Good stuff, though I’d like to point on some of your reflections.
> Part of it was due to laziness. I was a fast reader and had an excellent memory. This allowed me to excel in most subjects without much work. In contrast, numerate subjects required more dedication and systematic study.
It is important you say “laziness”. Usually laziness is about taking less energy-demanding activity across lots of choices. So it looks like “solving problems” was energy-demanding for you, but other activities were not. Whenever you had to solve problems, it felt “tough”, and coupled with lack of reason, you avoided this activity.
But it is interesting to understand, what’s happening to other children, who actually do math. Suddenly you realize, that “solving problems” for them is less energy demanding, which is awkward! How can it be that same puzzle has different energy-demanding levels for different children?
If you say this is due to difference between children, you are correct, but what exactly is different? Interest itself can’t change energy balance. Ability to read may also be same. As you said, you have good memory, so it also isn’t a factor which increases energy level of a puzzle.
Let’s look next.
> It was programming that opened my eyes. As I started learning Python, I understood the difference between the label and the thing. When coding, one works on two levels: the namespace, which contains the labels for the objects, and the objects themselves.
How do you feel this understanding? What exactly makes you able to “see” namespace and objectspace in distinct? Have you had that ability before? What were subjective “energy levels” before doing programming and after?
> At some point, I realized that doing maths is not so different. You are manipulating names that refer to objects.
You say “manipulating”, but you do this manipulation in brain, right? What allows you to do this “manipulation”? Did it feel energy-demanding before?
> I didn’t give myself the chance to be mistaken. I didn’t have a mission that forced me to either learn or fail. At the end of the day, all I did with most of my knowledge was think about it verbally and sometimes talk about it with other people.
This is good. Which kind of “manipulation” gives you chance to be mistaken? You know, if you do “verbal” talk, it often is generated like GPT-3 one—just created word pattern is predictor for next word pattern. It just can’t feel “wrong”, it is what follows. But “manipulation” isn’t like pattern-after-pattern, it is something different. What is it?
> Later, you could have them simulate the models of physics, chemistry and biology. They could engage in competitive or cooperative games which reward curiosity and stimulate them to think. You could have them design the games themselves, or send them to gather data and test theories. The possibilities are endless.
And here it is important to show, that something is omitted. To be able to simulate physics you first must have physics model based on rules in your head. → Exact this ← part is tough, not the subsequent simulation. If you don’t have rules mindset in your head, simulations just won’t “click”.
Whole programming won’t “click”, if you feel mental rule-based transformations energy-demanding.
So yeah, it is not enough to know what math is good for. It is not enough to teach children programming for them to like to understand world. This never taught stuff I talk about—is a special mindset, which reduces energy-demanding levels for most puzzles, so they no longer feel “tough”, but “interesting”.
What is this mindset? How does it look like? How to pass it to other people?
This is false, there are a few genius mathematician who early in childhood proved it is easy for some humans.
Exactly! There is even more specific concept in programming psychology, it is called “notional machines”. Small little machines in your head which can interpret using rules.
I think those also can transfer to math learning, as after rule-based machines concept is grasped, all the algorithmic, iterative, replacable and transitive concepts from math start making sense.