> In math you can't often solve a more advanced problem such as Calculus problem without understanding the more foundational math such as algebra, fractions, etc.
Yep, this is the number one reason people think they aren’t suited for math. Everything is built on everything else, and if you missed anything you’re screwed. It takes a while to realise you are screwed, you can get by on rote for a surprising distance.
Ultimately, “there is no royal road”, but a good tutor will help you find those gaps and build out the missing bricks.
This does depend on the curriculum to some degree, and whether you’re just trying to grasp a concept firmly enough to move onto a more advanced concept or whether you’re trying to build a practical skill in solving problems. For instance, it’s entirely possible to understand higher level mathematics without having much skill at all in pencil-and-paper arithmetic. I know this because one of my best friends in college got straight A’s in upper level mathematics and EE classes but, due to his unusual background, only bothered learning arithmetic when he needed to prepare for the GRE.
I didn’t enjoy math as a child, and I used to be a lot more bitter about this when I first started to grasp what mathematics actually was. As a child, mathematics seemed like a small amount of “learn and understand a new abstract concept” (which I was pretty good at) bogged down with a huge amount of “okay now you have to solve a a bunch of problems based on that concept over and over again before we’ll trust you with another concept”. Eventually I figured out that mathematics itself really is the concepts, and that the concepts eventually build up to a level of complexity where it was increasingly challenging and fun to grasp them.
Maybe the reason it’s taught this way is because the vast majority of people aren’t mathematicians and aren’t really attracted to mathematics out of an abstract intellectual appreciation for the beauty of mathematical concepts; they just want to solve problems. And this is perfectly reasonable. But if I had it to do over again, I probably would have put more effort into mathematics and study more of it, at much higher levels, if I knew it would eventually get a lot more interesting.
And eventually things do start to branch out a bit. The standard K-12 curriculum up through calculus mostly builds up like a single tower where everything is built on everything else, but there are parts of mathematics where you can just sort of go in a different direction for awhile.
> Yep, this is the number one reason people think they aren’t suited for math. Everything is built on everything else, and if you missed anything you’re screwed. It takes a while to realise you are screwed, you can get by on rote for a surprising distance.
That's exactly what happened to me!
This is why I'm learning about differentiation yet struggling to factor simple fractions with a surd.
Yep, this is the number one reason people think they aren’t suited for math. Everything is built on everything else, and if you missed anything you’re screwed. It takes a while to realise you are screwed, you can get by on rote for a surprising distance.
Ultimately, “there is no royal road”, but a good tutor will help you find those gaps and build out the missing bricks.