I’ll second it about the teachers not being able to teach. I tutor middle school math. The kids are confused, the teachers are either math-illiterate or used to be engineers and cannot remember ever learning math; the math tutors are in high demand. The books are awful, too - seem to be written by drama majors not those who think math. I use the older texts whenever I can.
I think I take offense at that remark.... I’m an engineer who has a teaching certificate in middle / high school math.
Personally I think engineers make the best math teachers. They have application experience and can bring it alive with actual problems, and labs.
Some math teachers use the state guidelines and simply teach the test or teach the book - which works but doesn’t inspire.
Algebra is easy and I can prove it. There are two reasons for student troubles, one is bad teachers, and the other is mental blocks (the “math is hard” meme).
Story #1 (bad teaching), my friends kid was in town (from a supposedly very good school system). He is fairly good at math, but was absolutely cratering in one area in his algebra two. This was in graphing rational equations (basicaly stuff like (X-2)/(x^2 + 2x +1) kind of stuff. Granted, I had done nothing of the sort in over 25 years, so I thought about it for a few, and came up with a plan to show him. I first asked him how the teacher explained how to do it. He rattled off the most ridiculously overly complicated list of nonsense I have ever heard. I then show him...first solve both the numerator and the denominator for x...where the numerator is zero that is where it crosses the Y axis, where the denominator is zero, that is where it approaches infinity. Then on either side of zero and infinity determine whether the whole function is positive or negative, and draw accordingly. After one or two examples of this he looked at me and said “It’s this easy, really”, I said “yes, really”, he said “My teacher spent weeks and weeks unable to explain what you taught me in 5 minutes”...I made him do all of the problems, which he had no problem with...then to make sure he had it I created a few and had him do them the next day...then I instructed him to teach his buddies who were also having trouble when he got home. Having him teach it, would cement it for him. Needless to say, he aced it when he got home.
Story #2 (Mental Blocks), I used to tutor all levels of university math when I was in school for extra money. One of my students was a very very stereotypical blonde sorority girl who was absolutely failing college algebra and was completely desperate. For the first two weeks it was pure hell. I tried in every way to make her understand even the simplest concepts to no avail, sometimes she would get so frustrated, that tears would come to her eyes. From my perspective it seemed to me that she was willfully not understanding it, and I was getting very frustrated (but could not show my frustration). I was convinced she was so hung up on math being hard that even if she was understanding it, she refused to believe it because she knew that math was hard, therefore, even if she thinks she is understanding it, it can’t be true. There was some point at some time that after attempt number 1067 of rewording my explanation, that I could see the lights suddenly fire up in her eyes, and a virtual earthquake went through every one of her synapses simultaneously. She looked down at the book, then looked up at me, and said...”What? Is that it? Is it really that easy?”. With that one question, the years of mental blocks came tumbling down, and from then on all new material was easy for her (with just a little explanation)..she ended up with a B as her final grade.