Why Johnny Can't Add; The Failure of American Education

On a recent visit to my sister's, I witnessed as my niece engaged in a struggle familiar to me; math homework.  The difference; I struggled to juggle the numbers to come up with the correct answers.  She was struggling to learn how to come up with the wrong answer.

I kid you not.  The state of the art flavor of the day shit-for-brains educational theory is called "compatible numbers."

In proper math, you deal with the actual numbers to come to the correct answer.

In compatible math, you round up the numbers (or one of them) to one that's easier to deal with, to come up with an answer that is close to the actual number the problem should result, but isn't actually the number the problem should result in.

Is your head hurting yet?

OK, let's take 28-13.  We round up 28 to be 30, because it's easier to deal with; 30-13=17, which is close to the correct answer of 15.  Of course, even though 15 is the correct answer to the problem of 28 minus 13, it's wrong for the homework because they are looking for the wrong answer.

In essence, our schools are teaching that 28-13=17.

Just so you don't get as confused as I did, with two digit numbers, you only round up if the second digit is greater than five.  Thus 69x14 becomes 70x14.  And of course, you get completely different answers when you solve the equation.

Educators, however, have decided that "close is good enough."

Of course, this kind of sloppy thinking can actually kill people.  Can you imagine the results if an engineer using this technique to design aircraft, or bridges?  "Oh, the parts ALMOST fit, but close is good enough."  Or if a pharmacist or nurse gave you "almost" the correct dosage?

It's completely unacceptable.

Some of you might remember "new math."  New math differed from old math (or simply "math") in that the processing of the equations was broken down so that the student could work with smaller units.  Sometimes this process was outrageously complicated.  So complicated, that Tom Lehrer satirized it in song.

But the end result was still expected to be the actual, correct, answer.  A number that was close, but incorrect, was still  incorrect. 

Proponents of this educational malpractice make an extremely lame argument.  "We're teaching them how to estimate," they coo reassuringly.  "WHYYYYY?" I hiss back at them.

Yes, many adults have been doing this kind of estimation for years; many of us can look at the multiplication example I gave earlier and say "yeah, that's gonna fall somewhere between 900 and 1000."  And when we do the actual math, we nod our heads because the correct answer is close to what we projected. 

But that's not what you teach kids.  When you teach that at a primary level, sloppy thinking becomes a primary process instead of something you know you can get away with later in life.  What you learn first is what sticks; it is the foundation for everything that follows.  What you learn first usually ends up being what you learn.

Morris Kline, Professor of Mathematics, in his 1973 book Why Johnny Can't Add: the Failure of the New Math addressed this issue directly:

"abstraction is not the first stage but the last stage in a mathematical development"
- Why  Johnny Can't Add, page 98

I doubt there will be funny songs about the use of compatible numbers. Teaching kids how to arrive at the wrong answer just isn't very funny.