But

everyone needs to know about interest rates, compounding, and the time

value of money. And if you don't take business courses in college,

you will never learn about these kinds of things. One of the main

reasons for the economic mess we are in now is that people simply do

not understand what it means to borrow a lot of money.

Now, algebra does help you work with the interest rate equations. If

you don't have algebra skills, you have to learn half a dozen formulas

instead of just one or two. But people are much better at

memorization than symbolic manipulation. Most people simply do not

possss the kind of mind that is required to be comfortable with

algebra, and it is foolish to expect them to learn this esoteric skill

at the expense of things that you need to know to live a good life.

Teaching imaginary numbers in elementary school is far, far worse than

teaching algebra in high school. Instead of something that 10% of the

population needs, it is something that 0.01% of the population needs.

It is also worse than useless. The kids, if they have any sense, will

forget everything they ever learned about imaginary numbers right

after they take the test. This creates horrible habits. Not only do

they learn to forget the useless routine of the week, they also learn

to forget the basic life skills that they will really need.

I have seen more and more evidence that our education system is

completely failing to provide students with a useful, science-based

mapping of reality. Instead, it all seems to be devoted to putting

random facts and arbitrary routines into short-term memory. Now,

memorizing facts is important. Facts are the bricks that you use to

build the structures in your mind. But you need something to connect

that knowledge to, so it becomes long-term knowledge. Facts without

context are soon forgotten.

Education should be about teaching people how to understand and work

with reality. I have seen little evidence that our system

accomplishes this.

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