Year

2004

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Information Systems - Faculty of Commerce

Abstract

This thesis uses a theoretical framework derived from activity theory to investigate the introduction of computer algebra systems (CAS) in first year university mathematics subjects. Both qualitative and quantitative data relevant to a case study of a group of approximately one hundred students, and two academics, were collected and analysed using a range of methods. The major question for this study was: What are the socio-cultural dynamics of learning with a new tool? More specifically, there are three questions: first, how do students in a particular context respond to their initial experience with a CAS as part of their first year mathematics subjects? Second, what relationships exist between aspects of students personal histories, their goals for mathematical learning, and the range of experiences they report concerning using a CAS for the first time? Third, in a particular case in a particular setting, how do academics see their role in the introduction of computer algebra systems into mathematics teaching? The main findings include the identification of the critical nature of purpose, or multiple motivating objects in activity systems. Personal identity as a learner of mathematics is constructed through choosing to engage at surface or deep levels, alone or with others. Students with a low level of computing background who had a high level of engagement and sense of purpose in their mathematical learning reported that they appropriated the new tool for their own personal use. Students with a high level of computing experience who were unable to form goals congruent with the learning tasks were less likely to appropriate the tool. In a similar way, lecturers with different purposes and different epistemological views of mathematics, in responding to contexts and personal goals, planned different teaching and learning experiences for their classes. The significance of this study is that it demonstrates how activity theory can be used successfully as a framework for an investigation that takes an expansive view of learning as a socio-cultural activity. Personal socio-cultural histories and motivations and social contexts influence students and academics as they form and reform their goals for engaging in learning and teaching activities. The study also highlights the gap between high school experiences of learning mathematics, dominated by rule following and the replication of pen and paper algorithms, and the more creative and challenging possibilities for making mathematics opened up by new technologies such as computer algebra systems.

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