Introduction

Many college and university faculty routinely publish educational materials for their classes on publicly accessible Internet websites. While these websites are intended to allow registered students the opportunity to access course material online, faculty and students from other institutions often access this available information and use it for their own purposes.

A publicly accessible course website can serve as an invaluable tool for faculty seeking to develop related courses or revise existing ones. With the availability of course syllabi, homework problems, quizzes and exams, the task can be mostly reduced to that of course organization rather than content development. Recognizing the benefits of sharing educational content online, in 2001, MIT announced an initiative to share the educational materials for nearly all of its courses [2]. Utilizing the OpenCourseware website, Internet users from around the globe are able to access materials from MIT courses. Faculty seeking to develop a new or revised version of these courses can utilize this information on the OpenCourseware website as a starting point.

Despite the availability of publicly available course content, the task of adapting material for use in a new course can be daunting. For example, if course material is borrowed from an institution that is on a semester schedule and is intended for use in a quarter system, a significant amount of rework might be necessary due to the difference in the number of meeting days. Often times, an in-depth understanding of the underlying implicitly defined topic dependency graph is needed to determine which topics can be added, removed or abbreviated. This topic dependency graph is rarely made explicit and often resides in the mind of the people intimately familiar with the course. In order to reduce the amount of work needed to create or modify a course, there is a need to make available the topic dependency graph for others to use.

Approach

We view each course as a partially-ordered sequence of fine-grained requirements, each involving certain pedagogic resources (such as a lecture, homework problem, or laboratory exercise) and satisfying some particular pedagogic goal (such as gaining the ability to simplify Boolean expressions using Karnaugh maps). Our plan is to support an extensible universe of such resources, coded in a form that makes them shareable and exposes their interdependencies. Within this universe, course development takes the form of (1) contribution of new resources, and (2) assembly of resources into concrete courses.

The success of course building tools in this universe depends on the explicit representation of enough of its structure to allow acceptable learning sequences from those that violate basic dependencies. In describing rational numbers, for example, we assume of the student some understanding of integers; if both concepts are to be taught, this dependency dictates a natural ordering (see Figure 1). A step toward the representation of such constraints is the organization of course material into concept maps [1] that prescribe assumed dependencies. While intriguing, the construction of ontologies for subject material (1) ignores the multiple levels of understanding a student might have of each concept, and (2) rapidly leads one into the infinite tar-pit of knowledge representation.

Figure 1 - A partial ordering of requirements. Rational numbers and integers are
pseudo pedagogic goals and Lecture, Tutorial and Homework Problem are pedagogic resources.

To avoid this slippery slope, we base the structure of our universe on concrete pedagogic goals, each defined by some measurable characteristic of the student (such as her ability to solve quadratic equations of one variable). For each such goal, a variety of techniques may be specified for its satisfaction; each of these may involve one or more resources. In figure 1, we show a partial ordering of requirements for rational numbers. A trivial pedagogic goal for rational numbers could be to measure a student's ability to identify the numerator and denominator for a rational number p/q. If the student understands the prerequisite knowledge for Integers, there are three resources associated with Rational Numbers. The Lecture resource (shown in yellow) is a teaching technique to introduce the Rational Numbers. The Tutorial and Homework Problem resources (shown in red) are satisfying techniques to get a measure if the student can identify numerators and denominators. There could a plethora of techniques for each pedagogic goal measuring various characteristics related to each topic.

Given a substantially complete partial ordering for a course, we intend to build a planner capable of compiling courses that takes as its input (1) a list of pedagogic goals, and (2) a set of constraints. The constraints might specify requirements such as the length of each lecture, the number of meeting times and the type and number of problems to include. The planner would consult the universe of pedagogic goals and techniques to build a partial ordering of resources satisfying the requirements. In the event the planner can not create an acceptable educational plan or modifications are necessary, an intervention component will allow the user the ability to change constraints in real-time to construct new plans. We envision the output of this system would be akin to a course website.

The notation of creating goal-oriented approach is not new. Azadegan [3] utilized a configurable course material system for computer security courses. While his system was limited to the topic of computer security and does not explicity utilize the notions of goals and educational techniques, it demonstrated great promise in this area.

References

[1] Darina Dicheva and Lora Aroyo. Concept-based Courseware Authoring: An Engineering Perspective. In The Proceedings of ICALT'2002, pp. 46-49, Kazan, Russia, September 9-12, 2002.

[2] MIT Open Courseware. http://ocw.mit.edu.

[3] Shiva Azadegan. A Web-Based Configurable Course Material System. In The Proceedings of ICEUT'2000, pp. 163-167, IFIP, Beijing, August 21-25, 2000.