How to Study STEM Courses With Practice Problems

Why rereading does not work

Rereading notes feels productive because the material becomes familiar. Familiarity is not the same as being able to solve a problem you have not seen. Research on learning consistently finds that practice testing, trying to retrieve or apply what you learned, produces stronger and longer-lasting learning than rereading the same material.

In STEM courses this is especially true, because the exam asks you to do something, not to recognize something.

Start with worked examples, then fade them

When a topic is brand new, studying a worked example closely is efficient. Read it step by step and ask why each step happens. Then try a similar problem on your own, and look back at the example only when you are stuck. As the topic becomes familiar, drop the examples and solve from scratch.

Mix your practice

Textbook problem sets are usually grouped by section, so you always know which method to use. Exams mix topics, and choosing the method is often the hardest part. Once you have learned several topics, practice mixed sets where you have to decide what kind of problem you are looking at. It feels harder, and research suggests it leads to better exam performance.

Keep an error log

For every problem you get wrong, write one line: what the problem was, what you did, and what you should have done. Group the entries by type. A short list of repeated mistakes is the most valuable study guide you can have, because it is specific to you.

Space your practice

Come back to each topic a few days after learning it, then again a week or two later, instead of doing all of its problems at once. Short, spread-out practice sessions build memory that lasts until the final exam, not just the next quiz.

Simulate the exam

Before each exam, do at least one timed set of problems without notes. Treat it as information, not judgment: it tells you which topics you can do alone and which still need work.

A two-week plan before an exam

• Days 1 to 3: list every topic on the exam. Do a few problems from each without notes to find your weakest areas.
• Days 4 to 9: study the weakest topics first, with worked examples, then problems, then mixed sets. Update your error log daily.
• Days 10 to 12: timed practice exams or past exams under real conditions, with full review.
• Days 13 and 14: read your error log, redo the problems you missed, and sleep normally.

Common mistakes

• Looking at the solution too early. The struggle before the answer is where much of the learning happens.
• Doing only problems you can already solve. They feel good but teach little.
• Treating practice exams as a final check instead of a study tool you use early and often.
• Studying with highlighters. Highlighting feels active, but it rarely improves problem-solving.

Frequently asked questions

What is the best way to study for STEM exams?

Solve problems without looking at the answers, mix topics once you have learned them, keep an error log, and space your practice over days and weeks.

What is interleaving?

Interleaving means mixing different types of problems in one practice session instead of doing all of one type at once. It helps you learn to choose the right method, which exams require.

Do worked examples help?

Yes, especially for brand new topics. Study them closely, then switch to solving problems on your own as soon as you can.

How plue helps

plue turns your course material into lessons and fresh practice. Its adaptive practice starts with what you know, gives you new checks to move ahead or revisit an idea, and counts hints separately so you can see what you solved alone. Spaced recall brings topics back when they are due.