Revisiting Zeno's Paradoxes: The Evolution of Number Line Models - Couverture souple

López, Jorge Marcial; Hernández, Omar; Velázquez, Aileen

 
9781534990227: Revisiting Zeno's Paradoxes: The Evolution of Number Line Models
Couverture souple
ISBN 10 : 1534990224 ISBN 13 : 9781534990227
Editeur : CreateSpace Independent Publishing Platform, 2016

Synopsis

Zeno's four paradoxes epitomize the natural tension between discrete and continuous mathematical thinking and succeed in challenging human basic intuitions about space and time. Sorting out the difficulties posed has taken close to twenty-two centuries, and has required the work of the best minds of humankind. Our argument is that Zeno's paradoxes are paradigmatic of the problems that ensue when discrete models are used in lieu of continu- ous ones. We document our presentation with results of tests given to entering students at the Natural Sciences College of University of Puerto Rico at Río Piedras who evidence similar hesitations as those associated with Zeno's paradoxes, and evidence a lack of understanding of the basic number models of mathematics. Exemplary among these models are: the discrete number lines used to represent natural numbers and integers in arithmetic, the infinitely divisible number lines (Archimedean ordered fields) and the continuum number line (complete or- dered fields). We present a reflection on the evolution of these number line models showing how they build upon each other and propose a unified didactical phenomenology for their mathematical structures, linking them to the mental actions involved in the teaching of arithmetic and measurement. Our approach, while based on an idea of Freudenthal, differs significantly from his approach, and is novel to the extent that it reveals simultaneously, the geometry as well as the relevant arithmetic and algebra. Examples of didactic activities for the classroom are presented to illustrate the teaching of the proposed didactical models.

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Présentation de l'éditeur

Zeno's four paradoxes epitomize the natural tension between discrete and continuous mathematical thinking and succeed in challenging human basic intuitions about space and time. Sorting out the difficulties posed has taken close to twenty-two centuries, and has required the work of the best minds of humankind. Our argument is that Zeno's paradoxes are paradigmatic of the problems that ensue when discrete models are used in lieu of continu- ous ones. We document our presentation with results of tests given to entering students at the Natural Sciences College of University of Puerto Rico at Río Piedras who evidence similar hesitations as those associated with Zeno's paradoxes, and evidence a lack of understanding of the basic number models of mathematics. Exemplary among these models are: the discrete number lines used to represent natural numbers and integers in arithmetic, the infinitely divisible number lines (Archimedean ordered fields) and the continuum number line (complete or- dered fields). We present a reflection on the evolution of these number line models showing how they build upon each other and propose a unified didactical phenomenology for their mathematical structures, linking them to the mental actions involved in the teaching of arithmetic and measurement. Our approach, while based on an idea of Freudenthal, differs significantly from his approach, and is novel to the extent that it reveals simultaneously, the geometry as well as the relevant arithmetic and algebra. Examples of didactic activities for the classroom are presented to illustrate the teaching of the proposed didactical models.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
CreateSpace Independent Publishing Platform
Date d'édition
2016
Langue
anglais
ISBN 10 
1534990224
ISBN 13 
9781534990227
Reliure
Broché
Nombre de pages
86
Coordonnées du fabricant
Manufactured by Amazon on behalf of the author
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