Margo Alexander, Jean Bevis, and Draga Vidakovic
Georgia State Univeristy
A version of a precalculus course incorporating web based activities is being developed at Georgia State University. In doing so the authors should address three fundamental questions. What are the most pedagogically effective uses of the web and related technologies? What does it mean to "Put a mathematics course on the web"? Will it really take three years to develop the course, or are there some short cuts? Although, the answers to the first two questions may remain incomplete for some time, we can report a strategy to reach the initial offering of the course very quickly.
Course Design, Pedagogy
The Precalculus course at Georgia State University contains a review of functions, trigonometry from the point of view of functions, polar coordinates, vectors, and conic sections. There are usually 30 sections per year with over 1200 students. Students majoring in mathematics, computer science, or the natural sciences take the course as a prerequisite to the calculus sequence, but some take precalculus as the sole mathematics requirement in their college program. Many of these students have rather weak backgrounds in the prerequisite college algebra course, but based on experiences from high school, still feel they can successfully complete the course.
All of the authors had previous experience with lower division mathematics courses using group work and interactive computer laboratory based materials. The computer laboratory materials in these earlier courses ran under StudyWorks, Maple, or ISETL. This experience led to certain decisions. First, web technology would be used instead of a specialized mathematical software package as before. Although, mathematical software packages provide interactivity quickly and easily, they require the purchase of a site license, and tie the instruction to a laboratory where the packages are provided, or require students to purchase the package. Two of the key features of these software packages, a graphical user interface and interactive graphing of functions, are easily provided with web technology.
Previous experience indicated that a combination of lecture and group work was a highly effective way of using class time. However, great care needs to be taken to keep students focused on the mathematical activities. In a previous computer based college algebra course, in which students were required to work in groups in a computer lab, students often cruised the web or played solitaire while the remainder of their group completed the assigned activity. In that course lectures had been quick ten to fifteen minute summaries. In the new precalculus course, we decided to use twenty-five to thirty minute lectures giving fuller coverage of core topics, followed by group activities taking twenty to twenty-five minutes. The terms group and activity are never used. Rather, these activities are called daily quizzes. Each person must complete his or her own quiz, so everyone participates. There are four versions of each quiz, so students cannot simply copy from one another. Students are made aware of this and are encouraged to discuss with one another how to find a solution rather than the solution itself. Groups form naturally without any effort from the instructors. During the daily quizzes, the instructors and graduate assistants move about the room working with the various groups that have formed.
Finally, the use of web based materials was to be optional during the initial offering of the course. This option allows for differences in student preferences and learning styles. It also gives greater flexibility in scheduling the development of materials. At this point all lectures and quizzes are available on the web. An optimum strategy for a student would be to work on a quiz with a group in class, but not turn it in. The student can then have more study time after class and take the quiz on the web that evening. Web quizzes are slightly different from the ones given in class and contain random variations. The option to take quizzes and "attend" lectures on the web eliminates the need for make up work. Students complete the course requirements by taking four traditional in-class tests and a final exam. The class could be offered as a distance learning course if arrangements were made for these tests.
Putting A Course on the Web
The administration at Georgia State University has encouraged faculty to "put their course on the web". However, it is not always clear what is meant by this phrase. Our interpretation involves more than putting a syllabus and assignment sheet on the web (of course these steps are appropriate for all courses). It is our desire to put a substantial portion of the course content on the web, and to incorporate features that are best suited to the abilities of web technology. These features include interactive lecture materials, regular self-grading and self-recording assignments, interactive demonstrations or animations, electronic office hours, chat rooms, and the publication of projects. (In other disciplines the web also provides a research tool for gathering basic data.) Luckily most of these features can be imported or developed with a few elementary tools. Further, the work can be organized so that much of it is completed after the initial offering of the course has begun.
Course Development, Technology Tools
In this section we describe the strategy we used for putting the precalculus course on the web, and discuss the tools we used in the process. This strategy produce the materials very quickly, that were needed for the initial offering.
The first step was to outline the content of the course. This used paper, pencil, existing outlines, present textbooks, and other sources we had found attractive. We determined that there were 44 meetings during a term, four for class tests, five for review sessions, and thirty-five for presentation of material. The course content was organized into thirty-five lessons. In the second step MS Word was used to produce class notes for each of the thirty-five lessons. Each lesson was limited to about three pages of 14-point type. There are several reasons for this. The lengths of these lessons influence the length of the lectures, both the online and in-class versions. The attention spans of students are limited in the lecture hall and in front of a computer monitor. At three pages the lesson is probably already too long.
The third step completes the first phase of the course development. The material was now completely organized into a number of lessons, so the course syllabi were written, textbook readings planned, and homework assignments detailed. Finally we cruised the web to find calculators, demonstrations, and animations that can be incorporated into the lessons and provided on a page of links. Some highly recommended sites include
Faculty at Georgia State University have available a tool called WebCT which is helpful in establishing a web based course. It will easily manage student identities and work records, provide chat rooms and other forms of web communications, as well as display web pages that are uploaded to it. We also used it to administer the online quizzes that were developed as the course progressed. Also during this phase the class notes were converted into two other forms. In one form the type size was changed to 20-point. After reformatting the pages, they were printed on overhead transparency film and used in the lectures. The final version of the class notes was uploaded to WebCT for presentation. The first step was to save the files in html (now a standard feature in many word processors). These files were then edited with Netscape Composer before they were uploaded.
The class notes contain mathematical equations, drawings, and graphs that required special handling in conversion to html files. Equations were entered into the original Word files with the equation editor that comes with MS Word. When Word files are saved as html files, these equations are converted to gif image files and embedded at the appropriate position in the html file. Other image files embedded in a Word document receive similar treatment. One needs to intercede in this process only if some changes are to be made. For example, one may wish to give the gif image a transparent background. Diagrams for the class notes were drawn with MS Paint, which comes with the windows environment. Graphs and grids for drawing graphs are first produced in StudyWorks and then pasted into MS Paint for touch ups and addition of legends. There are a large number of paint programs and function plotters that could be used in place of these two programs. Another useful tool for dealing with graphic images is Lview Pro. This shareware program has an excellent screen capture feature, converts bmp files to gif files, can be used to give an image a transparent background, and can define the pallet to be used for an image file. These are all helpful utilities. One can accomplish a great deal with a few simple and readily available tools. More sophisticated drawing and web editing tools can be acquired and learned later as interests and needs develop.
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During this initial offering of the course all web components have been optional, and no effort has been made to encourage students to use them. We wanted to know how many students would freely choose these options. In order to have a significant sample size the initial class size was set at 110. After the usual first week withdrawals about 90 students remain. Of these 10 to 15 percent use the web to take the daily quizzes. By chance, the classroom is unscheduled in the hour following this class, and the group activities usually continue into the next period. Many students perceive this extra time as a reason to take the daily quizzes in class rather than on the web. Without this bias a larger number of students would be choosing to take the quizzes on the web.
Another 5 to 10 percent of the students have attempted to use the web, but have reported difficulties in getting on the system. They usually report that the system is not working properly, when in actuality they have been careless in following instructions.
Another readily observable item is the nonparticipation of students in many of the intended activities, including lectures, assigned readings, and homework, but not the daily quiz/group activity. In a traditional lecture type course, the instructor may not readily observe this behavior, and have no indication of it other than low grades on the examinations. In a class with group activities observed by an instructor, the instructor quickly discovers that many students have not listened to the lecture, not read the assignments, and not done the homework. Consider the following evidence. The daily quizzes contain problems similar to ones presented in the previous lesson. Similar problems are presented in the assigned readings and homework associated with that lesson. After a lesson is presented, students are encouraged to review the three pages of class notes for that lesson, which often contain additional problems of a similar nature. Yet when confronted with the quiz problems, students often claim to never have seen similar problems. When the students are shown the examples that are similar to the ones they are assigned, they do work as a group, explaining to one another their best understanding of the needed steps and concepts. Several students have been observed skipping the first half, the lecture half, of class, but entering class just in time for the group activity. These activities, whether on the web or in a classroom may be the only study efforts of these students before trying to cram for an exam. In addition, these interactions with students during group activities force these students to confront, on a regular basis, the inadequacy of their study habits, and offer an opportunity for the instructor to suggest improvements.
For a mathematics class it is important for students to be engaged in
course materials on a regular basis. Daily quizzes worked in groups is
a successful method for accomplishing this goal, and can be implemented
using web based tools. We plan to seek ways to improve the effectiveness
of these efforts. Using interviews, surveys, and other forms of feedback
from the students, the class notes and other elements of the course will
be revised and improved. Finally Java applets will be developed to complement
demonstrations found on other web sites.