Sometimes I feel like a calculator

[5ymmetrica1]

Ok so the title is a bit of an over-kill, but seriously sometimes I feel like when I'm doing math my brain is like a calculator. (though no where near as efficient of course)

I'm able to work a solution based on what I'm given, but I'm just a number cruncher, and I don't seem to understand what the consequences of my equations really mean a lot of the time. You give me some numbers or whatever and I punch them in and give you the answer.
But the concept and underlying processes of what's occurring with the numbers or letters in the equation sometimes is not always visible to me, I just do what I know the rules are for what I'm trying to solve, as if you typed in a problem on a calculator.

I'm a numbers person, and I seem to be able to manipulate numbers and equations very quickly but I have a lot of trouble conceptualizing those numbers to a particular phenomena or situation. It hasn't been a hindrance to me yet in my education, as high school physics isn't particularly hard to get a grasp of, but I'm concerned about university where I'm sure I'll be asked to relate mathematics to real world situations rather then just a set of problems on a sheet of paper.

what I'd like to know is, is this a common thing amongst people who enjoy math and physics, to be better at either one or the other? (E.g. conceptualizing and analysing, equating and manipulating numbers ect)

 

[Simon Bridge]

It is very common for students to find themselves more confident with the numbers than they are with the applications ... courses try to instill in you a feeling for the real-world applications by giving you word-problems and practical exercises.

If you are very proficient with algebra and manipulating equations, then your best path is probably towards using algebra as a language to describe real-world events. Then you will start to see the connections.

 

[5ymmetrica1]

Hey simon thanks for the reply.

I'm not above average in my algebra skills really, I'm not doing higher level math then anyone else whos doing well in my 2 math classes, I just find that once I know the rules I'm pretty good at manipulating the numbers, and re-arranging things as they need to be, I've never found that the difficult part of math. I don't have any problem with understanding the rules and laws of math either, It's the abstract word problems that force you to think outside the box that I have the most trouble with.

I guess I wondered if it was something that you either have or don't have, or rather if as you say it is something that you learn through doing a lot of these kinds of problems that force you to use a simple theorem or equation in a much more difficult real-world application.

 

[Simon Bridge]

I guess I wondered if it was something that you either have or don't have, or rather if as you say it is something that you learn through doing a lot of these kinds of problems that force you to use a simple theorem or equation in a much more difficult real-world application.

It is something nobody starts out with but some people have a background that gives them more natural aptitude than others.

It is exactly like learning a language - you learn best by immersion.
It is hard at first but just keep on doing and watching what others do and you'll get it.
The language idea is key - the word problems are a matter of, initially, extracting the important information from a description and representing that information in math. Once you have that part, the rest often writes itself.