WeBWorK is an open-source online homework system. I believe it is a very good idea to use WeBWorK in mathematics classes for the following reasons.

**It lends itself to active learning.**

When teaching by lecture or lecture-discussion, the teacher often has a coherent and insightful train of thought in mind, which, however, is often lost on the students, as any teacher knows. Indeed the lecture format is inherently problematic, and is based on an often naive and excessive faith in the power of passive osmosis. An alternative is to translate the same train of thought into a path of guided inquiry, where the students themselves have to supply various steps along the way. WeBWorK can serve as the infrastructure for creating an active classroom along these lines. Further thoughts on this here.

**It refocusses the teacher role from judge to guide.**

In a traditional course, when the student hands in a test or assignment, the teacher locks himself in a dark room for hours critically judging it, and a week later the student receives it back with red marks on it. Insofar as the teacher wrote feedback, the only grade-pragmatist use of this is to scan for point deductions that seem weakly motivated so that one can confront the teacher for a grade appeal. The teacher becomes an aloof judge, and his feedback becomes justifications for his harsh verdicts.

With WeBWorK, the teacher does not spend his time judging, but guiding. Instead of spending his time judging the students’ work after the fact, he spends his time alongside them as they are doing the work. He assists students when they get stuck. His feedback is of the form “try this” or “look at it this way” instead of “here’s why you’re wrong” or “this is what you should have done.”

**It incentivises persistent work.**

In a traditional course, students are typically assigned many practice problems that are never graded, since hand-grading is unfeasible for the volume of practice problems that students need. Students must be driven by their own conscience and discipline to complete these assignments. They will eventually be held accountable in the form of quizzes and exams, but this does not directly incentivise them to complete all assignments and to complete them on time. Many students are natural procrastinators who seek the path of least resistance. If they will not be held accountable for this week’s material until a quiz three weeks down the road, many will neglect the assignments and hope to make up for it with some last-minute cramming before the test. In fact, since a test can only contain a few questions and could not possibly cover everything from the assignments, doing all assignments is guaranteed to mean much “wasted effort” as far as crude grade-pragmatism goes.

With WeBWorK, all problems count toward the student’s grade. The students now have a direct incentive to complete all assignments and to complete them on time. Attending class, asking questions, discussing problems with classmates, using tutoring resources---all of these things are now more strongly incentivised, since the students can keep their WeBWorK assignments before them, on their smartphones for instance, and see concrete and direct contributions toward their final grade accumulate in proportion to the effort and time they put it.

**It incentivises learning from mistakes.**

In a traditional course, when students receive back a graded exam or assignment they have little incentive to do more than to check the final score. Ideally you would want them to learn from their mistakes, but since the grade has already been set anyway the only mechanism for this is a kind of self-shaming, which is not pleasant. Furthermore, even if they wanted to learn from their mistakes, the feedback comes much too late, several days after the students wrote it, meaning that the student will have to devote much effort to retracing their original reasoning before they could analyse their mistake and understand how to learn from it. Redoing the problem and relearning the material correctly in this way would cost much time, and since the grade is already set grade-pragmatism dictates that this time is better spent on the next assignment.

With WeBWorK, students receive instant feedback and have the chance to correct their mistakes right away while the problem is still fresh in their minds. They thus have a direct incentive to try to figure out what went wrong and to correct their reasoning. This also eliminates the demoralising phenomena, unavoidable in one-off grading schemes, that a small computational error can have a heavy effect on the final score.

**It encourages collaborative work and structural thinking.**

WeBWorK problems incorporate randomisation, making them ideal for collaborative work without direct copying, as the underlying idea or strategy rather than the answer must be conveyed to help a friend.

**It is suited for assigning a variety of conceptual questions.**

Traditional hand-grading tends to be focussed on a few quite substantial computational problems. The one-sided nature of these problems, however, can have a disastrous effects. Students can become masters in computational procedures while still understanding next to nothing of the visual or verbal meaning of what they are doing. It is crucial, therefore, to challenge them with conceptual problems that forces them to reflect and form a fuller mental image of the notions at hand. But this is not easily done in hand-graded homework assignments. Conceptual, explanation-type questions are much harder to grade fairly and objectively than clear-cut computational problems with a straightforward “right answer.” This difficulty can be avoided by focussing on true-false problems, multiple-choice verbal-interpretation questions, graph-matching problems, etc. But such questions are less suitable as hand-graded homework assignments since a large quantity of them are needed and the answers to such problems are easily copied. With WeBWorK, randomisation helps eliminate the threat of copying, and the volume of problems ceases to be problematic, thus making it possible to target conceptual understanding more efficiently.

**WeBWorK is free and open-source** and idealistically developed by actual mathematics teachers. This is the exact opposite of the scammy, filthy-expensive online homework systems pushed by major commercial publishers, which are designed to sell, not to teach. WeBWorK runs beautifully on any smartphone, tablet, or laptop right in your browser without any installation or complications. It also generates beautiful PDF output for printing.