On the math side... I remember that one of my kids was in 5th grade, and I went to a PTA meeting. The teacher was explaining to the parents how they were teaching division. It was quite complicated, with a whole lot of book-keeping. Of course, I could see the theory behind it, so I raised my hands and said to the teacher, “Your method is utilizing synthetic division rather than specific base-10 arithmetic, but the kids don’t understand polynomials, nor the positional notation for them that is implied in numbers.”
He wasn’t a bad sort, and said, “Well, if your kid can do the arithmetic by some other method you teach him, that’s OK, too.” Which, of course, I had done.
The funny part was after the meeting when several befuddled parents came up to me and said, “I know this method is screwed up, but I couldn’t put my finger on the explanation as to why it was so bad. I’m so glad you spoke up.” Well, their arithmetic instruction was good, and they remembered; but their algebra instruction and retention wasn’t. And, they probably taught their kids the old-fashioned way on the side, too.
I saw an explanation of looksay reading once. The reasoning is that adults who read do not sound out each word, they see the word and say it and it therefore made no sense to teach kids phonics since they would not use it as adults. Same with numbers. Adults don’t memorize things and it is better to teach kids to reason about things than to teach them all these datapoints to memorize. Biological reality , though, is that in the first 7 to 10 years for all but the very few prodigies, there is not reason but there is a huge capacity to memorize. It is far better to fill up those empty databanks with data so that they have something to reason about when their minds are a bit more developed. I taught all my kids starting as soon as they had a couple of dozen words to memorize a whole string of things starting with the Pythagorean Theorum as a series of questions and answers. What is the P- Theorum? The sum of the (or ‘Some of the’ as it may come out) etc- Who said that? ans. Pythagoras. Who was P- ans. a Greek mathematician etc. through Euclid and then branching to Archimedes and on and on. It impressed hell out of the grandparents and amazingly, when each was introduced to Geometry at the appropriate time, there was no intimidation. It sounded familiar. It was a great help in getting started and was far less irritating than memorization of Chocolate Frosted Sugar Bombs commercials.