ProblemSolving Strategies
Table of contents
One of the greatest physicists and teachers of the 20^{th} century was Richard Feynman. He summarised the process of problem solving like this:^{1}

Write down the problem

Think very hard

Write down the answer
For most of the rest of us, a more complete list is necessary. Here is one such list, from a textbook by Richard Wolfson.^{2} It is called the IDEA Strategy:
INTERPRET The first step is to interpret the problem to be sure you know what it’s asking. Then identify the applicable concepts and principle – Newton’s laws of motion, conservation of energy, the first law of thermodynamics, Gauss’s law, and so forth. Also identify the players in the situation – the object whose motion you are asked to describe, the forces acting, the thermodynamic system you’re to analyze, the charges that produce an electric field, the components in an electric circuit, the light rays that will help you located an image, and so on.
DEVELOP The second step is to develop a plan for solving the problem. It’s always helpful and often essential to draw a diagram showing the situation. Your drawing should identify the object, forces, and other physical identities. Labeling masses, positions, forces, velocities, heat flaws, electric or magnetic fields, and other quantities will be a big help. Next, determine the relevant mathematical formulas – namely, those than contain quantities you’re given in the problem and well as the unknown(s) you’re solving for. Don’t just grab equations – rather, think about how each reflects the underlying concepts and principles you’ve identified as applying to this problem. The plan you develop might include calculating intermediate quantities, finding values in a table or in one of this text’s several appendices, or even solving a preliminary problem whose answer you need in order to get your final result.
EVALUATE Physics problems have numerical or symbolic answers, and you need to evaluate you answer. In this step you execute your plan, going in sequence through the steps you’ve outlined. Here’s where you math skills come in. Use algebra, trig, or calculus, as needed, to solve your equations. It’s a good idea to keep all numerical quantities, whether known or not, in symbolic form as you work through the solution to your problem. At the end you can plug in numbers and work the arithmetic to evaluate the numerical answer, if the problem calls for one.
ASSESS Don’t be satisfied with your answer until you assess whether it makes sense! Are the units correct? Do the numbers sound reasonable? Does the algebraic form of your answer work in obvious cases, like perhaps “turning off gravity” or making an object’s mass zero or infinite? Checking special cases not only helps you decide whether your answer makes sense but also can give you insights into the underlying physics. In worked examples, we’ll often use this step to enhance your knowledge of physics by relating the example to other applications of physics.
Another wellknown textbook by Randall Knight, has another list:^{3}
MODEL It’s impossible to treat every detail of a situation. Simplify the situation with a model that captures the essential features. For example, the object in a mechanics problem is usually represented as a particle.
VISUALIZE Here is where expert problem solvers put most of their effort.

Draw a pictorial representation. This helps you visualize important aspects of the physics and assess information you are given. It starts the process of translating the problem into symbols.

Use a graphical representation if it is appropriate for the problem.

Go back and forth between these representations: they need not be done in any particular order.
SOLVE Only after modeling and visualizing are complete is it time to develop a mathematical representation with specific equations that must be solved. All symbols used here should have been defined in the pictorial representation.
ASSESS Is your result believable? Does it have proper units. Does it make sense?
ACTIVITY 1
Compare and contrast Wolfson’s and Knight’s problemsolving strategies. How are they the same and how are they different? How does Feynman’s problemsolving strategy fit into these two different lists?
David M Harrison, Dept. of Physics, Univ. of Toronto, modified Knight’s list as follows:^{4}

Form a model. The real physical world is very complex, and almost always we need to form a simplified model of it to solve a particular problem. As George Fox wrote, "All models are wrong, but some are useful." Explicitly writing down what model and simplifying assumptions are being made is often helpful.

Visualise. This is where most experienced problemsolvers spend most of their time. It is a crucial part of Feynman’s “Write down the problem” step. The visualisation can include freebody diagrams, graphs, sketches of molecules, pictorial representations, and more.

Guess the answer. Use any physical principle, intuition, symmetry, or conservation law that you can think of to guess the answer. A correct guess reinforces your instincts. A wrong guess brings the refreshment of surprise. Guessing the answer like this before going any further is called Wheeler’s First Moral Principle after John Archibald Wheeler, another great 20^{th} century physicist and teacher.^{5} Wheeler stated his principle as, "Never do a calculation until you know the answer!"

Solve. Usually this step means casting the problem into one or more equations, and then solving the equations to get a final answer. Casting the problem into one or more equations is Physics; pushing the symbols around on a piece of paper with a pencil to get an answer is just mathematics.

Assess. Often we get a final answer and just stop, or perhaps check the answer against the answer in the back of the textbook or posted online without further thought. This is a poor idea. Instead, think about the answer first. Is it physically reasonable? Is it consistent with your guess? Are the units correct? Do the equations that you ended up solving make physical sense? Checking special cases, such as “turning off gravity” or making a mass zero or infinite, is extremely useful and may give you new insights into the physics.
The major change is the new 3^{rd} step, Guess the Answer, between the Visualise and Solve steps.
ACTIVITY 2
How would you modify Wolfson’s list to include the new Guess the Answer step? Where would you put it? Why?
Besides the Guess the answer step are there any other significant differences between Knight’s list and Harrison’s list? If so, what are they?
Are any of Harrison’s modifications in Wolfson’s list but not in Knight’s? If so, what are they?
ACTIVITY 3
You now have five lists of problemsolving strategies: Feynman’s, Wolfson’s, Knight’s, Harrison’s modification of Knight’s list, and your modification of Wolfson’s list. Which of these lists is most appropriate for you to use in learning how to become an expert problem solver? Do you intend to make any changes before using it? Why have you made this choice? Note that different members of your Team may make different choices: if so explain to the other members why you have made the choice that you did.
Note that you may decide to change or modify this choice as the term proceeds and you become more expert in problem solving. Activity 4 will be done later in the term so that we may find out about this.
ACTIVITY 4
Now that you have some experience in problem solving, it is an excellent time to reflect on the strategy that you have been using and how it has changed since you chose a strategy at the beginning of the term. Do you think further changes in what you have been doing are called for? For each member of the Team, briefly summarise in the notebook what strategy he/she has been using, how it has changed since the beginning of the term, and whether any further changes are going to made.
This Guide was written by David M. Harrison, Dept. of Physics, Univ. of Toronto, in April 2016. Brian Wilson, Dept. of Physics, Univ. of Toronto contributed to the design.
1^{} Apparently this is from an interview with Murray GellMann in the New York Times. See, for example, http://c2.com/cgi/wiki?FeynmanAlgorithm (Retrieved April 28, 2016).
2^{} R. Wolfson, Essential University Physics, 3^{rd} ed. (Pearson, 2016), 9 – 10.
3^{} R. Knight, Physics for Scientists and Engineers, 3^{rd} ed. (Pearson, 2013), 22.
4^{} D.M. Harrison, Studying Physics (2011, last modified 2017), http://www.upscale.utoronto.ca/PVB/Harrison/StudyingPhysics/StudyingPhysics.pdf
5^{} E.F. Taylor and J.A. Wheeler, Spacetime Physics (Freeman, 1966), 60.