Why don't we use the math we learn in school?

I can remember failing math class hard throughout my entire academic career. I never passed a math class past primary school, and ended up dropping out of high school. The concepts simply never made sense to me, and as they were presented were just meaningless rote exercises of memorization. Math was something I had completely written off as ever being able to understand.

Then I took calculus and trig classes in college. Since I was also learning graphics programming at the time, I was able to actually make sense of math with a real world connection. Playing with little graph equations on shadertoy.com made me realize graphics was all just math. Everything immediately clicked. I was able to intuitively visualize the trig functions and graph equations and do transformations of them because I could picture what the resulting image would look like. Ultimately the problem for students I think is just creating this connection to reality.

My school rarely ever directed mathematics instruction in relation to another skill or problem. Sure math might be used in industrial arts, or in home economics, but the instruction phase of the math is always 100% abstract. If people knew all the interesting things you can do with math they would be more likely to use math more often and remember what they learned. This was certainly the case for me and may have been the only thing that made me even care about math at all. I am referring to only one math class I took in high school which did this, and that was geometry. I loved my geometry teacher. He was the only math teacher I ever found likable.

I loved the geometry class because it helped me a lot when thinking of practical considerations to 3D graphic arts I was creating on Amiga computers at the time not to mention the value of the discussion of area and volume. Did you know Pythagoras was a kind of cult leader?

Geometry wasn't just abstract, it was practical. How much carpet do I need for a room? How much water will fit in this cylinder? If I have a disc that has to be one square foot, what would the diameter be?

I had some enthusiasm for algebra one level math for solving an unknown variable using what is already known. I didn't learn the value in this at school. My dad was an electronic technician (Worked at Argonne Labs) and I was interested in what he did there. He taught me all there is to know about ohms law, finding resistance, conductivity, current voltage, using simple procedures. We did parallel circuits, tank circuits, ac theory. In less than a years time he gave me a complete 2 year associates degree understanding of dc and ac circuits.

Most of us found our math teachers some of the most arrogant people in the school. They demanded that we show our work and show it going down the way they personally approached solving problems. If the result was correct but if they didn't like your preferred procedure they would lower your scores. They never could offer a sound reason for their demands. Perhaps they did have a sound reason. They just didn't bother to sell us on it.

I suppose it isn't right of me to condemn all math teachers this way as my experience is kind of limited. This is just what I felt about it while being a student in high school and middle school 30 years ago.

It would be incredible if trigonometry classes had a lab component where students work on a 2D game, such as tower defense.

I ended up taking a fun programming elective in college where my team did exactly that -- we created a 2D game. That experience made me appreciate trigonometry more than my high school teachers and Khan Academy ever did.

Math is incredibly useful; probably everyone here knows that. But it's actually fine that most people don't use it.

What we really need is for every student to realize why math is useful -- so that if they want to, they can go learn it so that they can make some kind of technological contribution to the world. The fact is, you need to be good at math to make some new fundamental breakthroughs in technology. Those breakthroughs benefit everyone, even those who don't know any math at all. But you won't really get why that's the case until you know enough about sines and cosines to make sense of modern technological development.

The real issue is that we just teach the math, hoping that students will understand on their own that it's fundamental.

What we should do instead is try to instill that sense of wonder about the world that inspires people to study math. We don't need every person to know calculus, we just need everyone to understand why calculus is useful -- then they can be inspired to go further. Educators say that they're trying to do this, but I'm sorry "how many meters of fence does Farmer Bob need to keep the sheep inside the pen" is not inspiration -- it's drivel, no better than "find the perimeter given a=5, b=6."

If every person understood why math is so useful, we would have many more people who are motivated to work on improving the state of things.

I just did some regressions to model sprinkler head flow rates for variable pressure and spray angle.