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The onto-semiotic approach to research in mathematics education
- ZDM, The International Journal on Mathematics Education
, 2007
"... Abstract: In this paper we synthesise the theoretical model about mathematical cognition and instruction that we have been developing in the past years, which provides conceptual and methodological tools to pose and deal with research problems in mathematics education. Following Steiner’s Theory of ..."
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Cited by 23 (14 self)
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Abstract: In this paper we synthesise the theoretical model about mathematical cognition and instruction that we have been developing in the past years, which provides conceptual and methodological tools to pose and deal with research problems in mathematics education. Following Steiner’s Theory of Mathematics Education Programme, this theoretical framework is based on elements taken from diverse disciplines such as anthropology, semiotics and ecology. We also assume complementary elements from different theoretical models used in mathematics education to develop a unified approach to didactic phenomena that takes into account their epistemological, cognitive, socio cultural and instructional dimensions.
Elementary teachers' mathematics subject knowledge: The Knowledge Quartet and the case of Naomi
- JOURNAL OF MATHEMATICS TEACHER EDUCATION
, 2005
"... This paper draws on videotapes of mathematics lessons prepared and conducted by pre-service elementary teachers towards the end of their initial training at one university. The aim was to locate ways in which they drew on their knowledge of mathematics and mathematics pedagogy in their teaching. A ..."
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Cited by 20 (2 self)
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This paper draws on videotapes of mathematics lessons prepared and conducted by pre-service elementary teachers towards the end of their initial training at one university. The aim was to locate ways in which they drew on their knowledge of mathematics and mathematics pedagogy in their teaching. A grounded approach to data analysis led to the identification of a ‘knowledge quartet’, with four broad dimensions, or ‘units’, through which mathematics-related knowledge of these beginning teachers could be observed in practice. We term the four units: foundation, transformation, connection and contingency. This paper describes how each of these units is characterised and analyses one of the videotaped lessons, showing how each dimension of the quartet can be identified in the lesson. We claim that the quartet can be used as a framework for lesson observation and for mathematics teaching development.
Keeping meaning in proportion: The multiplication table as a case of pedagogical bridging tools. Unpublished doctoral dissertation
, 2004
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Rhetoric and mathematics
, 1987
"... ACCLAIM’s mission is the cultivation of indigenous leadership capacity for the improvement of school mathematics in rural places. 2 Copyright © 2004 by the Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics (ACCLAIM). All rights reserved. The ..."
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Cited by 13 (0 self)
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ACCLAIM’s mission is the cultivation of indigenous leadership capacity for the improvement of school mathematics in rural places. 2 Copyright © 2004 by the Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics (ACCLAIM). All rights reserved. The
An ontosemiotic approach to representations in mathematics education. For the Learning of
- Mathematics
, 2007
"... Abstract: Research in didactics of mathematics has shown the importance that representations have in teaching and learning processes as well as the complexity of factors related to them. Particularly, one of the central open questions that the use of representations poses is the nature and diversity ..."
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Cited by 9 (4 self)
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Abstract: Research in didactics of mathematics has shown the importance that representations have in teaching and learning processes as well as the complexity of factors related to them. Particularly, one of the central open questions that the use of representations poses is the nature and diversity of objects that carry out the role of representation and of the objects represented. The objective of this article is to show how the notion of semiotic function and mathematics ontology elaborated by the onto-semiotic approach to mathematics knowledge, enables us to face such a problem, by generalizing the notion of representation and by integrating different theoretical notions used to describe mathematics cognition. KEY WORDS: external and internal representations, mathematical objects, meaning, understanding, semiotics.
Empowerment in Mathematics Education
- Retrieved April 15, 2002, from the World Wide Web: http://www.ex.ac.uk/~PErnest/pome15/empowerment.htm
, 2000
"... this paper I explore the meaning of empowerment in the teaching and learning of mathematics. The main part of the paper is devoted to distinguishing three different but complementary meanings of empowerment concerning mathematics: mathematical, social and epistemological empowerment. Mathematical ..."
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Cited by 6 (0 self)
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this paper I explore the meaning of empowerment in the teaching and learning of mathematics. The main part of the paper is devoted to distinguishing three different but complementary meanings of empowerment concerning mathematics: mathematical, social and epistemological empowerment. Mathematical empowerment concerns gaining the power to use mathematical knowledge and skills in school mathematics
Implications of Experimental Mathematics for the Philosophy of Mathematics
- CURRENT ISSUES IN THE PHILOSOPHY OF MATHEMATICS FROM THE VIEWPOINT OF MATHEMATICIANS AND TEACHERS OF MATHEMATICS, 2006. [D-DRIVE PREPRINT 280
"... Christopher Koch [34] accurately captures a great scientific distaste for philosophizing: “Whether we scientists are inspired, bored, or infuriated by philosophy, all our theorizing and experimentation depends on particular philosophical background assumptions. This hidden influence is an acute emba ..."
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Cited by 5 (1 self)
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Christopher Koch [34] accurately captures a great scientific distaste for philosophizing: “Whether we scientists are inspired, bored, or infuriated by philosophy, all our theorizing and experimentation depends on particular philosophical background assumptions. This hidden influence is an acute embarrassment to many researchers, and it is therefore not often acknowledged.” (Christopher Koch, 2004) That acknowledged, I am of the opinion that mathematical philosophy matters more now than it has in nearly a century. The power of modern computers matched with that of modern mathematical software and the sophistication of current mathematics is changing the way we do mathematics. In my view it is now both necessary and possible to admit quasi-empirical inductive methods fully into mathematical argument. In doing so carefully we will enrich mathematics and yet preserve the mathematical literature’s deserved reputation for reliability—even as the methods and criteria change. What do I mean by reliability? Well, research mathematicians still consult Euler or Riemann to be informed, anatomists only consult Harvey 3 for historical reasons. Mathematicians happily quote old papers as core steps of arguments, physical scientists expect to have to confirm results with another experiment.
INTERCULTURAL PERSPECTIVES ON MATHEMATICS Learning -- Developing A Theoretical Framework
, 2004
"... This paper explores Alan Bishop’s assumption that all formal mathematics education produces cultural conflicts between the children’s everyday culture and the culture of mathematics. Existing empirical studies support the assumption that mathematics learning indeed has some intercultural aspects wh ..."
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Cited by 5 (3 self)
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This paper explores Alan Bishop’s assumption that all formal mathematics education produces cultural conflicts between the children’s everyday culture and the culture of mathematics. Existing empirical studies support the assumption that mathematics learning indeed has some intercultural aspects which can be differentiated in language factors, effects of overlapping, divergent aims and purposes and moments of foreignness. Analysing mathematics learning in this way from an intercultural perspective allows us to integrate perspectives and results from psychological and pedagogical research on intercultural communication and intercultural learning into mathematics education research. Since these results are located on the descriptive and on the prescriptive level, they can be activated both for analysing and for arranging learning processes in an intercultural setting. Hence, in the third part, prescriptive consequences and didactical orientations are formulated for organising mathematics learning as intercultural learning. I: Can you tell me what you think about the way your father did the sums, is it the same or is it different from the way you learned in school? S: It is a different way, he does it in his head, mine is with the pen. I: Which do you think is the proper way? S: School. I: Which do you think gives a correct result?
The problem of the particular and its relation to the general in mathematics education
- Educational Studies in Mathematics
, 2008
"... Abstract Research in the didactics of mathematics has shown the importance of the problem of the particular and its relation to the general in teaching and learning mathematics as well as the complexity of factors related to them. In particular, one of the central open questions is the nature and di ..."
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Cited by 4 (3 self)
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Abstract Research in the didactics of mathematics has shown the importance of the problem of the particular and its relation to the general in teaching and learning mathematics as well as the complexity of factors related to them. In particular, one of the central open questions is the nature and diversity of objects that carry out the role of particular or general and the diversity of paths that lead from the particular to the general. The objective of this article is to show how the notion of semiotic function and mathematics ontology, elaborated by the onto-semiotic approach to mathematics knowledge, enables us to face such a problem. Keywords Process of generalization and particularization. Generic element.
