• Distance Learning (DL)
• the Web
• the HTML, Java, and JavaScript languages

Imagine the following "Distance Learning" scenario:

Our student, "Miss T", sits down at her terminal after dinner to resume her College Algebra lessons. She is learning about exponential functions and their applications.

She logs on to her terminal, selects "College Algebra", and with a mouse-click or two on highlighted phrases, gets back to where she left off the night before. What she is viewing are some prepared lessons, presented to her much as a classroom teacher might provide transparencies for classroom presentation. But these "transparencies" are of a revolutionary different kind, both in mode of presentation and content, as you will see.

Miss T is in the middle of a lesson on exponential decay of radioactive isotopes. She has previously been given the mathematical model for the decay of the carbon-14 isotope. She has also been taught how to solve exponential equations.

She proceeds with today's lesson

Some bones are found by a bunch of teen-age boys wallowing around in the Buda Tar Pit. They take them to the Buda Branch of A&M, and inform the resident paleontologist there, Dr. Osseous, that "these are bones".

Dr. O dances around for a while, then settles down to his instruments and determines that the bones contain 10% of the radioactive C₁₄ that was present when the victim (affectionately referred to as "Mr. Bones") died.

Her answer:
"Right after the big party at the Buda Greyhound Station!  Right?"
 

Unfortunately, Miss T has forgotten the math model for the decay of C₁₄ !  She jumps back to that lesson (by clicking once or twice) and refreshes her memory. It is:

She is also reminded of the meaning of A(t) and A₀. She sets up the appropriate equation on paper:

or just

But now she is stuck again.  How to solve this equation for t? The lesson on solving exponential equations is only a couple of mouse-clicks away.  She goes there, follows the directions for solving her equation (by using logs), and arrives at an answer (she has a scientific calculator): t = 40,000.

The lesson prompts her to check the reasonableness of her answer by offering to graph the general exponential

for a given parameter a. She is prompted for a, types in "-0.000124", and sees the generated graph:

She notes that for t = 40,000, y << .10. Her computed answer is wrong!

She rechecks her calculations, finds an error, and gets a new result,  t = 18,600. Reviewing the graph again, she notes that for t = 18,600,  y = .10 (approx.). Success!

The lesson will show (graphically) what happens to the distribution as the s parameter varies from 10 down to 1/2.  It does this by showing a moving picture of the effects of varying s.  She sees a series of bell-shaped curves that cluster more and more closely about the mean (m=10) and become taller and taller..
 
   

This moving picture cements forever in Miss T's mind the role of s in the Gaussian distribution.
 

Now to a more sober discussion of some currents in education and technology that have contributed to making Miss T's life a

.

CURRENT ONE -- DISTANCE LEARNING

A recent article Lawmakers defend turf of Texas' universities (Austin American Statesman, June 1, 1996) is thought-provoking, perhaps even disturbing.  To quote:

...the plan approved by Senate committee would leave distance learning virtually unregulated in Texas, allowing competition to shape its course.  "It will cause a war," said Mickey Slimp, dean of learning for Tyler Junior College.  "When four-year colleges and universities start offering courses traditionally offered by two-year institutions, turmoil will break out."

One can envision an open marketplace of DL products and services, in which richer, more technologically advanced institutions can raid the turf of poorer, less-well-equipped institutions.  Such a scenario could be played out locally (University of Texas vs. Austin Community College), regionally (Temple Community College vs. UT), nationally (UT vs. Harvard), or globally (fill in the blanks). How are the less prestigious institutions going to fare in the face of such competition?

Community colleges are in a position of strength on at least some service issues: e.g. smaller classes and more personal service.  But because of the larger and larger numbers of students that they have to deal with, we see increasing signs of depersonalization: telephone registration, inadequate testing and advising, and the extensive use of part-timers, most of whom can't provide the same kind of on-campus accessibility for students that full-timers can provide (how many part-timers are in their offices 25 hours per week?).  But in the end, things still get personal in the classroom, and DL will be hard-pressed to overcome this inherent advantage of classroom instruction.

But in spite of its shortcomings, DL is rapidly gathering momentum, and those who are selling DL will surely be working hard at ameliorating its personalization shortcomings. Adding further to its attractiveness, DL will become a driving force towards the creation of truly superior pedagogical products (lessons). These lessons will be less and less influenced by the whims, behaviors, and idiosyncracies of classroom teachers; rather, they will be built, used, tested, studied and improved, each version getting better and better as more experience is obtained from its use.

This kind of evolution is not possible with old-style "teacher technology."  Each of us starts out as a new teacher, we stumble and fumble for a while (at the expense of our students), and eventually become "effective".  Then we retire, and are replaced by someone who goes through the same learning cycle.
 

In the technology-driven DL environment I foresee, the role of the teacher as organizer of materials, expert lecturer, and provider of learning tools will become a diminishing one. That role will be taken over by media materials that will be in a state of continuous evolution, incorporating the best of what works, and discarding what doesn't.  And because these media materials will be standardized and formalized, their efficacy will be subject to objective measures of quality.

This is not to say that the role of the human teacher will disappear. On the contrary, the teacher will be freed up to do the kinds of things that technology is poorest at! The teacher will have an expanding role in the personalization aspect of the course: providing diagnosis and remediation on an individualized basis, offering encouragement and inspiration, helping with study methods, and so forth.

The role of remediation can be significantly enhanced by the use of technological tools. For example, if a student is proceeding through a computer-mediated lesson, those interactions can be recorded for later playback by the instructor, thus aiding the instructor in the diagnosis of the student's problem. Such detailed analysis is totally impractical by virtue of the demands placed on teachers' time in today's environment. Incidentally, the discovery of wide-spread confusion over a particular topic will lead to an improvement in the materials.
 

CURRENT TWO -- THE WORLD WIDE WEB

You only have to read the paper, watch TV news, or read the billboards by the side of the road to be convinced that the Internet is the most significant social and technological phenomenon of the current generation.

There seems very little argument against the proposition that the Internet is will eventually provide DL in its most convenient form. Today's cable-TV DL, in a weak imitation of a classroom environment, pales in comparison to the spectrum of pedagogical tools that will be made available over the Internet. Technologies in many arenas are currently being developed to make the Internet a fast, cheap method of communication. New ways of increasing bandwidth are being developed and installed: satellites, fiber optics, ISDN, cable, and others, are all cooperating (or competing) to bring vast amounts of data at high baud rates into everybody's home.

New computer hardware technologies, even now in the making, will contribute significantly to the mass marketing of information. The Network Computer ("dumb terminal", but they are far from dumb when hooked up to the Internet and your home TV), now being announced, will offer home computing via the Internet at an initial cost of as little as $500. If this cost follows the trend of other hardware costs, that price will drop even lower as competition turns such computers into mass-marketing commodities. The Benjamin Cummings Publishing Company newsletter BC Link, Spring 1996, Number 5, contains a short article "Internet Box or PC?", citing the following articles from the popular media:

Don Clark, "Oracle is Demonstrating Network Computer Today," Wall Street Journal, 2/26/96, p. A3

Jon Auerbach, "One Small Box, One Giant Debate," The Boston Globe, 1/14/96, p. 45

Julia Pitta, "Industry Debates the Future of PCs", The Boston Globe, 11/16/95, p. 49.

The emergence of the Network Computer is being made possible by concomitant advances in software: the development of sophisticated client-server technologies, HyperText Markup Language (HTML) and the exploding phenomenon of the HTML-related Java language, which will be the third current about which I write.

The Internet was born distinctly user-unfriendly. Things have come a long way in the past two years, with the emergence of Web technology, Netscape, search engines, and similar tools. These tools paper over all the ugly underpinnings of the Internet, and allow one to easily do, for example, massive content-based searches for information stored on thousands of computers. You type in a topic, hit "Enter", and you get a list of all Web sites, world-wide, having information on that topic, which you can then access simply by pointing and clicking. This is made possible by the continuous maintenance of vast indices of information together with smart lookup programs which conspire to make fast global searches possible.

Netscape allows individuals to create "Home Pages" at their Web site, which can be made accessible to anyone who cares to look at them. You put whatever you want to put in your Home Page. Your picture,
 

your personal information, your

All of your Home Page information is easily structured into a coherent whole by the placement of appropriate pointers embedded in your documents. These "pointers" are uniquely highlighted phrases in your documents, which can be clicked on to allow a reader to see more about that particular topic. By thoughtful structuring of your materials, you allow your Home Page "visitors" to navigate through them in a non-linear, self-directed manner. They are allowed to ignore completely those parts that don't interest them, and concentrate on those parts that do.

Furthermore, all documents attached to your Home Page will automatically be searched by the giant indexing utilities referred to above. Consider the following scenario:

July 4: You insert a discussion of the analytic geometry figure The Witch of Agnesi into your Home Page. You refer to Agnesi using the pronoun "he".

July 5: Unbeknownst to you, graduate student Lisa Fibonacci in Pisa, Italy, doing research on female mathematician Maria Gaetana Agnesi, finds and reads your newly-completed notes.
 

  Maria Gaetana Agnesi (1718-1799)

July 5: Lisa sends you e-mail correcting your error! Thank you, Lisa!

But is this all we are talking about: the convenient dissemination of teaching notes? No; this is only the tip of the iceberg. We definitely do not think of the Internet simply as a tool for providing home use of the same notes you would use in a lecture. Nor are we talking about providing for home use the same kind math tutorials that are available in our Learning Centers and Math Labs today.  This would be a no-brain exercise, and would certainly represent a severe under-utilization of technology -- analogous to putting out a fire by beating it to death with a fire extinguisher. We envision something distinctly more imaginative than that.

CURRENT THREE -- HTML AND JAVA

Coinciding with all the other advances in hardware and software technology is the emergence of HTML ( "HyperText Markup Language", a rather pedestrian device for creating Netscape-compatible documents), and its more recent and more exciting adjunct: a software tool called Java (it's an object-oriented language), developed by Sun Microsystems expressly for use with HTML documents. Java promises to become a major force in the scenario we envision.

[The following paragraph was added in July, 1998]
A variation of Java, called JavaScript, which provides some of the programmability features of Java without some of the complications, and whose source code (unlike Java's) can be viewed by any reader of the document,  can also be used to provide some of the facilties provide by Java.  In fact, the animations in this document were written in JavaScript.  Many of the following comments about Java apply as well to JavaScript.

The article "Java -- Yet another Computer Revolution?" (from the aforementioned BC Link) comments:

But the real sizzle in the Java story emanates from the World Wide Web. Java ... promise(s) to make the Web come alive as never before. The prospect of Web pages that offer sound and motion, and that people can interact with, have (sic) spurred an explosion of interest in Java.

Another recent article from the Austin American Statesman (Monday, July 1, 1996), discusses some of the capabilities of Java and its impact on the Internet:

"Java stands a very good chance of revolutionizing the industry," says Geoffrey Fox, a professor of computer science and physics at Syracuse University. " It's already changing the look of the Web. It will also change the way software is written and distributed."

It is interesting to note that the "waving flags" on the home page of 1600 Pennsylvania Avenue are provided courtesy of Java.

All of this "media hype" about the impact of Java can easily be reinterpreted to suggest new ways to instruct and inform.

All Internet-conversant computers (even the $500 dumb terminals) will be equipped to translate HTML/Java documents into their screen images. But HTML (as supplemented by Java) is not simply a passive document markup language. The presentation of documents can be enhanced by display elements that are animated -- that move -- providing eye-catching graphics for visual appeal, but, more importantly, bringing to "life" certain aspects of a subject that cry out for visual, animated, illustration.

For example, the practiced mathematician easily visualizes the following sequence of functions:
 

He (or she) "plays a mental movie" which is an interior visualization of the series as it converges to a limit, as follows: on the range [-1, 1], the discontinuous function f defined by:
 

f(-1) = 1

f(x) = 0,                     -1 < x < 1

f(1) = 1

I suggest that playing for the student the "movie" of what the instructor easily plays in his/her own mind can illumine this whole matter almost instantaneously. The "movie" would be a display (at one second intervals, say) of the successive graphs of f₁, f₂, f₃, and so forth.

as opposed to the more conventional:
 

Keeping in mind that these lessons are teacher-constructed HTML documents, a natural question is:
 

Here is how:
An HTML document can consist, not only of static text and graphics, but also of active elements which will provide the animation aspects of the document. Those active elements will be specified in the procedural programming language Java, and embedded within the document, ready to be called upon to provide the animation upon request. Such pieces of Java code are referred to as "applets" (as in application-ets), and every Netscape-savvy computer (regardless of manufacturer) will be equipped with a mechanism for interpreting such applets, and showing the viewer the intended animation effects.

Applets can be programmed to be interactive. This will allow student investigations into mathematical topics that take on an "experimental science" feel by allowing the experimenter to plug in her own values of various parameters of a problem (half-life of a radioactive isotope, the value of p in a binomial distribution, the various parameters of the logistic growth curve), and observe the effects of this experiment on the graph of the function.

Interactive applets can serve up tutorials, ask questions, prompt for answers, and screen the answers for correctness. The possibilities are limited only by the energy and imagination of the developer. One can imagine an applet calling upon sophisticated mathematical or statistical software (Mathematica, Minitab) to graph a complicated three-dimensional function, or draw a regression line. Sound, color, and moving digital photographic imagery can all be incorporated seamlessly into a smooth presentation that is user-friendly, pedagogically sound, and interesting!

WHAT WILL BE A DISTANCE-LEARNER'S VIEW OF A LESSON?

We have already experienced Miss T's saga. To summarize:

• by using HTML pointers, Miss T will be able to jump around within a whole curriculum at will: replaying, reviewing, refreshing her memory
• the lessons, capitalizing on the capabilities of Java, will present Miss T with animated visualizations where such can contribute to her understanding
• Miss T can run experiments with her own parameters or data in order to view the mathematical consequences of her choices
• she may choose to be tested by the computer for understanding of a topic before moving on to the next topic
• she may elect a computer-mediated tutorial on certain topics

Of course, all these "options" are buttressed by lots of refined thinking and effort on the part of the materials developer. On the other hand, one would expect a virgin lesson to be neither full-fledged nor even perfect with respect its current fledging. But as teachers discover shortcomings, improvements will be made and augmentations provided to meet them. Unlike a textbook, these lessons can be in a continuous (day-by-day) cycle of improvement*.

* The down side of this is that some mechanism would have to be in place to prevent the addition of hastily-provided amendments that are either ill-thought-out or buggy.

WHAT ABOUT CLASS ADMINISTRATION FOR AN INTERNET-BASED DL PRODUCT?

The above discussion tries to elucidate what the "feel" of an HTML/Java-based lesson would be. There are, of course, a host of other more peripheral aspects of DL that need to be considered.

How can a student interact with the teacher?

The possibilities are many. The Internet already has a whole array of time-tested mechanisms for interaction. Discussion groups, chat rooms, documents that answer FAQ's (frequently asked questions), are just some of them. These ready-made mechanisms can all be used directly (no reprogramming or adaptation needed) to provide useful modes of teacher-student and student-student interaction.

Will there be live and real-time conferencing sessions (assisted by video images of participants) that will try to simulate the interactions of a real classroom?

Will there be traditional lectures, either live, or taped?

The merits of trying to simulate a classroom-style of pedagogy needs further study and evaluation. It is conceivable that we could discard all our old teaching paradigms if we discover technology-based paradigms that work.

Will students progress in lock-step, or at their own pace?

Will they register in "sections" or as individuals who will be assigned to a "course coordinator (teacher)"?

How will the teacher gauge and ensure the progress of individual students?

How will the teacher do evaluations?

These are all non-trivial issues that need to be addressed by the application of appropriate technology in the context of DL.

These "administration issues" have the potential to overwhelm the pedagogical issues. But this should not deter us from starting to think about the narrower issue of how best to deliver instruction in a DL environment.

CLASSROOM VS. DL: DIVERGENT CURRICULA?

Of real concern is the following:

Are we now going to have to manage two curricula, two handbooks, two testing scenarios, two of everything: one for the classroom, and one for DL?

And if so, where are we going to get the people-power to manage all this?

It is conceivable (and fondly to be wished) that the quality of the DL materials will seduce the ordinary classroom teacher into using them. To the degree that this happens, there will be one curriculum and one handbook, with appropriate "footnotes" here and there with regard to variant usage in the two settings.

The classroom teacher will still control the overall structure of his lessons, but will also be free to pick and choose from the wide selection of "technology transparencies" available if s/he chooses to devote some portion of classroom time to "lectures and demonstrations". The handbook would be re-written with the DL materials in mind, but the classroom teacher would, presumably, still only be bound by the general provisions of the syllabus.

WHO IS GOING TO DO ALL THE WORK TO PROVIDE THESE MARVELS?

As we embrace DL, and find that it is having a profound influence on classroom teaching, as well, we will find ourselves discarding the old paradigm that teachers provide their own notes, lecture materials, and teaching tools, just as today we discard the notion that every instructor writes his/her own textbook. Materials will be donated by their developers, bought from "publishers", or constructed by home-grown committees. For starters, they will be based on textbooks (it's hard to let go of old paradigms).

As time goes by, it will become easier and easier to build home-grown materials. Not every aspiring curriculum developer will want to endure the pain of learning Java. Nor will he or she have to. Educational system specialists will build tools on top of HTML/Java that will allow curriculum developers to pose lessons in a non-procedural, "pedagogically-oriented" style, and then let the tool do the work of turning it into HTML and Java-code applets.

But in the short run, those that have the passionate belief that there is something here that is worth exploiting will roll up their sleeves and get started (by learning Java or JavaScript, if necessary),  in order to test and demonstrate the power and potential of these methods.

WHAT DOES THIS HAVE TO DO WITH YOUR COLLEGE MATH PROGRAM?

The confluence of the three revolutionizing themes discussed above seems compelling enough to me to suggest that it will only be a matter of time (measured in months) before we begin to see curricula in the style mentioned above appearing for popular appraisal and consumption. We can wait and be passive recipients of materials developed by others, or we can decide that we want to be active participants and try to influence the course of pedagogical events. This is a decision that needs to be made intentionally, and not left to chance.

Note that the revolution being spoken of here is orthogonal to what is currently referred to as the mathematics reform movement.  Math reform has to do with approaches to conveying the intellectual content of mathematics to students in an optimal way. What is being discussed here is a different kind of "reform":  it is not unique to mathematics, but addresses the modalities of presentation needed for delivering any kind of materials in new educational environments. The instructional technologies envisioned here will serve to enhance and make even more viable the advances being sought by the math reform movement.

The Internet, Netscape, and the world of opportunity they open up has come to my institutions.  Other institutions are now or will soon be devising creative ways to exploit the "Information Revolution" that is taking place right now. There is no reason to believe that we cannot make a contribution to this revolution.

HOW CAN AN INDIVIDUAL TEACHER START TO GET INVOLVED IN DL?

Experimenting with these methods will not require (at least for starters) a large organizational effort with committees, subcommittees and endless discussions. We don't need DL or any technology (other than a word processor) to get started. We can begin right in our own classrooms, and gradually evolve from what we do today through several stages of increasing dependence on more and more sophisticated technology.  Here are some ideas on how we as an individual instructors can proceed:

1. Make up some good lecture notes on selected lessons or a whole course, put them on a word processor, and make them into transparencies.
2. Teach from these notes in a conventional classroom setting. Observe successes and failures. Revise and improve.
3. Give the notes to other faculty to read, perhaps even use, and criticize. Have discussions. Revise and improve.
4. Convert these notes to "raw" HTML format (there are utilities to do this). These documents will now be viewable on a computer screen, and by a class via a projection device attached to a PC (or Mac). They will appear, when shown, pretty much as they did as transparencies, but you will now be loosed from the burden of transparencies and hard copies. These documents are Web-ready, but you don't need the Web to use them. You can store and display them from a local computer, or if the computer is attached to Internet, pick them up from a Web page.
5. Start putting in HTML pointers, so that the notes become usable as "point and click" documents.
6. Use these notes in a classroom setting. You will need an ordinary PC that is HTML-ready, and a display device.
7. Put these notes in your home page for perusal by students, other faculty, other departments, other schools, and the whole world.
8. Start thinking about the real "teaching goodies" that can accrue from the use of Java applets. Learn Java (or enlist a programming-literate friend), and start putting these goodies in (you will need Java software, available from the Web). Try them out, revise and improve.
9. Ask other faculty to try out your notes. Revise and improve.
10. Work on the peripheral aspects of setting up and running a DL course. It is at this point that the Mathematics Task Force will have to start playing a role. Offer an experimental DL course. Revise and improve
11. to oo.  Teach, revise, improve.

WHY SHOULD I SPEND THE TIME NEEDED TO GET INVOLVED IN THIS?

I believe that anyone who gets involved in developing HTML-based materials will, regardless of the outcome from a global point of view, become a better teacher. This comes about because he or she will have been in the process of thinking deeply about and codifying exactly what is the best way of getting various topics across to students. Successes will be noted and retained; failures will be noted, and improvements attempted.  This process occurs even during steps 1 and 2 above, which requires one to get his or her ideas down on paper (or transparencies) in an teachable way.

Aside from serving as a teaching improvement device, other benefits may accrue from this exercise. Good materials may be adopted by other faculty. This is efficient -- let others benefit from what you have tried and found to be true. Give others the advantage of not having to make the same mistakes you did the first time around.  New part-timers may welcome a tested set of materials as a way to get started, even if, later on, they abandon the materials for some of their own.

Good materials may come to be accepted and used outside of your own institution.  This will mark your school as an innovation-oriented, and other schools will look to yours for future offerings. You will be serving others as you serve your own institution.