# 5 Mistakes Students Make While Learning Calculus

While calculus is not known for its simplicity, students can destroy their odds of success with some very simple mistakes on top of the expected mathematical ones. Here are several things you shouldn't do if you want to succeed in your calculus course.

## 1. Skipping class

Mathematics can be learned by keeping up with the textbook, but the brain may store information more effectively if it is received through more than one sense. If you combine the visual learning of reading the textbook with the auditory learning of the lecture, you will likely retain more. Given the increased availability of distractions available to students today, it takes great discipline to stay offline, turn off the phone, and individually review the material that was learned in class.

## 2. Avoiding asking questions

Don't be self-conscious: if a question has occurred to you, it is likely that others in the class are wondering the same thing. Seeking clarity on a concept is a public service that can also enhance your understanding. Speak up.

## 3. Copying classmates' work

Mathematics cannot be learned through simply copying the image of numbers, symbols, and functions you see on the page. Students learn through grappling with homework problems, not by copying the work of others. Take the time to complete the assigned work and you'll likely have a better understanding of the lesson.

## 4. Coming to class unprepared

You will follow the lecture more easily if you read the assigned material before class. Reading the material and then sleeping on it may make the professor's presentation much more clear. It's amazing how an instructor's performance improves when the students are prepared and well-rested.

## 5. Make mathematical errors

Common student mistakes in calculus include improper use of substitution, improper handling of indefinite integrals, matrix algebra issues, wrong linearity of determinant, inappropriate linearity, inappropriate commutativity of composition, and inappropriate cancellations. Also, watch out for unclear brackets, unit confusion, inadvertently dividing by zero, square root errors, and sloppiness about signs, particularly in connection to the chain rule. "The SAT pitfall" describes students' tendency to apply facts that are true for integers to all real numbers. The inversion formula for polar coordinates must always be complete. Be particularly careful with signs when the chain rule is relevant.