UM Math on-line homework

Noting that in all of 115, 116 and 215 there are individual homework problems drawn from the book that may or may not be collected or graded, and that these are frequently more-or-less routine problems, we consider a Web-based homework system that may serve to easily grade homework without increasing the instructors' workload, thus increasing the likelihood that students will do the assignments.

Desirable characteristics of such a system include:

the automatic grading of any submitted homework, that each student get a homework problem set which is in some way different from those given to other students, that students get the same problem set each time they log on to work on the problems, that each student be able to rework errors in submitted homework, ideally for reduced credit, that it interface with some sort of on-line tutorial system that would allow students to do additional work on areas in which they are weak,

that instructors be able to view results for the homework easily, and download the results in tab-delimited or csv format for easy incorporation into a spreadsheet, that it include an easy way of generating problems for any given course, and that it support multipart questions.

It may be that some of these are mutable -- for example, with homework given from the book objective (2) isn't satisfied, so that it may be tolerable for an on-line system to fail to provide this as well. (3) could be supplanted by having the problems be different each time, but be sufficiently similar that it was clear that the same skills were tested. Similarly, (4) might be as well served by having a cap of two or three homework submissions.

existing systems

Some of the packages that already exist for the delivery of homework over the Web include:

• WeBWorK - Developed at the University of Rochester, WeBWorK is designed to be a homework delivery system. While non-trivial to set up and run, and moderately demanding of the webserver running it, it has many properties which are desirable for a homework system.

  Webwork is free to educational users.

• eGrade - John Orr of the University of Nebraska's brainchild, now marketed by John Wiley publishers. Easy to set up and configure, it supports modes which are appropriate for homework as well as testing.

  eGrade is generally free to users of Wiley textbooks, but includes licensing fees for students buying used texts.

• COW (Calculus on the Web) - A site at Temple University with a remarkably complete set of problem modules for calculus I-III and precalculus. The organization is book-like, with each course having a book, which is broken into sections, each of which has one or more modules of similar problems. The interface is clean and consistent.

  COW affords that ability to record student grades for instructors to review, but this requires a login, and nowhere on Temple's site is there obvious provision to aquire such. (Or use the software elsewhere.) It is therefore unclear the extent to which they promote the use of COW at other institutions (though its funding from the NSF would argue for that).

detailed analysis

Recall the objectives were

The success had thus far at meeting these objectives may be summarized in the following table (* = I have a working implementation that does this; a-d = see notes). Another analysis with more written explanation and additional points is on a separate details page.

1. To give each student a different problem set, eGrade must give a different problem set every time a student logs in, so that (3) is impossible. If a student gets the same problem set each each time they log in, then every student gets the same problem set.
2. eGrade can give reduced credit on repeated submissions, but effectively only by reducing credit on the entire set for subsequent submissions, rather than on a problem-by-problem basis. That is, if a student takes the set and does not get all of the problems correct they could retake it for, say, 70% of the credit available for the set. However, both (or all) scores would be reported to the instructor, and he/she would have to manually determine which to use.
3. both eGrade and Webwork admit the possibility of including HTML links to other problem sets or Web sites. It is not necessarily straightforward to configure eGrade to generate the links on the basis of scores on a given set. In Webwork it appears that there is a relatively simple fudge to make do this, though it would not be elegant.
4. the problem generation in eGrade is generally easier than in Webwork. However, Webwork allows greater flexibility in the manner in which different problems are presented and graded.

examples of homework systems

In these examples, the sample course includes one or two homework assignments developed from or for math 215 (calculus III). The problem sets have the characteristics described in the detailed analysis above, except where noted otherwise.

1. Webwork course.
2. eGrade course allowing full credit on arbitrarily many retakes. (This could obviously be changed to limit retakes to two or three.)
3. eGrade course allowing reduced credit on a limited number (5) of retakes. Note that this is done by having 5 versions of the homework, e.g., 13.1, and 13.1a-d; it is not possible to start 13.1y before having attempted 13.x, and each successive version allows less credit.