# How to teach modeling physical systems?

While working as a teaching assistant for introductory experimental physics classes (newtonian mechanics and electromagnetism) for the last couple of years, I faced a certain kind of issue again and again. Of course the course material is hard and some students cope better with it than others. But almost all attendants are struggling with analyzing a given real life problem and modeling it with the tools from the lecture.

Once the formulas are written down, most of them have very little problem arriving at the correct solution, even if it involves some difficult integrals or long calculations. The most extreme case of this was a math student who took the class for her minor. I learned some things about math through discussions with her, and the equations posed no challenge at all. But she just could not graph the forces acting on a rotating point mass correctly or add them together in the right way once they were drawn on the blackboard.

This problem is amplified in exams, where errors creep in because of stress and time. But most students don't even get to the point where they can start calculating things, because the basic premise is often wrong. And because of this they lose a lot of points, as they can't make much progress from a wrong start.

Because we separate the exam into three parts and one of these focuses on "understanding" (very simple one line calculations, the goal is to reason correctly about the physical system and predict its behaviour), we actually have some data on that. In general, this part has by far the lowest mean score while the calculation heavy part fares much better. Also compared to past exams, it seems to have been getting worse, because six or seven years ago this part had a higher mean score.

I am certain, that I had the same problems in the beginning and just learned these things over time through practicing with many examples. But in what way can a teaching instructor or professor teach students to model real life physical systems?

Remark: I chose this site over "Mathematics Educators", because it is strictly about teaching modeling in a physical sense, so I think it fits better here. Also I am not sure, if the "models" tag is appropiate here.

Also if you think this might have something to do with the education system, I am talking about first year bachelor degree courses for physics majors and minors at a German university.

Edit: I will give some examples from memory to clarify the issue.

Example 1 (from the third week): Consider a chairoplane with a given height, rope length and mass of the person inside it. The whole system rotates at a constant angular velocity. Task: model the situation appropriately and draw the acting forces. Problems: a tangential force is drawn, so the person would constantly accelerate in the direction of movement and no force along the rope is considered.

Example 2 (from the 4th week): a ball sits on a table, that stands on the ground, and everything is at rest. Task: draw all forces in the schematic and in the abstraction (that just consists of blocks for ball, ground and table). Problems: no force between the table and the ground is included and forces are not transferred correctly to the abstraction

Example 3(from an exam): a metal rod is lying on a metal loop and there is a current running through everything. The whole system is inside a homogeneous magnetic field and tilted 30 degrees. Task: consider all forces acting on the system and describe its motion. Problems: Lenz's law is not identified to work here; even if it is identified, some ignore it when describing the motion afterwards (so it is described as a rolling motion with the acceleration given by earth's gravity and the slope of the system).

• Could you give an example or two of what the students may be struggling with? It is in the category of conceptual questions, I can see, where the student must learn to "think physics". Jun 21, 2018 at 7:48
• Is it that the students are presented with a real-world problem and struggle to make the connection to theory? For example (over-simplified), they struggle to connect, "A car starts from rest and reaches a speed of 60 km/h in 15 s. Calculate the acceleration."?
– Mick
Jun 21, 2018 at 8:28
• My professional career centered around math modeling of physics systems. The first requirement is that the students have a firm understanding of the physical fundaments. Secondly, for a given problem, they need to be able to articulate (in words) the physical mechanisms involved. The ability to do this all-important step evolves from practice in solving many many problems. Thirdly, they need to be taught good modeling practices, such as always using free body diagrams. Jun 21, 2018 at 12:08
• I have roughly six years experience teaching intro courses, and I would agree with @Chester that being able to express their thinking verbally is a mark of students who will do well. But I don't have any really good suggestions for how to teach the skills. I use some group problem solving ala Heller to get the students to talk to each other, plus scaffolded sequences of related exercises, and as much personal attention as I can afford. And then I just kinds hope the students muddle through. Overall results on learning gains are only modestly better than "sage on a stage". Jun 21, 2018 at 16:52
• "because there should be general techniques and approaches to teaching modeling, shouldn't it?" The wide variety of techniques suggested under the moniker Physics Education Research, and the variation in results both between instructors using the "same" technique and between different techniques in the hands of individual instructors suggests that it may not be that simple. Jun 21, 2018 at 16:56

This is a challenge faced by physics (and other) teachers the world over. There are various pedagogical approaches and students respond differently depending on their preferred/dominant learning styles.

One approach is to:

• sketch out the problem (draw a picture). From the example in my earlier comment ("A car starts from rest and reaches a speed of 60 km/h in 15 s. Calculate the acceleration."), it can be as simple as a rectangle with circles - a box with wheels - and some labels, arrows, etc. to help visualise the problem.

• identify the variables:

• initial speed (0 km/h)
• final speed (60 km/h)
• time 15 s
• convert non-SI units to SI units

• identify the relevant formula

I think from this point your students are ok with the calculation side, it is identifying which equation is needed from the description.