Plenary 1. Anna Sierpinska
Concordia University, Montreal, Quebec, Canada
Title: Research into elementary mathematics methods courses in preservice teacher education.
Abstract: Considerable effort has been made in mathematics education research towards the development of knowledge that could serve as a basis for a professionalization of the work of mathematics teachers. A similar effort is now being expended with regard to the work of the mathematics teacher educator. Three years ago, I joined this current by engaging in a research project on the so-called ‘elementary mathematics methods’ (EMM) courses with Helena P. Osana, a researcher in educational psychology and an experienced elementary mathematics teacher educator. The goal of this research, ultimately, is to make public, communicable and open to critical analysis the personal experience of university professors teaching EMM courses to future elementary school teachers. In the talk, I will present some results of our research so far, focusing on the experience of those of the professors we have been collaborating with who have taught such courses for a decade or more. Based on observation of their classes, study of their course descriptions, and long interviews with the professors, we have tried to understand the nature of, and reasons for, the changes they have introduced over the years, the aspects they have abandoned and those they have kept. I will also speak about a framework for analyzing the EMM courses that we have started developing in our research. This framework, we hope, could be useful for other researchers aiming at the professionalization of the work of elementary mathematics teacher educators.
Plenary 2. Markku Hannula
University of Helsinki, Finland
Title: Structure and dynamics of affect in mathematical thinking and learning
Abstract: In this presentation, I will review the development of research on affect in mathematics education since the late 1990s and forecast some directions for future development. One trend in the development has been the elaboration of the theoretical foundation. I will suggest that a useful description of the affective domain can be based on distinctions in three dimensions: 1. rapidly changing affective states vs. relatively stable affective traits; 2. cognitive, motivational and emotional aspects of affect; and 3. the social, the psychological and the physiological nature of affect. Another direction of development has been to explore the structural nature of affect empirically. I will review some instruments that have been developed to measure different dimensions of beliefs, motivation and emotional traits. Moreover, I will look at some empirical results concerning how the different dimensions are related to each other, and how they develop over time.
Plenary 3. Maria Alessandra Mariotti
University of Siena, Italy
Title: Proof as an educational task
Abstract: In this talk I will discuss proof from an educational perspective, situating "proof as an educational task" within the context of current research. This point of view sets out to combine three perspectives: epistemological, what we mean by proof; cognitive, the main difficulties that students meet when engaging in proof; and didactical, the kind of didactic interventions can be proposed (selecting from interventions that have been tested and whose effectiveness has been demonstrated). The examples that will be presented are drawn from the current literature, but also from research studies in which I have been directly involved. In particular, I will discuss some results from long-term teaching experiments related to the use of computer-based artefacts as tools of semiotic mediation that teachers can exploit to develop the mathematical meaning of proof.