Study Tips for Math 51
Study tips developed by Math 51 instructors and Academic Coaches to help students succeed.
Read the textbook to establish a strong foundation
The Math 51 textbook was designed with specific features to help you navigate the information and determine what content to prioritize. Be sure to read the Introduction to the textbook and watch the videos on how to read the course textbook, as these two resources will help you refine your reading approach for this course and for future math courses as well.
As you read, make sure that you have something to write with (notebook, tablet, etc.) to help you actively engage with the material. When you encounter worked examples, try writing out solutions on your own as practice.
Though these strategies can help guide your reading, you may still find it challenging to understand all of the concepts presented when you first read a chapter. That’s okay! Similar to how you might write a first draft of a paper and then go back to revise, you can think about the pre-class reading as providing you with a baseline understanding that will be refined as you attend class, revisit the text after class, and practice solving problems.
Practice is key
While reading the textbook and attending class (both lecture and discussion section) are important components of Math 51, being able to solve problems yourself requires practice. Homework gives you the opportunity to apply concepts and check for gaps in your understanding. When you watch someone else solve a problem it may seem straightforward, but the only way to know for sure whether you’re able to solve the problem is to try it for yourself.
It’s important to keep in mind that practice problems will require you to stretch your thinking and apply concepts in new ways. Practicing math isn’t simply a matter of repeating a pattern or process you saw demonstrated in class. You may get stuck on particular problems, and that is expected. Solutions often take several steps, and the process is like exploring a maze - you may not be able to see the center of the maze, but it’s important to start somewhere and explore different options. If you’re not sure where to start, try to translate the problem from words to equations. Identify the general topic the problem is about and look up some examples on that topic. Grappling with challenging problems is where growth occurs!
Because solving problems isn’t always a straightforward process, be sure to have lots of scratch paper or digital note space available. Also, consider ways to reduce distractions so that you can fully focus on the task at hand. This might include closing open tabs on your computer, turning off your phone or placing it out of reach, and identifying quiet places where you can work.
Starting the homework early is a good idea, as it is less stressful than working right up to the deadline, and it also gives you an opportunity to go to office hours and ask questions. If possible, set aside some time to start working on the homework problems after the discussion section since the material will be fresh in your mind.
Finally, identify ways you can work with others as part of your learning. You might be used to working on math largely on your own, but working with others gives you the opportunity to explain your thinking, brainstorm, and ask questions. These active learning strategies are necessary for learning math at the college-level, and you should connect with your classmates and course staff for guidance and interactive problem-solving.
Check your understanding
If you’ve tried various approaches and still can’t solve a problem, try talking through it with someone else from the class or attend office hours. It can be helpful to explain to someone else what you did and why, and where you got stuck. Sometimes simply talking through your confusion can lead you to discover a different way forward, and it can also help someone else pinpoint gaps in your understanding. When you get a homework or exam problem wrong, use it as an opportunity to learn. Review the grading and instructor feedback, and compare your work with the posted solutions to see how you can improve your understanding.
For problems that you were able to solve correctly on your own, it’s still a good idea to read the solutions sets for homework and worksheets in detail. If a solution set uses a different method than you did or expresses the same method differently, try to understand it. Getting the correct answer isn’t sufficient if you’re uncertain about how you got there.
Finally, it’s important to have a strong baseline of fundamental math skills to build on as you progress through Math 51. Spending some time engaging with the Stanford PreCalculus Refresher Canvas course, and completing all prerequisite courses up to and including Math 21, can make it easier for you to draw upon your prior knowledge when you attend class and perform calculations on your homework and exams.
Use active study techniques when preparing for exams
Exams will test your understanding of concepts by including questions that you haven’t done in class or on homework assignments. Re-reading your notes or skimming through past homework assignments might give you a feeling of familiarity with the content, but that isn’t a good indicator of whether you’ll actually be able to apply those concepts in new contexts. Use your study time to practice and test your understanding.
Completing a practice exam without the solutions on hand can be a good way to self-assess what you know and which areas you may need to spend more time practicing. It’s also a good way to practice working under similar conditions to what you’ll experience when you take the real exam. Going back to worked examples in the book, practice problems, and homework solutions can provide more opportunities to practice and test yourself. Studying with others can also be effective if you use it as an opportunity to explain concepts to each other and talk through areas of confusion.
Ask for help
Asking for help may feel uncomfortable, but it’s an important part of learning. When you’re no longer able to do something on your own, it means that you have the opportunity to expand your knowledge and skills, and that’s a good thing! Asking for help shows that you are committed to learning and engaging with challenges. Being proactive about asking for help is especially important in math because the concepts will build on each other.
Your first resource for getting help with the course are office hours. This is a great space to ask questions or work through points of confusion with the instructors and TAs. You can ask questions about concepts, examples, homework problems, or class logistics. It can also be helpful hearing the instructor or TA answer other students’ questions. Office hours will be most useful to you if you’ve spent time working on problems ahead of time, as it will allow you to ask more specific questions and apply what you learn immediately.
You can also work with a tutor; the Center for Teaching and Learning (CTL) offers drop-in and appointment-based tutoring for Math 51, and the Stanford University Mathematics Organization (SUMO) also offers drop-in tutoring. Working with an Academic Coach can be helpful if you would like to talk about your approach to Math 51, including note-taking strategies, reading strategies, or study strategies.
Adopt a growth mindset
Math skills can be developed with instruction, practice, and persistence; being good at math is not an innate ability. If you find yourself thinking, “I’m just not a math person,” consider other skills that you’ve developed over time. How did you work through challenges? What resources did you use? Even if you experience setbacks in Math 51, it doesn’t mean that you can’t be successful going forward. Think about what you can learn from the challenges you encounter, and use those lessons to inform your approach going forward. Talk to instructors, TAs, tutors, and/or Academic Coaches–they want you to succeed and can help you overcome roadblocks.
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Study Tips for Math 51
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