"What if we are Not Allowed to do it that Way?"

Here's a dilemma for a lot of parents and other people who are trying to teach their kids math:

The methods that many people use are far superior to the standard algorithms taught in elementary school, yet many benighted administrators and school policy-makers do not recognize this, and insist that students do things "the regular way." Of course they don't realize that other cultures  (besides the U.S.) have a different "regular way" that sometimes beat the poop out of our way - which is proven by our low ranking among most other countries of the world in most subjects.

I'm specifically thinking of math. I help teachers, parents and students learn math with methods that magicians have used for years. They are not "magic" -  just more effective, which make them seem like magic. Some of these methods are the norm in other cultures (the ones outperform us by far in elementary math).

Commonly, someone I am helping will ask, " But what if we are not allowed to do it that way?" Recently someone wrote in:

"I am fascinated with your approach to math but worry about teaching these kids differently from what their teachers are teaching.  Will I confuse them?  Because they are graded on the methods taught in the classroom, will I be doing more harm than good?"

Well, let me not be coy - yes, you will confuse them if you teach superior methods. But that is unavoidable, and not as big a deal as  it might seem. There really is no learning without some initial confusion. The common "show-and-tell" kind of inculcation that gets kids to jump through specific hoops is not really learning. It is "training."

If the children aren't getting it the "normal" way (and all statistics point out that most kids in U.S. public schools don't really have a grade-appropriate grasp of math), then it is really time to bite the bullet and face a little confusion.

They will get over the bit of confusion, as soon as they finally "get" what they are supposed to get, using better methods. Besides, the alternative methods do not give different answers, they just use different algorithms to arrive at the answer.

Let me give you a trivial, yet representative example:

You know that when you multiply a whole number by ten, you basically just tack a zero on to the end of the number. 34 x 10 = 340. Would anyone really expect any child to write out the example, complete with partial products, each time they were to multiply by ten? That would be ludicrous.

As long as the child understands the concept that there are ten groups of the number, therefore the number is to go into the tens column instead of the units column, it's fine - no, it's necessary - for him or her to just "know" the answer is 340.

So when you teach them a better algorithm for the standard algorithm to perform multiplications like 28 x 63, it would be appropriate - no, much better! - for the child to be able to simply write or call out the answer "1,764", without showing any "work." (For the algorithm for this, check out http://www.mathmojo.com/chronicles/2007/01/27/algorithm/ - which also has some more thoughts about "showing the work." )

Yes, some teachers will frown on a student doing things like this. Fortunately, I live in the twenty-first century, where most of the teachers I have shown this to can't wait to embrace it. There are still some hold-outs, but that says more about them than about the methods, or their students.

The real problem lies with administrators and school-boards who don't really understand what teachers face "in the trenches."

There are ways to deal with that, and I'll have to deal with this in another article, soon. Stay posted!

Written by :

Brian Foley