Teaching Students to Solve Problems

In this section, Prof. Hazel Sive describes this course’s focus on problem solving.

Problem Solving at MIT

I think the unofficial motto of MIT is "We solve problems." Everything that we do here is to prepare our students to be problem solvers in the world. This idea permeates all the disciplines at MIT: engineering; science; business; architecture and urban planning; and humanities, arts, and social sciences. No matter what degree students earn at MIT, they leave with the ability to solve hard problems. When faced with a new problem, they know how to understand it, think about ways to solve it, try those ways, and ultimately get some kind of solution. That kind of philosophical and also real power gives students a big edge when they leave MIT and enter the workforce, go to graduate school, or go to medical school and become a physician.

It’s a difficult way to learn, but it’s a fantastic way to learn. I believe that learning should be a struggle; without struggle, you don’t get anywhere new. I think the courses at MIT are very challenging, and the introductory courses here are much harder than the introductory courses at most other universities.

Learning Terminology and Facts in Order to Solve Problems

Our course does include some rote learning, but the purpose of this rote learning is for our students to develop enough background to be able to speak the subject and understand and tackle challenging problems. They have to know what DNA is, what a gene is, and what a cell is. Very often, I’ll give them a term and I’ll say, “This is the scientific term. You should know it because it’s in your book, it’s in the scientific literature, and you’ll hear it on the news. But what’s most important is the concept underlying the term.” If you look at our problem sets and exams, you’ll see that there are no questions where students have to label a diagram, give a definition, or regurgitate facts.

Learning to Problem Solve through Practice

In this course, students learn to solve problems through practice. Every two weeks, we give the students a problem set with six long problems. The problems are all about problem solving. The students look at the problems and realize that this isn’t just a matter of taking the lecture material and giving it back to us; we assume they know that information, and they’re expected to build from there. It’s very challenging for the students.

This is a shock to many of our students. In most high schools and even universities, biology is about learning facts. This was the case for me. I went to a very good university in South Africa. I learned all about the anatomy of the skull. I learned all about bones. I could classify fish. I learned many things that are very useful, but no one ever taught me how to solve a problem. Many of our students arrive at MIT having gotten the highest possible mark on the Advanced Placement^® biology exam, and when they get the first problem set in our course, they are stunned. They haven’t encountered biology as a kind of detective story where there’s a problem that they need to understand and solve. We explain that biology is a rigorous problem solving discipline; in fact, biology is all about using information to solve problems. It’s a terrific moment when a student realizes that this is different from any way they’ve been taught before, and they’re going to be challenged in ways in which they never knew they could be challenged.

The first problem set has to do with biochemistry. By the time they get the problem set, we’ve taught them about the various classes of molecules and macro-molecules that are found in living cells. We give them a problem set where not only do they have to be able to recognize something about the macro-molecules we present to them, they also have to recognize something about how the macro-molecules are put together, about bonding between the different parts of the macro-molecules, and about what that means for the structure of the macro-molecule, especially proteins. We do that both on paper and then also using a visualization program that was developed in the biology department called StarBiochem. In this program, the students are given a 3-dimensional structure of a protein, and they have to be able to understand what they’re looking at and what it means for the actual function of the protein, which is usually an enzyme that can catalyze a particular reaction. As soon as they see that problem set, they realize that this is going to be different from their high school biology experience.

As another example, when students learn about medical disorders, we don’t ask them to regurgitate the typical symptoms. Instead, we might say, “Here’s a patient that’s presenting with a funny disorder, and if she tries to move too quickly, she collapses. Her muscles look normal. Her nerves look normal, but if you do certain tests to them, you can see they’re not firing properly. Here’s what the trace of their firing pattern looks like. Suggest what’s wrong with the patient.”

The Problem Set Process

I tell the students that they have to practice these problems on their own. We can give pointers about how to solve the problems, but they need to think through the material. I tell them that when I’m thinking hard, I get a headache. For them, it might come as some other manifestation, but they should be getting their own personal version of a headache when they’re doing their problem sets. It shouldn’t be easy, but once they learn how to do a problem and get somewhere with a problem, it’s powerful. It empowers them to then go and tackle another one.

For each problem set, I tell the students to print out three copies. First, students should take one copy and attempt the problem set all by themselves, without their notes and without help from others. They can identify what they don’t understand right away. They might get halfway through the problem set and panic upon realizing that they don’t know very much, that they went to lecture but didn’t absorb a lot of the material.

At that point, they can review their notes and their textbook, or go to the library, or search for information on the web. They learn what they can, then try the second problem set copy. Again, this is without help from other people; they need to personally struggle with the material. They always get farther the second time. The headache, the struggle, and then the triumph with bits of the problems is really powerful. Through this process, students show themselves that they can triumph over the work, and they come out actually having some power over the material.

Usually there will still be some holes in what they’re able to do and understand. Then, they can go and talk to their friends, their teaching assistants, and me or my co-instructor. They have to hand in their own work, in their own words, but they can work together and their work can have all these inputs. If they work as a group initially, they may miss getting that headache because they’re relying on their friends and people who may get it more quickly or in a different way than they do. I really discourage them from working together initially because I think they just don’t learn the material properly that way. They need to learn by doing. As they do more and more problems, they get better at addressing these questions. Students get substantial practice throughout the semester, and they come out really knowing something about how to solve problems in this particular area of life science.

Crafting Good Problems for 7.013

A critical part of our job as teachers is crafting good problems. We aim to create problems that have the following characteristics:

• Rooted in problem solving. A good problem should challenge students to think and to apply their knowledge in novel ways.
• Clearly written and easily understandable. The point of the problem should be clear.
• Built upon multiple aspects of the course material. Although the course is taught in a modular way, students cannot forget the earlier material as they learn new material. The early, fundamental material is used for all of the later lectures and problem sets. The best problems not only address the current module that they’re learning, but also draw upon and integrate past modules. For example, while learning about neurobiology, students should still remember that proteins only function properly if they’re put in the correct place in a cell.
• Informed by current literature. When possible, we like to draw upon real, current examples from the news and/or scientific literature. We usually take just one aspect of it and use it in a problem. When possible, we try to pick topics that we think students can relate to. This way, our problems are fresh, current, and interesting, and we never run out of ideas for problems.