Organizers: Davide Cervone, Michael Gage, and Arnold Pizer

August 6, 2007 - August 10, 2007

At many colleges and universities, calculus and other elementary mathematics courses are taught in large, impersonal lecture environments. Often there are insufficient resources to grade homework. An obvious and unfortunate upshot is that the students do not do the homework, they become disaffected with the class, they fall behind, or they drop out.

The new software WeBWorK, developed by these organizers at the University of Rochester and allied colleges, addresses this problem head-on. WeBWorK is an OnLine system that allows the student to do homework problems in real time and have them graded immediately. Different students are assigned different versions of the same problems (with different answers), so that they can collaborate to learn new techniques without literally copying each other's problems. The computer actually calculates whether each answer is correct, so it can recognize different forms of the correct answer.

WeBWorK is now used at over 100 institutions around the country. Johns Hopkins University was the first institution to adopt this new tool after Rochester, but now it is used at the University of Michigan, Washington University, and a variety of institutions nationwide. All report decreased dropout rates, an increase in the number and quality of student questions, better retention of women and other under-represented groups, and an overall higher success rate in lower-division teaching.

Curiously, WeBWorK grew out of experiences that Gage and Pizer had with an earlier software product (emanating from the scientific community at Michigan State University) called CAPA. CAPA also featured immediate answers to questions and questions tailored to the individual student. But it had severe syntactical limitations, it could not handle functions, and it had serious programming issues. Gage wrote a front end for CAPA that eventually evolved into the new product WeBWorK.

Certainly one of the key virtues of WeBWorK is that students get feedback on their work while it is fresh in their minds. Contrast this with the traditional scenario of the student submitting his/her work on paper and not getting it back for 7 to 10 days. In the interim the student has forgotten all about that set of ideas as he/she has moved on in the course to the next several lessons. WeBWorK is an effective teaching tool that has changed the way that both students and instructors view the course. Of course WeBWorK does all the bookkeeping, scheduling, and grading that is connected with homework so it is a timesaver in that regard as well.

The purpose of AIM's WeBWorK workshop was to explore means to make problem-authoring in WeBWorK easier. Most users now download ready-made problems from an existing library of over 20,000 problems. But it is clearly desirable for each user to be able to manufacture problems for a particular course. Documentation for WeBWorK is scattered and incomplete; so a second goal of this workshop is to create comprehensive documentation for this important tool. Lastly, organizer Davide Cervone has created a new WeBWorK tool called MathObjects. This device makes functions and other object in WeBWorK dynamic, so that they are easily manipulated and plugged into other functions and routines. In technical terms, MathObjects makes WeBWorK more object-oriented. It makes programming WeBWorK problems much easier. Participants in the workshop learned how to use {\tt MathObjects} both effectively and fluidly.

WeBWorK is a well-developed and versatile tool. The student sees a typeset version of his/her answer--much as it would appear in a textbook--as he/she enters the answer to a WeBWorK question. The student can get a printout of the work done in a WeBWorK session.

There are other software products, some of them commercial, for helping students to do homework (and helping professors to create the homework and to grade it). Most of these provide only multiple-choice questions, and do not provide the kind of productive feedback for which WeBWorK is justifiably noted. WeBWorK offers great flexibility in the format of answers, and also in the ways in which questions can be formulated. The fact that different students have different versions of the questions promotes collaboration, which is a critical part of educational discourse. Students learn from each other, as well as from the software and from the instructor.

The AIM WeBWorK workshop was an active and productive time for thirty WeBWorK afficionados and rising afficionados. The workshop offered tutorials on special features of WeBWorK, planning sessions for developing new programming tools and writing documentation, and tips on how design special kinds of problems and how to use WeBWorK as an effective teaching tool. Many of the workshop participantsw will now go back to their own departments and make another institution a WeBWorK institution. This software is starting a slow revolution in the way that we view the mathematics teaching process; the AIM workshop has played a significant role in supporting the effort and moving it to the next stage.