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How can I tackle problem sets?

Various math equations and diagrams overlappingProblems are a critical part of STEM studying and an opportunity to apply important concepts presented in lecture.  As mentioned in Reviewing and Studying, don’t jump to the answer. Take the time to work through the entire process of the problem.  Use the following techniques to take full advantage of homework, course provided questions, and problem sets.



Before Attempting a Problem

Ask yourself three questions:

1. What are the important words in the prompt?
  • It could be a disciplinary word. It could also be something simple like “most” or “least.”
  • Highlight or underline these words to keep them in focus.
  • If you aren’t sure what the term(s) mean, take a few moments to look them up.

2. What are the concepts behind the question/problem?
  • Jot the key concepts down. Doing this increases your ability to analyze question prompts and builds processing fluency.

3. Do you know the concepts well enough to attempt the problem?
  • If yes, you’re ready to start.
  • If no, take some time to review your notes so that you can use your problems to assess your understanding of key concepts.
  • Don’t look at the solution before starting. Treat your homework and practice problems like exam problems and start with a blank space.

Color-Coding Strategy

Having a color-coding strategy when solving problems helps you build awareness of how you process information and what steps you may need to take to improve.

Color 1

Red, orange, green, and blue squiggles meet to create a pencil

Use your first color or pencil to try doing the problem from scratch. This color represents your “how far can I get without looking anything up” tool.


Color 2

Use your second color as your “I could solve the problem on my own, but only after looking at my resources” tool.

Did you solve the problem completely but get the incorrect answer? Did you get partway but then get stuck? Or, even though you feel confident in your conceptual knowledge, were you unsure how to start?

  • Don’t start by looking at the solution. Look through notes or your textbook to find a similar problem.
  • If you can’t find one, then compare your solved problem with the solution.
  • Use your second color to annotate what went wrong.
  • If you got stuck but had to look at the solution or a similar problem to figure out the next steps, use your second color to solve the problem the rest of the way.
  • Don’t give up! Put it aside for a while and maybe try a different problem. Or sleep on it and try it again in the morning. Sometimes coming back to a problem after a bit of time can help jog your memory. Your brain can process challenging problems in the background and sometimes when you look at it again, things will click into place.

Color 3

Your third color represents your “this problem was a challenge that I solved with the help of a peer/instructor” tool.

If you are still not sure about the steps in a problem or why your answer isn’t correct, ask someone!

Go to office hours, a friend, a study group or a tutor and work through the problem with them. Use a third color to make a note of what went wrong, what was missed, and why.

Note: If your practice problems are mostly in your second or third color, then it might be an indication that you need to spend more time really making sure your conceptual knowledge is solid!


How to Use Textbook Questions

Questions presented in your textbook are a great tool for early problem solving and later to test yourself as you prepare for an assessment.icon textbook

Embedded Questions
  • Do not skip the embedded chapter questions you stumble upon as you are reading over the chapter—these are perfect starting points to learn how the concept can be applied. Many textbooks offer detailed explanations for these problems.

End of Chapter Questions
  • When you are feeling more confident with the material, move to the end of the chapter questions to check how you can work through the material. Avoid referring to provided answers to assess if you really understand the topics from the chapter.  Use the color-coded technique to see the individual parts to the solving process.
  • The textbook questions can be a great resource for a practice exam. Copy a few questions and mix them up.  With main concepts out of the normal chapter order, you will work on recall of the material and forming connections between major topics.  Simulate an exam by timing yourself to make sure you can work through the problems in the right amount of time.

Working Through Multiple Choice Questions

Lined paper with the word Questions and circled letters as answers to multiple choice questionsDifferent forms of multiple-choice exams can be popular with STEM disciplines.  Students often struggle with the option of more than one true answer.   Here are some steps to practice for multiple-choice tests

Gather the information
  • Read over the question first and cover up all the answers. Take time to sort through the provided information. The question is probably full of details and you may not instinctively understand all of the material.
  • Carefully move through the words and highlight key terms.
  • Write or draw concepts and ideas to the side of the problem if possible.
  • Is the information presented in a slightly different form than you have seen before?  Can you relate it back to a lecture topic?
  • Try to form a clear image in your head of the presented information.

Focus on the prompt
  • Read the prompt and think about what it is asking. Do you understand the terms in the actual question?  Can you develop an answer in your own words?

Develop a possible answer
  • Think about an answer and fill in any drawings or notes on your paper.
  • Take note of any possible explanations. Do not always rely on memory, as it is easy to start talking yourself out of these ideas while you read the possible answer choices.

Review your choices
  • Carefully go through each answer choice to see if it fits with your explanation. Does it make sense and is it true compared to your notes?

After completing problem sets, ask yourself if you have mastered the concepts. If not, complete additional problems. Remember that on an exam, you have to demonstrate mastery.  Use this handout from Biology 201 for an example of this method.

Focus on Faculty
Model the different types of solutions that are appropriate in your discipline. Consider offering examples of exceptional, acceptable, and unacceptable responses to the same question and allow students to “grade” them early in the semester. Students will better understand your expectations and practice problems accordingly.