Thanks to Professors Eric Egge, Deanna Haunsperger, and Steven Kennedy for their advice on how to succeed as a Carleton calculus student, reflected in the content below. Also, view their handout: Succeeding in the College Mathematics Classroom.

Use your calculus course as an opportunity to establish strong study strategies that can positively impact all of your courses at Carleton.

Intelligence, including mathematical ability, is not fixed (e.g. Oakley, 2014)
Asking questions, practicing, and engaging with the material increases your ability to learn. The strategies outlined below are will help you become an efficient and effective math student.

Myth: You’re either good at math or you’re not.
Reality: Intelligence is dynamic and improves with engagement and practice. Being intentional about how you approach learning will help you be successful.

Keep up with the pace of class

Falling behind in a math course makes it nearly impossible to succeed, since the next concept builds upon the previous one. Consider doing the following to keep up with the pace of your class: 

Show up to class, and show up on time (or early!)

If you show up late and the class has already answered questions and started new content — you are behind!

Be fully present in class

Spend your mental energy on understanding the topics presented in class. Take notes, but don’t let your note-taking distract you from critically thinking about the content. If you have a gap in your notes, you can always revisit that topic with a friend or during office hours. It is more important to understand the content than jotting everything down.

  • Are you slow at taking notes? Take a picture instead. Spend class time understanding the content, and rewrite the notes from the picture after class for review.

Ask questions

Questions not only help you understand the material better, but are also a useful mechanism to provide feedback to the professor about how class is going. To that end:

  • Come with any unanswered questions or items that you found particularly challenging from your homework.
  • If you’re confused or stuck, asking questions is an excellent way to slow the class down and catch up. You are not alone, and if the class moves on without you, you’ll get further behind. If you’re not quite sure what to ask, try something low-stakes such as: “Can you show me an example of that?”

Study Actively

When learning to drive a car, we don’t just read about driving, or highlight the drivers ed book, or sit in a car looking at the wheel — these are very passive strategies. We learn using active strategies, in this case by driving. In a real car. On real streets. We have a teacher there to help and correct mistakes, and we learn from past mistakes. We have to experience the real thing over and over before we can take the test. It’s hard at first, but with determination and practice, we get better. What does that look like in math?

Here are some examples of active strategies for studying:

Read actively

Expect math readings to involve a lot back and forth: read a little, look at an example, look back at your notes, read it again, make a list of questions… and so on.

Do all example problems as you go

The reason your book includes so many examples is to give you a chance to practice. A particularly strong strategy is covering up the answer, and working through the answer. If you get stuck, uncover the solution little-by-little.

Make connections with previous and future course content

Ask yourself “how does this relate to what we’ve done already?” “How might this be presented on a quiz?”

Track spots where you have trouble

Find a way to keep track of problems or concepts that were particularly difficult for you (even if you figure it out). This could be making a notecard with the question, starring your homework, or keeping a list. In this way, you’ll have a record of the items you need to spend more time studying.

Spend time practicing

For each class period, spend at least 3.5 hours doing homework and studying. If you finish a homework set early, find ways to continue engaging with the material: do some extra problems, quiz yourself, work with a friend, etc.

Talk through problems in a study group

Give yourself enough time to study. Cramming is not as effective as engaging with the material over a longer period of time. There is a lot of cognitive science that backs this up. The more times you recall information, the more likely you are to remember it. Quiz yourself often to practice recalling information out of context.

Create a practice test with note cards (and trade with friends!)

For each homework session, write example problems on notecards without the solution and without the section heading (put the page number on the back in case you get stuck). In this way, you’ll have a set of out-of-context problems you can mix up and test yourself with before an exam. Can you figure out where to start? Can you recognize problems out of context? Trade with friends to get even more practice!

Double-check — does my answer make sense?

When finished with a problem, be sure to double-check the answer and the question. Did you answer what the question asked? Do the units make sense? If not, go back and try again (or ask someone where you went wrong)

Use wrong answers as a chance to get better

Why do we have tests and homework? To give ourselves feedback on what we’ve learned and what we still need to work on. If you get something wrong, be sure to find out why, and practice doing it right!

Use Resources Effectively

Many students rely solely on class notes and the textbook, but these are not the only resources available to you (nor are they effective on their own). Keep in mind that the top-performing students are the ones utilizing all of these resources. Incorporate the following resources strategically into your study plans:

Faculty office hours

If you have any questions about the material, go to office hours. Faculty love to see you and work with you (that’s why they became professors). If you’re nervous, bring a friend! You can even stop by just to say “hi”, so that when you do have a question, you’ve already done a first visit. (Plus, many of them have candy!)

The Math Skills Center

This is a great place to do homework individually or in a group. When you get stuck, there are other students, student workers, and Russ available to answer questions right away. Plus, if you’re working before or during office hours, your professor is just a hallway away.

Math tutors

The Math Skills Center also provides group and one-on-one tutoring (there is a sign-up sheet at the Math Skills Center). This can be a great resource to help answer questions and give you some extra practice working through problems.

Classmates

A study group can help you work through homework and you can quiz each other to get ready for a test.

Sleep

Sleep early, sleep long, sleep often. Every time you sleep, your brain consolidates your memories, moving information from short-term memory to long-term memory. In other words, a crucial part of your learning happens while you sleep. So if you sleep less, you learn less.

References and Resources