Recent Developments on Introducing a Historical Dimension in Mathematics Education

cover
copyright page
title page
Preface
Contents
Teaching with Primary Historical Sources: Should it Go Mainstream? Can it?, David Pengelley
	Introduction
	A Personal Odyssey as an Illustration of Issues
	Motivations: Why or Why Not?
	Logistical Obstacles
	A Sample Project: Pascal on Induction and Combinatorics
	Finale
	Bibliography
	About the Author
Dialogism in Mathematical Writing: Historical, Philosophical and Pedagogical Issues, Evelyne Barbin
	What is Dialogism?
	Dialogism in Mathematics: A Paradox?
	Dialogism and Innovation in Mathematics
	Dialogism and History of Mathematics: The Question of Addressivity
	Dialogism and History of Mathematics: Reading Original Sources in Classroom
	Conclusion
	Bibliography
	About the Author
The Process of Mathematical Agreement: Examples from Mathematics History and an Experimental Sequence of Activities, Gustavo Martinez-Sierra and Rocío Antonio-Antonio
	Introduction
	The Process of Mathematical Agreement
	The Fractional Exponents
	The Square Root of Negative Numbers
	The Radian and the Trigonometric Functions
	An Experimental Sequence of Activities: The Square Root of Negative Numbers
	In Conclusion
	Bibliography
	About the Authors
Researching the History of Algebraic Ideas from an Educational Point of View, Luis Puig
	Introduction
	Babylonian Cut and Paste Operations: A Tool for Analysis
	Cut and Paste Operations in Al-Khwarizmi's Algebra
	A Reading of Jordanus de Nemore' De Numberis Datis
	Didactical Comments
	By Way of Conclusion
	Bibliography
	About the Author
Equations and Imaginary Numbers: A Contribution from Renaissance Algebra, Giorgio T. Bagni
	Editors' Introductory Comments
	Introduction
	Theoretical Framework
	History of Mathematics and Imaginary Numbers
	Imaginary Numbers from History to Mathematics Education
	The Semiosic Chain
	Final Reflections
	Bibliography
	About the Author
The Multiplicity of Viewpoints in Elementary Function Theory: Historical and Didactical Perspectives, Renaud Chorlay
	Introduction
	The Interplay Between Four Viewpoints
	A Historical Case-Study of f' and Variations of f According to Cauchy
	Ways of World-Making: The Case of Functions
	From Historical Research to Didactic Engineering and Research in Didactics
	Conclusion
	Bibliography
	About the Author
From History to Research in Mathematics Education: Socio-Epistemological Elements for Trigonometric Functions, Gabriela Buendia Abalos and Gisela Montiel Espinosa
	Introduction
	Socio-Epistemological Theoretical Approach
	Didactic Difficulties with the Trigonometric Functions
	Socio-Epistemological Review: Towards Trigonometric Functionality
	A Socio-Epistemological Approach to the Introductio in Analysin Infinitorium
	A Socio-Epistemology Based on Uses and Significations Developed in a Historic Setting
	Problem Situations
	A problem-situation to identify the unit of measurement
	Final Reflection
	Bibliography
	About the Authors
Harmonies in Nature: A Dialogue Between Mathematics and Physics, Man-Keung Siu
	Why is an Enrichment Course on Mathematics-Physics Designed?
	How is Such a Course Run?
	A Sketch of the Content of the Course
	Some Sample Problems in Tutorials
	Conclusion
	Bibliography
	About the Author
Exposure to Mathematics in the Making: Interweaving Math News Snapshots in the Teaching of High-School Mathematics, Batya Amit, Nitsa Movshovitz-Hadar, and Avi Berman
	Introduction: The Ever Growing Nature of Mathematics
	The Problem: A Gap Between School Mathematics and Mathematics
	A Proposed Solution and its Rationale
	The Challenge for the Teacher
	The Study
	A Snapshot: ``The Search for Prime Numbers"
	Analysis of Observed Reactions to the Snapshot
	Closing Remarks
	Bibliography
	About the Authors
History, Figures and Narratives in Mathematics Teaching, Adriano Demattè and Fulvia Furinghetti
	Introduction
	Using Pictures as a Special Case of Using Original Sources
	The Experiment
	Didactical Implications and Conclusions
	Bibliography
	About the Authors
Pedagogy, History, and Mathematics: Measure as a Theme, Luis Casas and Ricardo Luengo
	Introduction
	The Innovation Project
	Evaluation of the Project and Conclusions
	Bibliography
	About the Authors
Students' Beliefs About the Evolution and Development of Mathematics, Uffe Thomas Jankvist
	Introduction
	The Danish Context
	Students' Beliefs About the `Identity' of Mathematics
	Evaluating Students' Beliefs Against the `Goals'
	Final Remarks and Reflections
	Bibliography
	About the Author
Changes in Student Understanding of Function Resulting from Studying Its History, Beverly M. Reed
	Introduction
	Theoretical Basis for the Study: APOS Theory
	Procedure for the Study
	The Research Instruments
	The Worksheets and Readings
	Findings
	Discussion
	Conclusion and Summary
	Bibliography
	About the Author
Integrating the History of Mathematics into Activities Introducing Undergraduates to Concepts of Calculus, Theodorus Paschos and Vassiliki Farmaki
	Introduction
	The Historical Background of the Teaching Experiment
	Designing Didactic Activities Inspired by History of Mathematics
	The Multiple Linked Representations Between Rates and Totals
	Analysis of the Data CollectedŠ--Results
	Bibliography
	About the Authors
History in a Competence Based Mathematics Education: A Means for the Learning of Differential Equations, Tinne Hoff Kjeldsen
	Introduction
	Mathematical Competence and the Role of History
	A Multiple Perspective Approach to History of Mathematics
	A Student Project on Physics' Influence on the History of Differential Equations
	Some Conclusions and Critical Remarks
	Bibliography
	About the Author
History of Statistics and Students' Difficulties in Comprehending Variance, Michael Kourkoulos and Constantinos Tzanakis
	Introduction
	Classroom Observations
	Looking for Solutions: History Enters the Scene
	An Important Predecessor
	The Normal Distribution and the Central Limit Theorem
	Bibliography
	Appendix
	About the Authors
Designing Student Projects for Teaching and Learning Discrete Mathematics and Computer Science via Primary Historical Sources, Janet Heine Barnett, Jerry Lodder, David Pengelley, Inna Pivkina and Desh Ranjan
	Introduction
	Pedagogical Goals and Design Principles
	Incorporating Pedagogical Design Goals: Two Sample Projects
	Implementation
	Conclusion
	Bibliography
	About the Authors
History of Mathematics for Primary School Teacher Education Or: Can You Do Something Even if You Can't Do Much?, Bjørn Smestad
	Introduction
	Background
	Ways of Working with History of Mathematics
	Discussion
	Bibliography
	About the Author
Reflections and Revision: Evolving Conceptions of a Using History Course, Kathleen Clark
	Introduction
	Course Context
	The Capstone Project: The First Three Semesters
	Reflections for Further Course Revision
	Conclusion
	Bibliography
	About the Author
Mapping Our Heritage to the Curriculum: Historical and Pedagogical Strategies for the Professional Development of Teachers, Leo Rogers
	The English Curriculum: 2008--2009
	A Pedagogical Tradition
	The History of Mathematics and our Mathematical Heritage
	Mapping Our Heritage
	Trialling, Qualitative Results, and Development
	Heritage Maps and Canonical Images
	Bibliography
	About the Author
Teachers' Conceptions of History of Mathematics, Bjørn Smestad
	Introduction
	Background---Norway
	Background---International
	The Research Question
	Method
	The Participants
	Discussion
	Conclusion
	Bibliography
	About the Author
The Evolution of a Community of Mathematical Researchers in North America: 1636--1950, Karen Hunger Parshall
	The Seventeenth and Eighteenth Centuries: Mathematics in Colonial Settings
	The Nineteenth Century: A Period of General Structure-Building in Higher Education and in Science
	A Mathematical Research Community Emerges in the United States: 1876Œ-1900
	The Twentieth Century: The Consolidation and Growth of Research-Level Mathematics
	The North American Mathematical Landscape by 1950
	Bibliography
	About the Author
The Transmission and Acquisition of Mathematics in Latin America, from Independence to the First Half of the Twentieth Century, Ubiratan D'Ambrosio
	Introduction
	Independence
	The 20th Century up to the End of World War II
	After the End of the Second World War
	Concluding Remarks on Contemporary Developments
	Bibliography
	About the Author
In Search of Vanishing Subjects: The Astronomical Origins of Trigonometry, Glen Van Brummelen
	Introduction
	False Beginnings
	Heavenly Foreshadowing
	A Union of Opposites
	Cultural Divergence: Trigonometry in India
	Conclusion
	Bibliography
	About the Author
About the Editors