Preview
Before class, skim the lesson and write down one question you want the class to answer.
Student resource
Study strategies for mathematics
The goal is not simply to spend more time studying. It is to notice what you understand, practice what you do not yet know, and adjust your approach using feedback.
Start here
- Identify the gap. Try a problem without notes and name the exact idea that stopped you.
- Repair it. Revisit one example or resource, then work a similar problem independently.
- Check later. Return to the idea after a delay, rather than deciding you know it after one successful attempt.
Each week
Use a study cycle
Attend & participate
Work through examples actively. Predict the next step before it is shown.
Review
Soon after class, rewrite the main idea in your own words and redo one example from memory.
Study & assess
Practice representative problems, then check what you can do independently and decide what needs another pass.
Study cycles and focused study sessions help turn studying into a repeatable habit. See the short guides to study cycles and focused study sessions.
Learn how you learn
Practice metacognition
Metacognition means thinking about how you think and learn. It helps you become a self-aware problem solver and take control of your learning. After each study session, ask: What did I understand? What evidence do I have? What will I do differently next time?
Metacognitive Study Strategies from the UNC Learning Center offers additional ideas.
Build fluency
Practice beyond first understanding
Overlearning means practicing a technique beyond the point where it first makes sense—until you can use it quickly, accurately, and without consulting notes or the textbook. This is especially useful when an exam gives limited time for each problem.
Set a timer and quiz yourself with homework, textbook, or exam-archive problems. Use the result to decide which technique needs more practice, not as a verdict on your ability.
Before and after exams
Practice under realistic conditions
Before
Choose a set of questions that matches the exam’s length and topics. Time yourself and use only the resources permitted on the exam.
After
Sort missed problems into conceptual gaps, process errors, and time-management issues. Relearn the idea, then solve a fresh problem without notes.
For more on deep versus shallow processing, watch the five-part How to get the most out of studying series. If an exam did not go as hoped, I Blew the Exam, Now What? offers a constructive next step. You may also find 14 Tips for Test Taking Success useful.
Get support early
Bring a specific attempt and a specific question to office hours, recitation, or tutoring. The Purdue Academic Success Center offers workshops, peer success coaching, and academic consultations. For a deeper introduction to study cycles and metacognitive learning, see Saundra Yancy McGuire’s Teach Yourself How to Learn; Chapter 5 is a practical place to start.