A good online system should repair the problems found in the other two paradigms and not introduce too many new problems. Some of criteria I feel are desirable:
- Adaptive Testing
- The duration of practice should be individually tailored to each student. Students who need more problems should get as many as they want.
- Context-Sensitive Help
- Students should get formative assessment appropriate to their needs.
- No new major difficulties or drawbacks should be introduced. The system should be stable, unambiguous, and mathematically correct.
- Instant Assessment
- Problems should be graded instantly -- students should get immediate feedback.
- On-The-Fly Question Generation
- Problems should be individually tailored to each student; so no two students get the same problems. This will discourage collaboration for its own sake, while permitting appropriate collaboration. Also, students may repeat the practice without encountering the same questions.
- The system should not be plagued with security flaws that would allow students to cheat and hackers to disrupt the works.
- The system should be extremely easy to use for both students and instructors.
- It should require learning an absolute minimum of non-subject material.
- It should be friendly to people with varying degrees of computer literacy.
- Summative Assessment
- Statistics should be kept about the difficulties students have with the problems. This will eliminate the need for separate assessment later.
Furthermore, I believe the system should be free to use, for two philosophical reasons and one practical one:
- First, the spirit of the World Wide Web is that of free and easy access to information. For example, consider the growing popularity of Linux and projects such as Wikipedia.
- Second, the spirit of fair educational use is also that of free access.
- Finally, budgets of students, educators, and educational institutions are often quite slim and do not allow for unnecessary expenditures. If a fee is charged, a significant portion of the potential users will stay away. The increasing popularity of for-pay systems only reflects a frustration with the lack of equally good free alternatives.
Vadim Ponomarenko, "DRILL 3.1 - Philosophy," Loci (December 2004)
Journal of Online Mathematics and its Applications