Why is understanding underlying concepts crucial for success in calculus?

[delphii367]

Hello, everyone.

I'm trying to earn a Bachelor's Degree in Computer Science, and my problem is that I have to learn college-level Calculus and Physics.

I managed to get through College Algebra and Trigonometry without too much trouble, and I'm taking Precalculus now. I'm taking all these classes at a community college, before I transfer to a four-year school.

I'm running into all kinds of problems with my Math classes, though. I feel like I'm essentially having to learn everything on my own and that I'm not getting much insight beyond what's written in the textbook by attending class.

So, I'm coming here in order to try and figure out a different perspective on Math. I feel like I need to be learning to see it as a series of underlying concepts rather than just a frustrating mental torture that involves a lot of memorization and practice, but I'm not getting there. This is especially unpleasant because I'm an abstract thinker and enjoy things like computers and science because I see all these patterns and connections, but I just don't understand Math in that way. That's probably why I never liked the subject, and what made me wait so long after High School to pursue the degree I wanted.

 

[axmls]

All of the technique's you're learning in algebra/trig/precalc really don't come together until you learn calculus. Then you finally see the reason for the manipulations you learned. You see the reason you need to factor polynomials and understand logarithms and all that.

So just keep it up, and I've seen that it often starts clicking with people when they get into calculus (provided you have the necessary drive to understand it well).

 

[delphii367]

So, if what you're saying is true, then it sounds a lot like how I stumbled blindly through grade school Math, struggling to memorize multiplication tables... and then when they taught me Algebra and Geometry, I suddenly got a lot better at Math, because Algebra and Geometry were the tools I needed in order to understand Arithmetic.

I was basically the kind of student who was awful at memorizing multiplication tables or understanding place value, but I was good at doing weird things that confused my teachers... like forgetting the answer to 3 x 7, and choosing instead to pretend like I was multiplying 3 x 5, and then adding the result of 3 x 2 to that in order to get a result equivalent to 3 x 7. I was never able to explain what I was doing, so it caused issues for me. I'm good at seeing patterns and predicting results, but bad with memorization and keeping track of details. A lot of my teachers told me the I have exactly the opposite problem with Math that most of their students have, and that my strengths and weaknesses are "backwards" in a puzzling way that they can't quite put their finger on.

All I know is that before Algebra, Math was completely unmanageable for me, and I struggled to get Cs... and after Algebra, I was able to get As and Bs consistently if I applied myself. It went from "This doesn't make any sense and I'll never be able to do this," to "I can do this if I have to, but it's very messy."

 

[axmls]

Yes, that's correct. For me, at least. Why do you have to know how to find the zeroes of polynomials? Because the zeroes of the derivative tell you where the maximum and minimum parts of a graph are, which is useful in optimization, physics, etc. Why do you need to know trig identities? Because many problems in calculus are vastly simplified my applying the proper identity to the terms.

There's a reason for everything you learn leading up to calculus, and you'll use all of it.