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Map** the effects of policy on mathematics teacher education
Changes in school mathematics curricula, pedagogy and assessment, and as a consequence the pressure for changes in initial teacher preparation, are...
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Ethnomathematics and Philosophy
Any concept of ethnomathematics must eventually meet philosophical debates about the nature of mathematics. In particular neo-realist positions are...
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Beyond motivation: history as a method for learning meta-discursive rules in mathematics
In this paper, we argue that history might have a profound role to play for learning mathematics by providing a self-evident (if not indispensable)...
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Dawn of Science
Foundations of calculus were developed by a school of mathematicians in Kerala during 1400–1600, years before similar developments took place in the...
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Why Proof? A Historian’s Perspective
The history of mathematics provides evidence that proofs let mathematicians distinguish between true results and merely plausible ones; that the...
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Zooming in on infinitesimal 1–.9.. in a post-triumvirate era
The view of infinity as a metaphor, a basic premise of modern cognitive theory of embodied knowledge, suggests in particular that there may be...
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Approaches to Calculus Using Geogebra
This chapter outlines how GeoGebra can be used to facilitate a high school treatment of calculus, including differentiation of polynomial,...
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Historical Objections Against the Number Line
Historical studies on the development of mathematical concepts will help mathematics teachers to relate their students’ difficulties in understanding...
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New Avenues for History in Mathematics Education: Mathematical Competencies and Anchoring
The paper addresses the apparent lack of impact of ‘history in mathematics education’ in mathematics education research in general, and proposes new...
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Drawing space: mathematicians’ kinetic conceptions of eigenvectors
This paper explores how mathematicians build meaning through communicative activity involving talk, gesture and diagram. In the course of describing...
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Dynamic mathematics and the blending of knowledge structures in the calculus
This paper considers the role of dynamic aspects of mathematics specifically focusing on the calculus, including computer software that responds to...
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Abstract Tools and Technologies of Learning: An Evolving Partnership
This discussion begins by placing the human use of tools in an evolutionary context. This helps in understanding the many ways educationists need to...
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Towards a Critical Professionalism in University Science and Mathematics Education
Descartes is often referred to as the first modern philosopher, as he introduced a new way of looking at knowledge and nature. This new way is...
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Gestures as semiotic resources in the mathematics classroom
In this paper, we consider gestures as part of the resources activated in the mathematics classroom: speech, inscriptions, artifacts, etc. As such,...
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The transition to formal thinking in mathematics
This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university....
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A historic overview of the interplay of theology and philosophy in the arts, mathematics and sciences
The etymology of the word “mathematics” can be traced to Greek roots with meanings such “a thing learned” (mathein is the verb “to have learned”)...
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Computational Construction as a Means to Coordinate Representations of Infinity
In this paper, we describe a design experiment aimed at hel** students to explore and develop concepts of infinite processes and objects. Our...
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Proof as a practice of mathematical pursuit in a cultural, socio-political and intellectual context
Through examples we explore the practice of mathematical pursuit, in particular on the notion of proof, in a cultural, socio-political and...
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A Never-Ending Braid: the Development of Mathematics
The evidence from language is brought together to discuss the nature of mathematics. Different conceptions of the way it develops are described, and...