Your suggestions are the real problem with teaching mathematics; do people learn science only to learn practical stuff? Read literature only to gain literacy skills? No! That is not how classes are taught.
Mathematics is seen only as a tool, but if it was taught as an art, or even a science, people wouldn't hate it!
See (A Mathematician’s Lament by Paul Lockhart) http://www.maa.org/external_archive/devlin/LockhartsLament.p...
"In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soulcrushing ideas that constitute contemporary mathematics education."
> Rigor
My trigger word!!! Rigor, the most hatred word in all of education philosophy!!!!
> Three Dirty Words are Killing Education by Deb Jensen
RIGOR VS. RELEVANCE The second problem term is rigor (also known as “high” standards). The term is associated particularly with college readiness. The term might call up images of learned individuals from the 1800s, but today's rigor is imposed artificially — it requires only more algebra or more credits. While the mind needs information to build beyond the concrete to the abstract, much of the random information is actually screened out.
http://journals.sagepub.com/doi/full/10.1177/003172171009200...
These topics are much more fascinating than mere calculus could ever be, but this requires people to stop viewing mathematics solely as a tool, and start viewing it as a way to reason about the world.
https://betterexplained.com/articles/a-gentle-introduction-t...
A note on rigor (for the math geeks) I can feel the math pedants firing up their keyboards. Just a few words on “rigor”.
Did you know we don’t learn calculus the way Newton and Leibniz discovered it? They used intuitive ideas of “fluxions” and “infinitesimals” which were replaced with limits because “Sure, it works in practice. But does it work in theory?”.
We’ve created complex mechanical constructs to “rigorously” prove calculus, but have lost our intuition in the process.
We’re looking at the sweetness of sugar from the level of brain-chemistry, instead of recognizing it as Nature’s way of saying “This has lots of energy. Eat it.”
I agree. I did some research on teaching the concept of instantaneous speed to 5th graders. Building on their intuitive understanding—from a young age on we are continuously confronted with dynamic systems such as (loco)motion, weather, computer games, cooking, and so on—and connecting to their understanding of a constant speed, I devised a learning trajectory to explore and deepen their understanding of instantaneous speed more mathematically, including quantifying it.
If anyone is interested, you can read more about it here: https://heerdebeer.org/DR/thesis/ch5.html
That's moderately complex math, and goal oriented.
What ends up happening is the people good at math prey on those who are bad at it. You tell a kid "you learn this so people can't take what's yours" and most of them will pay attention.
Calculus can be explained in terms of algebra, sure, but it can also be explained with visualizations and with experiments (and/or you can learn the algebra at the same time).
