Physics Study Group: How to Solve Problems Together

A physics study group solves problems best in threes, with a role for each member: one runs the steps, one checks that everyone can explain them, one argues. The University of Minnesota built that format from years of research on group problem solving. Add three habits: a free-body diagram before any equation, sorting problems by principle, and checking units.

What working problems in a group does

At Minnesota, Patricia Heller, Ronald Keith and Scott Anderson taught a large introductory physics course an explicit problem-solving strategy (American Journal of Physics, 1992). Students then practiced it in mixed-ability groups. Groups produced better solutions than individuals working alone. The course improved problem solving for students at every ability level.

A companion paper traced well-functioning groups to specific rules for how members work together (Heller and Hollabaugh, 1992). It tested the format in two very different places: a large introductory course at a state university and a small modern physics class at a community college. Groups used the strategy more often on context-rich problems, realistic situations from students' lives, than on standard textbook exercises. Group size, the mix of members, seating, roles and testing each made a difference.

Interactive work also moves understanding. Richard Hake pooled pre- and post-test scores from 62 introductory courses with 6,542 students (American Journal of Physics, 1998). Courses that made heavy use of interactive engagement averaged a normalized gain of 0.48 on mechanics concept tests. Traditional courses averaged 0.23.

Forming a physics study group of three

Minnesota's instructors explain their choices in their guide to cooperative group problem solving:

• Three members. Groups of three worked "a little better than pairs or groups of four". Pairs often lacked enough physics knowledge, and in fours one member tended to be left out.
• Mixed ability. Mixed groups worked better than matched ones, so the instructors put one student from each third of the class in every group.
• Watch the mix. Groups of two men and one woman worked poorly early in the course. "The men tend to ignore the woman, even if she is the highest ability student in the group."
• Rotating roles. Each member takes a role, and the roles rotate every time the group meets.

A fourth member takes the energizer and summarizer role, restating what the group has decided. To find members, start with your discussion section, where everyone has the same problem sets. StudyDuo's Find Partners includes Physics among its interests, searchable by country and city, if your section meets online or your class is small.

The five-step strategy, said out loud

Minnesota teaches one five-step strategy, and early in the course students write each problem on a sheet with a space for every step. In the algebra-based course, its graders assigned the 25 points for a problem like this in the first quarter:

Fifteen of the 25 points went to the two steps before any equation is chosen, because those were the steps students found hardest, the guide says. In the second quarter, the split moved to 5, 6, 6, 6 and 2. In a group, the Manager calls each step, the Recorder writes it where everyone can see, and the Skeptic asks whether a step is done before the group moves on.

Free-body diagrams before equations

David Rosengrant, Alan Van Heuvelen and Eugenia Etkina studied a course built around physics representations (Physical Review ST Physics Education Research, 2009). Over two years, they coded the free-body diagrams students drew on 12 multiple-choice exam problems. Nobody was asked for a diagram or got credit for one. The share who chose the right answer depended on the diagram's quality:

A wrong diagram did worse than no visible diagram at all. The authors note that "no diagram" may include diagrams drawn in someone's head or on scrap paper they didn't collect. In interviews, high achievers also used the diagram to check their work, not only to start it.

So in a physics study group, the diagram gets its own turn. The authors' steps make a checklist for the Skeptic:

1. Sketch the situation and circle the object you're analyzing.
2. Represent it as a dot.
3. Find everything touching it, plus Earth.
4. Draw one arrow per interaction, starting on the dot, with lengths showing relative size.
5. Label each force with two subscripts: who exerts it on whom, such as "rope on box".

Count the forces against the interactions before anyone writes Newton's second law.

Sort problems by principle before solving

Before the group solves a set, sort it. In Michelene Chi's classic 1981 study, eight introductory students sorted problems by what they looked like: 75% made a "springs" category and 50% an "inclined plane" one. The graduate students sorted by the principles that solve them, and none used "inclined plane", as Andrew Mason and Chandralekha Singh summarize it. Their own study at the University of Pittsburgh gave the task to three introductory classes (Mason and Singh, 2011). Students in the calculus-based class put 34.4% of the problems in good categories on average; those in an algebra-based class, 18.7%. Professors were the likeliest to file a problem under two principles when it could be solved two ways.

For the group: each member labels every problem in the week's set with a principle, such as Newton's second law, energy, momentum or kinematics. Compare labels before solving anything. Any problem with two labels is the one to solve twice, once each way.

Units and estimates: checking the answer

The evaluate step earns the fewest points, and it's the one that catches errors. Run it as a group ritual:

1. Estimate first. Before any algebra, each member writes the order of magnitude they expect: a few meters per second, or hundreds?
2. Check units in the symbols. Before numbers go in, the Recorder checks that both sides of the final equation have the same units.
3. Test a limit. Set a mass to zero or an angle to 90 degrees, and ask whether the formula does what physics says it should.
4. Compare with the estimate. An answer a hundred times off sends the group back to the diagram, not the calculator.

Mason and Singh count estimating quantities and examining limiting cases among what's expected of an expert in physics.

An evening's session

1. Sort, 10 minutes. Label the week's problems by principle and pick one context-rich problem; Minnesota keeps an archive of them.
2. Solve in roles, 40 minutes. Five steps on paper, the free-body diagram checked against its interactions.
3. Evaluate, 10 minutes. Units, a limit and the estimate.
4. Rotate, 5 minutes. Swap roles for next time and split the solo problems.

Solo problem sets fill the rest of the week, and a physics study group can still do them side by side. StudyDuo's Study Hour gives the group one shared start each day: an hour of focus for everyone at once, at a time each member sees on their local clock. Focus Room stays open around it. With one partner instead of three, a 1:1 has sound, and the camera can point at your diagram.

For a group on the FE exam, where physics meets an official handbook, see the FE exam study group plan. For more formats, there are 20 study group ideas; how a group can share rooms on video is on the online study group page.