PHYS 310, Lecture 1 – Fundamentals of Problem Solving
Research in Expert Problem Solving
 Studies that examine experts solving problems
 Comparing to novices and journeymen
 Development of problem solving ability
o Works best with explicit instruction and practice using
expert-like process
Problem solving strategies utilized by experts
 Modeling
o Restatement of the physical situation/phenomena/etc.
o Determination of relevant and irrelevant information
o Explicit statement of what is known and unknown
 Visualizing
o Multiple representations of the situation/phenomena/etc.
o Before and after for transformations
o Graphs, charts, cartoons, etc.
 Solving, analytical process
o Devise a plan
 Principles
 Assumptions
 Simplifications
 Mathematical representations
o Execute a plan
 Manipulation
 Substitutions
 Assessing
o Right units
o Consistent with assumptions/simplifications/etc.
o Limiting cases
Criteria for Assessment of Problem Solving in this class
Modeling
 Explain physical situation using original and full sentences
 Describe what information is given in the problem
 State what the problem is asking for
 Use correct physics terminology
 Include all relevant information
 Exclude irrelevant information
Grading:
o 2 points if all criteria are met
o 1 point if one of more criteria are NOT met
o 0 points in no attempt is made
Visualization
 Draw a representational cartoon of the situation, including before
and after if some kind of transformation takes place
 Draw a physics representation of the situation (motion diagram,
free-body diagram, energy bar chart, P-V diagram, a ray, a wave
snapshot, etc.)
 Choose and show coordinate axes, if needed
 Record all quantities in appropriate places on the diagram AND in
a table
 Identify symbolically all given and unknown quantities with
appropriate variable names
Grading:
o 8 points if all appropriate criteria are met
o 6 points if 1 or 2 criteria are NOT met
o 4 points if 3 or 4 criteria are NOT met
o 2 points if only 1 criterion is met
o 0 points if no attempt is made
Solving
 Devise a plan
o State the general topic of physics needed to solve the
problem
o State the specific physics principles, concepts, laws, or
theories needed
o State the assumptions and/or simplifications you need to
make
o Construct a mathematical representation which is based on
the physics principles and simplifying assumptions
 Execute the plan
o Use algebra, calculus, or other mathematical techniques to
manipulate the equations in a manner appropriate for the
solution
o Substitute numbers and units for known variables if
numerical quantity is required (only AFTER analytical
solution)
o State clearly your final answer in a complete sentence.
 Grading:
o 8 points if all appropriate criteria are met
o 6 points if 1 or 2 criteria are NOT met
o 4 points if 3 or 4 criteria are NOT met
o 2 points if only 1 criterion is met
o 0 points if no attempt is made
Assessing
 Explain why your answer is a reasonable quantity or expression
 Demonstrate that it has the correct units
 Demonstrate that it is consistent with any assumptions or
simplifications you made
 Demonstrate that the expression makes sense in limiting cases, if
applicable
 Grading:
o 2 points if all criteria are met
o 1 point if one of more criteria are NOT met
o 0 points in no attempt is made
General Tips
 Strategy design tips
o Look before you leap
 Whenever you face a problem, there is an immediate
temptation to rush in, roll up your sleeves, and begin
tinkering with it. Resist that temptation. If you start
with the execution stage, you will likely write down a
lot of correct statements that do not lead to an
answer. Instead, think about the problem on an
overview level. What sort of conceptual tools will you
need to solve the problem? What path will you take to
the solution, and in what direction should you start
off? Concretely, it often helps to classify your problem
by its method of solution.
 Example: If you are looking for a child lost in the
woods, your first step is to sit down, think about what
the child probably did and where he probably is, and
devise a strategy that will allow you to effectively
rescue him. If, instead, you just rush about the woods
in random directions, you're likely to become lost
yourself.
o Where are you now, and where do you want to go?
 Before you can design a path that takes you from the
statement of the problem to its answer, you must be
clear about what the situation is and what the goals
are.
o Keep the goal in sight.
 Don't get caught in blind alleys that lead nowhere, or
even in broad boulevards that lead somewhere but
not to where you want to go. It sometimes helps to
map a strategy backwards, by saying: "I want to find
the answer Z. If I knew Y I could find Z. If I knew X I
could find Y . . . "
o Ineffective strategy
 Do not page through your book looking for a magic
formula that will give you the answer.
o Make the problem more specific.
 You're asked to find the number of ways that M balls
can be placed into N buckets. Suppose you can't even
begin to map out a strategy. Then try the problem of 3
balls in 5 buckets. Solving the more specific problem
will give you clues on how to solve the more general
problem.
o Large problems.
 At times you will be faced with big problems for
which no method of solution is immediately apparent.
In this case, break your problem into several smaller
subproblems, each of which is simple enough that you
know how to solve it.
 Execution tips
o Work with symbols.
 Depending on the problem statement, the final
answer might be a formula or a number. In either
case, however, it's usually easier to work the problem
with symbols and plug in numbers, if requested, only
at the very end.
 Easier
 Some things cancel OFTEN!
o Define symbols with mnemonic names.
 If a problem involves a helium atom colliding with a
gold atom, then define mh as the mass of the helium
atom and mg as the mass of the gold atom. If you
instead pick the symbols m1 and m2, you stand a good
chance of mixing up the symbols and their meanings
as you solve the problem.
o Keep packets of related variables together.
 In acceleration problems, the quantity (1/2)at2 comes
up over and over again. This collection of variables
has a simple physical interpretation, transparent
dimensions, and a convenient memorable form. In
short, it is easy to work with as a packet. Take
advantage of this ease. Don't artificially divide this
packet into pieces, or write it in an unfamiliar form
like t2a/2. Packets like this come up in all aspects of
physics--some are even given names (e.g. "the Bohr
radius" in atomic physics).
o Neatness and organization.
 it is easier to work from neat, well-organized pages
than from scribbles.
 2 vs. Z, t vs. +, l vs. 1 etc.
 Answer checking tips
o Dimensional analysis.
o Numerical reasonableness.
 If your problem asks you to find the mass of a
squirrel, do you find a mass of 1,970 kilograms?
 20 m/s is about 40 mi/hr
o Algebraically possible.
 Would evaluating your formula ever lead you to
divide by zero or take the square root of negative
number?
o Functionally reasonable.
 Does your formula agree with common sense?
o Limiting values and special cases.
 In the projectile travel distance problem the range is
obviously zero for a vertical launch. Does your
formula give this result? If you solve a problem
regarding two objects, does it give the proper result
when the two objects have equal masses? When one
of them has zero mass (i.e. does not exist)?