Integrating Experiments and Computer Simulations To Promote Learning
Over the past decade several co-authors and I have been involved in the development of three physics and physical science curricula, one for middle school students  and two for college students, especially prospective elementary teachers [2,3]. Each curriculum was designed to guide students through a sequence of laboratory experiments and computer simulations to test their ideas about phenomena, and to provide the opportunity for students to consider both the laboratory and simulator-based evidence in small group and whole class discussions.
In writing the curricula we did pay careful attention to the difference between the hands-on laboratory experiments (including the use of probeware) and the computer simulations that modeled physical experiments. We viewed learning science as making sense of physical phenomena (through observations with hands-on materials) and making sense of models of phenomena (through observations with computer simulations). The evidence from laboratory experiments help students develop models that explain phenomenon. They use computer-simulation evidence to develop models of someone else's (the programmer's) model of a phenomenon. Although there are epistemological differences between these two ways of constructing knowledge, we found that students rarely were concerned about the difference; they usually saw the results of both as equally believable and equally helpful in developing their own ideas.
Among the various issues we had in mind as we designed the activities for these curricula were these two questions. How can a sequence of experiments guide development of ideas or models? How can computer simulations complement what students learn from laboratory experiments? Below I describe in some detail an example from the Physics and Everyday Thinking curriculum, or PET,  to illustrate one way that we addressed these questions.
An Example: Students Developing a Model of Magnetism
One of the six units comprising the Physics and Everyday Thinking Curriculum focuses on providing the opportunity for students to develop a model for magnetism. (In this class students take primary responsibility for developing models, using observational evidence as the arbiter of model validity; the instructor only plays a supportive and facilitative role.) The unit consists of three activities and a homework assignment that engage students in the process of constructing, testing and revising models to explain and predict observations of some magnetism phenomena, a fourth activity where students apply their final model to explain other magnetism phenomena, and a fifth activity and two homework assignments that focus on the history and nature of science and the nature of learning. Each of the magnetism activities takes about 2 hours to complete. Here I will describe just the first three activities and the homework following the third activity. My purpose is to show how the sequence of laboratory experiments and computer simulations help promote the development of a model of magnetism that can both explain and predict a certain range of phenomena. The magnetism activities were adapted from a previous curriculum development project.
The purpose of the first magnetism activity is for students to make a set of observations involving magnets and nails to establish a base of evidence that they could draw on to support their construction of a model for magnetism. Students use bar magnets and nails to explore the interactions between two magnetized nails and between a magnetized and unmagnetized nail. To magnetize a nail, the student holds one end of the bar magnet (either the North Pole or South Pole) against one end of the nail and slides the magnet from that end to the other end. She then lifts the bar magnet and repeats the process several times, always rubbing the nail in the same direction. (At first, students are told to do it this way so the class would start with a common set of observations. Later, after students develop a model, they can understand why they need to rub it in only one direction.) A nail prepared in this way is referred to in the curriculum as a rubbed nail. To test the interactions between nails, the student places a nail (either rubbed or unrubbed) on a small, flat piece of Styrofoam floating in water in an aluminum pie tin. She then brings the head end of a rubbed nail near the head end of the floating nail and then near the point end of the floating nail and observes what happens. After making several similar observations with rubbed and unrubbed nails and with different ends of nails, students conclude that: (1) each end of a rubbed nail attracts each end of an unrubbed nail; and (2) each end of a rubbed nail attracts one end of a rubbed nail and repels the other end. Thus a rubbed nail is seen as being two-ended, in the sense that each end behaves differently when near one end of another rubbed nail. As part of the same activity, students also notice that a floating rubbed nail, when spun on the Styrofoam floater and left by itself, would always end up oriented with one end pointing toward the geographical north. That end is defined as the North Pole of the rubbed nail; the other end is the South Pole. Students then develop a strategy for how to rub the nail so that a specific end would become a North Pole.
The second magnetism activity focuses on constructing, testing and revising models. Students start the activity by proposing a model for what happens in a nail when it is rubbed that could explain their observations from the first activity. Each group in the class then shares its model with the rest of the class. (Whole class discussions are an important part of the PET pedagogy, since it is in these settings where students both need to clarify their own thinking in order to share their ideas with others, and also become aware of what other groups are thinking.) Almost all the groups in the class propose what we call a 'separation' model. In this model there are two types of entities, either plusses and minuses, or norths and souths, which are arranged randomly throughout the unrubbed nail. The act of rubbing in one direction with a magnet causes one type of entity to move towards one end of the nail, and the other type of entity to move towards the other end of the nail. Figure 1 shows a representative model of this type presented by one of the groups in the class. Students justify how this separation model can account for the interaction between two rubbed nails in terms of opposite entities attracting and like entities repelling. [Most students actually use plusses (+) and minuses (-) as the entities, but some, like the group whose model is shown in Figure 1, use norths (N) and souths (S). Students often refer to the entities as 'charges,' regardless of whether they are represented as +'s and –'s or as N's and S's. Later in the unit the class considers evidence for whether magnetic phenomena is the same as or different from electrostatic phenomena, agree that they are different, and thus it would not be appropriate to use plusses and minuses to explain magnetic phenomena.]
In the next part of the second activity students are asked to use their model to make a prediction: What would happen if you cut the nail in half? When arguing from their separation model, students explain that since each half of the original nail will contain only one type of entity, the tip of a rubbed nail should attract both ends of one of the half-nails and repel both ends of the other half-nail. See Figure 2.
When they actually do the experiment, they observe that contrary to their model's prediction, each end of the rubbed nail attracts one end of each half-nail and repels the other end. This suggests that each half-nail is two-ended; that is, it behaves like a rubbed nail. Students then try to revise their model to account for this new evidence. Most try to modify their original separation model for the rubbed nail by including a mixture of both entities in the middle. See Figure 3. When asked to use their model to account for the new evidence, students tend to say something like: when the nail is cut, the mixed charges in the middle separate, making each half have two different poles. However, they do not provide any mechanism for why the mixed charges in the middle re-arrange themselves this way.
During the last part of the second activity the students cut their nail in either 1/3-2/3 pieces or 1/4-3/4 pieces and share results with the whole class. They observe (again) that each piece is still two-ended. To account for this additional evidence, students often make further revisions to their separation model. See Figure 4 for an example from the same group represented in Figure 3.
By the end of the second activity, all students are dissatisfied with their separation-type models, since by now they can generalize their observations: you could cut the nail anywhere along its length, and you'd still end up with two pieces that were each two-ended. They realize that a model that assumes the entities are separate N's and S's (or +'s and –'s), which move one way or the other during the rubbing of the nail, is not workable.
I have taught PET over ten times and the above description is pretty characteristic of what happens in the class. (Others who have taught PET have also confirmed a similar experience with their students.) So how is the class going to make progress? The third magnetism activity, where they work on further revisions to their model, was designed to provide a hint that helps most students. They are introduced to an analogy for the nail: a test tube filled with small iron filings. The students do some experiments with the test tube that are similar to what they had done with the nail. First they observe that each end of the test tube attracts each end of a floating rubbed nail. Thus, the test tube acts like an unrubbed nail. Then they rub a magnet over the test tube from one end to the other and observe that one end of the rubbed test tube attracts one end of the rubbed nail and repels the other end. Hence the rubbed test tube is two-ended; it behaves like a rubbed nail. Students are then encouraged to look closely at what happens to the filings when the magnet slides along the test tube. Some students, especially if they slide the magnet too slowly or if they don't pay careful attention claim that the magnet drags some filings to the end of the test tube; similar to what they had imagined happened in the nail, that the magnet drags one type of entity to the end of the nail (separation model). At this point in the activity, to help ensure students are seeing what the curriculum intended them to see, they run a computer simulation that models a magnet being moved near two other magnets that are each constrained to rotate around a fixed pivot. See Figure 5. They observe that as the magnet is dragged from one side of the screen to the other (along the dashed line in Figure 5), each of the lower two magnets rotates around its fixed point.
They return to the test tube experiment and again look carefully at what happens to each iron filing as the magnet is dragged along the glass surface of the test tube. Assuming they don't move the magnet too slowly, they now 'see' that each filing is lifted up and then falls over on the other side as the magnet passes by. See Figures 6a and 6b. In this case, the computer simulation played an important role: it either guided them to make a critical observation, or it confirmed the original observation they had made.
After considering these observations with the test tube and computer simulation, some students in the class come up with a whole new way of imagining what is going on inside a nail when it is rubbed. Instead of imagining that there are separate entities of opposite types inside a nail, they now imagine that the entities are now paired. That is, they imagine that opposite types of entities (N and S, or + and -) are paired off in a self-contained magnet-like entity. Each individual entity has its own north pole and south pole. In an unrubbed (unmagnetized) nail, the paired entities are randomly organized, with just as many north pole ends as south pole ends pointed in the same direction. See the 'Before Rubbing' representation in Figure 7, where this student has used a + charge to indicate a north pole end and a – charge to indicate a south pole end in each entity. Thus, the nail as a whole does not have a North Pole or a South Pole. The act of rubbing the nail with a magnet causes all the paired entities to re-orient and align with all the north pole ends pointing in one direction and all their south pole ends pointing in the opposite direction. Thus, the nail as a whole has a North Pole and a South Pole. See the 'After Rubbing' representation in Figure 7.
The students in the class who come up with a similar model can then explain to the class why a rubbed nail cut at any place would produce two pieces that were each two-ended. The students assume that the paired entities are intact and could not be broken apart. Thus, when the nail is cut at any place, the cutting always goes in between paired entities. That leaves two pieces, of any size, with the paired entities still aligned. Thus, each cut piece has its own North Pole and South Pole. As soon as some students in the class propose this new model, many others adopt it immediately.
The purpose of the homework that immediately followed the third activity was to provide additional simulator-based evidence to support the new model proposed by some students in class. Students worked with a new computer simulation to explore what happens when a large number of magnets are combined with different orientations. Figure 8 shows some screen shots from the simulation. In (a) the students place four magnets on the screen with their North Poles facing towards the meter and four magnets with their South Poles facing towards the meter. The magnetic field meter reads a very low value. In (b) they orient all eight magnets the same way and the field meter reads a much higher value.
In the class period following this homework the class comes to a consensus on a final model for magnetism. They imagine the entities inside the nail are like 'baby magnets.' In an unrubbed nail the baby magnets are randomly oriented and the nail has no North or South Poles. The act of rubbing the nail with a magnet causes the baby magnets to reorient themselves with all their north poles facing in the same direction. That end of the nail will then be a North Pole, and the other end will be a South Pole. Rubbing the nail, then, makes it two-ended. The baby magnets model is a simple version of the Domain Model of Magnetism. In the fourth magnetism activity, students apply their baby magnets model to explain several new observations with magnets.
The description above illustrates how a carefully designed sequence of experiments can help students construct, test and revise their own models to explain some magnetism phenomena. In this example, computer simulations are used either to reinforce observations made during class, to help focus students attention on critical aspects of their observations, or to provide further support for ideas developed by the students. In other activities and units within the PET curriculum the sequence of activities were carefully designed to enable students to construct and test ideas or models, and computer simulations were used in a supportive or generative manner to complete the hands-on experimental work.
The work described in this article was supported by the National Science Foundation Grant Number 0096856.
 Goldberg, F., Bendall S., Heller, P. and Poole, R. InterActions in Physical Science. It's About Time, Herff Jones Education Division, Armonk, New York, 10504, 2006.
 Goldberg, F., Robinson, S. and Otero, V. Physics and Everyday Thinking. It's About Time, Herff Jones Education Division, Armonk, New York, 10504, 2007.
 Goldberg, F., Robinson, S., Otero, V., Kruse, R. and Thompson, N. Physical Science and Everyday Thinking. Second Edition. It's About Time, Herff Jones Education Division, Armonk, New York, 10504, 2008.
 Hickman, P., Morse, R. A., Otero, V., Johnson, A. and Goldberg, F. Static Electricity and Magnetism module, in Goldberg, F. et al. Constructing Physics Understanding Simulation Software and Curriculum Units. The Learning Team, Armonk, NY, 2000.
 The computer simulation is not exactly analogous to the test tube experiment. The iron filings are not magnets, like the pivoting magnets in the simulation, but the filings become magnetized when the bar magnet is slide across the test tube. Nevertheless, because the behavior of the filings is similar to the behavior of the pivoted magnets in the computer simulation, the simulation helps focus the students' attention on what happens to each filing.
Fred Goldberg is a professor of physics at the San Diego State University (SDSU) and is affiliated with the Center for Research in Mathematics and Science Education at SDSU.
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