Sensemaking is an important step in problem solving and critical thinking. Physicists use it to check their work while they analyze systems. The basical premise is to evaluate whether procedures or results pass a number of sensemaking tests. Very closely related to these tests are the different multiple representations that are used to analyze problems. Below is an overview of the various representations and sensemaking techniques used to help improve your problem solving skills.
Sensemaking
Sensemaking
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Sensemaking - Problem Solving - 2min
Multiple Representations
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Sensemaking - Multiple Representations - 2min
Multiple Representations is the concept that a physical phenomena can be expressed in different ways.
Sensemaking Techniques
Problem Evaluation Tests | Overview of Sensemaking Techniques (5 min)
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Sensemaking - Solution Evaluation Tests - 5min
There are many different types of sensemaking. In this course, we will focus on evaluative sensemaking. This is often phrased as checking if your answer is reasonable or not. Usually, the evaluative sensemaking process consists of three pieces: a prediction, a comparison, and an explanation. First, make a prediction of what you would expect your answer or solution to look like, based on one of the techniques below. Then, make a comparison between the answer that you did find and your prediction. Finally, either your prediction or your comparison will need an explanation based in physical reasoning.
Sign: Explain a prediction for the sign of your answer or a quantity in your solution. Compare your prediction with the found quantity (e.g. if you are asked for a mass, your answer should be a positive number since there is no such thing as an object with negative mass.)
Sensemaking | Check the Sign (2 min)
Dimensionality: Explain a prediction for the units or dimensions of your answer or a quantity in your solution. Compare your prediction with the found quantity. (e.g. a length should be in m, not m2)
Sensemaking | Units and Dimensions (2 min)
Order of Magnitude: Explain a prediction for the order of magnitude of your answer or a quantity in your solution. Compare your prediction with the found quantity. Order of magnitude is a very rough estimate (is it 1, 10, 1000?) of a value. The order of magnitude of the length of a cat is about 1 meter. We can approximate the momentum of a 65 kg human running at 12.0 m/s to have a magnitude of p = mv = (100 kg) (10 m/s) ~ 1000 kg-m/s. A way to express relative orders of magnitude is that 4500 is three orders of magnitude bigger than 5.
Order of Magnitude (3min)
Graphical Analysis: Explain a prediction for your answer or a quantity in your solution based on arguments made from analysis of a graph. Compare your prediction with the found quantity or relationship. (e.g. the speed increases as time increases).
What to do:
In solution evaluation sensemaking we should...
- Predict something about our answer and explain why using a technique
- Compare our answer to our expectation
Graphical analysis sensemaking has several options as a solution evaluation sensemaking technique. We could state what we expect the shape of a graph to look like and then explain why we expect that shape. Alternatively, we could explain why the graph given in the problem statement leads us to expect our answer to have a certain property, like being positive or of a certain order of magnitude (another sensemaking technique may be used in conjunction here). Once you have made a prediction based on graphical analysis, we need to compare our prediction to our result. Do they match? Yes, or no.
Proportionality: Usually using a symbolic solution, explain a prediction for the behavior of one quantity in your solution when another or others are changed. Compare your prediction with the found quantity. Does the answer vary as you expect?
Sensemaking | Proportionality (2 min)
Special Cases: Explain a prediction for your answer or a quantity in your solution by examining the behavior as another quantity is taken to a limit or special case, such as 0, infinity, 0 degrees, or 90 degrees. Compare your prediction with the found relationship. This technique also usually uses a symbolic solution to make an argument for what happens as a quantity is taken to a limit.
Sensemaking | Special Cases (4 min)
Self-consistency: Explain or show that your answer is self-consistent. Usually this involves using your found answer within an earlier part of your solution and showing that the result is as expected. (e.g. check that the slope of a derived position plot matches the values of the given velocity plot)
What to do:
In solution evaluation sensemaking we should...
- Predict something about our answer and explain why using a technique
- Compare our answer to our expectation
For self-consistency sensemaking, we can take the final solution we found and plug it back into a previous step or parallel step in the solution process. We can then work out the algebra to make sure that we arrive at an expected result. Commonly this will result in an equation that shows 0 = 0, or that a different quantity equals itself. Make sure to explain what you are doing with a brief explanation.
Known Values: Explain a prediction of your answer or a quantity in your solution based on a known value, such as the speed of light or the density of water. This can involve research and citing a source. Compare your prediction with the found quantity. (e.g. solving for the speed of a car should probably give a value between 0-100 mph, unless it is a race car).
What to do:
In solution evaluation sensemaking we should...
- Predict something about our answer and explain why using a technique
- Compare our answer to our expectation
For this sensemaking technique, we should compare our answer with a known value and explain why we expect our answer to be similar or different from this known value. You should also show that your answer is reasonably close or different from this value. Also, don't forget to cite your sources for information that is not common knowledge!
Related Quantities: Explain a prediction for the relationship between two quantities within your solution. Compare your prediction with the found relationship. (e.g. a vector at 70 degrees above the x-axis should have a larger y-component than x-component).
What to do:
In solution evaluation sensemaking we should...
- Predict something about our answer and explain why using a technique
- Compare our answer to our expectation
For related quantities sensemaking, we should compare two quantities in our solution path. We need to explain what relationship we conceptually expect there to be between the two quantities. Finally, we need to show that the quantities do have the expected relationship. For example a few examples, check out the video below.