Now that my kids are entering the public school system, I'm starting to think about how they should be educated. After reading A Different Kind of Teacher, by John Taylor Gotto I can no longer afford to trust the public education (nay, schooling) system to the education of my children. The problems in that system range from the inconvenient to the malevolent.
Unfortunately, I'm not in a position to fully home-school my kids nor am I convinced that the premium I would pay at a private school would offer any significant advantage to my childrens' education.
While my first son is just starting Kindergarten, I've spoken to enough parents to realize that I'll be helping them with a whole lot of homework in the coming years. The thought that keeps coming to my mind is just how much will I be fighting with the cirriculum of the teachers.
After reading a paper written by one of my old professors from college, I can certainly see the signs of war on the horizon.
In a paper entitled, Let's Abolish Pencil-and-Paper Arithmetic, Anthony Ralston argues, essetially, that long division, multiplication of large numbers, and most manual methods of computing results to high precision without the use of a calculator is an outright waste of time.
He says
Not only does being able to do long division have no practical value whatever but, in addition, the time required to teach this algorithm to students is far, far in excess of any benefit which might accrue from learning it. Of course, students must learn what division is, when to apply it, what remainders are and how to do simple division problems mentally. But teaching long division is pertinent to none of these aims; it is as nonsensical as teaching the square root algorithm which was staple fare until recent times. I cannot help but believe that those who favor teaching long division in elementary school (and these include some research mathematicians [Klein, 1998]) are in the grip of some fantasy about what is important and useful in school mathematics6.
He stresses the need to develop mental arithmetic skills, say the multiplication of 2-digit numbers together:
...many children aged, say, 10 or 11 would find learning to multiply $46 \times 83$ mentally hard and would require many days, weeks or months to learn to do such calculations accurately. But does any reader of this paper believe that you can't teach as many children to do this as you can, say, teach to do 5-digit by 5-digit multiplication with pencil-and-paper. (Of course, it is simple madness to try to have anyone become effective at 5-digit by 5-digit multiplication; such calculations should always be done by calculator.)
At the end of the paper, he outlines what seems to me the right way to teach math skills. Hint, it heavily relies on in-memory arithmetic and calculators.
Alas, he concludes toward the end of the paper that even if, "A detailed curriculum could be developed, textbooks could be written, lessons planned etc... let's even be optimistic that politicians, parents, mathematicians - all those antediluvian groups - could be convinced of the rightness of abolishing PPA," that elementary school teachers are probably not ready to teach using the new methods. He calls for specialist math teachers, like those used for art and music.
Sigh.
