Teaching Theory Before Data

I had no idea it was this bad.  I have been hearing that parents were puzzled at math methods being taught to their children, but I figured it was just a mild inefficiency of method that they were not familiar with. We forget things, and when Jonathan and Ben were in more advanced maths I had to stare at things a while and look at the previous chapters (which I never did in high school) to figure it out.  But they were in Christian schools which taught math in more old-fashioned ways.  I recognised what was in front of me, but had forgotten it.  I could get it back. (Though they usually got there first while we were staring at it together.)

Holly Math Nerd, who I have seen quoted before on the internet, has an essay I can only describe as chilling, Light Bulb Moments Are Not Accidents.

 The clearest example came with a real-world problem: 6,990 ÷ 260. Framed concretely, this was a question about how many more paychecks it would take to pay off my car loan if I stopped making extra payments, with each paycheck covering half a payment.

Without prompting, she immediately saw that 260 × 2 = 520 meant 2 was the first step — and did the multiplication mentally. No boxes. No number lines. No written explanation of her “strategy.” No developmentally inappropriate requirement to do meta-analysis of her strategy in real time.

Just fluency, surfacing the instant the problem was allowed to be orderly.

This is the part that’s hard to explain to people who haven’t watched it happen: the so-called “conceptual” method didn’t deepen her understanding. It buried it.

It increased cognitive load, scattered attention, and replaced a stable procedure with constant decision-making.

The standard algorithm didn’t feel old-fashioned to her. It felt like relief.

Some of you are familiar with Richard Feynman's experience on the California State Curriculum Commission in 1964 New Textbooks For the "New" Mathematics. This is the same type of error allowed to continue unchecked for 60 years.  It stems from the idea that the theory should be taught first, before there is any data to apply it to.  Children's brains don't work that way.  Heck, our brains don't work that way. Even in later years, when children have some abstract reasoning ability, you don't teach the idea of the periodic table and expect the student to figure it out, labeling it as they go.  You put the periodic table in front of them and then start pointing out the patterns and connections. Once they get the general idea, then it doesn't necessarily matter much if neodymium drops out of their memory.  But they aren't going to get the idea cold. If you want to teach maps, you start with places the child already knows, not the idea of a map.