MentalMultiplication

I just got off the phone with an old friend. Gerry, Bernie and I all used to be colleagues in the Florida Atlantic University math department, and we more or less independently left and moved to take up new lives in the greater Denver area. Bernie and I went into industry, and Gerry went into teaching; he now teaches mathematics at a private Catholic girl's school in Denver. We see them occasionally (not often enough!).

Gerry is a great innovator when it comes to math education, and a prolific inventor of new and creative math manipulatives, including one of the largest math manipulatives ever: the Sugar Sand Park Moebius Climber, designed with the aid of Mathematica.

Gerry is an extremely thoughtful individual. We are both fascinated by developmental issues and how they affect math education, and we began a conversation tonight that I hope will continue over a long period of time on this website.

But just for tonight: here is a tip he dropped on me for teaching the essence of multidigit multiplication.

At the core of multidigit multiplication is the distributive property of real numbers: (a+b)c = ac+bc. The standard algorithm utilizes it more or less explicitly. But often, these days, the standard multidigit algorithm is not taught: either it's eschewed completely, or some variant like the lattice algorithm is taught instead. If kids are not explicitly taught the distributive property, it will come back to bite them in algebra, where it is used all the time in algebraic simplification and in factoring polynomials.

Here is Gerry's tip; if you want to be sure your kids understand the distributive property, get them to do problems where they multiply one-digit numbers by two-digit numbers entirely in their heads.

Working memory can't hold too much in storage, but it can do that much. If a kid knows his single-digit multiplication tables cold, then he can multiply a multiple of ten by a single-digit number, and add it to a multiple of two single-digit numbers, all in his head. And in doing so, he'll internalize the distributive property, because he has to use it in order to do this sort of problem.

Because unless you have an incredible visual memory, the lattice method isn't of much use for doing mental math.

Brilliant and simple. Like all of Gerry's other math ed innovations.

Back to main page.

Comments

Users must register to comment.

One night last week when I was having trouble sleeping, I decided to amuse myself while lying there by recalling and/or calculating squares in my head, from 1^2 up to whatever. I knew it was working when I had to repeat 37^2 several times because I kept drifting off.

I used (a+b)^2 = a^2 + 2ab + b^2 quite a few times during that exercise, where a was 30 or 40 and b was +4 or -2 or whatever.

That worked so well that I think I am going to work on my times tables up to 40x40 the next time I can't sleep.

-- GoogleMaster - 20 Jan 2006

That would certainly finish me off.

-- CarolynJohnston - 20 Jan 2006

A whole new way of counting sheep??

-- KarenA - 20 Jan 2006

Square sheep, like square tomatoes.

-- GoogleMaster - 20 Jan 2006

Goodness, you can even find results googling "square sheep".

-- GoogleMaster - 20 Jan 2006