A WEB-BASED CORE MATH COURSE: REINVENTING THE CURRICULUM
Kristina Pfaff-Harris
University of Nevada, Reno
<kristina@greatbasin.com>
INTRODUCTION: ISSUES TO CONSIDER
In designing a course to be offered on the Worldwide Web (WWW), it was necessary to consider many key differences between such a course and traditional face-to-face (F2F) learning. In addition, the WWW offers more of an opportunity to expand our base of learning material to encompass resources outside the classroom. Suddenly, taking the students on "field trips" to other states or even other countries was possible, and we wished to take advantage of that fact.
At the same time, we realized that students in online courses could have difficulty feeling as if they were part of a class. The competition and communication which is taken for granted in a F2F course is necessarily somewhat limited in an online version. Because we intended to offer this to any student with the ability to access the web, we needed to take into account the possible differences in technology available to the students. Specifically, web access does not necessarily mean that the user has their own e-mail account, nor does it mean that the student has access to software which will allow them to use online real-time "chat" programs such as MOO [1] (Multi-user-domain, Object Oriented) or IRC (Internet Relay Chat) [2].
ADDRESSING THE ISSUES
COURSE MATERIALS
Dr. Donald Pfaff (PhD, Mathematics), was the Instructor and writer of the actual mathematics course materials for Math 120 Online. Since Math 120 is usually taken by students in non-mathematical or scientific disciplines, a common problem is helping students to overcome "math anxiety" or fear of mathematics. We questioned previous instructors of the F2F course and found out several areas where students seemed to have the most problems; Dr. Pfaff then re-worked the presentation of the material to give more time to some of those topics.
Another common problem students have is the terminology or specialized vocabulary of mathematics. The actual calculations may not be difficult, but students are often intimidated by terms such as "asymptote," "quadratic equation," "exponential function," or "logarithm." To address this, we created a vocabulary database where for each lesson, students could search for unfamiliar terms using a simple form on a web page.
For the past three years, the F2F Math 120 classes have integrated a writing component into the course, where students write two essays, stories, or other papers using the math concepts presented in the course. In our online version of Math 120, we expanded that concept to include a writing component in each lesson (Pfaff, 1996/97). The idea behind the writing assignment is twofold: first, the more practice students have in writing, the better writers they will become. Since good writing skills are important in many areas outside of the academic environment, thare important in many areas outside of the academic environment, the University of Nevada, Reno (UNR) encourages participation in its "Writing Across the Curriculum" project. Secondly, as many teachers know, explaining an answer or a concept in words often helps to strengthen the understanding of that concept. We had hoped thus to strengthen our students' understanding of some of the material in this way as the course progressed.
The tone of all course materials was above all intended to be friendly and humorous, in order to reduce students' resistance to the mathematical concepts. Most of the lectures included personal anecdotes, or "pep talks" to encourage the students to believe that learning math was by no means "only for the super-intelligent."
TAKING ADVANTAGE OF THE WORLDWIDE WEB
A very common lament of students in a course such as Math 120 is "I'm an English/Art/Physical Education major. Why do I have to learn Math?" Thankfully, the WWW offers us many opportunities to answer this question. Each lesson in Math 120 Online includes a section called "What's it For?" (Pfaff-Harris, 1997, March) where we discuss who uses the math from this lesson, why someone might want to use it, how it can help the student in life, historical background on some math concepts, and where we present links to sites on the web where this math is being used or talked about.
A lesson on finance and interest presents links to First Citizen's Bank interest calculators and Mastercard International. A lesson on exponential growth presents links to papers on population growth and a "Race Time Calculator," which calculates a time in which you can run a certain distance based on your time running another distance. A lesson on linear equations allows students to view experiments done by students in another state and published on the web. Other lessons present examples of math used in Biology, Geography, Art, English, and other courses at UNR by linking to materials on the website for the Mathematics Across the Curriculum project.
While some of the "What's it For?" sections are little more than explanations of how the type of reasoning used in mathematics can help in other areas, or discussions of why we are presenting the material in a certain way, we have tried to take advantage of the WWW environment to offer students a chance to see real-world examples of the course material across the country and the world.
THE TECHNOLOGY
Of course, all this material could not be a static collection of print on web pages if we wished to fulfill our goal of an interactive course at least equal to a F2F course. To obtain that interaction, we integrated many different CGI [3] (Common Gateway Interface) programs written in the Perl programming language [4]. These programs fall into two separate categories: those used to enhance or encourage communication between students and the Instructor, and "utility" programs used to perform course-related functions such as quizzes, the vocabulary search, and homework submission.
The simplest of these programs is used on our "Panic Page." Each page in the course has a small graphic at the page in the course has a small graphic at the bottom which reads "Panic Button." This "button," when selected, takes the student to a page where they may contact the Instructor or the Technical Designer of the course in order to get help. The program used on the Panic Page simply takes the student's name, email address, and a brief message, and e-mails it to the person selected. The panic page also includes photos of the Instructor and Technical Designer, so that students have a picture of whom they are contacting. This is a simple means of giving the feeling that "there are real people out there," but it is a start. The Panic Page uses a simple cgi program called MailStuf [5] which is freely available.
The next level up from the Panic Page in communication is our Message Board, which uses Matt Wright's WWWBoard [6] cgi program. The message board is linked to most of the lesson pages, and allows students to post public messages, questions, or comments to be read by others in the class. When enrollment increases, we plan eventually to have tutors monitor the newsboard in order to help students with their posted questions. We instituted the public messaging system in order to increase the sense of community in the course by letting students see and benefit from the questions of others.
The most complicated program is the Math 120 Mail System, which students can access from the "My Mail" button at the bottom of each page. This is a completely web-based, self-contained mail system similar to regular email, except that the messages do not leave the server but rather are stored on site until the recipient chooses to read them. If available, we can scan and include photographs of each student with their messages in order to further enhance the sense of being in a class with others. The "Web-B-Mail" [7] program allows mail only within a designated system (in this case, students who are registered in the course) and has the benefit of allowing the instructor to easily add and delete mail accounts with a simple HTML form. This internal mail system allows private messaging between students or between students and instructor just as "regular" e-mail does, but it addresses the problem of students having web access and no e-mail address. Just as with "regular" email, the user can send mail to anyone on the system, and can receive, reply, delete, or scan through their messages at will. In addition, the instructor can add or delete users, delete an offensive message from a user's mailbox, or send a message to all users on the system at once.
As for "utility" programs, the simplest of these is the one used for our vocabulary database search [8]. On each lesson page, a hyperlink is available to allow students to quickly look up a term they might have forgotten. On the vocabulary search page itself, students may search for a term, or send e-mail to the instructor if the word they are seeking is not found. The program includes another form interface for the instructor to add words and definitions/examples to the database easily.
A more complicated example is the program we use for homework submission. Since HTML does not incorporate mathematical symbols very well or (in some cases) not at all, we needed to devise a way for students to submit homework with such symbols online without forcing them to learn complicated HTML codes. To accomplish this, first, we created our own HTML-like syntax for entering mathematical symbols such as exponents and Greek letters, and included a tutorial for students on how to enter these special symbols. (The tutorial is linked from every homework submission page, in case students forget.) The syntax was fairly simple: ^x would translate to an exponential "x," x would translate to a subscript "x," 
a would translate to the Greek letter "alpha," and so on. We then created a set of small graphics files for various sub and superscript digits and letters, and for special characters, saved them in GIF (Graphics Interchange Format) files, and placed them on the website.
Once the student has entered these symbols, the program replaces them with HTML code which will show the graphics. For example, 2^x gets converted by the program into
2<img src=http://www.unr.edu/math120/math-symbols/powerx.gif alt=^x>
which then shows up as 2
in a web browser, while <alpha> gets converted to
<img src=http://www.unr.edu/math120/math-symbols/alpha.gif alt=(alpha)>
and shows up as .
The formatted code is then e-mailed to the instructor, who can view it in his own web browser in order to grade it.
The third and most problematic utility program used, is the one which handles the online quizzes. For this program, we had to consider how to avoid cheating while still giving students a reasonable amount of time to finish a quiz in what might be an unfamiliar online environment.
The quiz program has several features. It is password-protected, so that unauthorized people may not access a quiz. In addition, it is set up such that actual quiz materials may only be accessed through the program, and not as a regular web page. Because the materials are accessed through the program, we can time the students, and allow only a fixed number of minutes in which the students must complete the quiz or lose credit. (We allocated 45 minutes per quiz.) The quiz program then takes the students' answers, scores the quiz, and returns the result to the student immediately, while e-mailing the results to the instructor, and writing the scores to a results database in the same directory where the quiz is located. The program also gives the student the opportunity to go back and try the quiz again, but only the first attempt is e-mailed and written to the database.
While we have addressed several security issues with online quizzing here, it should be pointed out that there is no way to be sure that the student has not given out her password to a friend in order to have someone else take the quiz. Because of this, only certain quizzes count towards the student's final grade, and thesetowards the student's final grade, and these are awarded points similar to homework assignments, i.e. they will not be a majority of the total points awarded for work in the class. (The final exam for the course is proctored in a F2F environment, so any cheating will not help the student in the long run.) Ultimately, students themselves are responsible for maintaining their own academic integrity. Students determined to cheat at all costs will do so, while most others will not. With this in mind, we believe that these online quizzes are analogous to "take-home" tests, where the student is expected to honor the rules. We have placed limits on possible means of cheating, but take possible cheating into account in the way the quizzes are added to the final grade.
CONCLUSION
Of course, as with any new technology, there are still issues to consider and aspects of the course which can be improved upon. (We're certain that the students in this course will bring many such possible improvements to our attention as the course progresses.)
With Math 120 Online, we have attempted to take many things into consideration, from different learning styles to different available technologies. Through the use of CGI programs, links to other sites on the WWW, rewriting of the typical Math 120 curriculum, and other means outlined above, we believe we have created a non-threatening and interesting environment in which to learn mathematics. Although due to the mathematical symbols involved, students should use a graphical web browser of some sort, the course is readable to those with non-graphical and other "low tech" browsers as well, thus we have made the course accessible to a wide range of students.
It is our hope, then, that online courses such as this will prove to be as effective as traditional courses, and that by the use of Internet-based technologies we may reach a broader range of students than was possible before.
ADMINISTRATIVE SIDE NOTES
Many instructors at other institutions have indicated an interest in how we induced students to take our course, and how we publicized it. As of this writing, we have enrolled 6 students in this course, due in part to the fact that our Independent Study office agreed to reduce tuition by 50% for the first five students enrolled. In keeping with the spirit of the course, we sent out advertisements to local newsgroups proclaiming the benefits of the course and shamelessly using phases such as "We're practically giving away this tremendous opportunity!" (see http://www.unr.edu/math120/demos/ad.html), and this may have helped to reduce students' apprehensions about taking the course.
Currently, another issue is being investigated by administrators at UNR: that of how to figure an online course into teacher workload. This course has been intended to be offered as a regular semester-based course, but is, for the time being, offered through Independent Study in order to give us a chance to see what sort of problems may be encountered by the students. We believe that a course of this nature with a normal enrollment (say, 20 - 30 students) will create a workload similar to a F2F course. Although many of the materials are already online, grading and answering student questions should require as much or more time than a "regular" course.
ENDNOTES
1. MOO: A synchronous chat environment. The user logs in and sees a description of the "room" he is in. Others logged in can then type comments, and all users in the same "room" will see what the typist "said" on their own compu"said" on their own computer screens almost immediately. By typing commands such as "north," "south," "up," or "down, "users can "move" into different "rooms" each with its own description. It is sometimes referred to as a "text-based virtual reality" environment.
2. IRC: A synchronous chat environment composed of different "channels," each with its own topic of discussion. When a user joins a channel, whatever others on that channel type is displayed on the user's computer screen almost immediately. In this way, it is possible to hold real-time conversations over the Internet. IRC does not have a "virtual environment" as does MOO.
3. CGI: Put simply, CGI programs are those which interface with HTML forms on web pages. The HTML form calls the program, and sends it data in a certain format. The program then parses the data, and returns a result based on what the user entered into the form.
4. Perl: Practical Extraction and Report Language. Designed by Larry Wall, Perl is one of the most common languages in which CGI programs are written, due to is exceptional handling of text-data and its ease of use.
5. MailStuf is a freely available program which sends email to a designated recipient from a web page.
6. WWWBoard is freely available from http://www.worldwidemart.com/scripts/
7. Web-B-Mail is available free to educational institutions, but must be registered. Information is available from the author (kristina@unr.edu).
8. VocabSearch is freely available from Scripts for Educators on the WWW at the URL: http://www.linguistic-funland.com/scripts
REFERENCES
Johnson, J. et. al. (1996, August). Mathematics Across the Curriculum at the University of Nevada, Reno. [WWW document] URL: http://www.unr.edu/mathcenter/mac/
Pfaff, D. and Pfaff-Harris, K. (1996, December) Math 120 Online at the University of Nevada, Reno. [WWW document] URL: http://www.unr.edu/math120/
Pfaff-Harris, K. (1997, March) Scripts for Educators [WWW document] URL: http://www.linguistic-funland.com/scripts/
Pfaff, D. and Pfaff-Harris, K. (1996, October) Math 120 Online Vocabulary Search [WWW document] URL: http://www.unr.edu/math120/demos/vocab.html
Pfaff-Harris, K. (1997, March) Math 120 Online: What's It For? [WWW document] URL: http://www.unr.edu/math120/demos/whatsitfors.html
Pfaff, D. (1996/97) Math 120 Online: Writing Assignments [WWW Document] URL: http://www.unr.edu/math120/demos/writing.html
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