Visit by Anna Sfard
On February 17-21, 2014, Anna Sfard from the University of Haifa visited Umeå Mathematics Education Research Centre (UMERC). During her visit, she participated in different seminars and worked together with members of UMERC.
Anna Sfard was the second invited researcher for the Hans Wallin Lectures.
Monday, February 17
13:00-14:30, room N370
"Development of numerical thinking – the discursive view"
The point of departure for this presentation is that the language in which researchers conduct their investigations influences their ability to ask questions and interpret data. The rest of the talk will be devoted to one extended example that illustrates this claim: I will show how our thinking about numerical thinking changes when we make a transition from the dualistic to non-dualistic talk about numbers.
The traditional language of research on numerical thinking implies that the child is aware of the existence of the abstract objects called numbers prior to being able to apply them in any way. Those who adopt discursive approach conceptualize thinking at large and numerical thinking in particular as forms of communication. In this way, they remove the assumption about the pre-existence of numbers: by portraying them as discursive constructs, they imply that numbers are products rather than pre-given objects of human communication. In this talk, after presenting the basic tenets of the discursive approach to cognition, I will explore the question of how the proposed reconceptualization impacts our understanding of numerical thinking and how it may impact the practice of fostering children’s numerical development. Theoretical arguments will be supported with empirical examples coming from my own and other researchers’ recent studies.
Wednesday, February 19
13:00-16:30, room MA356
Anna Sfard will participate in a workshop.
Thursday, February 20
15:00-16:30, room N380
"Using commognitive tools to evaluate opportunities for learning created by mathematics teachers"
The aim of this talk is to demonstrate with the help of an example how the discursive (commognitive) perspective on mathematics learning and the analytic tools it engenders allow to get deeper insights into the process of classroom teaching and learning. In this talk, after introducing the fundamentals of discursive conceptualization, I will present a study, in which commognitive tools were applied in analyzing the way a teacher taught high school mathematics and in finding out the impact of his kind of instruction on the students' mathematics. The example that will be used comes from the lesson in which students were introduced to quadratic inequalities. (The study was conducted in South Africa with Jill Adler).
Anna Sfard is Professor and head of the mathematics education program in the Department of Education at the University of Haifa. She is affiliated with the University of Michigan, where she was the first Lappan-Phillips-Fitzgerald Professor of Mathematics Education, and she is also affiliated with the Institute of Education, University of London, where she has been the Chair of Mathematics Education and a visiting professor.
In 2007, Anna Sfard was awarded The Hans Freudenthal Medal by the International Commission on Mathematics Instruction,
in recognition of her highly significant and scientifically deep accomplishments within a consistent, long-term research programme focused on objectification and discourse in mathematics education, which has had a major impact on many strands of research in mathematics education and on numerous young researchers.
Her work on issues of objectification in mathematical discourse focuses on those discursive mechanisms that are active when new mathematical objects emerge, and her interest is with the development of discourses both at the individual level and also in the course of history.
Although focusing on mathematics education, the work of Anna Sfard also encompasses aspects of human thinking more generally, where relationships between communication and cognition are in focus. Much of her work on these issues is summarized in her book from 2008: "Thinking as communicating: Human development, the growth of discourses, and mathematizing".