That seems so simple as to be tautological. After all, you were a layman yourself once.Ideas/jobs/researches don’t spring whole-spun from the ether. You have to be led along that same path yourself—either by a teacher, or by your own mind bumping along down dark corridors.
But it’s not true. Consider by analogy: if you can’t explain something to a 4-year-old, you don’t understand it yourself. After all, you were a 4-year-old once yourself.
No, actually, sometimes you can’t explain something to someone because you don’t have a good enough understanding of their mental processes. It doesn’t matter if you once experienced those same mental processes; the relevant memories of that time are very likely lost to you now. Explaining math to novices is a different skill than understanding math. It requires the ability to figure out why the other person has got it wrong and what they need to hear. That isn’t a mathematical skill.
A distinguished math professor is probably inferior at explaining arithmetic to 8 year olds than an experienced mathematics educator, but it doesn’t mean the latter has the better understanding of math. They just have a better understanding of 8 year olds.
That seems so simple as to be tautological. After all, you were a layman yourself once.Ideas/jobs/researches don’t spring whole-spun from the ether. You have to be led along that same path yourself—either by a teacher, or by your own mind bumping along down dark corridors.
But it’s not true. Consider by analogy: if you can’t explain something to a 4-year-old, you don’t understand it yourself. After all, you were a 4-year-old once yourself.
No, actually, sometimes you can’t explain something to someone because you don’t have a good enough understanding of their mental processes. It doesn’t matter if you once experienced those same mental processes; the relevant memories of that time are very likely lost to you now. Explaining math to novices is a different skill than understanding math. It requires the ability to figure out why the other person has got it wrong and what they need to hear. That isn’t a mathematical skill.
A distinguished math professor is probably inferior at explaining arithmetic to 8 year olds than an experienced mathematics educator, but it doesn’t mean the latter has the better understanding of math. They just have a better understanding of 8 year olds.