Mr. Miyagi taught young Daniel son karate via repetitive actions such as Sand the Floor, Paint the House, and of course, Wax on Wax Off. The idea behind this is to develop muscle memory that can be translated to karate moves.

This methodology is no different than Place Kickers in the NFL continuously practicing, Basketball players practicing free throws, and most importantly, those of us within stem learning mathematics and science.

In order to perform at the “show”, you need to practice those fundamentals repetitively. This means that the amount of homework normally assigned is not sufficient to guarantee success on an exam. You may be able to follow along with a given solution for a given problem, but can you replicate it with minimal effort? This only comes from practice. Luckily the vast majority of the problems within the Calculus series for engineers as well as Linear Algebra and Differential Equations, are very formulaic. Given problem statement X, perform operations, A, B, C, and D.

As professors, sure we’re intelligent. However, I say time and time again, a PhD is a measure of hard work and not a measure of intelligence, nor is it a measure of a good teacher. Academia respects, praises, and holds to the highest esteem, hard work and dedication towards their discipline. This is no different in the undergraduate realm. If you work hard, study hard, and practice, most everyone can be successful.

So practice. Go through the problems. Talk the process through. The process is more important than forgetting a minus sign, or accidentally forgetting that the the sine of 0, is 0. If you don’t know the plan of action, the process to follow, the directions that will lead to the answer, your screwed from the get go.

I like to use the analogy that the problem solving process (at least for the Calculus series) is very similar to traveling to a new place. Imagine you just moved from out of state to Phoenix and you have never been to your new apartment / house. The first time you may have to use google maps (your lectures from your instructors). The second time you head there, you know the general direction but need to perhaps reference which street to turn on to get into the neighborhood and which ones within (your review of your notes). On your 3rd and 4th attempt, you know the general vicinity but make small mistakes on missing a side street left or right (your homework). However, eventually you’ve made that trip so many times that you day dream whilst driving, and before you know it you got there without even realizing it. Hopefully, given the practice of math / science / engineering, this principle will hold true on your exams.