Carl Winsløw

University of Copenhagen, Department of Science Education, Faculty Member

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Papers by Carl Winsløw

Ultraproducts, QWEP von Neumann Algebras, and the Effros-Maréchal Topology

Based on the analysis on the Ocneanu/Groh-Raynaud ultraproducts and the Effros-Maréchal topology ... more Based on the analysis on the Ocneanu/Groh-Raynaud ultraproducts and the Effros-Maréchal topology on the space vN(H) of von Neumann algebras acting on a separable Hilbert space H, we show that for a von Neumann algebra M ∈ vN(H), the following conditions are equivalent: (1) M has the Kirhcberg's quotient weak expectation property (QWEP).

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Mathematical analysis in high school : a fundamental dilemma

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Studying Student Teachers’ Voices and Their Beliefs and Attitudes

Learning to teach mathematics is a complex undertaking, and in the last twenty years there has be... more Learning to teach mathematics is a complex undertaking, and in the last twenty years there has been a great deal of research looking at aspects of the process. There are many ways one might structure an analysis of research on learning to teach mathematics. It is clear, though, from all the research on learners in all kinds of situations that what student teachers bring to their teacher education courses in terms of prior knowledge, experience, attitudes, beliefs, goals, fears, hopes, and expectations has to be a key factor in preparing for and teaching those courses and hence for research.

Components of Mathematics Teacher Training

Initial mathematics teacher education is primarily concerned with knowledge–the acquisition of kn... more Initial mathematics teacher education is primarily concerned with knowledge–the acquisition of knowledge required for the teaching of mathematics. Opinions as to what exactly comprises this knowledge and how it is best delivered and best learned varies widely across different contexts. In what follows, we will look more closely at this concept of teacher knowledge and how it plays itself out in the context of initial mathematics teacher education.

CERME7 Working Group 14: University mathematics education

Research in Mathematics Education, 2012

The WG14 papers presented at CERME7 provide ample evidence of growth in this area of research. Th... more The WG14 papers presented at CERME7 provide ample evidence of growth in this area of research. The nutshell descriptions of WG14 papers that follow are structured around the main themes of the Group&amp;amp;amp;amp;amp;#x27;s Call for Papers (such as the teaching and learning of particular topics, pedagogical and curricular issues at university level, the transition from school to university mathematics) and the observation that, beyond staple references to classic constructs from the AMT era, several works employ approaches such as the ...

DIDACTIC CODETERMINATION IN THE CREATION OF AN INTEGRATED MATH AND SCIENCE TEACHER EDUCATION: THE CASE OF MATHEMATICS AND GEOGRAPHY

This paper presents an application of the Anthropological Theory of the Didactic to describe and ... more This paper presents an application of the Anthropological Theory of the Didactic to describe and analyse the genesis of an integrated mathematics and science preservice teacher education. Reporting from the pre-experimentation phase, it is shown how the levels in the scale of didactic codetermination enable us to understand more clearly how integration is envisaged.

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Anthropological theory of didactic phenomena: some examples and principles of its use in the study of mathematics education

Abstract: The founder of the anthropological theory of the didactical, Yves Chevallard, was recen... more Abstract: The founder of the anthropological theory of the didactical, Yves Chevallard, was recently awarded the Hans Freudenthal medal, given in recognition of “a major cumulative program of research” in mathematics education. The aim of this paper is to present, to a Nordic audience, an outline of this theoretical programme, and to highlight some of the features which we believe to be of particular relevance to research on mathematics education.

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正当化することについて

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MATHEMATICS AT UNIVERSITY: THE ANTHROPOLOGICAL APPROACH

In this presentation I propose a theoretical framework to study these questions more precisely, b... more In this presentation I propose a theoretical framework to study these questions more precisely, based on the anthropological theory of didactics. As a main application, the links between the practices of mathematical research and university mathematics teaching are examined, in particular in the light of the dynamic between “exploring milieus” and “studying media”. Key words: university mathematics, tertiary, anthropological theory of the didactical

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Hvorfor gik de ud?: en analyse af frafald på årgang 2006 af matematikstudiet

IMF har bedt IND identificere årsager til matematikuddannelsens' tidlige'frafald, dvs årsager til... more IMF har bedt IND identificere årsager til matematikuddannelsens' tidlige'frafald, dvs årsager til at studerende forlader bacheloruddannelsen i matematik inden for de første par år af studiet. Navnlig faktorer som instituttets uddannelsesansvarlige har mulighed for at reagere på er af interesse her. Vi har valgt at belyse spørgsmålet ved at se nærmere på de studerende der påbegyndte matematikuddannelsen i efteråret 2006.

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Competencies, version ground floor

As the title of this conference indicates, there is strong pressure on universities to change. Th... more As the title of this conference indicates, there is strong pressure on universities to change. The agenda is well known from abroad, in particular from UK where it has been prevalent since the Thatcher era, and is often formulated in terms of implementing strategies from the private sector into the public. With a, perhaps typical, delay of a couple of years, it is dominating the political discourse on education in Denmark.

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A GRADUATE COURSE ON DIDACTICS AS DESIGN SCIENCE

Didactics is the science which investigates the conditions for teaching and learning. These condi... more Didactics is the science which investigates the conditions for teaching and learning. These conditions may arise from a number of sources: societal and institutional (from outside the teaching/learning system), cognitive and social (from teachers and learners as interacting individuals) and epistemological (from the knowledge at stake).

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Didaktiske elementer: en indføring i matematikkens og naturfagenes didaktik: en indføring i matematikkens og naturfagenes didaktik

Developing and assessing specific competencies in a first course on real analysis

Research on Collegiate Mathematics Education VI, Jan 1, 2006

A model of mathematics teacher knowledge and a comparative study in Denmark, France and Japan

A model for mathematics teacher knowledge based on the anthropological theory of didactics is pre... more A model for mathematics teacher knowledge based on the anthropological theory of didactics is presented together with a methodological discussion of how to assess such knowledge in practice. To this end we propose a concrete method involving "hypothetical teacher tasks" and individual as well as collaborative work of the teachers to be assessed. This discussion is illustrated by a small scale comparative study of how future lower secondary mathematics teachers (just about to graduate) from Denmark, France and Japan approach two hypothetical teacher tasks (related to teaching geometry and arithmetics).

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The flow of weights in subfactor theory

Publications of The Research Institute for Mathematical Sciences, Jan 1, 1995

We define a Connes-Takesaki type flow of weights for any inclusion of factors. It is shown that P... more We define a Connes-Takesaki type flow of weights for any inclusion of factors. It is shown that Popa's classification of strongly amenable subfactors as well as some new structural results on type III-subfactors can be stated in a unified way using this invariant. The invariant also separates certain "exotic" examples of subfactors which are not covered by that classification.

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Classification of strongly amenable subfactors of type

We define strong amenability for subfactors of type III_0 as a special case of a general strong a... more We define strong amenability for subfactors of type III_0 as a special case of a general strong amenability type property (called strong injectivity) for subfactors. Using the “relative” flow of weights for subfactors, we then give a complete classification of strongly amenable subfactors of type III_0.

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Semiotic and discursive variables in CAS-based didactical engineering

Educational Studies in Mathematics, Jan 1, 2003

This paper presents a semiotic analysis of the (often claimed) potential of computer algebra syst... more This paper presents a semiotic analysis of the (often claimed) potential of computer algebra systems (CAS) for enabling mathematical activity on a conceptual level higher than usual. Theoretical points are illustrated by examples from a development project in the context of a first year university course on calculus. We also discuss how they may be used in 'a posteriori' didactical analysis and in didactical engineering.

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Strongly free actions on subfactors

Internat. J. Math, Jan 1, 1993

For actions on arbitrary inclusions of factors with finite index, we define an algebraic property... more For actions on arbitrary inclusions of factors with finite index, we define an algebraic property called&amp;amp;amp;quot; strong freeness&amp;amp;amp;quot;. In the case of strongly amenable subfactors of type II∞ or IIIλ (0&amp;amp;amp;lt; λ&amp;amp;amp;lt; 1), this property is shown to be a characterization of centrally free actions. We then classify strongly free actions of discrete amenable groups on strongly amenable subfactors of type II∞, and strongly free actions of a class of discrete amenable groups (which include ℤn, n∈ ℕ) on strongly amenable subfactors of type IIIλ. Namely, we show that the (generalized) ...

Semiotics as an analytical tool for the didactics of mathematics

Nordic Studies in Mathematics Education, NOMAD, Jan 1, 2004

This paper is an introduction to (what the author perceives to be) one of the most exciting and p... more This paper is an introduction to (what the author perceives to be) one of the most exciting and promising directions in research on the didactics of mathematics: studying the learning of mathematics as the initiation to, and internalisation of, certain semiotic systems. Three principal ways in which this point of view can contribute crucially to didactical research are presented and exemplified; they concern the cognitive, social and cultural aspects of mathematics education. Finally, as a topic transcending the three aspects, we discuss the use of digital semiotic appliances in mathematics teaching.

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Carl Winsløw

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