Why is Mechanics Taught Separately from Electricity & Magnetism?

Almost all undergraduate physics curricula start with one term studying mechanics.  In the first term, students learn about motion and the forces that cause motion.  Then they learn a (different) way of explaining motion in terms of energy conservation.  The second physics term is spent studying electricity and magnetism.  Students learn about the motion of charged particles and the forces that cause that motion.  Then they learn a (different) way of explaining motion of charges in terms of energy conservation.  There seems to be a nice sort of symmetry between the two courses, but I encounter a problem each year, namely, my Electricity and Magnetism students have a hard time applying the skills they learned in Mechanics to Electricity and Magnetism.  I’m sure that one culprit is time; the students have probably forgotten what they had learned before.  But I’m wondering if part of the problem is the lack of a unified approach to representing physical situations in their first physics course.  The students spend a little time learning how to use Newton’s Laws, then a little time with Conservation of Momentum (which is sometimes presented as a separate topic when in fact it easily combines with Newton’s Laws), then a little time learning about Conservation of Energy.  From a student’s perspective, I wouldn’t be surprised if his or her Mechanics class felt like this:

  1. There are quantities called position, velocity, acceleration, and time — sometimes you have to use kinematic equations to answer questions
  2. There are these things called forces  — sometimes you have to use force equations to answer questions
  3. There is this thing called momentum — sometimes you have to use momentum equations to answer questions
  4. There is this thing called energy — sometimes you have to use energy equations to answer questions

The students don’t have to think too much about which physical principles (i.e. Newton’s Laws, Conservation of Momentum, or Conservation of Energy) to apply in order to answer a question because the questions that are asked are pretty much always aligned with the current chapter.  It should be no surprise, then, when students have difficulty knowing which physical principle to apply to a generic situation.  In fact, when presented with a generic situation, the solutions that I see from students are often “Equation Soup”.

Equation Soup


1.  A collection of partially-worked formulas from the Equation Sheet that have letters in them that correspond to the quantities that were given in the problem statement

The problem is perpetuated in the Electricity and Magnetism course because the curriculum goes through exactly the same process, except now it gets applied to the property of charge instead of the property of mass.

What if, instead, the courses were organized as follows:

First Course – Interactions as Forces

  1. Objects and systems have properties such as mass and charge.
  2. Interactions between objects can be described by forces.
    1. the gravitational force is an interaction between two objects with mass
    2. the electric force is an interaction between two objects with charge
    3. the magnetic force is an interaction between two objects with charge that are moving
  3. Knowledge of the forces acting on a system can be used to describe the motion of the system.

Second Course – Interactions as Energy

  1. Objects and systems have properties such as mass and charge.
  2. Interactions between objects can be described using energy.
    1. gravitational potential energy is the energy of interaction between two objects with mass
    2. electric potential energy is the energy of interaction between two objects with charge
  3. Knowledge of the energy transfers within a system can be used to describe the motion of the system.

In this course curriculum, the different subtopics in each course are the types of interactions (i.e. gravitational, electric, or magnetic), not how you choose to represent those interactions (i.e. forces or energy).  For example, in the Interactions as Forces course, you learn that the Earth interacts with all other massive objects (i.e. moon, other planets, the sun), you represent all of those interactions with an arrow called a “force”, then you apply the rules of forces to determine the resulting motion of the Earth.  Next you learn that a charged particle interacts with all other charged particles, you represent all of those interactions with an arrow called a “force”, then you apply the rules of forces to determine the resulting motion of the charged particle.  The same goes for the magnetic force and every situation that is a combination of the gravitational force, the electric force, and the magnetic force.  In the Interactions as Energy course, you take exactly the same situations as before, except now you represent those interactions with a scalar quantity called “potential energy”, then you apply the rules of energy transfer to determine the resulting motion of the object.  The process of how to represent and analyze a situation is always going to be the same for every type of interaction.  In terms of teaching, the advantage of this is that the students will get practice in applying the same process over and over again, and they should eventually start to see that any interaction can be represented either with forces or energy.  The choice of which representation to use comes down to ease and efficiency.  The other advantage here is that rather than promoting the idea that there is the “mechanical world” and the “electromagnetic world”, there is only one world, and we choose to represent it in whatever way is most convenient.

I’m sure this has been considered before; in fact, I remember reading somewhere about some schools that actually do separate their courses this way.  Is there a compelling reason that I am missing for why the vast majority of curricula are divided into Mechanics and E&M instead?

Why I Decided to Change the Way I Teach

When I was hired as a teaching assistant in graduate school, I taught in the same way in which I had been taught…lecture.  I had never received any formal education in how to teach.  In fact, the extent of my teacher training was someone telling me, “You’ll be fine”.  (That’s not completely fair, actually, because there was a two-day workshop for teaching assistants that I missed for reasons I can’t remember.)  I was in charge of four recitation sections in which I was supposed to do practice problems from the material that was covered in lecture.  When the students had difficulty with some piece of material from lecture, I tried to explain it to them in my own way. The students seemed to think I was doing a pretty good job.  I had a problem, though: while  the students understood me as I explained something, they often couldn’t replicate what I did when they were on their own.  I couldn’t quite figure out what else I could do.  After all, I explained everything the best I could.  Wasn’t the rest of it in the students’ hands?

In retrospect, I shouldn’t have been too surprised at the fact that the students had trouble communicating ideas and making connections on their own because similar issues arise in other aspects of life.  As an example, many people who have been immersed in a foreign language find that they can understand the language but they can’t speak it themselves.  This suggests that the ability to comprehend doesn’t necessarily translate to the ability to speak.

It was around this time that a friend of mine suggested group work.  To be honest, I thought it was just a waste of time.  I had heard about group work before, but I never really trusted the theories in favor of group work because they were based on words that I didn’t feel had a precise meaning, and they didn’t have measurable outcomes.  Proponents of those theories reminded me of those New Age treatment peddlers that are able to make wild claims because of how nebulous the terminology is.

“Use these crystals to protect against negativity and attune to your higher self.”

I needed to hear something that was more scientific.

Last summer, I took two physics pedagogy courses at Buffalo State College, and that is when I was finally exposed to a lot of the hard data:

In order to understand this graph, you need to know something about the Force Concept Inventory, or FCI.  It is a conceptual assessment test that was designed to gauge a student’s understanding of Newtonian concepts.  It has been around for about 20 years, and it has been extremely thoroughly vetted.  Typically, the FCI is given on the first and last day of class in order to see how much students learned.  The normalized gain is calculated by: (post-test % – pre-test %)/(100% – pre-test %).  This is a measure of how much a student learned relative to how much they could have learned.  Anyway, what Richard Hake did in his 1998 paper was to compare the FCI scores of 6,542 students from 62 classrooms.  He divided the classrooms into two categories: Traditional Instruction — defined as relying on passive-student lectures, recipe labs, and algorithmic-problem exams — and Interactive Engagement — defined as classes designed at least in part to promote conceptual understanding through interactive engagement of students in heads-on (i.e. minds engaged) and hands-on activities which yield immediate feedback through discussion with peers and/or instructors.  This graph shows the results, with normalized gain on the horizontal axis and the fraction of courses of that style that achieved that particular gain on the vertical axis.  Traditional Instruction courses are in red and Interactive Engagement courses are in green.  As you can see, there is a huge difference; in fact, the average gain of an Interactive Engagement course is roughly double that of a Traditional Instruction course.

I also watched Derek Muller’s Veritasium video in which he describes his doctoral research on how students understand and interpret physics material from video explanations.  He gave his own pre-test and post-test that was much like the FCI, and in between he showed a video that gave the answers to the majority of the questions on the test.  The students were quite confident that they did well on the post-test, yet the average score only went from a 6/26 to a 6.3/26.  So not only was the direct instruction not helpful, but it actually made the students more confident about their misconceptions.

Lastly, I was informed that Interactive Engagement physics classes produce nearly double the number of STEM (Science, Technology, Engineering, Math) majors as Traditional Instruction classes do.

That was enough data to get me to at least try teaching using Interactive Engagement methods, and actually experiencing Interactive Engagement for myself fully convinced me that this was the way to go.