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WIMS: An Interactive Mathematics Server - Virtual Classes

Xiao Gang

WIMS is designed to support intensive classroom applications. To this end, it incorporates a structure of virtual classes. A virtual class under WIMS can be created and managed entirely online by the teacher (supervisor) of the class. Students can then be registered in the virtual class, either by the teacher or by themselves, with the registration mode definable by the teacher.

A user can connect to WIMS in one of three ways: as anonymous visitor, as the teacher of a virtual class, or as a student. The first is open-access, while the other two are protected by passwords.

The content of a virtual class is a number of worksheets, which are created and maintained online by the teacher. Each worksheet contains a number of items, and each item is the address of a WIMS module, which may be an exercise (for which the teacher has determined the difficulty level), an online tool, an online lesson text, or other.

The design of the system requires that the teacher of a virtual class takes responsibility for choosing the exercises for his or her students, as well as determining the difficulty level of the chosen exercises. For this purpose, pages sent to virtual class teachers contain special links. The teacher has only to click on these links, in order to add a chosen exercise into a worksheet. The difficulty level and configuration of the exercise added to the worksheet will automatically be set to that of the exercise containing the link.

When adding an exercise to a worksheet, the teacher can also set up the number of points each student is required to make, as well as the weight of these points in the computation of averages. Sample worksheets are also created and can be inserted directly in virtual classes, helping teachers to make their choices.

Student who log in to the virtual class are presented the list of active worksheets. While working on the exercises contained in a worksheet, the scores they obtain are automatically gathered by the server. However, points exceeding the assigned number are discarded by the system, preventing students from gathering extra points by repeatedly working on one (easier) exercise.

Each time a student answers an exercise, the score and the resulting change in average are shown on the page. Experiments show that this instantaneous feedback is very efficient in inducing students to work hard.

In the current version of WIMS, a complete list of scores of a virtual class can be consulted only by the teacher. For each student and each worksheet, the system computes a score based on two numbers: the percentage of assigned work done and the average of individual scores (between 0 and 10). The computation depends on a formula according to a (modifiable) severity level determined by the teacher.

In principle, the system allows students to log in to the virtual class any time and from anywhere, to work on the assignments. Some people object to this possibility, because some students may ask others to log in, work, and get points for them, especially when the points are used in student evaluation. For this reason, teachers' pages include menus allowing them to change the score registration status of a given worksheet: open, close, or open for a selected number of sites. With this feature we can let students score only during monitored classroom sessions.

Each virtual class also has a discussion forum to host electronic discussions between teacher and students, or among students. Mathematical expressions can be inserted in a very easy way into messages within the forum (see Page 4).

All manipulations within virtual classes (for teacher as well as for students) are done online, via html links and forms. This is straightforward in most cases: For example, to create a new worksheet, the teacher can click on the link "create a new work sheet" in the teacher's home page. And online help pages are available at many places.

The least obvious manipulation is for the teacher to add an item into a worksheet. Usually the item is an exercise, and most exercises on WIMS accept various configuration parameters that vary the difficulty level in a very wide range. So, in selecting the exercise, the teacher not only designates the module but also sets the parameter configurations. In practice, this is done in a quite transparent way. Once a choice of configuration is made -- usually when a new exercise is generated -- a link "Insert into a work sheet" will appear at the bottom of the page. Clicking on the link brings up a form page allowing the teacher to determine insertion parameters (number of worksheet to insert into, number and weight of required points) and to insert the exercise.

We have made a large-scale use of virtual classes (400 students) at Université de Nice - Sophia Antipolis during the year 1999-2000. Practice shows that students usually have no difficulty getting used to the interface, and they start to work very quickly after registration. Some of them are also very quick in starting attempts at cheating -- and getting warned by the server.

Student behavior under this environment is usually quite different from that in a classical environment. They become very active, trying to find out the most efficient way to get points. When they have difficulty getting solutions to some of the exercises, the demand for help from the teacher present in the classroom becomes very pressing. When the teacher is not immediately available, discussions among students start quickly, with the most advanced helping those in difficulty. However, nobody can copy another, because everybody is working on a different exercise, and the difference in the question may often lead to radical differences in solutions.

In our setup, worksheets are installed days before the working session, to allow students to practice on them. However, they can get scores only during the work sessions, and only from computers within the classroom. With this precaution, the individual scores registered by the server are sent directly to the administration for calculation of each student's credit, and there have been no contests of the server-generated scores.

Xiao Gang, "WIMS: An Interactive Mathematics Server - Virtual Classes," Convergence (August 2004)