5 ms·

Functions? Algebra? How is comprehending any of that, possible without the sort of abstract/counterfactual thinking that develops around age 12?

berg01 8y ago
It's not, but do you really think that's going to stop true FP believers from upvoting this article?
cdelsolar 8y ago
I was programming functions in my brother's calculator when I was 8..
nnq 8y ago
...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...
- mmirate 8y ago
  > ...who told you that lie? An educational psychologist? https://en.wikipedia.org/wiki/Piaget%27s_theory_of_cognitive_development#Formal_operational_stage https://en.wikipedia.org/wiki/Piaget%27s_theory_of_cognitive... Fine, I was off by one year.
  - fiatjaf 8y ago
    Still a lie. And you still believe in it even after seeing an example in contrary.
    - mmirate 8y ago
      It takes far more than one anecdote to outweigh the evidence in support of Piaget's model.
  - gowld 8y ago
    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.
wahern 8y ago
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/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3582172/
abecedarius 8y ago
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.
tathougies 8y ago
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.

berg01 8y ago

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

cdelsolar 8y ago

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

nnq 8y ago

...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...

mmirate 8y ago
> ...who told you that lie? An educational psychologist? https://en.wikipedia.org/wiki/Piaget%27s_theory_of_cognitive_development#Formal_operational_stage https://en.wikipedia.org/wiki/Piaget%27s_theory_of_cognitive... Fine, I was off by one year.
- fiatjaf 8y ago
  Still a lie. And you still believe in it even after seeing an example in contrary.
  - mmirate 8y ago
    It takes far more than one anecdote to outweigh the evidence in support of Piaget's model.
- gowld 8y ago
  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.

wahern 8y ago

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/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3582172/

abecedarius 8y ago

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.

tathougies 8y ago

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.