Using Cases in Introductory Physics

Debora M. Katz

If you teach physics to non-physics majors for a long enough time, you are bound to be asked, "Why do I need to know this?" This question may seem hostile, and so we appeal to the student’s most selfish interest and answer, "Because it is on the test," or "Because you need to it know it for the next required class." Perhaps the student’s question is born out of a genuine curiosity. It seems likely that students may want to know how the physics that they learn in our classroom fits into their experience of the world. In fact, being able to answer that question may be the single most important thing you do for your students. Many students cannot learn physics without knowing why they are required to do so. 

For the moment, imagine that you are a student who hopes to become a medical doctor, an electrical engineer, or a United States senator. You are in a physics class either in high school or college, and you have just spent three hours in a laboratory measuring the kinematics of a cart. A bright, curious student is likely to wonder why such a laboratory is important. Think of the sort of answers that might satisfy you.

 For example:

  1. Studying the motion of a cart may seem trivial and perhaps boring. However, we work with the cart because it is simple, and this allows us to focus on the mathematical description of motion. This is the foundation for studying more complicated motion.
  2. Since so many things (our hearts, particles in a conductor, people on public trains) are in motion, the description of motion is the beginning of understanding a wide variety of phenomena. So whether you want to be a doctor, an engineer or a legislator, understanding motion is an important part of your preparation.
  3. The laboratory helps to develop your skills. You practice making quantitative measurements and estimating the error in those measurements. You learn the difference between experimental errors and mistakes.
  4. For over 1500 years, people did not understand the nature of motion. One of the great achievements of science is developing a mathematical description of motion. It was an important step in our understanding of nature. Understanding nature allows us to know ourselves better, and determines how humanity works together. All educated people should understand nature in general, and motion in particular.

I think you would be more satisfied with one of these answers than with just knowing that you will be tested on the laboratory.

These are terrific answers, but what is the best way to persuade your students that these claims are true? You have probably seen the ancient Chinese proverb:

I hear and I forget
I see and I remember
I do and I understand

The proverb tells us that when our students listen to a lecture or watch us demonstrate a concept, they don’t learn as much as when they are actively engaged. You probably use some active learning techniques in your classroom, in the hope that your students will better understand important concepts such as Newton’s laws or Maxwell’s equations. But while a laboratory measuring the kinematics of a cart is likely to deepen students’ understanding of motion, such experiences do not answer your students’ most fundamental question of why they should learn these physics concepts in the first place.

Just as lecturing is not an effective way to teach physics concepts, it is not an effective way to address this fundamental question either. Case studies are active learning projects that address not only particular physics concepts, but also the importance of physics. In general a case study has two parts: a motivating or exciting setup and a challenge to be solved by the students. A student working on a case study is like Sherlock Holmes solving a mystery. The student sees the importance of the challenge and is excited to find the solution.

A case study may be used to draw a connection between the concepts learned in the classroom and challenges faced in the outside world. For example, suppose a trucking company is being sued because one of its drivers collided with a car. Based on data taken at the scene and reported in a newspaper article, students can determine whether the truck driver was exceeding the speed limit. The motivation is making sure that justice is done. The challenge is for students to find the driver’s speed. Such a case study shows students that the basic (and sometimes boring) concepts they learn in our laboratories make a difference in people’s lives. (Will the trucking company lose the suit?)

A case study may also be used to show the importance and the process of scientific discovery. For example, a case may include an imaginary dialogue between historic figures such as Galileo and Aristotle. Aristotle would argue that a force is required to keep an object in motion. Galileo would disagree; he would argue that a net force will cause the object to accelerate. The debate is exciting. Students are challenged to evaluate each figure’s argument. Working through the same struggle that took people more than a millennium to sort out helps students to see the important place of science in human understanding.

This particular case study works nicely as an introduction to a kinematics (or dynamics) laboratory. In order to understand the difference between Aristotle’s and Galileo’s theories, students learn to take friction into account as a source of error. Then they are better able to distinguish between laboratory errors and human mistakes.

There is another benefit to using a case study that involves fictional dialogue; it allows students to address their own preconceptions. It is possible to include many common preconceptions in a fictional dialogue. When students work through such a case study, they learn how their preconceptions are connected to their formal study of physics. This process of connecting their preconceptions to physics concepts helps to break down the notion that there is one sort of physics used in the classroom, and another sort of physics used in the more complicated outside world.

My students wrote some of the best case studies I have seen. Whenever I teach non-physics majors, I always include a term project in which students ask and answer a question using the physics covered on our syllabus. Students are willing to tackle complicated and interesting problems when they choose the problem for themselves. The problems they choose to solve are generally more involved than any homework problem, and there is no doubt that in solving them, students see the importance of physics in their lives. Here are some examples:

  1. One runner wanted to know if she should buy a new type of running shoe. She borrowed a piece of the track from the coach and a new shoe from another runner. She used these to measure the coefficients of static friction between the new shoe and the track, and also between the old shoe and the track. She used techniques similar to ones she used in one of our boring laboratory exercises. She found that the old shoes had a slightly higher coefficient of static friction.
  2. A movie fan wanted to know why we haven’t built a light saber as featured in the Star Wars movies. He learned to isolate a single answerable question, "How many batteries would it take to power a light saber?" Based on particular scenes in the movies, he estimated the number of batteries that would be required. He applied principles from thermodynamics and electricity and magnetism. He found that great number of batteries required would make the light saber too heavy to be practical.
  3. A student interested in the classics learned that in ancient Greece, self-propelling carts were used to move scenery around in theatrical productions. He wanted to know if such a cart could be used to move the actors. His analysis involved free-body diagrams, rotational kinematics and conservation principles. While he had done more than enough work to complete the assignment, he also decided to build a scale model of the device. It looked something like the carts we use in our laboratories.

Debora Katz has been teaching physics at the United States Naval Academy since 1995. She is currently working on a case-based textbook for university physics.
