My friends kid was up from Texas (where he is actually in a very good school). She told me he was having some trouble in his algebra 2 class (mostly in graphing rational functions stuff like (X^2 - x + 6)/(X^2 -4)), and asked if I could help. Though I use fairly high level math all the time, I hadn’t done that particular kind of thing since I was his age 28 years ago. I thought about it for a while, and formulated a plan in my head. The next day, as we got started, I asked him how his teacher explained how to do it. I was entertained with the most complicated explanation I had ever seen. I proceeded to show him the simple steps I had formulated in my head the night before, and one hour later he had fully got it. He was amazed that in one hour I made him fully understand with simple concise rules what his teacher was unable to explain in 3 weeks.
oops, X^2 -4 is irrational, meant X^2 + 4, lol
I tutored a sophmore in high school recently in mathematics, chemistry and cellular biology. I was utterly appalled at how convoluted the teacher's procedural explanations were in math, and how crazily the subject matter bounced around - yet demanded ridiculous levels of detail - in chemistry and cellular biology. There was simply no way for the student to grasp functional relationships, because they seemed to be deliberately destroyed by the curriculum organization, which demanded rote memorization of thousands of apparently disconnected facts.
It was so extreme, it was evil - teaching, in order to prevent comprehension. ALL of the students had private tutors (no surprise). And this was at a highly accredited high school in a wealthy area. It's just madness.
When I started college I took all my math classes via ‘math lab’, no teacher unless needed. All the books are simple, get it done, every step spelled out in examples. I kept them and have used them over and over for my daughter and now her daughter to help them with math. It is funny how quickly the light bulb goes off using the examples from the book.
Old saying: Them that can, do. Them that can't, teach.