Video analysis to understand e-learning of vector calculus

Abstract

At RMIT Mathematics, we have been using Computer Algebra Systems Maple or Mathematica in undergraduate teaching for more than 15 years. Many of our courses use computer algebra systems in some support mode for what are otherwise traditional courses. However a few courses have been developed and run in a Maple ``immersion" mode where Maple is used for class presentation, computer lab classes and assessment entirely with Maple. All course materials (including the examination) are delivered electronically over the web (using the course management software BlackBoard). This is a fundamental change in the paradigm by which we teach and learn mathematics. Teaching materials (Maple files) have been developed for a vector calculus course. Technology is used increasingly in teaching mathematics at all levels and studies show that mathematics learning is enhanced by using technology. However evaluations have been limited. Video analysis methodology is well established and utilized in large international studies in school settings but has not been used for undergraduate mathematics, much less for computer algebra immersion mode teaching and learning. Computer mediated learning is highly visual in form, but, unlike conventional instruction, generates no written paper record that might be collected and analysed. The adaptation of existing video analysis techniques offers new possibilities for the investigation of learning in such new undergraduate computer laboratory settings. The teaching and learning environment is intrinsically electronic and includes some elements of new e-learning which do not exist in a paper and pencil environment. As an example, animation is used to illustrate the generation of the 2D domain for double integration. Video captures both the visuality of the medium of instruction and the dynamics of the connections between representational forms, both by the instructional medium and by the learner. The research design for this study was deliberately exploratory in character: both in terms of understanding the new e-learning occurring and in the adaptation of the techniques of video-based data collection and analysis.