A lot of incoming and lower division students experience a bit of a shock when they find that Berkeley math just does not suit them, even though they may have done really well in high school Calc or similarly advanced courses. The reason for this comes down to basically how college math classes want you to think. I actually was not a fan of mathematics in high school, but after taking Math 54 here I fell in love with the subject and began pursuing a pure math major. What I’ve noticed is that too many students try to utilize “plug-and-chug” methods in classes like Math 1B or 53, where they simply memorize equations for any possible problem type and then plug in values to solve problems on homework and exams. The problem with this approach to problem solving in college mathematics is that “real” math is not so much concerned with getting to an answer as it is about approaching problems for every possible unique angle. A lot of pure math is about proving characteristics of constructed structures and ideas, and there is very little actual answer finding. Of course there is applied mathematics which focuses on a lot of computation which is of course geared towards finding an actual answer, but even then the main focus of computational math is still considering a lot of interesting characteristics of systems and then representing behaviors in mathematical language in order to find “rules” that give desired answers, like gas laws or optimization algorithms.So how does knowing this help a student actually enjoy classes like Math 1B? Well personally I found it a bit liberating to not be as focused on finding answers. Once I moved from the problem solving format of “plug-and-chug” to actually thinking about the interesting points of given problems, I started to jot down interesting observations about problems or my methodology on homework and exams, and surprisingly I would actually get points for that!

Professors and GSIs always tell you to show your work on exams and problem sets to get partial credit, and I really started to understand why after I started doing this. Obviously the faculty of the math department have the job they do because they love the practice of math, so what they appreciate most from math students is real evidence of grappling with the problem is novel ways. I believe that if lower division students can slowly move away from “plug-and-chug” the will not only find their scores improving (and thus remove a great source of stress) but also actually thinking about problems will help them appreciate the theoretical and philosophical underpinnings of mathematics!