...who told you that lie? An educational psychologist?

More like "at age 12 even the most incompetent teacher can teach things involving abstract/counterfactual thinking to even the least intelligent child"... the bad ol' "lowest common denominator thinking" and the other horrors of our standardized educational systems :| Unfortunately it's not economically feasible to lecture to children in a classroom unless you calibrate on the lowest common denominator.

Also, it's the huuuge difference between "understanding" and "being able to communicate efficiently in words". People can "grok" very advanced stuff even if they don't fully command the language for expressing it. Unfortunately most incompetent teachers are totally incapable of "trying to explain something beyond the level of the language" but the human brain's pattern matching engines are not always tied to language...

> ...who told you that lie? An educational psychologist?

https://en.wikipedia.org/wiki/Piaget%27s_theory_of_cognitive...

Fine, I was off by one year.

Piaget's classification of thinking skills is good, but the theory that these kinds of thinking are developed in discrete stages at those ages has only vague experimental support.

Young children can engage in basic counterfactuals. Ask one.

Still a lie. And you still believe in it even after seeing an example in contrary.

It takes far more than one anecdote to outweigh the evidence in support of Piaget's model.

Uh... what? Counterfactual thinking develops well before the age of twelve. Kids that I know are asking 'what if' questions in pre-K and kindergarten. It's a natural thinking mechanism that children engage in all the time.

Counterfactual reasoning is a subset of abstract reasoning which is a subset of abstract thinking more generally. Children are capable of abstract thinking (e.g. pretend play) and even abstract reasoning (e.g. basic conditional reasoning) very early on. I haven't studied this field (though my spouse has), but a cursory reading of this paper shed light on the distinctions: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3582172/

Don't underestimate how big a difference is made by actually being interested, not worrying about how you'll look to the other kids in class, etc.

I was programming functions in my brother's calculator when I was 8..

It's not, but do you really think that's going to stop true FP believers from upvoting this article?