In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia (Vol. 2). Palmerston North, NZ: MERGA. © MERGA Inc. 2009 Relative Values of Curriculum Topics in Undergraduate Mathematics in an Integrated Technology Environment Greg Oates The University of Auckland <g.oates@auckland.ac.nz> Changes to the relative value of curriculum topics, when using computer algebra systems in secondary school mathematics, have been previously considered in several studies (e.g. Artigue, 2002; Stacey, 2003). This paper extends these findings to an examination of particular topics in undergraduate mathematics, as part of a wider study investigating issues of integrated technology at the tertiary level. This study suggests that issues of curricular value are a critical factor in the successful implementation of integrated technology, and that a re-examination of the relative values of fundamental topics remains a significant challenge for undergraduate mathematics in a rapidly evolving technological environment. A study by Oates (2004) identified the variety of ways in which integrated technology is interpreted in the literature. Responses from an exploratory survey of undergraduate mathematics colleagues conducted for this pilot study were used to propose an initial framework for describing integrated technology. Following this earlier study, a wider international survey of undergraduate mathematics educators was conducted, that received responses from forty-one tertiary institutions representing eight countries (see Oates, 2009). In addition to examining further the elements identified in the pilot study, this latter survey aimed to investigate a number of factors subsequently identified in the literature, particularly those associated with the use of technology at the tertiary level. These issues include student instrumentation (Artigue, 2002; Stewart et al., 2005); the effect of research mathematicians’ beliefs about mathematical knowledge, technology and pedagogy on their use of technology (Anguelov et al., 2001; Keynes & Olsen, 2001; Kersaint et al., 2003); and the relationship between mathematicians’ experience with different technologies within their own research domains and their pedagogical technical knowledge (PTK). PTK is characterised as the necessary knowledge of the principles and techniques required to teach mathematics using a given technology (Hong & Thomas, 2006). A taxonomy of integrated technology was then developed, refined from the model proposed in Oates (2004), and informed by responses to the international survey. The complete taxonomy is not reproduced here, but a summary of the major components is provided in Table 1, along with some exemplars from the survey to illustrate the focus for each of the components. The full taxonomy describes a complex range of factors that should be considered for each of the six main components depicted in Table 1, and some examples of the factors from the Mathematical Factors and Staff Factors are provided later, in a closer examination of content issues (see Oates, 2009, pp. 202-203) An observational study of technology implementation in undergraduate courses at The University of Auckland over the period 2001 to 2008 was then used to examine the effectiveness of the taxonomy, in describing the outcomes of technology integration initiatives. Evidence was sought to measure the effects and significance of each of the factors identified in the taxonomy. Several elements of the taxonomy were found to have played a critical role in the comparative success of the technology implementation. More importantly, the findings emphasise interdependency between the elements of the taxonomy. The results highlight that it is essential to recognise the inter-related structure of the taxonomy. Oates (2009) concludes that addressing the factors in a comprehensive