Department of Physics
Problem Solving Sessions (PSS)
Student Guide
Spring 2013
Contributors (in alphabetical order):
Robert Beichner, Jon D.H. Gaffney, Mary Bridget Kustusch, Eli Owens, Evan
Richards, Jeff Polak, Michelle Snyder, and Shawn Weatherford
Compiled by Robert Beichner
Updated: January 8, 2013
Problem Solving Sessions
Overview:
The purpose of these sessions is to help you become better a problem solver. You will be presented with
difficult problems (as compared to typical end of chapter “exercises”) that will be quite challenging. The
difference between an exercise and a problem is that you will not know how to solve the problem after
a quick reading or examination of the situation. Just because you cannot immediately see a path to a
solution, doesn’t mean you should give up. By following a systematic approach to problem solving you will
always know what needs to be done next, leaving the “only” difficulty being how to actually do it.
Your TA’s task is to teach you how to solve problems. THIS DOES NOT MEAN HE OR SHE WILL
SIMPLY SHOW YOU THE SOLUTION! If all they do is tell you directly how to do the problem, then
you will only learn how to do that one problem. We have much bigger plans for you! We want you to solve
problems that no one else has ever seen before. That will take practice and a lot of hard work. The best
jobs go to the best problem solvers!
Grading:
Your team will be handing in your solutions to the TA to during each PSS. You should be working closely
with them throughout the session, getting guidance whenever you need it. (Don’t rely on them so heavily
that you don’t strengthen your own problem solving skills.) You will be graded using a 0, X-, X, X+
system indicating missing, inadequate, adequate, or exemplary. These count as 0, 1, 2, or 3 points out of 3
possible for the problem. (Even a multi-part or extensive problem only gets a total of three points.) Your
goal is to get a X+ for every assignment. Your team might need to revise and turn your assignment in
several times during the PSS to accomplish this. If a group does not attain X+ quality before the class
is over, then they get whatever grade they’ve earned up to that point. If your group gets done early, stay
around and help the other teams. Everyone learns something that way!
Groups:
You will be randomly assigned to a new group of three every week.You do NOT get to select your own
groups because we want to encourage you to work with many different people. Make sure you a chance to
practice each group role (Manager, Recorder, Skeptic) multiple times during the semester.
Makeups:
Your lowest PSS score will be dropped and there will be no makeups. You may not attend a PSS different
from the one you have registered for since that unfairly disadvantages those people registered for sessions
later in the week. They wouldn’t be able to sit in on a different session if they were sick during their session
time.
1
GOAL Problem Solving Protocol
This particular approach was based on the work of George Polya, from the mid-1940’s, so it is hardly an
original idea. What is new is the mnemonic ”GOAL” that helps students remember the steps.
•
Gather information
The first thing to do when approaching a problem is to understand the situation. Carefully read
the problem statement, looking for key words and phrases like “initially,” or “freely falls.” What
information is given? Exactly what is the question asking? Don’t forget to gather information from
your own experiences and common sense. You might need to look up something in a manual or on
the web. Put as many bits of data as you can into “physics jargon” like v0 = 0 when something is
said to start from rest.
What should a reasonable answer look like? You wouldn’t expect to calculate the speed of an
automobile to be 5 million m/s. Do you know what units to expect? Are there any limiting cases
you can consider? What happens when an angle approaches 0◦ or 90◦ or a mass gets huge or goes
to zero? Also make sure you carefully study any drawings that accompany the problem. You will
almost certainly need to make a sketch or two of your own.
•
Organize your approach
Once you have a really good idea of what the problem is about, you need to think about what to do
next. Have you seen this type of question before? Being able to classify a problem can make it much
easier to lay out a plan to solve it. If you haven’t already, you should almost always make a quick
drawing of the situation. Label important events in your sketch. Indicate any known values, perhaps
in a table or directly on your sketch. Some kinds of problems require specific drawings, like a free
body diagram when analyzing forces. Once you’ve done this and have a plan of attack, its time for
the next step.
•
Analyze the problem
Because you have already categorized the problem, it should not be too difficult to select relevant
equations that apply to this type of situation. Use algebra (and calculus, if necessary) to solve for
the unknown variable in terms of what is given. Substitute in the appropriate numbers, calculate the
result, and round it to the proper number of significant figures. It is usually, but not always, best to
wait to the end of the analysis to plug in numbers.
•
Learn from your efforts
This is actually the most important part. In the real world, you would use this as an opportunity
to consider what experience you have gained by successfully solving this particular problem. In the
more artificial academic world, try to put yourself in your instructor’s place. Why did he or she
assign this specific problem? You should have learned something by doing it. Can you figure out
what? Examine your numerical answer. Does it meet your expectations from the first step? What
about the algebraic form of the result before you plugged in numbers? Does it make sense? (Try
looking at the variables in it to see if the answer would change in a physically meaningful way if
they were drastically increased or decreased or even became zero.) Think about how this problem
compares to others you have done. How was it similar? In what critical ways did it differ?
For complex problems, you may need to apply these four steps of the GOAL process recursively to subproblems. For very simple problems, you probably don’t need this protocol. But when you are looking at
a problem and you don’t know what to do next, remember what the letters in GOAL stand for and use
that as a guide.
2
Group Role Definitions
These are the basic group roles used in labs and PSS:
• Manager or Organizer: oversees the group’s efforts through planning, maintaining focus, time
management, and ensuring appropriate participation from all group members.
• Recorder: maintains the integrity of the group’s record of the activity through recording data,
ensuring all agree with the results, and ensuring that all understand the group’s plan. This is the
person who writes up the solution that all agree upon.
• Skeptic or Questioner: ensures that the activity has been explored from all angles through questioning results (and the group’s interpretation of the results), suggesting modifications to the group’s
plan or providing alternate paths.
• Summarizer: provides the large picture through expressing a summary of the activity, the plans
raised by the group, the data and results along with denoting the overarching ideas that the group
should take away from the activity. (Only create a summarizer when you need a four-person group.)
See ‘Group Roles Table’ for description of what each role looks like for each activity.
Note: The person who is assigned the role is not restricted to that role, but is ultimately
responsible for making sure that particular job gets done.
From: Gaffney, J. D. H., Richards, E., Kustusch, M. B., Ding, L. and Beichner, R. Scaling up educational
reform. Journal of College Science Teaching 27 (5): 48-53, May/June 2008.
3