f all the species on earth, Homo sapiens is the only one, so far as we know, that uses models. We invent models for many, often conflicting purposes: to provide parsimonious descriptions of observed phenomena, to predict what will happen under prescribed circumstances, and sometimes to explain why things happen the way they do. Models are the indispensable tools of modern science, and increasingly they run on computers, which enables us to predict, and to varying degrees control, the exact landing spot of a Mars probe, the three-dimensional configuration of a molecule, or the chance of rain tomorrow. Such uses of models, in fact, have given rise to a new kind of research, aptly described by the phrase "computational science."

But whereas the research laboratory has embraced computer-based models as an aid to understanding, the same cannot be said for schools, where pre-college science classes all too frequently concentrate on teaching facts, rather than scientific reasoning. The question naturally arises, then, whether the use of computational models in a school environment might not help students, literally, to think like scientists. Indeed, several efforts have been made to introduce models similar or identical to those used in research into the classroom.

Varieties of models
Scientific models may vary quite dramatically across disciplines. A physics model, such as the theory of relativity, is very different from a model in biology, such as Mendel's model for genetics. As a result, scientists in different disciplines often differ considerably as to what they consider a model, and how they judge its utility. Physicists tend to place great store in the simplicity of a model, its fundamental nature, its explanatory power. Those models are particularly prized that start from an axiomatic base (e.g., Newton's Laws of Motion or the constancy of the speed of light), particularly so if they can be shown to apply to a wide range of phenomena. BioLogica™l models, in contrast, are judged primarily on their explanatory power. They are expected to be approximate, somewhat ad hoc, and to admit of exceptions.

Teaching models
Computational models used for research in whatever discipline are not necessarily much good for teaching. The design of a good teaching model starts with several simple but important questions. What exactly do we expect the students to do, and when they do it, what do we think they will learn? What do the students think they are doing when they use the model? What semantics or purpose do they associate with their manipulations of it?

A question one should always ask of any piece of software is, why do this on a computer? In the case of computational models, what educational value does the computer bring to the enterprise, and what special role does it play that couldn't have been filled as well or better in some other way?

A good teaching model should be simple, but not too simple, capturing the essence of the professionals' mental models of the domain, but stripped of unnecessary complications. It is also useful if the model is modifiable --either by the teacher or by the students themselves -- which may enable it, among other things, to change to meet the needs of students as they become more versed in the subject matter. For example, at first we may want certain aspects of the model to be inspectable by the students; later on, we may wish to turn this feature off, in order to force the students to make inferences indirectly by experimenting with the model.

A useful starting point for designing a computer-based model for teaching something is to choose the set of objects and manipulations that it will incorporate. If we choose them carefully, these will be familiar and interesting enough to "jump start" the students' learning, but a formless and unstructured environment will not be enough to sustain the process. Often, we must impose a higher level semantics and purpose on the model. It is not enough, in other words, that the students be able to manipulate the objects. They must have a reason for manipulating them, a reason that motivates their investigation and connects it to the science concepts we hope they will learn. This semantic overlay can also serve to link the features of the computer model to their analogs in the real world -- a crucial aspect of the learning process and, as we shall discuss below, by no means an automatic consequence of students' interactions with the model.

Thinking along these lines, my colleagues and I at The Concord Consortium (and earlier at BBN) have created several game-like environments that pose problems to students and offer them powerful computer-based tools with which to solve them. Each tool embodies an underlying model of a specific scientific domain, and each offers a set of representations and affordances appropriate to that domain. In each case, the student learns the domain by exploring the operation of the model. We call these open-ended exploratory environments "computer-based manipulatives" (CBMs for short) in order to emphasize their close pedagogic analogy with the mathematics manipulatives commonly used in the elementary grades.

Choice of representations
In choosing what objects to represent, the educational software designer is not limited to those that would be accessible in real life. On the computer we can show students many things that are ordinarily invisibl. And we may choose, for pedagogical reasons, to hide others that would normally be visible. Nor is it simply a matter, for example, of showing the user things that are too small to be seen with the naked eye, or too difficult or hazardous to approach. Many scientific models, for example, include abstractions (e.g., the center of mass of a collection of objects) that are invisible because they are not real, but are often more important for understanding the working of the model than the real objects themselves.

Often we can get an educational advantage from hiding information that would normally be available to students. Here is an example. Imagine that our goal is to help students understand, at a qualitative level, the nature of elastic (energy and momentum conserving) collisions between point particles. We could simply tell the students to watch the motions of the particles very carefully and try to figure out what is going on. This might work, but it would be a lot more motivating if we simply made one of the particles invisible and challenged the students to locate it by studying the motion of the visible particles. Every so often one of these will bump into the invisible one and make a sharp turn. From a careful study of the motion -- and a pretty detailed knowledge of the dynamics of the collision -- the students should be able to figure out where the invisible particle is and where it is going. To dress this activity up and make it more fun, we could invent a tool that acts like a "butterfly net." Once a student has figured out where the invisible particle is, the object is to place the net over it and click the mouse button. This action turns the invisible particle visible and freezes all motion. If the invisible particle lies within the butterfly net, we award the student a point, create a new invisible dot at a random location with a random velocity, make the butterfly net just a wee bit smaller, and start the cycle over.

Choice of affordances
Just as we may take away an ability they would normally have, for pedagogical purposes, we sometimes enable students to do things on a computer that they would not be able to do in real life. GenScope is a manipulable model of genetics that we have designed (see Winter '98 @CONCORD). It offers students a multi-level view of genetics and enables them to move easily between the levels. Clicking on an organism with the chromosome tool, for instance, will bring up the textbook view of the organism's chromosomes, represented as short, fat rectangles like popsicle sticks with lines across them representing the loci of various genes. The labels on these genes are in the form of popups that enable a student to change a gene, for example, from its dominant to its recessive form. When they do this, the organism that "owns" the genes changes too -- its phenotype changes to reflect its genotype.

Obviously, in reality no one can alter a gene from one allele to another, nor would such a change, if it were possible, have any effect on the organism from which the gene came. Thus, the operation of changing genes in no way simulates a laboratory or clinical procedure. The affordance is included in the software in order to allow students to discover Mendel's laws of inheritance for themselves by observing their consequences in a direct and motivating manner. This phase of exploration by direct manipulation of genes usually lasts two or three days, after which the power to change, and even to observe genes directly is taken away and the students are forced to make inferences about genotype from phenotypic and breeding data, just as real geneticists do. Thus, by a carefully sequenced set of moves that progressively limit students' interactions with the software until they are similar to those available in the real world, we guide them bit by bit to reason in ways analogous to those of the professional scientist.

Evaluation for redesign
It is not enough to design a model for teaching -- one must observe it in use, evaluate its effects, and modify it as required. Moreover, students are not simple, predictable robots. They do not bring identical attitudes and preconceptions to the learning process, and what they learn from working with an interactive model may differ, often dramatically, from what its designer intended. When this happens it may suggest the need for substantial redesign of the model and/or its accompanying pedagogy.

The management of inquiry-based classrooms, in fact, poses problems unrelated to the use of CBMs. Open-ended exploration that enables students to "construct their own knowledge" is a powerful teaching tool, but in practice it can be a very inefficient process, as students perseverate on a misconception, or "play around" for a significant fraction of the class time without making visible progress. It's all right -- some might argue that it's essential -- for students to struggle in this way, but if it goes on too long, they will become frustrated and turn off. Ideally, a tool for open-ended inquiry should help the teacher to intervene at just the right moment.

Moreover, the designer of a CBM must bear in mind that, just as teachers have different teaching styles, students have very different learning styles. In some situations it may be appropriate to let the student loose to explore a model with little or no direction, but at other times a more structured and linear approach may be called for. What is needed is a way to script how the software interacts with the student.

Scripts are not a new technology. Most business applications are scriptable, allowing one to write simple programs that will cause them to perform a specified sequence of often used functions with a single mouse click. In an educational context, scripts can display information to the student in the form of text, animations, audio, or video material. They can also gather information from the student, in the form of text entry or mouse clicks, and to receive updates from the CBM itself. Thus, they can monitor the students' actions. By constraining the problem very precisely, a curriculum developer can use this monitoring capability to identify "teachable moments" and can tell the script to intervene when such opportunities present themselves.

Linking models to the real world
Models, by definition, are not real and it is not always obvious how they connect to the real things that they represent. The most carefully crafted computer model, designed to teach important scientific concepts, may come across to students as just another videogame. When this happens what they derive from the computer may not go deeper than the skill required to "win" the game. In particular, it may not extend to reasoning about real-world phenomena or processes. Moreover, many scientific discoveries carry with them important implications for society. Consider, for example, the legal, ethical and moral dilemmas that seem to arise almost daily from scientific advances in genetics. In a world increasingly confronted with such issues it is unacceptable to teach science without encouraging students to consider its social implications, and this requires that one make explicit the links between the model and the real world.

Conclusion
Models, whether on or off the computer, aren't "almost as good as the real thing" -- they are fundamentally different from the real thing. From an educational standpoint, they are neither better nor worse than "hands on" methods -- the two approaches are complementary, and neither works very well in isolation. We have concentrated in this article on a particular kind of computerized model -- the computer-based manipulative -- as an example of one way to use computers to teach science. We have examined the design of CBMs with particular attention to such issues as selective intervention, sequencing of problems, and linking activities on the computer to real world analogs. The CBM paradigm, powerful though it may be, must be brought to bear in the context of conjunction with many other tools -- "wet" labs, textbooks, classroom activities -- that can help students to link the various features of the CBM to the real world facts, phenomena, and procedures that they represent.

The most important question that still confronts us in the use of CBMs is "what are the students learning?" In careful experiments, repeated in many classrooms, we have observed striking discrepancies between students' performance on the computer, captured in observation notes and on videotape, and their scores on written tests. We do not lay the "blame" for this discrepancy on the tests themselves, which have been designed to assess what we think the students are learning. Rather, it appears that learning accomplished entirely within the context of interactions with a CBM may become learning about that CBM, rather than generalizing to learning about the domain. It is very important, therefore, to broaden the learning process so that students are made explicitly aware of the model underlying the CBM, and of its application to real world phenomena. This broadening process has implications for the teacher, the curriculum developer, and the software designer. We hope that the scripts that we are currently designing for BioLogica™ (see Spring '98 @CONCORD) will help to make students conscious of what they are learning when they explore and solve problems on the computer, and how what they are learning applies in the broader world outside the classroom.

Paul Horwitz is senior scientist for the GenScope and BioLogica™ projects.
paul@concord.org
This article is excerpted from the forthcoming book Modeling and Simulation in Science and Mathematics Education, published by Springer-Verlag.

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