# Think Out of the Box

### by Gaurav Punj, IEOR

#### Teaching Effectiveness Award Essay, 2003

Imagination is more important than knowledge.

Albert Einstein

Issue addressed: Students usually tend to limit their thinking by getting bogged down by formulas in algebra, trigonometry and geometry rather than trying to understand the “Physics” behind the problem. This has been a perennial problem and one of the main motives for starting discussion sections. But, as I soon found out, students usually think of discussion sessions as just problem-solving sessions where the GSI will work on some numerical problems that are relevant for their midterms and finals. I realized that they were more interested in the final answers rather than Physics.

Teaching method used to address the issue: The reason that Physics is the most interesting branch of science (with all due respect to Chemistry and Biology) is because you get to experience in your everyday life whatever you learn in class (unlike Chemistry and Biology) — for example, simple things like walking, driving a car, etc. And, once you begin to understand the physics behind everyday processes, not only does it make learning fun but it also opens up your imagination. That’s exactly what I tried to do in discussion sections. I asked my students to imagine themselves inside the system they were working on to see how it would affect them. They didn’t have any formulas with them and they had to think logically, trying to use only the basic concepts of physics. I will give some examples, which although straightforward, helped in understanding some fundamental concepts:

1. Usually students tend to take the direction of tension force for granted without understanding why it is so. I asked them to visualize themselves inside a simple system in which a mass is hanging from a rope, and place themselves on the rope somewhere. They will experience the mass m trying to pull them down. Therefore, to counter that, they have to pull the mass upwards. That’s what actually happens, and we call that force the tension force and it acts upwards. This approach helped them a lot in complex pulley problems where direction of tension is not immediately apparent.
2. Drawing correct Free Body Diagrams (FBDs) is one of the most important concepts in Physics 7a. Students usually have a very methodical understanding of FBD’s, which they get by looking at the similar diagrams. But, they struggle in exams when they see something different. Using this strategy, they can actually visualize the interaction of different forces by placing themselves at the contact points.
3. This method works really well for rotational motion problems, with which students usually struggle most. Just by using some imagination and placing themselves inside the system, they can get a better understanding of what is happening than they would ever get by writing a number of equations. Thus they can realize why the acceleration is towards the center, why a force is required to keep them on the circular path, how various forces create torques and how more torque makes them go faster. I had the best time teaching rotational motion because of the possibilities that topic provides, and I am sure the students did, too.

Assessing outcomes: Once they got used to this mode of thinking, students really took to it. They realized that Physics is not just plugging numbers into equations, but rather it’s a very interesting science that they can use to explain everyday phenomena. For me, the biggest satisfaction was that they were using their imagination almost uninhibitedly. This was obvious from the questions they asked me during the discussions and the topics they discussed about amongst themselves when I divided them in groups. Instead of the numerical answers to the problems, they were more interested in understanding the concept behind them, and they found it fun, too.

Probably the best assessment was provided by the answer to a question I asked them once at the beginning, and then at the end of semester: “Do you like physics?” A lot more did.