# At what stage during an undergrad degree should a student move beyond just 'doing' the equations?

I ask "At what stage during an undergrad degree should a student move beyond just 'doing' the equations?" because I am taking some Year 1 maths papers in 2015. I am worried I won't be able to actually see the deeper meaning and reasoning behind the equations. I may be able to plug numbers into the formula and remember the procedures to follow, but I feel this is different to really knowing what is going on and why.

I asked a 3rd year student and he said during years 1 and 2 that I shouldn't get too worried about the deeper meaning, rather the teachers/lecturers are wanting to see that I can do the work and arrive at the correct answer.

Is anyone able to shed some light on this and how they see it, or share their experiences?

I am not fresh out of high school, rather an adult trying to get an education later in life.

thanks

• This is a very tricky subject and depends very much on what you mean by "just 'doing' the equations", e.g. some mathematicians never go beyond manipulating symbols. If you are struggling with geometrical interpretation of a derivative then I would be concerned; on the other hand, in logic or universal algebra one might not have any intuitions for a long time. – dtldarek Oct 30 '14 at 10:53
• @dtldarek A geometric interpretation of a derivative is something I'd never thought of. My experience with derivatives so far has been along the lines of "here is x^2, in this case apply the power rule, so it is now 2x". So while I may have come up with the answer, I start to wonder what does it really mean? how do you prove that ? and what does it look like to look at ? I guess now it should include what is its geometric representation. My problem is as I have just come across derivatives I don't understand the material that proves why it works (it seems like a whole new topic) – user3754366 Oct 31 '14 at 21:40

## 1 Answer

My experience has been that this can happen as early as you like.

I teach College Algebra, Calculus, and Differential Equations at a community college. In all of these courses, it is possible to see connections and ask "why" questions. I truly believe that if you start asking why and finding out what is going on, it is significantly easier to learn and retain the material.

Even as early as the identity $x^0 = 1$, it is very productive to ask why!

Your professors will almost certainly have office hours available. Appearing in their office to ask these questions is a very good idea.