An examination of a didactical procedure to engage first year university students in meaningful mathematical activity

Abstract

The challenge to empower learners whose mathematical powers have been underdeveloped has lead the author to search for and implement teaching innovations designed to enhance students learning of mathematics. Undergraduate students receive much of their exposure to mathematics during lectures which are characterised by frontal teaching, a demonstration only by the lecturer. Students are passive recipients of the lecturer's knowledge and end up coming to lectures to gather information to learn at a later stage. The low level activity inherent in traditional lectures results in most students not developing the skills to grapple meaningfully with mathematical concepts and ideas. This has prompted the author to investigate changing the format of lectures in the quest to provide an environment in which students can engage more meaningfully with mathematical concepts. Adopting the position of education theorists who advocate that mathematics as a meaningful activity is engendered by "doing" mathematics and that students must be allowed to enter the culture of the mathematical enterprise, the author has designed a teaching procedure called the "workshop-lecture". This mini-thesis reports on an examination of the design and implementation of the "workshoplecture" which affords first year university students the opportunity to be involved in meaningful mathematical activity. This examination provides evidence that the format of the "workshop-lecture" is conducive to more meaningful interaction amongst students and between lecturer and students than would be the case in a traditional lecture, even with constraints such as venues with fixed, tiered seating and a relatively large class size of 56 students. It also highlights issues such as lecturer intervention, and the learning materials and aids that facilitate student interest and involvement in meaningful mathematical activity. A way of expanding the notion of the "workshop-lecture" to create opportunities for students to recognize more their own responsibility for their learning is proposed, as well as a strong recommendation for changing the curriculum to allow for meaningful involvement by students.