I have never been much of an academic. In high school, all my friends were accelerated 1 year and allowed to test out of algebra 2; my scores were too low to allow me to skip it. Not wanting to be left behind, I resolved to take algebra II over summer.
That was a mistake.
That Summer I took algebra II with some laughably bad students at an inner city school. It was surreal. We would spend 4 hours a day in class, doing almost no real learning. I believe one kid was actively jerking off in the back of the room. One girl was pregnant and was taking life advice from another teen mother. By the end, we had covered maybe 3 out of 15 chapters. It was a complete failure. Somehow everyone who showed up passed. I later heard that Texas had so many "super seniors" clogging up the system that they created summer classes like this which were guaranteed passes; the goal was not education, the goal was to move people out of the system.
Like an idiot, I then took my "pass" in algebra II to my own school. I was happy, I could stay with my friends! Mathematically, things quickly fell apart. I realized that I was in over my head. The prospect of admitting that I couldn't hack it was even worse than my previous fear of being left behind (teen logic at its finest). For the next 3 years, rather than understand anything, I built elaborate workarounds to avoid exposing my ignorance. I didn't know how to actually solve most problems, I did however understand that my TI-83+ calculator could approximate the solution to most everything. With a little bit of flourish I could provide something that looked like I worked through a problem, despite the fact that the only thing I really had was a solution and an understanding of my calculator.
I graduated missing around 4 years of high school mathematics.
I feel like failing to understand some of the basic concepts in Algebra II substantially retarded my progress in mathematics. I lacked the basics that were necessary to move forward.
The plural of anecdote is not data. With that said, this video resonates with me. I like the idea of mathematics being a small graph of deeply connected nodes. Failing to understand one of the axiomatic/deeply-networked nodes can make understanding the interconnected nodes very difficult.
Contrast this to history with its much larger number of nodes. These nodes are interconnected, but not as dependent on each other. They might provide context or contrast relative to one another, but they are not required for understanding.
I though this was an interesting point.