Monday, May 9, 2011

Just Un-Multiply

Today a friend on Facebook asked for ideas to help her young daughter who is having a hard time learning long division. I suggested she un-multiply until it makes more sense. She didn't understand my answer, so I offered to go into more detail on my blog.

As I child I counted my schools for a while. When I stopped in 7th Grade, Hill School at Fort Belvoir, Virginia, it was my 13th school. My dad was military—U.S. Army to be exact, and during most years I was in more than one school. In case you don't realize it, there is no relationship to what a person is taught in 3rd grade, for instance, in Illinois and Idaho; none whatsoever between what is offered for a sophomore in Virginia and one in Southern California.

I'll discuss another time what this did to my ability to make deep friendships. Today I'm just going to touch on one of the educational aspects of the classroom experience. I managed to learn addition twice, while missing subtraction completely. I left one school just before they started it, arriving at another when they had already finished and were starting multiplication.

We did multiplication and were preparing for division when my family was reassigned again. The new school had just begun multiplication. It was an easy (read that to mean boring) time in math for me. We were gone again, of course, before that class was ready to tackle long division. If you're following the pattern here, you realize that the next class I got to had already finished long division.

I figured out ways to compensate. With double the normal practice on addition and multiplication skills, whenever I hit a subtraction problem, I would un-add. If the numbers were 15-7=something, I would automatically read it 7 and something equals fifteen. Un-adding, I would know it was 8.

Multiplication and division worked the same way. If you had 24 divided by 3, I would say, what times 3 equals 24? I knew that answer was 8. With long division, just write down the answer and carry down the numbers. Then, since subtraction is in order, I would just un-add the balance and bring down the next number.

Eventually I learned how to do it correctly as a student, but I'm out of practice now, so I do it the old way, as I taught myself growing up. I un-add and un-multiply. It works. So it's not the most normal method you've ever heard of. I've never tried to be the most normal person. I've never even understood what normal was, or why it should be deemed important. I found something that worked. I could move every 6 months and still get A's in school.

Now, if I could only remember why that was important...


Kat said...

LOL...Had to laugh...I un-multiply too :). It's just quicker for me.

Ben said...

I call that Algebra.

Kathleen said...

Huh. You know, Ben, you're right. Maybe that's why algebra was so easy for me. I figured it out by myself so early. If Daddy had done something besides setting up nuclear reactors, we wouldn't have moved so often, and I would have been in one classroom, learning the right way. Maybe then algebra would have been a problem. It never occurred to me why it seemed so logical.

Dean K Miller said...

So goes one of the challenges in teaching. I think the processes are just as important as the correct answer, for most cases anyway. However, how would a teacher grade a student who's process is altered, but still arrives at the correct answer?

I follow your same logic...if we can call it that...on certain types of math problems as well.

Kathleen said...

Most of my teachers didn't care how I got the answers, as long as I did. The few who asked were bewildered or amazed by my explanation. I always said I'd be glad to learn their method if they wanted to teach me. I never had any takers.