# How It All Began

I’ve been teaching my kids math since before I became a homeschooler. I had never planned to pull my kids out of school (ah, the best laid plans of mice and men…), but I always figured I’d need to supplement their educations, and accordingly, I started my 8-year-old’s math lessons when she was about 4.5 and attending preschool.

As I had taught many products of our educational system over the years, I had deep knowledge of what could go wrong with their mathematical education. The main issue I’d seen over the years is something I like to call “symbol shuffling.” When they were doing math, they weren’t thinking logically: instead, they had a poorly memorized set of rules, and they tried to apply them. This would lead to equations like (﹣4)＋(﹣5) ＝ 9, because, after all, “two negatives make a positive.”

The problem, as I saw it, was that a lot of the mathematical symbols weren’t producing mental images of anything in particular. They were simply symbols on a page, and they were to be manipulated accordingly. The rules were rules not because they were logical inevitabilities: they were rules because the teacher had said so. In the context of that mindset, (﹣4)＋(﹣5) ＝ 9 makes just as much sense as (﹣4)＋(﹣5) ＝﹣9. After all, how can something make sense when the symbols don’t actually refer to anything?

I was resolved to do better with my kids. So when my 8-year-old was 4.5, we started some very gentle math lessons, starting with simple addition and subtraction. My one overriding concern was that she needed to understand everything she used﹣I’d seen the outcome of the opposite approach far too many times. So I was determined to teach her to true conceptual mastery, and to let everything take as long as it needed to…

As you’ll see if you keep reading my blog, this worked far better than even I expected. Stay tuned!