I went through engineering school, and 20 years of work (not as an engineer), before finding a calculus text that explained why the derivative of x^2 is 2x+C. Along with many practical applications of calculus.

That book was Calculus Made Simple, published in 1914. Thanks, Project Gutenberg!

Somewhere in middle school they give up on the “if you have two apples and buy two more apples you have four apples” or “if you have 3 pizzas cut into 8 slices each and your family eats 13 slices how many pizzas do you have left?” and they start trying to teach 11 year olds by making them memorize proofs and phrases like the transitive property of equality.

To a lot of high schools and colleges, the aesthetic of academia is much more important than students actually learning anything useful, so they teach math class with a chalkboard full of squiggles rather than any kind of practical approach.

From Algebra class on up, it’s taught as a rules following exercise. “Okay, now we do this, and then who knows what we do next?” And it is amazing how many of them are set up as trick questions, how often out of the infinite span of numbers there’s often one right answer and one wrong answer. “How many of you got five? Well you’re wrong, it’s negative 3.”

Meanwhile, I was learning how to fly. In flight school, you learn how to navigate by dead reckoning. I want to fly this course on the map, which is x distance and x degrees from true north as measured from the chart. Given a weather brief and the performance characteristics of the plane from the pilot’s operating handbook, calculate: true airspeed given indicated airspeed, altitude and temperature wind correction angle, given true course, true airspeed, wind direction and wind speed ground speed, given true course, true airspeed, wind direction and wind speed true heading given true course and wind correction angle magnetic heading given true heading and local magnetic variation time aloft given distance to travel and ground speed fuel consumed given time aloft and fuel consumption

The tool you’re taught to use to calculate all of this looks like this:

It’s basically a circular slide rule, that has a vector plotter on the back. The trigonometry is done by accurately drawing and measuring the triangle, the ratio problems (anything “per hour”) is done by rubbing a couple of logarithms together, and you’re on your own for the addition and subtraction. Ever used a slide rule? They don’t keep track of the decimal point for you. So you have to do these built-in sanity checks, like “Wait, no, the plane doesn’t even hold 70 gallons of gas, there’s no way I’ll burn that much in ten minutes.”

I learned how to do that before I took physics class, and surprised my physics teacher that I knew how to do “boat crossing a river” problems with a weird piece of cardboard. Later on, when I was teaching flight school, I taught that procedure to “It’s been 30 years since math class” boomers and “Trigonometry is next semester” teenagers. They all picked up on it without much problem, because “the wind is blowing you to the right” is a real thing they’ve felt in their own asses by now.

Part of it has been how it is/was taught. Math was always the subject I had to work harder on than any other. The problem is that I was never taught to really conceptualize the problems. Once I started taking physics and real world applications came into play, it all sort of clicked and got much easier.

Edit: Also, math is really all about relationships and conceptualizing interesting problems or ideas. If it had been presented to me that way, I think I would have been more adept at it earlier.

Studying mathematics is a difficult but also rewarding activity. This requires having a positive relationship with the effort. By analogy we could compare this to sport. To give up practicing mathematics because it is difficult is equivalent to giving up sport because it tires.

For those interested in the education of mathematics, I would recommend this book by mathematician David Bessis.

Mathematica: A Secret World of Intuition and… by David Bessis

https://www.youtube.com/watch?v=KJafasuk4NQ

Where in other subjects the knowledge you gain is related but not completely contingent on everything else you were taught, e.g. you don’t need to remember too many exact details about the Mayflower pilgrims to understand the American Civil War, math requires a solid throughline from the basic arithmetic, through algebra, geometry, and so on. You can’t really do anything with trigonometry if you didn’t understand algebra well. You can’t really do algebra if you didn’t understand arithmetic. You definitely can’t do calculus if you struggled with any of the previous areas.

So the problem is the continuity required, combined with the way most students learn simply not being thorough enough to completely internalize the intuition for each math concept they’re being exposed to. Ask a 9th grader about the differences between rational numbers and irrational numbers that they may have learned in 7th grade: you’ll probably get answers that are about right, but might start to get a little vague or confused. Thankfully I might be overstating the interconnectedness a bit, but I know I definitely had some hiccups in college related to how I had only learned some of the advanced concepts halfway in previous courses, which led to me just barely understanding the really abstract concepts I started to get into like Stokes’ Theorem and Greene’s Theorem at the end of Calc 3.

Disclaimer: I have always been good at math, and have asked myself the same question. This is what I came up with by asking others:

It heavily depends on how your brain works plus your teacher’s abilities.

1. Most stuff can be done by taking educated guesses, that’s just not possible in math/physics etc. There is only right or wrong, no in between, thus if you are good at creative thinking, it doesn’t help at all. Also, since one rule is based on other rules, you really need to get the first rule to get the next. This requires a ton of abstract thinking to get the depenencies. A lot of people are good at memorizing stuff, which can be done without understanding it.

2. For you to get and stay interested in a topic, it needs proper presentation. Lots of logical thinkers are not good at presenting stuff to people who’s brains work differently. They just try to eyplain things the way THEY understood it, which is why their presentations are simply boring to others.

I think it’s a topic that just doesn’t interests most people, especially children. Where I live, solving problems like 10 - x = 4, solve for x is taught to 10 year olds in grade 5. How many 10 year olds would think this is interesting?

In comparison, grade 5 science teaches cells are the building block of life, energy can exist in forms like electrical and light and can transform between them, and matter has states like solid, liquid, and gas. It’s stuff that ends up being naturally more interesting.

Personally equations with too much symbols make mw feel overwelmed

Personally, my problem was always that math concepts were never presented in a way that actually made sense in the “real world.”

I was taught that complex numbers were real numbers with imaginary parts that had something to do with the square root of -1. Yeah, I get it, but… why?

Fast forward a few decades and I’m writing code that processes a digitized waveform. Now it makes sense. Math isn’t hard when you have a frame of reference. Learning math concepts solely for the sake of learning them is very hard.

Science and math pedagogy is fucking trash world over and it only serves to raise students’ anxiety levels on the subject matters until they check out of them entirely and the only ones left are those who have somehow evaded the microtrauma imposed on them

Most people are fuckin’ stupid, when you really get down to brass tacks

Mathematicians are shitty communicators who like feeling special because they can understand their obscure language.

I’m a programmer and in this field there have been tons of books published, conference talks, and heated internet arguments about how to make your code as readable as possible: formatting, function length, naming of variables and functions, keeping number of cross references low, how to document intent, etc. Mathematicians do none of that - it’s all single-character names (preferably from the Greek alphabet to complicate it further) and they rarely communicate intent before throwing formulas at you. You can easily tell when a mathematician has written code because it’s typically hot garbage in terms of readability.

Maths by its nature is a bit abstract, but I think that the primary issue is that it is sequentially learned for the most part in primary and secondary education. If there is ever a point that a student is struggling with a concept and the teacher/parents don’t identify it in time, the student is then faced with not understanding new concepts afterwards, and may just be left behind.

This is starkly different to other fields a student will be presented, they generally will have multiple topics that are not strictly reliant on parts learned before, and that can be relatively easily co-developed in everyday life.

I can’t speak to most people but I have dyscalculia.

For me, a lot of it has to do with how it’s presented in schools

Pi, for example. One day my teachers just kind of dumped this magical 3.14… number on me without any real explanation. Just basically “use this number to do stuff with circles,” no real explanation on what pi actually is on anything, just “remember this”

Years later I found a gif of a circle sort of unraveling that showed how the circumference is π × the diameter of the circle

And sure, mathematically, the formula tells you that, but actually seeing that animated out made a hell of a lot more sense to me.

Now I got most of my basic math education before those gifs were so readily available, and smart boards were just becoming a thing when I was in high school, so it would have been a little hard to show that to a bunch of elementary or middle school students without having us huddle around a desktop.

But that’s something that could have been illustrated pretty well with a couple circles of different sizes (cardboard cut-outs, printed on paper, different jar lids, etc,) a piece of string, and a ruler.

And the same goes for a whole lot of different math things.