Using multiple theoretical perspectives to connect , clarify and convey research results

Using multiple theoretical perspectives to connect, clarify and convey research results Gerd Brandell Centre for Mathematical Sciences Lund University Contribution to WG 5 ICMI, Rome, 2008 Introduction Documented teaching qualification becomes increasingly important for academic staff. Besides teaching experience, courses on teaching and learning are required to get an appointment as a lecturer or a promotion. PhD-students and newly appointed lecturers therefore demand opportunities to qualify as university teacher. One possibility to meet this demand at large mathematics departments is to design specific courses in teaching and learning mathematics at university level. During the process of developing and delivering such a course for two Swedish universities, it became clear, that the existence of many competing theories in the areas of mathematics education and in general education tend to obstruct the learning outcomes of the course. One reason is that almost all participants in the course have their background solely from mathematics and science and are unacquainted with the use of theories in social sciences. In this paper I will briefly describe the course in question and its relative success as well as shortcomings. The difficulties for the students to appreciate and learn about competing theories and theoretical perspectives are discussed. The pedagogical question arises if there are any opportunities to reduce the complexity by connecting different theoretical perspectives. I claim that such possibilities exist and will show by examples the strength of using a connecting strategy. I also argue that such connections – when they exist – will deepen and enhance our interpretation of the research results and therefore are in the interest of the researchers themselves. The main part of the paper is devoted to a couple of examples from the mathematics education literature, both addressing learning obstacles and dealing with tertiary level mathematics (Vinner, 1997; Lithner, 2003). I will identify connections between the analysis presented by Vinner and Lithner and more general theories of learning in higher education. Finally I will discuss these findings in the light of the ongoing discussion about multiple theories in mathematics education research and specifically to the idea of a networking strategy (Bikner-Ahsbahs & Prediger, 2006). A course in teaching and learning mathematics in higher education The course in question was a graduate courses offered to doctoral students and young lecturers, first at the Centre for Mathematical Sciences, Lund University in 2005/06 and later at the Department of Mathematics, Stockholm University and KTH Mathematics, Royal Institute of Technology in cooperation in 2006/2007. The latter course was a development of the first version. About 15-20 students participated in each course. The majority of the students in the course were PhD-students, while a minority were newly appointed lecturers. The participants represented several subjects and divisions in their departments: mathematics, mathematical statistics and numerical analysis. The aim of the course was for students to learn to describe and evaluate students’ learning on scientific and empirical grounds, and to develop their ability to plan, teach, supervise, assess and examine courses in mathematics at undergraduate level. An orientation of research in mathematics education with emphasis on higher education was included in the course. Theory and praxis were integrated in the course. The workload corresponded to five weeks full time study while the course was stretched out during seven months. John Mason’s book on teaching and learning mathematics at university level (Mason, 2002) was chosen to be the main literature. This book focuses on practical aspects and is partly inspired by investigations among mathematics lecturers. Chapters from other books, scientific articles and papers supplemented the main book. Lectures, seminars, classroom observations, workshops and teaching