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Web Visualization for Teachers
     Alistair B. Fraser

This stuff is so bad,
it must be educational.
Aunt Selma, The Simpsons

For another pedagogical resource by the same author, visit:
 Bad Science   and 
 Bad Meteorology 
Web Visualization for Teachers was created as an aid for teachers who are exploring the Web as a medium in which to build better metaphors for their students.

In the summer of 1999, my opinion piece in the  Chronicle of Higher Education  distinguished the academic use of the Web for the purpose of administrative and expanded access, from those which improve pedagogy. This was not done to denigrate the democratizing power of Web-wrought access, but to emphasis the pedagogical power of the medium, which, I felt remained largely untapped by those who used the Web primarily to redistribute material which had been conceived under a more constraining medium.

In discussing pedagogy, I provided a measure of merit (or demerit) which noted: The extent to which a student gains the same pedagogical benefit from a printout of your Web resources as from the resources themselves is the extent to which you have done nothing of pedagogical value by using the Web.

Rule: If you are successful in moving backward, you have been unsuccessful in moving forward.
In response, some academics wrote me to say that they could accept my point in principle, but it would be nice if I provided them with some examples of the improved pedagogy possible with the Web. Of course, I have many examples imbedded within my own course material, but, they are structured to offer meteorology to my students, rather than Web visualization to other teachers.

So, I created this site as an extension to issues raised in the article. I encourage you to start by reading it first; then what follows here make more sense.
The Chronicle article (Aug. 6, 1999, B8):
 Colleges Should Tap the Pedagogical 
 Potential of the World-Wide Web 

Objectives and caveats
In presenting the examples which follow, I pay scant attention to how one might create them, and only rarely mention the software. My primary concern is to discuss what can be done, rather than how to do it: the game is to tickle the creative imagination not explain the technicalities. There are instruction manuals and workshops galore which offer the technical details.

Further, I draw (almost all) of my illustrations from my own work. I do this not just because it is obviously most familiar to me, but because it is appropriate for the reader to think about how one adapts approaches from other disciplines. Besides, it avoids issues of copyright. And yes, I reserve copyright on all the material not in the public domain. You may view my examples as they arrive from my domain, but not make copies or redistribute it.

On building better mental models
The scientific method,
so far as it is a method, is nothing more than doing one's damnedest with one's mind, no holds barred.
P.W. Bridgman (1882-1961)
1946 Nobel Prize for Physics
In the Chronicle article, I recognized that a good teacher operates on many levels, but that certainly one of them is that of communicating the mental models of a discipline. Variously referred to as mental models or mental constructs, they can take many forms. They range from the discipline-dependent mastery (and understanding) of tools, techniques, and concepts, to the supra-disciplinary meta models such as critical thinking, research methods, and even how to think about and build mental models themselves. Media employed in communicating mental models range from gesticulation, speech, text, and images to the interactive animation.

In the past, we relied on words, diagrams, equations, and gesticulations to build those models piece by piece in the minds of the students. We now have a new tool -- not one that replaces the older ones, but one that greatly extends them: interactive computer visualization. Today, a teacher can build a pedagogical model, and both student and teacher can interact with it to explore the behavior of the system in a way inconceivable in earlier times.
The pedagogical method,
so far as it is a method, is nothing more than doing one's damnedest with one's mind, no holds barred.
The clue to doing this well, can be found in Professor Bridgman's somewhat irreverent restatement of the scientific method. Applied to teaching, it suggests that the pedagogical method, so far as it is a method, is nothing more than doing one's damnedest with one's mind, no holds barred. And that is the way to approach the exercise of building a better metaphor for your students.

Any attempt to exhaustively catalogue mental models probably involves an exercise comparable in magnitude to that of the human genome project, but without the established methodology. Nevertheless, some generalizations can be made at the elementary level. Most important among these are clearly those concerned with the phenomenology of temporal and spacial structures. These do not address issues of processes or concepts directly, but they are usually a prerequisite to them. Thus, before attempting to understand plate tectonics, a prerequisite is a piece of phenomenological information about spacial structure: the Earth is spherical (or nearly so). And any attempt to understand human aging must start with the phenomenological information about a temporal structure: the way in which humans do age. As such models of spacial and temporal structures is (at least initially) more concerned with what than why. The thrust of models is why; they illustrate the way in which various states are linked by processes.

Temporal models
World Wide Web,
an extension of the Internet, because available to the public in February 1993 with the release of Mosaic, the first graphical browser.
The construction of temporal models was greatly eased by the technology of the moving picture (c. 1890) although, previously direct observations of nature, pantomime, and verbal descriptions and even image sequences were widely employed. Instructional use of movies abounded from the mid-twentieth century on, but usually they were merely used as a substitute for the normal presentation, and were rarely employed to help the construction of mental models. The computer had digital video have greatly lowered the opportunity cost for individual instructors to create or tailor things to the needs of their own students. Finally material could be created which did not require the dedication of a corporation and used on demand for students. These ideas are illustrated in the document:
 Temporal Models 
Plugin required:  QuickTime .

Spacial models
Browser plugins:
In Jan. 1996, the capabilities of the Web moved beyond that of a medieval manuscript when Netscape allowed plugins and thus interactivity in movies, spacial objects and mathematics.
Millennia before the movie camera eased the communication of temporal models, spacial models were routinely represented by drawings, paintings, and sculpture. The word, sculpture, is taken to include things such as architectural models of things like buildings and boats and even a wide variety of toys and dolls --- miniatures of the real thing used for purposes of visualization. The ability of the drawings and paintings to communicate three dimensional structures was greatly enhanced in the 15th century by the development of perspective drawing. Of course, the invention of photography (the daguerreotype was given to the world in 1839) greatly eased the process of capturing and displaying images. Yet, a long time elapsed before teachers were able to make much use of the process for their students; indeed, it was an other half century before it even became commercially viable to reproduce photographs in newspapers. From its inception, the Web has been able to present static images (two-dimensional projections). Only after the release of Netscape 2.0 in January of 1996, did the web gain the capability (through plugins) of presenting models of manipulatable three-dimensional structures. These ideas are explored in two documents owing to the number and size of the illustrations in each. They are:
 Two-dimensional spacial models 
Plugin required:  QuickTime .
Three-dimensional spacial models 
Plugins (viewers) required:  QuickTime ,  Metastream1 .

Parametric models
Often one wants to illustrate how the way a system behaves in response to the change in some input parameter, in effect to illustrate some functional relationship. If that parameter is time, then of course we have the temporal models discussed above. Similarly if it is a view angle or depth, then of course, we have the spacial models.

But the idea is far more general and the parameter could represent anything: cost, temperature, wind velocity, heart rate, and on and on. Further, there might be multiple parameters (like multiple spacial coordinates) such that the teacher wishes to present the behavior of something across a multi-parameter space. These ideas are illustrated in,
Parametric Models
Plugins required: QuickTime, Shockwave.

Process models
These are models that mimic natural processes. Of course, a parametric model can do that also, and indeed, one of those illustrated, above, does so. Clearly, these two categories are not mutually exclusive. Yet the thrust of process models is that of familiarizing student with the behavior of nature. Consequently, they tend to have a much higher level of interactivity than parametric models. These ideas are illustrated in,
 Process Models 
Plugin required:  Shockwave .

You built it; now what?
The building of a good visualization is only the first step. Now, how do you use it? It seems to me that you have four choices and probably you will have created you visualization with the intent to use two or more of the possibilities. They are: use it in class during a lecture to enhance your ability to communicate concepts; give the students direct access to it to explore on their own; make it part of an assignment; make part of a test.
Sage on the stage:
Denunciations of the efficacy of lectures are usually made during a lecture --- for the very reason that a good lecture is such an effective way to promote thinking.
Lectures: A funny thing has happened on the way to the 21st century: lectures have been demonized. Now it goes without saying that some poor teachers deliver abysmally bad lectures. Further, collaborative student projects of discovery can be very effective. Nevertheless, the success of the standard mantra which contrasts the sage on the stage with the guide on the side relies heavily on the dishonest tactic of comparing the best of one approach with the worst of the other. The bottom line is that a good teacher should use both lectures and collaborative discovery. The good lecture is efficient, effective and inspirational. It engages and challenges the mind of the student every bit as much as collaborative learning. Collaborative learning is a far less efficient way to gain insight, but is far better than the lecture in providing the student with the necessary tools for exploration and discovery. Use both.

I use visualizations in my lectures (indeed, that is the primary purpose for building them). They are projected on a large screen in the front class, and become another tool in the arsenal of means of building insight in the minds of my students. By interacting with them myself, I set the stage for the student doing likewise outside of class.

Individual and group exploration: Before the web, it was far more awkward to share visualizations with students. It usually required a special lab provisioned with not only the visualizations, but also some special, usually expensive, proprietary software to run it. With the advent of the web, resources can be built such that they are available to any student with a computer and an Internet connection (which is most of them these days). Students can then explore and discover individually or in groups in the school or at home. This combines the versatility of discovery using a computer with the traditional versatility of access offered by a textbook.

Assignments: In the discussion, above, of individual and group exploration, I implicitly assumed that this was being driven by student's internal motivation to gain insight. Yet, the potential is great here to use such visualizations as part of explicit assignment: I explored these aspects of a model in class; you extend this exploration to broader issues and use it to address the following questions.... For example, if one, say, used the Coriolis visualization in the process model portion of this site with an assignment, one could ask the following question: the Coriolis force always acts to the right (in the northern hemisphere) of an objects track, yet when one clicks on the lower portion of the turntable, there is brief period when the track seems to bend the wrong way. Why is this?

Examinations: And, if one can use such visualizations and pedagogical models to prompt exploration through assignments, why not use them with examinations to go well beyond the normal means of either formative and summative evaluations?

Aunt Selma
Let's prove her wrong.

  |  Web Visualization  >  |  Chronicle article 
|  Temporal Models 
|  2D Spacial Models 
|  3D Spacial Models 
|  Parametric Models 
|  Process Models 

The initial version of these pages, Web Visualization for Teachers, was posted to the Web in early September, 1999.