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> Why can't we just provide a simple real life example first and then go on explaining the details?

That's a very good approach, which I try to follow in all my writings. Basically, I imagine a reader that is generally uninterested in the material, so the first thing to do is to "pitch" the mathematical concept using a simple example, or just say why the concept is useful. In the remainder of the lesson, I assume the reader might lose interest and stop reading at any point, so this is why I put the most valuable content first (definitions and formulas), followed by explanations, and finally a general discussion about how the material relates to other concepts.

> I was one of the best in that class, but when I asked what we need this stuff for the other people in the class looked at me and said the following: "if you ask this question you're in the wrong class"

I am always so disappointed when I hear people express this. Being able to place an effort in a broader context is so helpful in being able to approach the work well. A few teachers in the Literature department in high school had the same attitude and it was incredibly demoralizing and left me kinda directionless in their classes. I wish things like https://youtube.com/watch?v=suf0Jdt2Hpo had existed back then to give me some idea of what useful and interesting literary analysis looked like and could do.

I think there are teachers for whom rote repetition is teaching.

I used to know a math lecturer, and his attitude was very much that it was his job to throw proofs at his students, and the bright ones would put the rest together for themselves.

He wasn't even remotely interested in the less bright ones, and certainly not in presenting the material in a way that made it easier for them to follow.

Digital has real potential here, because you can build animations and virtual math labs to explore concepts and give them a context, and suddenly math becomes practical and not just an excuse for wrangling abstract symbols for the sake of it.

> Why can't we just provide a simple real life example first and then go on explaining the details? This. People learn differently, in my case, if I can't get the 'Why' first, I'm not that excited to learn it. I guess making 'simple' real life examples in many cases is hard. I also tend to learn things much better if they came from a real problem/need I have. There was a good discussion about a 'project based university' here: https://news.ycombinator.com/item?id=10989341

I actually think you're in the norm. The "why" helps create a belief; a belief is something that ignites action. Without it, someone's belief as to why they should learn [X] is too often defined as "to get a good grade."

High school math was awful at this in the US. I went through a year of calculus and never knew what the heck it was for.

When I asked in high school what math was for to some professors, they said it was more to 'improve your thinking' than to use it in 'real life'. Now, a math course designed to be progressively easy to grasp, personalized when needed, entertaining and showing lots of examples from real life (e.g. relating algebra with 3d and video games) requires a very talented educator; teaching well is really hard and usually there's not enough time or resources to do it. That's why I think one of the most important skills to develop is to learn how to learn.

I think it very much depends on the teacher.

It's not difficult to explain the first few topics on calculus in terms of distance, speed and acceleration. Other examples I remember were washing lines (a catenary), the path traced by a stream train's wheels and rocketry.

My teacher in England always had a real world example, but students with the other teacher didn't.

Yup. I don't recall actually learning anything in math class from 7th grade through my senior year.

I learned trig and geometry from my shop and programming courses... Trying to do graphics in QBasic and determine lengths and angles in carpentry gives concrete examples. It's not as though most math sprang spontaneously from pure thought-stuff - at some point, architects, inventors, astronomers and others in concrete endeavors discovered these rules.

Yeah, teaching the basics of an abstract concept without first explaining how it fits into the bigger picture is IMO not the best way to motivate some people. I'm also a person who wants to understand why it's important instead of just trusting someone that it'll be useful "later".

It'd be cool if, once you start your major, there was basically an overview class explaining why each of your courses is important and what concepts (at a high level) you should be grokking with each course and semester; basically some context to frame your learnings.

I took an automata class where the professor talked into the chalkboard and refused to explain why we were required to learn any of the material. It wasn't until later in the compilers course that we had a teacher who actually took the time to explain how all that mysterious theory actually had a place in the real world. So many light bulbs went off in my head during that class.

I had a similar experience from a different perspective -- I took a course on Theory of Computing, which was 50/50 gate-level CPU design and mathematical work on computability, automata and so on. I found this interesting as an intellectual exercise and to get a grasp on what is computable and what isn't, but then the next semester it proved super useful in the compiler design course.

I am also much more happy with an answer along the lines of "it has no practical use currently but is interesting because of...." than no answer at all.

> Why can't we just provide a simple real life example first and then go on explaining the details?

But sometimes there is no real life example. Fundamentally, math is abstract. Yes, mercifully, its models often have analogues in nature, making its purpose utilitarian and intuitive. But sometimes no analogue exists. As in much of modern physics, in math, often you have only abstraction.

I think that's why math is difficult to learn. Without compelling illustrations based in the physical world the student must follow the concepts and proofs using the rigor of math's legal transformations, fortified only by the faith that these formalisms will sustain truth. But too often the practitioner must remain oblivious to the utility and implications of both the end and the means.

I even asked at university (statistics course) regarding to some specific test "what do I need this for", the professor looked at me and said "you'll never need this". I packed my things and left (and finished the course about 3 years later with a different professor).