Innovative uses of digital technology in undergraduate mathematics

The ways in which digital technology is often used in university teaching of mathematics can be quite different from how it is employed in schools. This has the potential to form a discontinuity between school and university, making the transition less than smooth for students. In this chapter we consider several examples of how digital technology has been used with first year mathematics students in both New Zealand and South Korea. The approaches employed include: intensive use of technology, including formative and summative assessment practice; lecturer modelling and privileging of technology use; a versatile approach to calculus concepts that encourages epistemic exploration of local properties of functions; and novel orchestration of mathematical thinking through smartphone communication technology. We analyse each of these approaches using the theory of instrumental orchestration and outline some innovative aspects and benefits of them. The student perspective is also considered, with some evidence of the influence on student engagement and attitudes. We conclude by suggesting that in order to teach with digital technology in the manner described here good pedagogical technology knowledge (PTK) is required.