The recent revolution in information technology exemplified by increased awareness of the Internet and by rapid advances in World Wide Web technologies introduces exciting opportunities and challenges for educators. This paper presents an account of experiences gained at the University of Illinois at Urbana-Champaign since early 1995 in utilizing the Web for instruction in the field of mechanics. The Department of Theoretical and Applied Mechanics at the University has established a Web site called Mechanics on the Internet. This site links to a general introduction to the Department, logistics of programs and activities, such as curriculum, procedures for applying to the program, ongoing seminars and related activities, biographical data on faculty and staff, recent research reports, and a database of conferences and workshops in mechanics. It also includes a number of detailed course notes and interactive courseware materials with various utilities, help engines, search engines, and interactive interfaces. During Fall semester 1996, the speaker even taught a graduate course in fracture mechanics entirely over the Internet from a remote location. The course was repeated for a class of extramural students during Spring semester 1997. This paper describes several lessons gained from all these efforts. We also present some general views regarding the implementation of the new technologies towards an improved learning model for students of mechanics.

In recent years we have witnessed a remarkable, if not breath-taking, evolution of information technology, particularly in the utilization of the Internet for transporting and sharing information world-wide. Although the Internet has been in place for more than 20 years, the strong presence of this information-processing tool in a form resembling what we see today is only about 4 years old. Indeed, the University of Illinois at Urbana-Champaign (UIUC) has played a key role in the surge of the Internet: In 1993 computer scientists at the National Center for Supercomputing Applications (NCSA) released the first version of Mosaic, a software tool that today is known as a browser. This new software opened the Internet to non-academic uses and users and triggered numerous commercial developments. The rapid evolution and availability of Internet-based technologies has, in turn, fueled extensive efforts and discussions in the areas of education, professional development, and distance learning.

The ease with which the Internet bridges distance and access barriers between teacher, student, and resources such as libraries, has suggested new models of teaching and learning that are expected to mature and prevail in the 21st century. The numerous interconnected computers communicating over the Internet, and the nature of the software services now available on them, has led to the notion of a World Wide Web of information resources. We will reserve the name "Internet" for the physical vehicle allowing connectivity and communication, and use the term "Web" for this vehicle augmented by rapidly developing software tools and repositories of data. When we use such terms as "Web technology" we mean primarily the software interface seen by a computer user, and we are less concerned with issues of physical connectivity or bandwidth. It is from the development of software on a distributed computer system, with strong communications tools and utilities, that we expect to see the most profound influences on education. The interested reader is referred to the universal resource locator (URL)

http://e2.tam.uiuc.edu/Edu-Tech

where the speaker has organized much of the material used in the presentation of this paper.

The University of Illinois at Urbana-Champaign is an active member of a select group of U.S. universities pioneering Web technology. During the fall of 1994, the College of Engineering at UIUC initiated a number of pilot projects utilizing the new Web technology as a supplement to in-class teaching. The Department of Physics (which at UIUC is part of the College of Engineering) and the Department of Theoretical and Applied Mechanics (TAM) have been most active in view of our large teaching loads in several "service courses." These courses, which include introductory physics, statics and dynamics, strength of materials, and so on, are required in most engineering curricula. At a large public university this requirement quickly leads to large course enrollment counts. For example, in TAM we are providing instruction to some 2000 students from various curricula each year in our courses, and we have been doing so for the better part of a century. Although the courses under discussion are the same courses that majors in Physics and TAM take, most of the students in these courses do not have Physics or TAM as their home departments. Thus, conventional vehicles for disseminating information, such as bulletin boards or notes in mailboxes are ineffectual or simply unavailable.

In TAM we have always maintained an expanded "interface" for students, through office hours by the faculty, racks for returning problem sets to students, a system of display cases with posted assignments and problem solutions, and a study hall staffed by teaching assistants more-or-less continuously during the week. The Web is a useful supplement to these conventional modes of keeping in touch with students, and is, in turn, supplemented by software tools that UIUC has developed, such as the GradeBook software, which allows instructors to post grades and students to look them up with the confidentiality of login and password access.

In the Physics Department, Prof. Alfred Hubler and his group are developing a Web-based, courseware authoring system known as CyberProf. The philosophy of this effort is to develop extensive software capabilities within a single program framework, consistently with an eye to educational use. The CyberProf program is able to reduce and evaluate algebraic expressions offered by the student in response to questions, and thus, through instant feedback, to provide a certain level of on-line drill and evaluation.

In TAM we have taken a rather different approach. Our philosophy is to utilize as much of the substantial ongoing commercial software development as we can, which means remaining fully conversant with that technology and constantly assessing and adapting it to educational needs. We have developed an extensive Web site for the subject of mechanics, that we call Mechanics on the Internet. This Web site points to the usual logistical information that one expects to find, such as listings of programs and activities, curriculum requirements at both undergraduate and graduate levels, procedures for applying to the program, ongoing seminars and related activities, biographical data on faculty and staff, a description of facilities, abstracts of recent research reports, and a database of conferences and workshops in mechanics world-wide. There are a few special features, such as pages on the history of the Department and its founding Department Head Arthur Newell Talbot, and pages on the upcoming 20th International Congress of Theoretical and Applied Mechanics, to be held in Chicago in 2000, for which the Department is the lead in a consortium of primarily midwestern schools. There are also a number of detailed course notes and interactive courseware materials with links to various utilities, help engines, search engines and interactive interfaces. This part of the Web site currently includes materials for six courses, ranging from undergraduate to graduate levels, with electronic discussion groups, an e-mail interactive interface, a dictionary, and interactive interfaces to commercial mathematics software, such as Mathematica, MatLab and MAPLE. The reader may at this stage wish to peruse this Web site while continuing with the paper. The departmental site is at URL

http://www.tam.uiuc.edu

and the courseware materials reside at URL

http://e2.tam.uiuc.edu

Both the CyberProf and the Mechanics on the Internet projects have attracted interest worldwide. These projects show how the Web can be used as a flexible medium for a new model of teaching. On one hand, Web-based instructional materials are used by on-campus students as a valuable supplement to lectures and discussion sections. They are useful for students who fall behind, or miss a class for any of a variety of reasons. The materials on the Web are always those produced or approved by the instructor, and will usually provide a superior resource to the student than copying class notes from a friend. Assignments and worked problems are always the "official" versions. In some courses we have quickly evolved to a mode of operation where we do not hand out paper assignments or solutions to students (although we still collect and grade assignments done by students). On the other hand, the Mechanics on the Internet courses are being used for distance education, for example in offering extension courses to students at an industrial site. In some cases, the Web site is self-contained. In other cases, it provides a supplement to a videotape-based course.

In developing the Mechanics on the Internet site we shared the experience of many institutions with regard to courseware that we first saw--simple course outlines and logistics posted by faculty. Then more comprehensive collections of course material were prepared, including lecture slides, lecture notes or supplemental materials not covered in class, homework problems and their solutions, exams and their solutions, etc. At about this stage we understood how to include interactive program modules in our pages. Thus, we can now put examples of code written, for example, in Mathematica and the student can edit and execute this code, including the drawing of graphs and other figures, without having the Mathematica program resident on the student's machine. In this way the content of the Web site becomes genuine hypertext, and the beginnings of new types of textbook and lecture material are clearly discernible. We also understood that if we were going to serve large populations of students, say 200-300 in a given course, we needed to have dedicated servers to handle the requests. Thus, at this stage we began securing funds for computer servers dedicated to Web-based instructional materials. Upgrading such servers, and configuring them to meet demands, remains a departmental priority.

The use of the Web for teaching, and particularly the more ambitious projects mentioned above, are beginning to have an impact on the academic culture in the research university in several ways:

1. The technological challenges in producing well-thought-out instructional materials, and the general mastery of the technology of producing Web pages puts aspects of this activity close to the frontiers of research.
2. The availability of course materials for all to see is a new mode of operation for most faculty. The days of the informal hand-written notes, or the bungled derivation quickly erased from the blackboard at the conclusion of the lecture are numbered. With the Web materials, the record of what went on in a given course is there for everyone to access and assess.
3. The asynchronous element, and the ability to use communication tools to access several instructors or fellow students at once, improves the dialog in the course between student and instructor and among the students themselves. This connectivity can lead to heightened motivation and improved assimilation of the material.
4. Because of the potential of increased revenues from distance education, this type of teaching is being watched closely by administrators and business-affairs people in the university. The potential for licensing software tools and for selling course modules that can be delivered over the Web is of considerable interest to several administrative offices on our campus.

We expect these trends to grow in the next few years.

This section describes, in greater detail, highlights of the Mechanics on the Internet Web site and emphasizes the ingredients that appear to be most useful as evidenced by access statistics. The Mechanics on the Internet site includes an extensive collection of material covering six courses in the general area of mechanics. These courses are

TAM 221--Introduction to Solid Mechanics, a 3-semester-hour large-enrollment, sophomore-junior level undergraduate course that concentrates on strength of materials issues, offered every semester and during summer session, and used as a requirement by several engineering curricula and as an elective by all. The specific URL is http://e2.tam.uiuc.edu/TAM221/index

TAM 370--Introduction to Computational Mechanics, a 3-semester-hour senior undergraduate or first-year graduate course that provides a broad introduction to computational fluid dynamics and computational solid mechanics, emphasizing the communality of techniques and the general unity of purpose in computational investigations of continuum mechanical problems. See Fig. 1. This course is part of the Computational Science and Engineering program at UIUC. The URL is http://e2.tam.uiuc.edu/TAM370

TAM 441--Mathematical Methods for Engineers I, a 1-unit graduate course in applied mathematical methods for problems in the engineering sciences. It is followed by TAM 442 (for which the Web site is in preliminary stages). We require this course of all TAM graduate students, and it is used widely by other curricula as well. The URL is http://e2.tam.uiuc.edu/TAM441

TAM 451-452--Solid Mechanics I-II, a two-semester graduate course sequence on the fundamentals of solid mechanics. TAM 451 is required of all TAM graduate students, and the two-semester sequence is used widely within the College of Engineering as a fundamentals based introduction to the subject. The Web site is currently being expanded. The URL is http://e2.tam.uiuc.edu/TAM452

TAM 485 Fracture Mechanics, an advanced, topical graduate course on fracture mechanics theory. This Web site is our first "self-contained" site in the sense that it has been used as the sole resource for students taking this course. The Web site requires access permissions. Login as "guest" and use "tam" as password. The URL is http://e2.tam.uiuc.edu/Fracture

Interactive Mathematica Interface

This interface was first introduced during the Spring semester 1995 in TAM 221. The interface allows students to execute Mathematica commands from their browsers while the software resides and executes on the Web server. We have used this interface successfully in TAM 221, where the students may not know much about Mathematica, and later in TAM 370 (Fig. 1) and TAM 452, where we would encourage the student to spend some time learning more about a symbolic algebra language. The Mathematica code is prepared in such a way that it offers the student simple syntax while performing tedious and repetitive calculations. The student can then explore the concept in greater detail by editing the code, usually just by inserting different values for certain arguments. This experimentation allows the student to gain insight considerably beyond that obtained by studying the few worked examples in a text or working a couple of assigned problems. Typically, the theory is introduced and a few examples are worked in the "old-fashioned" way. Then the Mathematica based code is provided, with an easy-to-use syntax that lends itself to essentially unlimited exploration. For example, in TAM 221 we have provided code of this type for Mohr's circle, and for solving beam problems both numerically and symbolically. In TAM 370 we used Mathematica to explore the convergence characteristics of a number of finite-difference schemes and for studying repeated subharmonic bifurcations in the logistic map.

The usefulness of these "interactive interfaces" exemplified by the Mathematica implementation in our Mechanics on the Internet site suggests extensions of the same technology to popular mechanics software, such as finite-element packages. In addition, there are new technologies that allow for the remote execution of virtually any software on a server while the interface displays images through the Web browser on the client's side. This remote execution opens the door for very promising developments, especially in teaching mechanics concepts in elementary courses. A program such as WorkingModel from Knowledge Revolution, Inc., for dynamics simulations may be used, for example, to allow a student to explore instructor-authored examples in support of concepts treated in lectures. The opportunities presented by these evolving technologies for interactive learning appear to have no bounds

Problem Books

The benefits of "problem books," i.e. databases of worked examples, are evident. The Mechanics on the Internet site includes a collection of homework and exam solutions for TAM 221, a collection of Mathematica and MAPLE notebooks for TAM 370, as well as a variety of solved problems in other courses. The utility of these collections increases substantially as they grow in size and scope, since one can establish cross-links between related sets of problems, and between problems and the required theory. Furthermore, the availability of such collections in print is limited. Our problem collections on the Web have often experienced nearly 2000 hits per day. There are some intriguing issues here, given that many universities teach courses similar to ours, often using the same textbook. Entrepreneurial students may find it easier to secure the solution of a given homework problem by browsing the Web than by actually sitting down and solving the assignment! This problem is somewhat akin to the issues raised by repositories of papers on various subjects that have been posted on the Web and used by high-school students. Locally the problem can be controlled from semester to semester by timed release of solutions, but if several institutions are developing similar Web pages, conflicts are bound to arise. Of course, there are already such conflicts through the unauthorized distribution of solutions manuals and the collections of problem solutions maintained by student organizations. Ultimately, tests and exams will have to be designed as checks of students assimilation and retention of the material, suggesting that such tests and exams should not be administered by computer!

Software Manuals and Help Engines

Another popular ingredient of the Mechanics on the Internet site is its on-line set of help engines. These are electronic versions of the manuals for selected software packages, such as Mathematica, MAPLE:, LaTeX and MatLab. For example, we have developed a help engine for MatLab that is fully cross-linked and complete. It contains description, syntax, and file listings for hundreds of MatLab commands, and is much more convenient to use than a manual in book form. Similar engines are being prepared for other software. The availability of such resources adds to the enrichment of the learning environment for the students, and encourages both faculty and students to use a wider range of tools. An additional feature of Web-based course material is content indexing. This feature allows the students to search, through interactive Web forms, for their target course material. Evidently, this feature becomes ever more powerful as the Web content grows, since it presents the student with all related information at once. We have included search engines in our Mechanics on the Internet site, at the root level, as well as in major course sites, such as those for TAM 452 and TAM 485.

Enrichment of Context

The Web allows the instructor to provide students with a richer set of instructional materials through links to other useful sites. For example, one can bring in historical information on the individuals whose work in mechanics is being taught. One can provide the option for the student to explore what Newton would have experienced as contemporary developments in music, art, or literature, for example. One can link to sites containing material on the politics and history of that era. This is, clearly, non-essential and, for instruction in engineering, quite unconventional, but it may serve students well by allowing them to place the material in a broader context and, maybe, thereby gain additional motivation or assist retention. Providing links to courses in mathematics, physics or chemistry can give the student a better sense of the interdependence of the knowledge he/she is acquiring in science and engineering, and can provide a useful possibility for review or "just-in-time" instruction.

Virtual Laboratories

One of the essential things that is missing from distance education is laboratory experience. Two of our large undergraduate courses have a comprehensive laboratory component, one in behavior of engineering materials and another in fluid mechanics. The computers used in these laboratories are networked and are capable of running a browser. Hence, it is reasonable to put such things as the laboratory manual, and various laboratory guides, along with templates for data analysis, stylistic guides on writing lab reports, and related material on the Web. We are proceeding with projects of this sort. While these tools are primarily useful for our own students, since they are closely keyed to the experimental setups that we have on-site, they can in time be augmented with still photos and video-clips to provide a kind of "virtual lab," where a student without access to the real lab can get at least some feeling for what conducting a given experiment might be like. This "virtual lab" may be seen as a teaching counterpart of the "virtual instrument" access via the Web to sophisticated, one-of-a-kind equipment maintained at national centers. This type of software environment is also useful for physically disabled students who may not be able to turn knobs or take readings in a conventional laboratory setting.

The potential of the Web for distance education is very promising. TAM has been engaged in pilot experiments of Web-based distance education since the Spring semester 1995, when we enrolled a California-resident student in TAM 221 using our Web site for that course. We have used the TAM 441 site as a supplement to a videotape-based course offered to engineers at Caterpillar. Our most significant "experiment" in this direction has been the Web offering of TAM 485 during the Fall semester 1996. The course was offered while the instructor (TGS) was on sabbatical leave in Cairo, Egypt. It was offered again in Spring semester 1997 to engineers at Caterpillar. The home page for TAM 485 is completely self-sufficient. The student is presented with image maps linking him/her to all course ingredients. The "Today's Lecture" set of links takes the student to a presentation that explains the objectives of the day's lecture, and then moves to an HTML version of the lecture notes. The third link in this group points to an Adobe Acrobat version of the lecture notes for high-quality printing. The content of TAM 485 benefits from topics discussed in the course TAM 452. Hence, we have provided links within the TAM 485 site to relevant topics in elasticity theory in the TAM 452 site. We decided to avoid extensive use of audio- and video-conferencing in this particular offering. The rationale here has to do with the state of global networking infrastructure and its current inability to handle such technologies in a serious way. The bandwidth required for full utilization of audio/video ingredients is much larger than the existing capacity of today's networks. As an alternative, the instructor-student communications in TAM 485 take place through multi-media electronic mail and a Web-based discussion group. All course announcements are posted to the discussion group together with threads of student-to-student and student-to-instructor "conversations."

The process of homework/examination delivery and grading is a bit more complex. For TAM 485 we asked students to fax their hand-written homework solutions to a fax modem on the UIUC campus. The fax modem is attached to a computer that automatically notifies the instructor upon receipt of a new fax. The instructor then uses FTP to collect the faxed homeworks. The homeworks (which are essentially TIFF images) are graded manually using electronic annotation software. The graded images are then converted to HTML, and are posted to the Web site in secure directories. The security in this context refers to the fact that only the owner of a given homework can access the page with his/her homework. Thus, the TAM 485 model offers personalized grading to individual students.

The rapid evolution in Web authoring technologies has introduced significant tools for an improved teaching model. Recent key technologies include the Java authoring language, Java Script, NeXT/Apple Web Objects, Internet-Database Interfaces, Shockwave, Visual Basic scripts, and the new Dynamic HTML standard. These technologies add to a wealth of other technologies for on-line authoring that include frames, tables, server-push, active server pages, server-side includes (SSI), ActiveX, and a large array of plug-ins to provide a very powerful toolkit for creative learning environments. The aforementioned Mathematica interactive interface used in our Mechanics on the Internet site provides one example of the almost endless possibilities. Using Java, one can develop far more sophisticated "Web applications" that allow students a greater level of interactivity. For example, PWS Publishing has recently developed a Java-powered application called Dr. Beam. This product allows for a fully interactive exploration of solutions to beam problems. The student constructs the problem by dragging relevant ingredients, such as loads and supports, to the considered beam. The solution, expressed in terms of displacement, shear-force, and bending-moment diagrams, is generated dynamically. The student can move the load along the span of the beam in an interactive mode while the solution updates itself instantaneously. The interested reader may check out this software by visiting the URL http://www.pws.com/pws/vismech.html. A similar development has been undertaken by Addison-Wesley in their Interactive Series in Dynamics, Differential Equatlons and Physics. The AWI series also introduces interactive tutorials using Java-powered applets. Such tutorials take advantage of the underlying programming language to provide a very useful learning environment.

The pilot projects at UIUC and elsewhere have been useful as first steps towards a new learning model involving the use of the Web. We may summarize some of our early observations as follows:

1. Student acceptance of Web technology: Graduate (advanced or older) students appear to have a higher appreciation for Web-based education than undergraduate students. However, the early resistance exhibited by undergraduates fades as they become comfortable with the new technology and see it as an aid rather than an additional burden or requirement.
2. Faculty acceptance of Web technology: Faculty in research-oriented schools are typically encouraged by the university reward system to pursue research funding as opposed to increased teaching activity. However, interest in Web development can be strong if a case is made for possible revenue.
3. Nature of present Web technology: The majority of existing Web efforts in education are confined to static course material. There is a definite need for increased utilization of evolving technologies and more interactive Web-based course materials.

Towards a New Learning Model

It appears to us that Web technologies offer a remarkable medium for a new learning model that is destined to dominate education in the 21st century. Learning has generally been accomplished through a classical model involving direct instruction. The classical learning model is restricted by limitations of both time and physical space. This model confines the student to the experiences offered by the instructor, at the time scheduled, and to the locally available reference materials. When applied in schools with limited financial resources, the classical model often suffers from lack of resources (such as laboratories, software, and reference materials). Video-based instruction, as we currently offer to off-campus students, suffers from similar limitations except for the time limitation, since a videotape may be viewed at any convenient time. However, video-based course materials may quickly become out of date, and unless they are professionally produced, which can make the cost prohibitive, they may be exceedingly dull. Moreover, video-based courses lack the important component of student involvement and engagement in the learning process.

The Web potentially offers a world-wide forum in which to teach courses. One can assume that each student at any time has, for example, the Encyclopedia Britannica at his/her disposal as a "baseline" of factual information. This access immediately heightens the level of the course discussion. Course material can be dynamically updated. Course text, examples and exercises can be interactive in the sense that equations can be immediately illustrated with graphs, simulations and video-clips; the effect of changing parameters can be seen in "real time;" and links to other Web sites can be executed according to the interests of the student. The Web-based learning model is essentially free from limitations of space and time, while it reaches students around the world with great ease (given adequate bandwidth). In addition, the Web-based learning model offers students a wealth of information that was never available through the classical model. For example, the student who suddenly becomes interested in some fact or interrelation of facts may pursue such an avenue even though the instructor may not know the answer to a particular query, and certainly would have a hard time producing sample data or materials on short notice. The possibility of linking to information worldwide in a multitude of formats creates a remarkably rich leaning medium that opens the doors for great creativity and holds considerable promise.

Issues of Concern

We have outlined the potential of the Web in the development of a new learning model. However, effective utilization of this resource requires a re-thinking of faculty roles, training, and university reward systems. Faculty in science and engineering need to become familiar with the evolving technologies before they can utilize them to construct creative teaching environments. The need for such skill development is evident once one subscribes to the value of the new technology. Thus, faculty time and attention has to include yet another time-consuming activity in addition to the usual activities of research, classroom teaching, and university and public service. The university reward system must adjust to reflect this change. The creation of a major Web site is comparable in scope to the writing of a textbook--and it is well known that the rewards for textbook writing in a major research university are not always so clear.

Of great concern in most discussions of education and technology is the issue of copyright and intellectual property rights. These issues have already been faced and dealt with in the realm of textbooks and monographs, but the use of sometimes considerable computer resources to craft a Web site, and the necessity of providing servers on which to run it, naturally lead to a university's assertion of some claims on the material. Most universities are still in the very preliminary stages of sorting all this out. Course materials on the Web are also extremely easy to download or"pirate," and protection schemes are cumbersome and unnatural. How does an individual, or an institution, protect itself against such acts? Items such as curricula and syllabi now suddenly acquire value since they are being displayed and exported across the Web and are no longer confined to a localized institution, department, or program, as has been the case in the past. Quality offerings provided over the Web also pose a threat for smaller programs. If the student can access a given course from a major university, then why should he/she remain interested in the offerings of the local school, assuming these are not a match for what is on the Web? One can envision that certain Web offerings will dominate certain types of instruction, and that faculty in smaller programs may be reduced to conducting discussion and problem-solving sessions to supplement the main lecture course being delivered over the Web. In extreme cases one may speculate about layoffs or firings. It has been suggested that many colleges and universities will be reduced to locations that offer certification, and it has been pointed out that one only needs a rather limited number of such locations.

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