Using Computable Documents for Online Mathematics Instruction
with James Howard
University of Maryland University College
Teaching mathematics online introduces new problems and difficulties to an already complex task. Besides the normal issues of notation and anxiety, online instructions bring challenges introduced by the technology itself. First, there is almost no ability to work directly with a student who is having problems, though modern technology, such as video conferencing, partially addresses this. Second, asynchronous classes place a lag between a question and an answer, interfering with the learning experience. Third, static examples walked through in textbooks and videos cannot show the subtlety and nuance of responsive examples on a blackboard led by an instructor.
These issues manifest in distance learners in ways similar to the physical classroom. Students may be disoriented and confused during the transition to new application areas when skills are not mastered early. Students may also be frustrated early when the examples provided in textbooks do not provide sufficient guidance for generalized solutions. But for the instructor, these manifestations are less transparent in the digital classroom.
Mathematica and its Computable Document Format (CDF) provide mechanisms for interactive examples that give more insight than static examples in a textbook. Using three examples from developmental and precalculus mathematics courses, this presentation shows how CDF delivers interactive learning directly to students through a channel not available through other online or in-class resources. The examples show how even lower-level courses can benefit from the advanced features and interactivity inherent in CDF to give distance learners a better understanding of fundamental mathematical concepts.