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MATHEMATICAL IDEAS REPRESENTATION OF MATHEMATICAL IDEAS AND
, 2000
"... IMPROVING NUMERACY IN CANADA By John Dingwall ..."
The Nonlinearity of Mathematical Ideas
, 2010
"... Mathematics is a richly spun tapestry threaded with interconnections from a multiplicity of endeavors, perspectives, and disciplines, both theoretical and applied. Contrary to its typical presentation, mathematics is not a linear subject. For an instructor, this presents a number of challenges: • h ..."
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: • how best to address the nonlinear, interwoven nature of mathematical ideas while still maintaining sufficient pace through the material? • what is the appropriate tradeoff between guided exploration, which has the desirable element of personal discovery but takes longer, and between lecture, which
The Life and Survival of Mathematical Ideas
"... Nature and evolution provide the notion of a creative system: a core stable form (DNA), a fertile environment, a determination to survive, and random stimuli. Analogously, the mind of a mathematician provides a locus for creative systems, a place where mathematical structures live and evolve. Accord ..."
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Nature and evolution provide the notion of a creative system: a core stable form (DNA), a fertile environment, a determination to survive, and random stimuli. Analogously, the mind of a mathematician provides a locus for creative systems, a place where mathematical structures live and evolve
Inscriptions, Mathematical Ideas and Reasoning in VMT
"... In this chapter, we trace collaborative problem solving as an interactive, layered building of meaning among learners working as a small group. Our analytic aim is to investigate how students through their inscriptive signs collaboratively build mathematical ideas, heuristics and lines of reasoning ..."
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In this chapter, we trace collaborative problem solving as an interactive, layered building of meaning among learners working as a small group. Our analytic aim is to investigate how students through their inscriptive signs collaboratively build mathematical ideas, heuristics and lines of reasoning
Democratic access to powerful mathematical ideas
 In L. D. English (Ed.), Handbook of international research in mathematics education. Directions for the 21st Century
, 2002
"... Abstract. The emergence of the informational society creates the paradoxes of inclusion and citizenship, which call into question any simple interpretation of the meaning of “democratic access to powerful mathematical ideas”. In exploring this thesis we put forward ways of understanding what “powerf ..."
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Cited by 20 (6 self)
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Abstract. The emergence of the informational society creates the paradoxes of inclusion and citizenship, which call into question any simple interpretation of the meaning of “democratic access to powerful mathematical ideas”. In exploring this thesis we put forward ways of understanding what
Mathematical Ideas in Ancient Indian Poetry
"... Modern mathematics owes a big debt to India’s contributions to the subject. Of particular importance is the decimal, place value number system that appeared in India during the Vedic period or soon after, circa 1300 BC to 300 AD, and made its way to Europe during the Middle Ages. That period of time ..."
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of time in India also produced a heady mixture of poetic works: poems, songs, grand epics, biographies and books of instruction in verse covering millions of pages. Mathematical ideas are interwoven into the metaphysical, religious and aesthetic fabric of many of these works. This article brings a
pAdic TGD: Mathematical ideas.
, 1995
"... 2 pAdic numbers 6 3 Canonical correspondence between padic and real numbers 8 4 Algebraic extensions of padic numbers 11 ..."
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2 pAdic numbers 6 3 Canonical correspondence between padic and real numbers 8 4 Algebraic extensions of padic numbers 11
Constructing and sharing mathematical ideas: Some findings from the
"... This symposium will report the findings of the WebLabs project, a threeyear research study funded by the European Union, investigating students ' modelling of mathematical and scientific ideas. The fundamental idea of the project is twofold. First, to design and build "transparent modules ..."
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This symposium will report the findings of the WebLabs project, a threeyear research study funded by the European Union, investigating students ' modelling of mathematical and scientific ideas. The fundamental idea of the project is twofold. First, to design and build "
Epistemological analyses of mathematical ideas: A research methodology
 Proceedings of the Twentysecond Annual Meeting of the International Group for the Psychology of Mathematics Education
, 2000
"... This paper discusses a methodology for researching the question, “What does it mean to understand x, and how might people develop such an understanding?”. We call this methodology epistemological analysis (EA), and we view it as appropriate for creating didactic models of mathematical understanding. ..."
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Cited by 8 (5 self)
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This paper discusses a methodology for researching the question, “What does it mean to understand x, and how might people develop such an understanding?”. We call this methodology epistemological analysis (EA), and we view it as appropriate for creating didactic models of mathematical understanding
Using Computers Environments to Conceptualize Mathematical Ideas †
"... In addition to the computer providing us with new tools to use in mathematics, it also provides opportunities to develop flexible software to help students (and teachers) to understand fundamental mathematical concepts. The “Graphic Approach to the Calculus”, designed by the author, is an example of ..."
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School Mathematics 16–19 Curriculum using computer graphics to visualize ideas about functions, graphs and the calculus. This article outlines the theory underlying the use of such pieces of software – which I term generic organizers because they are designed to encourage the user to organize
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