[goldenkek]

I agree. Most of mathematics is taught as calculations without motivation. If it was taught as the study of systems, and a toolbelt to understand the universe, more people would be passionate about it. All we can do is show the light to others.

[cttet]

Actually if you dig in the calculation techniques taught in primary school(Like multidigit addition/multiplication/ division), you would find some of them are actually quite clever ideas (O(log n) algorithms), but what almost all school do is to ask the student execute the algorithm like a computer, not how to come up with ideas like those...

[chestervonwinch]

> If it was taught as ... a toolbelt to understand the universe ...

While true, I think that this is still a bit abstract. Rather than "a toolbelt to understand the universe", I would say "a toolbelt to formally characterize problems in order to analyze and solve them".

Let me add in addition that in order to learn to use the fun tools in the toolbelt, one must first grasp the basic ones. This (in my limited experience teaching lower level math courses) is another obstacle in teaching math: (continuing with the tool analogy) it would be quite boring to spend 3 months studying screwdrivers, another 3 months on wrenches, etc. without applying these tools to any "fun" problems.