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Norton, Anderson – For the Learning of Mathematics, 2019

Felix Klein's Erlangen program classifies geometries based on the kinds of geometric transformations that preserve key properties of their figures, rather than focusing on the geometric figures themselves. This shift in perspective, from figurative to operative, fits Piaget's characterization of mathematical development. This paper considers how…

Descriptors: Mathematics Education, Mathematics Instruction, Instructional Effectiveness, Geometry

Alshwaikh, Jehad – For the Learning of Mathematics, 2018

This article suggests a tool for analysing diagrams in mathematical texts. The starting point for this tool is Halliday's Systemic Functional Grammar (SFG), which considered language as a social practice. Kress and Van Leeuwen (2006) applied Halliday's SFG to images, suggesting a grammar for reading images. Morgan (1996) adopted Halliday's SFG and…

Descriptors: Mathematics Education, Visual Aids, Semiotics, Grammar

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

Rodd, Melissa – For the Learning of Mathematics, 2010

A well-documented experience of students of elementary Euclidean geometry is "seeing" a geometric result and being sure about its truth; this sort of experience gives rise to the notion of geometrical visualisation that is developed here. In this essay a philosophical argument for the epistemic potential of geometrical visualisation is reviewed,…

Descriptors: Geometry, Visualization, Epistemology, Mathematics Education

Fried, Michael N. – For the Learning of Mathematics, 2009

The first goal of this article to show the profound difference between how equality and similarity are understood in Greek geometry and how they are presented in modern mathematics classes. It highlights that the formula "equal-and-similar" reflects the distinct character of "equal" and "similar" as signs in Greek…

Descriptors: Modern Mathematics, Historical Interpretation, Mathematics Education, Mathematics Instruction

Barton, Bill – For the Learning of Mathematics, 2004

In this article, the author comments on the article "Solid geometry in the works of an iron artisan,'" Castro, 23(3). The author finds it interesting to read about the implicit mathematical knowledge of ironworkers, weavers, tailors and other practitioners as they undertake their various crafts and professions. In the article, Fernando…

Descriptors: Mathematics, Educational Practices, Mathematics Education, Geometric Concepts

Peer reviewed

Sharp, John – For the Learning of Mathematics, 2002

Discusses a number of Theo van Doesburg's paintings concerning arithmetic composition. (KHR)

Descriptors: Art, Geometry, Interdisciplinary Approach, Mathematics Education

Peer reviewed

Hanna, Gila; Jahnke, Hans Niels – For the Learning of Mathematics, 2002

Investigates what the role of arguments from physics within mathematical proof is, and how this role should be reflected in the classroom. Presents examples showing the fruitfulness of center of gravity arguments in terms of geometrical configuration and the laws of the lever. Discusses educational advantages of the use of arguments from physics…

Descriptors: Concept Formation, Curriculum Development, Elementary Secondary Education, Geometry

Peer reviewed

Sinclair, Nathalie – For the Learning of Mathematics, 2002

Describes episodes from work with a small group of 8th grade students who were working independently on a geometry course. Uses Geometer's Sketchpad for the tasks. Discusses students' reasoning skills and their interpretation of the painting in terms of the mathematical properties and relationships. (KHR)

Descriptors: Art, Computer Uses in Education, Geometric Concepts, Geometry

Peer reviewed

Gattegno, Caleb – For the Learning of Mathematics, 1980

Presented is an edited transcript of an interview with Dr. Caleb Gattegno exploring the teaching approaches used in a film of the same name. (MP)

Descriptors: Elementary Secondary Education, Geometric Concepts, Geometry, Instructional Films

Peer reviewed

Van Den Brink, Jan – For the Learning of Mathematics, 1995

Shows similarities between realism and radical constructivism by presenting examples of using children's ideas in order to create education in the context of teaching spherical geometry. (18 references) (MKR)

Descriptors: Constructivism (Learning), Geometry, Learning Theories, Mathematics Education

Peer reviewed

Shumway, Richard – For the Learning of Mathematics, 1990

Discussed are supercalculator capabilities and possible teaching implications. Included are six examples that use a supercalculator for topics that include volume, graphing, algebra, polynomials, matrices, and elementary calculus. A short review of the research on supercomputers in education and the impact they could have on the curriculum is…

Descriptors: Algebra, Calculators, Calculus, Cognitive Development

Peer reviewed

Zeitler, Herbert – For the Learning of Mathematics, 1990

Geometric axioms are discussed in terms of philosophy, history, refinements, and basic concepts. The triumphs and limitations of the formalism theory are included. Described is the status of high school geometry internationally. (KR)

Descriptors: Comparative Education, Foreign Countries, Geometric Concepts, Geometry

Peer reviewed

Gerdes, Paulus – For the Learning of Mathematics, 1988

The mathematics curriculum should be imbedded into the cultural environment of the student. Discussed is the mathematical educational potential of decorative motif. (PK)

Descriptors: Geometric Concepts, Geometry, Mathematical Enrichment, Mathematics Curriculum

Peer reviewed

Lopez-Real, Francis; Leung, Allen – For the Learning of Mathematics, 2001

Discusses reflections on a videotaped geometry lesson from a Japanese classroom. Contrasts the lesson with the work of a group of teachers on a B.Ed. program who were given the same problem-solving task as the Japanese pupils. (MM)

Descriptors: Comparative Education, Foreign Countries, Geometry, Mathematics Education

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