Making the Most of Problem Sets

We know that problem sets are the bread and butter of technical courses because professors of technical courses use problems to evaluate your knowledge of a concept or an idea. They test how well you know the idea by seeing how well you can apply it through a problem and so when you get problem sets for homework, you're not just getting homework, you're getting a tool that you can use to evaluate your knowledge of the material in the course and you're getting a powerful audit for how you might perform on an exam in the class.

The problem is that a lot of students think about problem sets as busy work, as things that need to be completed and submitted for evaluation, things that need to be checked off of a checklist. Instead, they should be thinking about problem set as a powerful tool to learn the material that's being covered in the lecture and as an opportunity to practice their skills doing the kinds of things they'll be asked to do on a midterm or a final exam. So problem sets are a huge opportunity and rather than miss that opportunity, we wanna seize that opportunity to increase our comprehension and retention of the material that's being taught in lecture and to achieve our goals in the course.

Here I'm going to talk a little bit about how to make the most of the problem sets that you're given in your technical courses to turn them into a real tool to bolster your studying. The first thing I would recommend is that you pre-read your problem sets. What does that mean? Well it means that before you sit down to actually complete your problem set, you take a few minutes to preview that problem set, taking a look at what kinds of problems you're going to be asked to solve and trying to understand where they fit in terms of the textbook material and the lecture material that you've either received or will receive. By looking at this, you not only get a sense of where the course is headed and you not only get a sense of what kinds of things you're going to be asked to learn, but it's also a really cool opportunity to try to determine what parts of the problem already seem familiar to you and what parts of the problem seem foreign and new.

The parts that seem new are the parts that you have yet to learn and so it's important to try to determine between these things because in general, you already know quite a bit of what you need to know to solve the problem. So again, pre-read the problem set. Not only will you get a sense of where you're headed in the class and not only will you get a sense of what things you already do and don't know, it also means that when it's time to do the problem set, you're warm and you're ready. Then you actually go through and do the problems. You can do these in isolation, you can do them with a group, or you can do both.

But once you've actually done the problems, you're going to come up with some places where you couldn't actually complete the problem or places where you completed the problem and you got a wrong answer. These are what I like to call stumbling blocks, when we think about problem sets, places where the student's progress is impeded by a lack of understanding and it's really really tempting, especially when you're up against a deadline to see that you got a wrong answer, look up the correct answer in the back of the book, say to yourself, oh I would have gotten that, and move on.

But doing so is a huge missed opportunity for learning because if you got something wrong in that problem on the problem set, when you're not in an exam setting, chances are you might make the same mistake on an exam where the stakes are much higher. So instead of moving along in the interest of trying to get it done, take a moment to really understand where you went wrong. Where is the gap in your understanding?

What part of the concept are you not fully comprehending? Are you calculating the values incorrectly, and if so, why? So if you do make a mistake in a problem set, try to understand where you went wrong. What happened? Was it a problem with you understanding the concept? Was it a calculating error? What is it that you're not understanding and how can you amend that gap in your knowledge?

This is an important moment because it really gives you a sense of where your strengths are and where your weaknesses are, and you can't handle your weaknesses or make them better if you don't know where they are, so the thing about the problem sets is they're a really powerful audit for your understanding before the test audits your understanding. Now one thing to be really clear about is that it's easy to pretend that you get it even though you don't get it, especially if you're working with classmates and colleagues.

And in attempt to not slow down the group, you pretend that you understand when you really don't. And again, not only does that do a disservice to you in your own learning, it also does a disservice to the group because if you admit that you're not sure what's going on, then someone has an opportunity to teach that information to you and teaching that information is a really powerful way to understand it better.

Finally, as you come up against these stumbling blocks and as you work through them and through the problem set, make sure to identify in each and every case what concept or major idea the problem is testing. Every single problem that you do in a technical course will be testing your knowledge of a particular concept or idea and so trying to reverse engineer the problem, trying to understand what concept is being tested, is a really great way to understand how to approach a problem and how to succeed in coming up with the correct answer.

Remember, as you work through problem sets, seek clarification actively. You have a host of resources at your disposal. Not just your instructors, your professor and your TAs, but also your classmates, your textbook, the people in your study groups, and online resources. Make sure to seek clarification early and often. Not only does it help you complete the problem sets in a successful and timely way, it can also limit the amount of frustration you experience as you do your homework.

Another idea is to try solving problems out loud. We know that teaching information to somebody else is a great way to determine how well we ourselves know the information, and so if you can do this with your problem sets, it's really helpful. Work with a classmate and alternate problem by problem, walking each other through how you went about solving the problem and identifying the concept being tested. Make sure to defend your approach because remember, on a lot of technical exams, you're going to be given partial credit for showing your work, so even if you don't come up with the correct answer in the end, being able to identify why you did the things you did can be really valuable. If you get the answer right, understand why it's right. And if you come up with a wrong answer, make sure you take the time to identify what went wrong and how to address that gap in your knowledge.

Again, if you can teach this information to someone else, chances are you understand it pretty well yourself and working with someone else gives you the opportunity to test each other before the test tests you. Means you can do some really good learning in a lower stakes environment before the stakes are raised in an exam. But one thing to remember about this: while working with another person is a really powerful tool for learning, you will be held accountable on the exam for answering these problems by yourself so make sure that even if you can teach this information to somebody else, that you can also solve a problem on your own. I also recommend making something called a master problem set. This means taking your problems from the assigned homework but also problems from lecture, problems from your textbook, even problems that you've encountered using online resources. This allows you to get the fullest possible sense of the kinds of problems you might encounter so that when you go to take an exam, you have a really clear sense of what the range of possible problems might be.

Professors really like to use new and novel problems on exams so the bigger your exposure is, the more robust it is, the more prepared you will be, and once again, always identify the concept being tested whenever you see a problem. What this really helps with is it helps mitigate the moments when you go into an exam and you feel like you've never seen this kind of problem before. I hear it all the time, students come back from a test and they say, I studied every problem in the assigned homework and I saw problems on the exam that I had never seen before.

Chances are you have seen similar problems but the problems on the test look a little bit different than the problems that you did in the homework. This is why it's so important to identify the concept being tested. If you're taking an exam on chapters three through five and you have an exam question, it's going to test a concept in chapters three through five, so even if the problem doesn't look like a problem you've solved before, it is testing your knowledge of a concept that you've seen before and that you understand.

So you've seen the problem before, it's just in disguise. These are just some ways to make the most of your problem sets to really increase your comprehension and retention and get the best use of the time you invest in doing your homework for technical courses.