"Imagining Numbers" (Particularly the Square Root of Minus Fifteen)

Mazur, Barry; Pesic, Peter; Sabbagh, Karl

doi:10.2307/4145034

Cited by 14 publications

(32 citation statements)

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“…Similar couplings have been made in mathematics education, where imagination is discussed as being important and useful (Davis & Simmt 2006;Hilbert & Cohn-Vossen 1952;Kasner & Newman 1940;Mazur 2003;Sfard 1997). Despite these connections, little is known about the ways in which imagination can be used as both a pedagogical and a mathematical tool for learning mathematics (Henderson 1995).…”

Section: Introductionmentioning

confidence: 81%

“…The work of Mazur (2003) led us to question whether teaching and learning mathematics can be thought of in terms of imagination. More specifically, we questioned whether the features and steps of Mazur's re-enactment of the imaginative work of mathematicians could be appropriated pedagogically in a middle-school setting.…”

Section: Introductionmentioning

confidence: 99%

“…2 Imagination and visualization: working definitions Mazur (2003) defines imagination 1 as a new way of "providing a natural home for that something in the mind's mind" (p. 138), that resists familiar "types of mental image-making activities" (p. 138). Commonly, imagination and visualization are taken as synonymous.…”

Section: Introductionmentioning

confidence: 99%

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Investigating imagination as a cognitive space for learning mathematics

Kotsopoulos

Cordy

2008

Educ Stud Math

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Our work is inspired by the book Imagining Numbers (particularly the square root of minus fifteen), by Harvard University mathematics professor Barry Mazur (Imagining numbers (particularly the square root of minus fifteen), Farrar, Straus and Giroux, New York, 2003). The work of Mazur led us to question whether the features and steps of Mazur's re-enactment of the imaginative work of mathematicians could be appropriated pedagogically in a middle-school setting. Our research objectives were to develop the framework of teaching mathematics as a way of imagining and to explore the pedagogical implications of the framework by engaging in an application of it in middle school setting. Findings from our application of the model suggest that the framework presents a novel and important approach to developing mathematical understanding. The model demonstrates in particular the importance of shared visualizations and problemposing in learning mathematics, as well as imagination as a cognitive space for learning.

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Section: Introductionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

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Investigating imagination as a cognitive space for learning mathematics

Kotsopoulos

Cordy

2008

Educ Stud Math

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“…For instance, as this list makes clear, although knitted from logic, mathematics relies on analogy. Indeed, as Mazur (2003) develops, many of the great leaps in the emergence of mathematical knowledge had as much to do with new analogies as with logical insight. 4.…”

Section: Resultsmentioning

confidence: 99%

Mathematics-for-Teaching: an Ongoing Investigation of the Mathematics that Teachers (Need to) Know

2006

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In this article we offer a theoretical discussion of teachers' mathematicsfor-teaching, using complexity science as a framework for interpretation. We illustrate the discussion with some teachers' interactions around mathematics that arose in the context of an in-service session. We use the events from that session to illustrate four intertwining aspects of teachers' mathematics-for-teaching. We label these aspects "mathematical objects," "curriculum structures," "classroom collectivity," and "subjective understanding". Drawing on complexity science, we argue that these phenomena are nested in one another and that they obey similar dynamics, albeit on very different time scales. We conjecture (1) that a particular fluency with these four aspects is important for mathematics teaching and (2) that these aspects might serve as appropriate emphases for courses in mathematics intended for teachers.

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“…It took two more centuries to arrive at a geometrical interpretation of complex numbers. This story is well covered by Barry Mazur (2003). For a mathematician, Mazur pays surprisingly much attention to the conceptual evolutions which have lead to imaginary numbers.…”

Section: Defining Imaginary Numbers By Operational Symbolismmentioning

confidence: 98%

On the Nature and Origin of Algebraic Symbolism

Heeffer¹

2008

New Perspectives on Mathematical Practices

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"Imagining Numbers" (Particularly the Square Root of Minus Fifteen)

Cited by 14 publications

References 0 publications

Investigating imagination as a cognitive space for learning mathematics

Investigating imagination as a cognitive space for learning mathematics

Mathematics-for-Teaching: an Ongoing Investigation of the Mathematics that Teachers (Need to) Know

On the Nature and Origin of Algebraic Symbolism

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