[syzarian]

Here’s an example that illustrates my position. Due to experience with teaching mathematics I know that it requires a lot of effort to convince a student that the reason 2x+3x is 5x is because of the distributive property. One could not possibly know this and why this is true without experience/knowledge. I haven’t the slightest idea of similar situations in other subjects. I know force is mass times acceleration but I have no idea how difficult a concept this is for new beginners because I have no experience with teaching this concept to beginners. I don’t know what examples to use when a student doesn’t grasp this concept.

[lemming]

But it's not like I sit down and just invent the classes I do with my daughter. There are really good programs, which scaffold all this information and explain it to the kid (and often, coincidentally, to the parent too). For example, I know how to add, but would not know how to go systematically through all the cases and explain them to her. Fortunately the Singapore Math curriculum we use does all that and much much more, and I work through it with her.

[Ntrails]

> Due to experience with teaching mathematics I know that it requires a lot of effort to convince a student that the reason 2x+3x is 5x is because of the distributive property

pffft. Put two skittles next to three skittles and ask what the resulting summation is in terms of skittles.

I'm being a bit glib, but the reality seems to be that many smart people think teaching is trivial, a simple case of knowledge transfer. If you understand it, surely you can teach it to someone else.

My personal experience at uni suggests that truly brilliant people who understand topics perfectly can be Not Good at instilling understanding in others. It's a different skill imo.

[syzarian]

Great example. It demonstrates you don’t know how to teach the subject. Your Skittles example won’t help with explaining how to add ax + bx. To generalize the concept of combining like terms we need to refer to the distributive property.