That's why calc is central. I wouldn't be surprised if it's the same in the US.
This means most people have no idea what the math they learn is used for, because they never reach a level where they have to use it.
So they leave school with the idea that math is annoying bullshit that they don't understand and can't use.
I think it would be better to stream math by ability much earlier. Make everyday math compulsory for everyone - interest rates and loans, basic stats, currency rates, areas/volumes, simple trig, maybe some slightly more advanced finance, perhaps touch on some calc ideas.
Only teach calc and scientific math to those with the talent and interest for it. Give everyone else a taste so they understand a little, but don't try and get them ready for a career they'll never go into.
Why most people don't understand the math they learned and what it is used for, I would argue has much more to do with how they are not taught to interpret what they see around them mathematically- granted that takes years of practice, but we do not care to teach this to children.
Now streamlining math is all well and good, but we may loose some of the greatest mathematical minds by doing so. Many famous mathematicians (Euler, Lagrange for example) were slated to be someone else- professionally that is. And it took other great mathematicians to notice them.
Yes. I agree generally--often even at relatively advanced levels.
The stats course I took in engineering grad school was so heavy on the math that I'm not sure I appreciated what the math was in service of. By contrast when I took a less math-heavy stats course later I much better appreciated the underlying principles.
But yeah, it's very easy to turn any of these math-related topics into: memorize the formula, plug the numbers, come up with a result.
Though stats/prob are perhaps more 'useful' in non-academic life. Imparting the notion of what probability actually is and how Bayes' rule fits into it requires a very gifted teacher with a fundamental grasp of the real mathematics and on top of that the ability to communicate it and link it to previously learned material aka algebra/ pre-calc. You can make it visual, but it would seem to require defining the concepts of sets, sampling, distributions etc.
The issue imo is that teachers tend not to teach the intuitions of math, rather they focus on the mechanics of it. As such, most students turn into machines calculating things as opposed to viewing math as a way to reason.