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Teaching in a Computer Classroom with a

Hyperlinked, Interactive Book

Robert O. Harger

Electrical Engineering Department

University of Maryland

College Park, MD 20748

Abstract

A first course in digital signal processing is being taught with an interactive book in a computer classroom. The interactive book is a set of Mathcad documents bound with navigation, full text search, annotation and special pasting facilities. The documents consist of editable and active text, graphical and mathematical regions. The computer classroom has twenty student PC workstations, forty seats and an instructor's podium with PC workstation, lighting and projection (computer screen, overhead, and video) controls. Discussed are the choice of software, interactive book, computer classroom, teaching methods, student evaluations and future plans.

I Introduction

Mathematical models are an important foundation for the practice of science and engineering . Much effort is spent on model creation, design, analysis, simulation and verification. This part of professional practice sets the content of much of the educational material taught engineers and scientists. High level mathematical programming languages, HLMPLs, are heavily used in this activity by many professionals. The recent maturing of some HLMPLs makes possible the direct expression of such models- e.g., in a traditional format- in an interactive interface, making possible the performing of important aspects of model creation, design, analysis, simulation and verification- and also the reporting of such activity- in a highly efficient manner. Indeed, one may argue that model and simulation are becoming synonymous [1].

These mature HLMPLs are admirably suited for the delivery of a substantial part of a modern professional science and engineering education. The conceptual level of discussion is raised by relegating unedifying calculation to the computer and by efficiently enabling the powerful learning methods of visualization [2] and trial-and-error experimentation [3,4]. An interactive book provides a logical and familiar structure to a collection of HLMPL documents by binding them with electronic links.

The computer classroom is a natural evolution of the traditional classroom [5]. It consists of individual workstations for students, each running applications such as an interactive book, and an instructor's console with a workstation and environmental and presentation controls. The computer classroom can enable active "learning by doing" to supplement the more passive "learning by seeing and hearing", nearly doubling the learning effectiveness [6]. The interactive book and the computer classroom provide an enriched environment for the application of learning methods such as student-selected syllabus, student-selected pace, group interaction, project presentation and instructor and group mentoring. The HLMPL allows implementation of electronic project and portfolio submission in self-checking form.

Specifically discussed here is teaching an introduction to Digital Signal Processing, DSP, with an interactive book in a computer classroom [7].

II HLMPL Selection

The selection of a specific HLMPL application package involves an evaluation of many attributes. The well known Mathcad software [8] was chosen because it is outstanding on several important attributes. It has some exceptional features for a very modest price: (i) an excellent graphical interface as a familiar worksheet, (ii) a low learning threshold, (iii) symbolic, in addition to numerical, mathematics, (iv) text editing and conventional mathematics formatting for self-documentation and reports, (v) easy document linking and (vi) interactive book capability. Mathcad also has (vii) an appropriate level of implementation of the required operations and (viii) can call lower level language programs. (x) It has wide use in the professional community with more than one half million registered users.

Mathcad's low learning threshold means meaningful activity can begin immediately. Its academic cost ($80) allows students to install it on their own computer: about one half do so. The excellent worksheet interface feels natural almost immediately. The most recent Version, 6.0, has programming structures, animation, e-mail and built-in Web browser. It can link and access documents in the local file system, in a Notes database and on the World Wide Web. Mathcad has been used frequently in teaching: see, e.g., [9]. While earlier versions of Mathcad are available for the Macintosh and Sun computers, the latest version is presently available only for the Microsoft Windows environment- which, however, is increasingly the dominant computer environment. The Windows 3.1 environment was used in this activity.

As is true of a good HLMPL, Mathcad is remarkable in that quite complicated mathematical problems can be solved in a small document- even a single page- that cannot be solved by paper-and-pencil analysis or, because of time restraints and limited student programming skills, by conventional computer languages. Mathcad's implementation level is well-matched to the course level, a senior elective. These capabilities allow re-orienting the teaching, as is the practice, of DSP toward numerical algorithms and solutions and raising the conceptual level of the course while covering the topics of a standard introduction [10,11].

III Interactive Book

While teaching digital signal processing over a number of years, a set of Mathcad documents was developed that exemplified all the topics covered in a first DSP course. These were made available to the students in varying states, with typical assignments being their elaboration, extension or application. In response to student requests, the set was brought closer to traditional text form using Mathcad's text editing feature. Of course, each document was interactive, unlike a traditional text. Each document, averaging about a dozen pages in length, corresponded to a chapter and roughly to one lecture of one and a quarter hours. The set was made available on a file server, along with hard copies in the library for short-term loan.

The Mathsoft Corporation made available to the author, for his educational purposes, an authoring kit with which the set of documents was bound into an interactive book, hyperlinking the documents to each other and a table of contents and index, with facilities for full text search, annotation, special pasting, book navigation controls and file compression. The interactive book has now been used for three semesters in the computer classroom. It is the primary text with traditional texts used as references [10,11].

The interactive book runs under Mathcad (version 5.0 or higher) running under Microsoft Windows. It is available on file servers in the College and in the computer classroom and can be downloaded for installation on student PCs. The compressed files, read transparently by Mathcad, fit on one 3.5 inch diskette. A hardcopy, of about 400 pages, is made available at very modest cost ($15) by the University's reprographic service and contains the installation instructions for the interactive book.

The interactive book will be described now, within the severe limitations of the print medium. Selected screen captures are available on the accompanying CD-ROM. We here show some cropped screen captures. After Mathcad 6.0+ is opened under Microsoft Windows 3.1 and the "Books" menu item selected, a drop-down menu appears (Fig. 1).

Clicking on "Digital Signal Processing" opens the title page of the interactive book (Fig. 2).

(Some of the menu bars have been suppressed to gain useful screen area.) The book's navigational palette is evident, with facilities for going to the table of contents, the index, preceding chapter, next chapter, previously accessed chapter, preceding page, and next page. Once the book is opened, the Books menu allows a choice of annotation options (Fig. 3): with these features the student can annotate his own copy of the book, the original copy always being available. Notice the full text search feature.

Each chapter of the book is a Mathcad document which consists of mathematical, graphical and text regions (Fig. 4).

These regions can be edited and copied and pasted to student-created documents. (There is a special pasting feature to drag regions across documents.) Since the mathematics regions are easily edited, trial and error experimentation is greatly facilitated. The "Graphics" menu item leads to a menu with easy formatting features. (There are several graph types, including surface, contour and vector plots.)

The book also has hyperlinks to a special type of document that can be used variously. In Fig. 5 is shown a typical project description: in the left margin the icon indicates this type of link.

Clicking once on it gives the message that it leads to hints on beginning the project; clicking on it twice produces the "pop up" window shown in Fig. 6.

This particular project is discussed in the third class period. A solution is presented with the students participating and creating their own documents. The class is led to moving average filters, noise reduction, decision rules, and probability of error assessment in an easy way. Such an early demonstration of the capability to solve a real problem is strongly motivating.

The contents of the interactive book are similar to standard choices. The core content covers an introduction to digital signals and systems (digital signals, digital finite impulse response (FIR) filters, and Discrete Fourier Transform (DFT) and Discrete Time Fourier Transform (DTFT) and their properties), FIR filters (linear phase types, geometric view, design by frequency sampling), sampling (decimation and interpolation), and infinite impulse response (IIR) filters (linear difference equations, geometric view, types, design for a specified magnitude).

Note that the discussion leads quickly to the DFT for which Mathcad has built-in fast algorithms, varieties of the Fast Fourier Transform (FFT). The FFT renders feasible both practical DSP and teaching with the interactive book! Focusing in the first part of the course on finite length sequences, which are literally the only kind encountered in practice, has major advantages. First, motivating topics such as image processing are reachable early. Second, analysis questions of stability, or convergence, are delayed, allowing DSP activity instead of preoccupation with mathematical analysis. There is no traditional chapter on the Z Transform: it is introduced while discussing the DTFT, mainly because singularities- important for the intuitive insight into filter operation- may lie off the unit circle in the complex plane. Little time is spent on conventional analytic transform computation and then it may be done symbolically.

Additionally there are chapters on FIR and IIR filter design, spectral density estimation, adaptive filtering, image processing and radar systems. These provide a source for independent student projects. The level of sophistication achievable in the course and with Mathcad is indicated in Figure 7 which is an edited extraction from the book. It shows a solution to a simple system identification problem using the LMS algorithm to determine, adaptively, an FIR filter model.

The Symbolic menu is shown in Figure 8: note the availability of Fourier and Z Transforms.

Some new features of Mathcad 6.0+ are mentioned that may be used in the future. It has an easy animation capability (Fig. 9) to create AVI files. This has been used to simulate the "eye diagram" seen on CRTs when testing digital communication channels for intersymbol interference.

It has an easy capability to link Mathcad documents that reside locally, in a Notes data base or on the World Wide Web (Figure 10). The documents to be linked are opened in two windows. A text region is selected in one window and the link effected by simply clicking in the other window!

Further, among other communication capabilities, Mathcad has a built-in Web browser (Fig. 11). This feature is being used by the instructor to get

.

student work.

IV Computer Classroom

The computer classroom used here contains 20 student Pentium PCs, recessed into custom-built tables, with 40 seats (Figure 12). The room is about 1000 sq.ft. in area, is carpeted, and has track lighting of controllable intensity, a white board and screen. The instructor's console is elevated and has a PC and controls for an Infocus LitePro Model 550 active-matrix LCD projector with VGA, video, and stereo sound capabilities and a sophisticated overhead projector. All computers are networked to a server which has a wide variety of software applications, including the interactive book, and

complete communications.

A more abrupt departure from the traditional classroom is the teaching theater, which generally requires a production staff. The computer classroom makes more modest demands on the production of the desired teaching material, clearly within the capability of the instructor himself. It is, e.g., well matched to the interactive book described here.

The computer classroom is fully scheduled until about 6 PM but is made generally available until midnight. Also, the conventional College computing facilities are open except for early morning hours and have computers running the interactive book from a file server with networked communications.

V Instructional Methods

Each class session can involve one or more of several learning methods. The students are asked to review the material to be discussed prior to the session. The instructor may go over parts of the chapter with the students participating by varying parameters in the examples, perhaps to answer posed questions. The book contains exercises for self testing and reinforcement. The students can work independently on the simpler exercises, with mentoring by the instructor. They like to have exercise solutions and many are now given en passant. They can work in the session on more difficult exercises and begin projects, especially in self-selected groups and mentored by themselves and the instructor. In the first part of the course several projects are jointly worked in class and the instructor's solution is made available electronically. Students maintain their own annotated copy of the book on one diskette. Little traditional note taking is done. An impromptu element is present in an active learning environment: supplementary material is delivered on the computer, the overhead, and, increasingly rarely, handouts. The white board is hardly ever used.

Each student develops a self-selected and self-paced schedule which must cover the course core and include design projects and a final project. This schedule can be revised at any time with notice to the instructor. (Some reminders are required for many students!) As a consequence, a student's interest in a specific session can vary from "need to know" to "nice to know".

Student work is evaluated in two or three portfolios and a final project, which are entirely Mathcad documents submitted on diskette or by file transfer. A portfolio is a purposeful collection of exercises and projects done over about a five week period, selected by the student, to exhibit his or her efforts, progress and achievements [12]. The final design project is presented to the class in the computer classroom. The evaluation criteria was this: to pass the course with an average grade, command of the core material is to be demonstrated; creativity must be shown for an above average grade. Examples of previous student work help define "creativity".

Supplementary tutoring and work periods totaling about five hours per week have been scheduled in the computer classroom in response to student requests. The backgrounds of the students are quite diverse and many have requested additional help. The department support normally made available for student assistance- e.g., grading- has been used to employ a graduate of the course as a tutor in these sessions as well as in class.

Communication between the instructor and students outside of class is by office hours, electronic mail and, recently, by file transfer. The interactive book is run in the instructor's office on a laptop computer driving an attached monitor for easier student viewing. Electronic mail is the preferred means of communication for a majority of students.

Trials with submission of work by file transfer is being conducted. E.g., the built-in Web browser in Mathcad makes it very convenient to access student work which is submitted as a Mathcad document. Efficiency and security problems are being studied.

VI Evaluation

Student evaluations of the interactive book, the computer classroom, the course and the instruction were routinely requested to assist in making improvements and lead to the following conclusions.

The students view both the interactive book and the computer classroom very positively. The third time the course was offered in this manner it was over-subscribed. Most say they would again take a course with an interactive book and/or a course in a computer classroom. The most frequent response to the question "What did you like most about the electronic book?" cites the ability to change parameters in examples and immediately see the consequences. The most frequent response to the question "What did you like most about the electronic book?" cites the hands-on experience of actually implementing what is being learned.

A substantial majority feel that both the interactive book and the computer classroom enable self-pacing, self-selection, diverse learning styles, and group learning. A few were uncomfortable with self-selection and self-pacing.

The self-selection of topics beyond the core works well and is thought to be a major reason for the apparent success of the course. Some students require direction- usually just by drawing out and elaborating on their interests and experience- but many already have well-defined interests from hobbies, employment and research projects.

The core content is delivered in the first two-thirds of the course. This gives students a degree of freedom in order to pace themselves. They are encouraged to spend more time to grasp the core if they require it. The material covered in the remaining third of the course is influenced by student interest. They are not "responsible" for it in the traditional sense.

The elements of interactive book, computer classroom, flexible learning options and future employers' requirements may have helped establish a relaxed atmosphere conducive to group work, which has usually been viewed negatively [13]. Assessment by interim portfolios and a final project was very much preferred to traditional testing.

Mathcad was regarded favorably nearly unanimously. Most thought it not difficult to learn and a pleasure to work with. The computer experience of students is increasing very rapidly: almost all of the latest class have experience with a windows operating system and have learned several applications. It is neither necessary nor desirable to fix on a uniform application for the undergraduate years. Notably, almost all purchase the hardcopy of the book.

The final projects, presented via active Mathcad documents in the computer classroom, have included a multi-band spectral estimator with FIR filters, a multi-band equalizer with Chebyshev IIR filters, sub-band filtering for speech compression and decompression for wireless transmission, a bass booster for audio (sound file and file conversion program found by the student on the Internet), the generation of Gauss-Markov random fields, image restoration from noise and blurring by inverse filtering, image restoration by a maximum entropy method, PAM communication with decision-directed equalization, Armstrong FM receiver simulation, image filter design by transformation of a one-dimensional design for surface wave detection, an audio cross-over network with FIR filters, sub-band image filtering, speech processing with LPC estimation, and, especially impressively, simulation of some parts of a v34 modem algorithm in conjunction with actual complete system implementation on a DSP board for a Texas Instruments Corporation competition! The students ask for very little guidance in their projects.

In conclusion, the introduction of DSP with an interactive book in a computer classroom is regarded as successful by the students and the instructor. This instructional method requires careful planning and dedicated staff support to avoid mischance which can quickly disrupt the learning atmosphere and degrade student motivation.

Creating the interactive book required directly about one man-year. The result is a markedly more effective way to present this material. This scholarly activity, as distinct from research and consulting, was supported by the Department, College and University, modestly in funds but importantly in spirit, and also by Mathsoft, Inc. Effectively using it and the computer classroom required new skills fairly easily learned. Relative to the traditional classroom, as much or more expertise is required but the instructor functions more as a mentor, resulting in a relaxed and more collegial atmosphere. The real reward is to productively participate with the students in one aspect of "teaching and learning ... in the age of the inconceivable" [4].

VII Future Plans and Possibilities

The author's department is planning a 36-seat computer classroom with the additional capabilities afforded by, e.g., servers for X-Windows- making use of UNIX software such as Khoros possible, selection of computer screen presentation and projection, and SVGA screen projection. All PCs will have a multimedia capability.

The linking feature of Mathcad 6.0 makes the binding of Mathcad documents into an interactive book quite easy once the documents have been developed. It provides an alternative, albeit more primitive, to the Mathsoft-supplied authoring kit. The built-in Web browser and the easy linking and accessing of documents anywhere on the World Wide Web implies that distributed joint authorship of, and a distributed audience for, interactive books is possible.

VIII CD-ROM Contents

A number of screen captures of the interactive book have been made available on the accompanying CD-ROM as "gif" files. They can be viewed by accessing a table of contents HTML document called screens.htm. These give an idea, though limited, of the nature of the interactive book.

Also made available on the companion CD-ROM are three chapters from the interactive book. One way to access these files is by installing Mathcad as a helper application in Netscape. (The application/subtype is application/x-mathcad and the extension is mcd.) Thus the reader will require Mathcad. The first two, 1_bk.mcd and 2_bk.mcd, show how finite length sequences and filters are introduced. The third, 29_bk.mcd, shows, with a discussion of adaptive filters, the sophisticated level to which the treatment can be carried.

Additional Mathcad documents exhibiting the interactive book, additional course material and student projects can be viewed at the site http://www.glue.umd.edu/~ harger/rohhmpg.mcd .

IX References

[1] P.K. Davis, "Distributed interactive simulation in the evolution of DoD warfare modeling and simulation ", Proc. IEEE 83, pp 1138-1155, August 1995.

[2] P.J. Davis, "Visual versus linguistic/symbolic understanding", SIAM News, March 1995, p. 6.

[3] J.G. Kemeny, "How computers have changed the way I teach", Academic Computing, May/June 1988, pp. 44-61.

[4] A. Kugachev, "Teaching, learning and publishing in the age of the inconceivable", FOCUS, Dec. 1993, pp. 13-14.

[5] K.L. Conway, "Putting Technology in its place: the classroom", Institute for Academic Technology, Spring 1991, p. 5.

[6] Kulick, C-L. C. and J.A., "Effectiveness of computer-based instruction: an updated analysis", Computers in Human Behavior 7, 1991, pp. 75-94.

[7] R.O. Harger, "Using an Electronic Book in a Computer Classroom", SIAM Minisymposium on Electronic Textbooks and Virtual Classrooms, Charlotte, Oct. 1995.

[8] Mathcad 6.0+ User's Guide. Cambridge: Mathsoft, Inc., 1995.

[9] D.Y. Northam, "Introducing computer tools into a first course in electrical engineering", IEEE Trans. Educ. 38, pp. 13-16, Feb. 1995.

[10] L.B. Jackson, Digital Filters and Signal Processing, 3rd Ed. New York: Kluwer-Academic, 1995.

[11] A.V. Oppenheim and R.W. Schafer, Discrete-Time Signal Processing. New York: Prentice-Hall, 1989.

[12] A.E. Woolfolk, Educational Psychology, 6th Ed. Boston: Allyn and Bacon, 1995, p. 565.

[13] R.B. Hilborn, "Team learning for engineering students", IEEE Trans. Educ. 37, pp. 207-211, May 1994.