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Physical Mechanism

In the Learning How to Learn Science project (NSF 2000-2005)[1], the University of Maryland's Physics Education Research Group (UMd-PERG) made extensive observations in the algebra-based physics class that included significant numbers of biology majors. These observations included hundreds of hours of videotapes of students working in tutorials and in groups on homework problems.

As a result of these detailed observations, we conclude that perhaps the single most important competency that students need to develop is the following:

Students need to learn to see situations and problems as representing a real-world phenomenon where "what happens" arises out of the structure and properties of the components of the system and the rules of how they interact and behave.

We refer to this orientation as seeing the physical mechanism.[2] While on the surface this sounds decidedly trivial -- What else would you do? -- in our experience, it is not only not trivial, students tend to frame what they are doing as not involving this step, and they find it extremely difficult to carry out even when they see it as appropriate.[3]

A students first step when presented with a problem is often to ask, "Do I know the answer?" This often activates what we might call the "keyword approach", where students note a keyword and reach for a simple association. If they have seen a problem that looks like this one before, they leap to the conclusion that the answers are the same. We refer to this as one-step thinking. While it can be extremely fast and even reliable in "very finite" situations where there are a small number of possibilities (like game shows), in real-world situations it has a tendency to go badly astray. Students -- even reasonably sophisticated ones, such as successful junior and senior science majors -- often come up with answers that make no sense at all and contradict things they know perfectly well.

A simple example of this comes from our multi-representational translation examples. A student drawing graphs of motion for an object might draw both the velocity and the acceleration as constant and non-zero, even though they know perfectly well (and would tell you when asked) that the acceleration is the rate of change of the velocity -- so a constant velocity implies an acceleration of zero. Another powerful example comes from Tuminaro and Redish,[4] who cite the case of a student solving a problem in which she decided with great delight and confidence that "her dormitory room was 1 cubic meter in size."

An essential element of building scientific competency is building a consistent web of self-supporting knowledge and to learn to check that web to be sure that one's reasoning makes sense. And the best way to build that web is to have an underlying picture of the system one is considering as a physics system with rich interacting properties. Referring back to the physical character of a system one understands is the best way to build strong scientific process. This competency interacts with all the others.

1. When given a physical situation or problem, students should be able to "tell the story" of the problem; that is, describe what the situation consists of, identify the relevant or controlling physical principles and properties, and describe "what happens" -- the relevant chain of events or relationships. This basically means building a rich mental picture of the situation.
2. Students should be able to relate their mental picture of the situation to the representations used to discuss and reason about the problem -- pictures, diagrams, equations, and graphs -- and to see the implications of physical constraints and properties for those representations.
3. Students should be able to use sophisticated mechanistic reasoning to analyze physical situations and problems. This includes:
1. Identifying the relevant system to consider.
2. Identifying the parts of the system, the relevant properties of those parts, and the relevant relationship between the parts.
3. Identifying physical principles that constrain and guide the development and analysis.
4. Creating "implication chains" -- reasoning steps (perhaps steps in time, but not necessarily) that tell "what happens".
4. Students should be able to use their mental picture of a situation or problem metacognitively to check that there reasoning and analysis makes physical sense.

Since this competency weaves tightly across many others, it is difficult to construct an assessment task that refers to this competency alone. But here is an example that illustrates how it might be observed and tested.

Sample Test Item

A small radio-controlled toy car can move to the right or left along a horizontal track.  Its position is being measured by a sonic ranger attached to a computer as shown in the figure at the right.

For each of the two situations described as A and B, select the number of the graph (or graphs) that could provide a correct graph of the position, velocity, and acceleration of the car as it would be shown on the computer screen and put it in the box at the right of the variable name. If none of the graphs could work write N.    A. When the motion detector is turned on (t = 0 on the graph), the car is moving towards the left and is slowing down at a uniform rate. ___1. Position       ___2. Velocity      ___3. Acceleration   B. When the motion detector is turned on (t = 0 on the graph), the car is moving towards the right and is speeding up at a uniform rate. ___1. Position       ___2. Velocity      ___3. Acceleration

Analysis

The challenge in this problem is in part in mapping the physical setup into representations. No coordinate system is shown, but students have a tendency to assume "standard coordinates" in which the x-axis is horizontal and points (has positive values) to the right and the y-axis is vertical and points (has positive values) up. But the sonic ranger measures position by sending using a speaker to send out a sound signal (click) and then measuring the returning echo using a microphone. The time delay is interpreted as a distance and internal calculations use difference rules to generate velocity and acceleration. This implies that the sonic ranger can ONLY measure positive values since the time delay is always positive, and cannot even see negative values (if the object is behind it). This means that the measuring tool has a built-in coordinate system as a result of the physical mechanism of how it makes the measurement. The problem has been set up so that this natural coordinate system is reversed from the "standard" one students use without thinking. If students choose graph 5 for part A (velocity) instead of 6, this indicates they may be using a standard rather than a physically motivated situation. Notice that the first correct answer (for A, position) is not present so the students must choose N. This is true even if students are using the standard coordinate system and is done to encourage them to be more thoughtful and cautious about their analysis.

[1] A good summary of the curricular approach developed by this project is given in Reinventing College Physics for Biologists: Explicating an Epistemological Curriculum , E. F. Redish and D. Hammer, Am. J. Phys., 77, 629-642 (2009). [supplementary appendix]

[2] This perspective, while initially based on years of teaching experience, is enriched considerably by research on this topic by philosophers of science, in particular, "Thinking About Mechanisms," P. Machamer, L. Darden, and C. Craver, Philosophy of Science, 67, 1-25 (2000).

[3] For implications for assessment, see "Making classroom assessment more accountable to scientific reasoning: A case for attending to mechanistic thinking," R. S. Russ, J. E. Coffey, D. Hammer, and P. Hutchison, Science Education: DOI 10.1002/sce.20320,875-891 (2009).

[4] Elements of a Cognitive Model of Physics Problem Solving: Epistemic Games, J. Tuminaro and E. F. Redish, Phys. Rev. STPER, 3, 020101 (2007).