Negative Numbers and Positive Children

My father had a PhD in Math from CalTech. He must have been confused when I grew up unable to deal with numbers. He had to tutor me through High School Algebra, which I barely passed. In my twenties, I decided it was unbefitting an educated person to go glassy-eyed whenever I saw an equation in Scientific American, and started an Algebra class via UC Extension. This lasted until we got to the multiplication of negative numbers. Now I always understood that multiplication was a short cut for addition. 3 + 3 + 3 = 9, or 3 x 3 = 9. And minus 3 is like spending $3, right? But when I add 3 $3 purchases in my checkbook, what I end up with is minus $9.00. So I decided that they had been lying to me all these years about Math (as opposed to English) being Reality and algebra was really magical thinking, and I dropped the course.

So now, all my grandchildren are doing variations of homeschooling. This means that I have much more opportunity to talk to them about what they are learning than families usually get. They are taking algebra, so I asked Evan and Mike to explain to me about negative numbers. My grandchildren are all bright, interesting people, and a lot of fun to talk to, and I was delighted to have a topic of mutual interest.

Various well-meaning people have explained the mystery of negative numbers to me over the years, and I have temporarily understood it. Temporarily. But after a lot of discussion with the kids, it suddenly occurred to me that maybe what we are talking about here is not subtraction, but negation. Negating 3 three dollar checks could leave me with a positive $9. This may be/probably is Really Bad Mathematics, but for the moment, it allows me to get my head around the problem.

On the principle that the best teacher is someone who just learned something, and explaining something is a good way to learn it, I think that maybe it’s time to let the kids teach me. But I’m going to have to have to go back to pre-Algebra to even get up to the point where they are.

Anybody got an old book or know any good on-line courses I could try?