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DRILL 3.1 - Three Paradigms

Vadim Ponomarenko

Traditionally, instructors have had to choose from only two paradigms for having students practice problems: in-class or at-home. Each suffers from certain inadequacies.

Problems done in class are subject to a very strong time restriction -- they consume a limited resource. Unless the course is structured to provide abundant in-class time, either some students will receive inadequate practice or some other goals must be sacrificed. This problem extends to assessment -- by using limited test/quiz time to assess, other class goals must be sacrificed.

Problems done at home suffer from two important defects. First, there is normally a significant delay between when a student performs the work and when that student receives formative assessment. This can range from days to weeks and often can completely erase the benefit, as the focus of the course has often shifted by then. Second, it is impossible to monitor the level of collaboration employed or the amount of effort students employed. Susie might have found the assignment difficult and spent ten grueling hours, while Sally found it easy and spent forty minutes, while Cindy copied her answers in ten minutes. How can an instructor properly teach all three students when their final work looks the same?

These two paradigms share another problem: lack of customization. Susie could have used more practice, since she didn't really understand the material, while Sally found the last few problems boring and lost interest in the subject. This issue is particularly acute in prerequisite material -- the variability among students is enormous, as their mathematical histories before a given course can be quite different.

We need a third paradigm that does not suffer from these drawbacks. Problems solved online are this needed alternative. Students work problems on their own time, which is an essentially unlimited resource. With careful design, an online system can repair all of the other problems as well. It can give the instructor assessment information, relieving the need to spend class time. It can give immediate feedback, while the topic is still fresh and relevant. It can be secure, reducing or eliminating collaboration. It can monitor the time students spend. And it can deliver assignments of varying lengths -- Susie will get more problems, and Sally will get fewer.

In fact, this third paradigm can completely replace the two traditional paradigms for reaching the Competency goal, permitting the instructor to focus more energy on the other goals. Online problems can be as intensive as homework and as secure as exams.

Vadim Ponomarenko, "DRILL 3.1 - Three Paradigms," Loci (December 2004)


Journal of Online Mathematics and its Applications