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Foster, Colin – For the Learning of Mathematics, 2011

In this paper I take a positive view of ambiguity in the learning of mathematics. Following Grosholz (2007), I argue that it is not only the arts which exploit ambiguity for creative ends but science and mathematics too. By enabling the juxtaposition of multiple conflicting frames of reference, ambiguity allows novel connections to be made. I…

Descriptors: Mathematics Education, Figurative Language, Scientific Concepts, Mathematics Instruction

Zazkis, Rina; Mamolo, Ami – For the Learning of Mathematics, 2011

This article extends the notion of "knowledge at the mathematical horizon" or "horizon knowledge" introduced by Ball and colleagues as a part of teachers' subject matter knowledge. Our focus is on teachers' mathematical knowledge beyond the school curriculum, that is, on mathematics learnt during undergraduate college or university studies. We…

Descriptors: Secondary School Mathematics, Mathematics Education, Knowledge Base for Teaching, Colleges

Ward-Penny, Robert; Johnston-Wilder, Sue; Lee, Clare – For the Learning of Mathematics, 2011

It is increasingly being recognised that a significant number of able students who embark on a mathematics degree become disenchanted and move away from mathematics after graduating. This paper reports on the experiences of four such learners, exploring their mathematical trajectories against ideas in current literature. Through a consideration of…

Descriptors: Learning Strategies, Interviews, Mathematics Education, Student Attitudes

Esmonde, Indigo – For the Learning of Mathematics, 2011

This paper contrasts public discussions about the educational troubles of boys and girls to consider what a gender equitable mathematics education might look like. Both public discussions and mathematics education research typically do not carefully define or theorize gender, tend to essentialize gender, and have narrow or unclear definitions of…

Descriptors: Mathematics Education, Gender Differences, Educational Research, Equal Education

Ethnomathematics in the 1930s--The Contribution of Ewald Fettweis to the History of Ethnomathematics

Rohrer, Andrea; Schubring, Gert – For the Learning of Mathematics, 2011

Ewald Fettweis (1881-1967) was the first researcher to develop and establish the term ethnomathematics. This article presents his contribution to ethnomathematics and its development as a scientific theory. We will show that he was the first researcher to realize and practice ethnomathematics in his research and to explain it in his lectures, thus…

Descriptors: Ethnology, Researchers, Mathematics Education, Theories

Tall, David – For the Learning of Mathematics, 2011

This paper introduces the notion of "crystalline concept" as a focal idea in long-term mathematical thinking, bringing together the geometric development of Van Hiele, process-object encapsulation, and formal axiomatic systems. Each of these is a strand in the framework of "three worlds of mathematics" with its own special characteristics, but all…

Descriptors: Geometric Concepts, Mathematics Instruction, Mathematical Models, Mathematical Concepts

Chazan, Daniel; Herbst, Patricio – For the Learning of Mathematics, 2011

Video recordings of instruction have been a mainstay for supporting conversations about teaching by representing particularities of instruction and by presenting the viewer with a multitude of details for interpretation. In this essay, we contrast non-fictional videotapes of actual classroom interaction with fictional animations of classroom…

Descriptors: Video Technology, Interaction, Algebra, Essays

Gerofsky, Susan – For the Learning of Mathematics, 2011

Drawing from sources in gesture studies, cognitive science, the anthropology of religion and art/architecture history, this article explores cultural, bodily and cosmological resonances carried (unintentionally) by mathematical graphs on Cartesian coordinates. Concepts of asymmetric bodily spaces, grids, orthogonality, mapping and sacred spaces…

Descriptors: Graphs, Anthropology, Cognitive Psychology, Cognitive Science

Renert, Moshe – For the Learning of Mathematics, 2011

Ecological sustainability has not been a major focus of mathematics education research, even though it has attracted considerable attention in other areas of educational research in the past decade. The connections between mathematics education and ecological sustainability are not readily apparent. This paper explores how mathematics educators…

Descriptors: Mathematics Education, Educational Research, Mathematics Teachers, Mathematics Instruction

Meaney, Tamsin – For the Learning of Mathematics, 2011

Children bring a wealth of mathematical knowledge from home to school. This paper describes one six/seven year old girl's home interactions over 20 weeks about measurable quantities. Almost all measurement discussions occurred when actions were not straightforward. Consequently the measurement attributes usually used to introduce measurement at…

Descriptors: Time, Mathematics Education, Young Children, Family Environment

Samson, Duncan; Schafer, Marc – For the Learning of Mathematics, 2011

This article explores the inter-relationship between the embodied processes of pattern generalisation and the visualisation of pictorial cues. A research framework is established for analysing pupils' multiple visualisations of figural cues in the context of pattern generalisation. The research framework centres on a novel combination of three…

Descriptors: Classroom Techniques, Cues, Models, Visualization

Borden, Lisa Lunney – For the Learning of Mathematics, 2011

As part of a larger project focused on transforming mathematics education for Aboriginal students in Atlantic Canada, this paper reports on the role of the Mi'kmaw language in mathematics teaching. Examining how mathematical concepts are described in Mi'kmaq gives insight into ways of thinking. Shifting classroom discussions to reflect Mi'kmaw…

Descriptors: Mathematics Education, Form Classes (Languages), Grammar, Foreign Countries

Radford, Luis – For the Learning of Mathematics, 2010

In this article, I focus on what can be termed "the domestication of the eye"--that is to say, the lengthy process during which we come to see and recognize things according to "efficient" cultural means. This is the process that converts the eye into a sophisticated intellectual organ--a "theoretician" as Marx put it. In particular, I focus on…

Descriptors: Grade 2, Perception, Culture, Individual Development

Roth, Wolff-Michael – For the Learning of Mathematics, 2010

As the end result of metaphysics, the Kantian and constructivist mind is not present in the world but withdrawn into the netherworld of its representations and constructions. First phenomenology then the embodied cognition research showed how there could be no cognition without the human body. There is something unsatisfying and lacking, however,…

Descriptors: Mathematics, Constructivism (Learning), Phenomenology, Social Systems

Tatsis, Konstantinos; Dekker, Rijkje – For the Learning of Mathematics, 2010

An episode of two students working collaboratively on a mathematical problem is analysed combining two approaches, namely the process model for mathematical level raising and role theory. The process model stresses the importance of key and regulating activities, while role theory deals with the inter- and intrapersonal concerns of the…

Descriptors: Mathematics Education, Cooperative Learning, Models, Role Theory