When taking a problem solving course, students often feel like they are spending too much time doing problems. Since these courses typically assign HW, it’s tempting to just go to lecture and do problems but not much else. It’s important to not only do practice problems, but to understand the concepts problems are based-on. If you fully understand the lecture/book material before approaching problems, you will gain a better understanding of how concepts fit together and will experience fewer roadblocks when doing problems later. This, in the end, will save you time as you will not need to waste time memorizing steps or practicing more than you need to.
Success in problem solving classes requires an understanding of the material before you try the HW. Spending time learning concepts and understanding how they relate to each other will make doing the HW faster and easier.
Do you spend too much time doing HW problems?
Do you have trouble understanding problems?
Do you feel your grades don't reflect your time and effort?
Follow the Problem Solving Study Cycle below to strengthen your problem solving strategies, improve your grades, and use your time efficiently. Start at the 1st gear and make your way to the final gear, "spinning" each gear as each step is completed. One gear cannot stop without also stopping the others. If a step is skipped or not completed fully, the problem solving cycle cannot continue "turning" and the learning process stops. Take your time working through each step completely.
When get a first look at material either in lecture or through a textbook, you’re familiarizing yourself with a new idea. The first step of problem solving is to identify a new concept you’re learning and begin thinking about its properties. The goal of this step is to get a broad understanding of the new material.
Ask yourself: What are we learning? How can I define it? Do I have a general understanding of what it is? Where can I go to learn more? (i.e. textbook, YouTube, Professor’s office hours, classmate, etc.)
Only move on to this step once you feel confident that you have a good grasp of the material you’re learning. For example, if you want to tackle stoichiometry problems, make sure you first understand what atoms, moles, atomic mass, and limiting reagents are and how that knowledge may help you do problems. The goal of this step is to begin to apply your knowledge to HW or other practice problems.
Ask yourself: What practice problems are available to me?What concepts do I need to know to answer each question? Do I know the concepts well enough to answer confidently? If I get stuck, what tools can I use to help me? Do I understand how/why I got unstuck?
Assess each problem that you solve. Was is multi-stepped, single stepped, challenging for you or simple? Think about how the problem could be changed and how it would affect your solving process. Compare it to other problems that you did and think about how they all might relate to each other.
Ask yourself: Are there other ways the problem could be solved? What are the differences and similarities between this problem and others? Can the problem be modified to become more challenging? What questions related to this problem might the professor ask on an exam?
In order to truly understand a new idea and be able to apply it confidently, it’s helpful to look at in from all different directions. Make connections to prior material you’ve learned and begin thinking about how the new material may be applied to HW problems and/or real life scenarios.
Ask yourself: How can I develop a better understanding of this concept? How does the book present the concept vs. lecture? What are some ways this concept could be applied? How is new material related to the material I’ve learned in the past?
Scrutinize the problem you are doing. Think about how you solved the problem and why you solve it the way you did. Write out an explanation for each step. The goal is to be able to interpret the problem and explain your process of solving it.
Ask yourself: What concepts, formulas or rules did I apply when answering this question? Why did I use them? What were the steps that I did? Why did I do each step? Could I teach it to someone else?