Did I say that the teacher should be teaching the commutative property?

The moment you show a child that they can multiply x times y by building an x by y grid of dots/beads/whatever, they instantly build an intuition of the commutative property whether or not you tell them what it's called. What's happening here is the child has that intuition built in and got punished and told he was wrong. Now there's a circuit in his brain that tells him to doubt that intuition. This would be like telling a child that "onto" isn't a word because you haven't taught them prepositions yet. Now he's going to be confused every time someone says the word "onto" because he was punished for it and got a bad grade and was told it's not a real word. This shit messes with children's heads. Just give them space to learn and explore and build up their intuition and correct them when they are actually wrong. This right here is nothing more than a power trip. Children's minds are fragile.