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Venkat, Hamsa; Askew, Mike; Watson, Anne; Mason, John – For the Learning of Mathematics, 2019
In this paper, we provide an elaboration of the notion of mathematical structure -- a term agreed upon as valuable but difficult to define. We pull apart the terminology surrounding the notion of structure in mathematics: relationship, generalising/generalisation and properties, and offer an architecture of structure that distinguishes and…
Descriptors: Mathematics Instruction, Mathematical Concepts, Algebra, Mathematical Formulas
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Hanna, Gila; Mason, John – For the Learning of Mathematics, 2014
This article discusses the concepts of "key ideas" and "memorability" and how they relate to the metric "width of a proof" put forward by the Fields medalist Timothy Gowers (2007) in a recent essay entitled "Mathematics, memory and mental arithmetic". The paper looks at the meaning of these concepts and…
Descriptors: Mathematics Education, Mathematical Logic, Mathematical Concepts, Teaching Methods
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Mason, John – For the Learning of Mathematics, 2010
Indulging in recounting a few salient memories of what seems now like a dim and distant past, I raise questions about the ebb and flow, the waxing and waning of salient themes in mathematics education. I mention some of the most inspirational influences on my thinking and on my behaviour with learners of all ages. I take the opportunity to ask…
Descriptors: Mathematics Education, Influences, Theory Practice Relationship
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Mason, John; Watson, Anne – For the Learning of Mathematics, 2009
While Socrates and Meno are discussing the nature of knowledge through considering the square-root of two with one of Meno's slaves, their wives are discussing the nature of knowledge through considering the square-root of three with one of the slave girls, using a diagram based on Raphael's "The School of Athens" being contemplated by Euclid.
Descriptors: Mathematical Concepts, Mathematics Instruction, Epistemology, Knowledge Level
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Mason, John – For the Learning of Mathematics, 1980
The roles and uses of symbols in mathematical thinking are discussed. The thinking process is further subdivided into specialization, generalization, and reasoning. (MP)
Descriptors: Cognitive Processes, Discovery Learning, Inservice Teacher Education, Learning Theories
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Sfard, Anna; Nesher, Pearla; Streefland, Leen; Cobb, Paul; Mason, John – For the Learning of Mathematics, 1998
Presents three schools of argument on mathematical communication: (1) cognitivist argument; (2) interactionist argument; and (3) neo-pragmatist argument. Distinguishes the mathematical versus talking about mathematics, talking mathematics versus learning the art of mathematical conversation, and the conversation of mathematicians versus students'…
Descriptors: Classroom Communication, Elementary Secondary Education, Mathematical Linguistics, Mathematics Education