Katz Victor J.,Tzanakis Costas (eds). Recent Developments on Introducing a Historical Dimension in Mathematics Education

The Mathematical Association of America, 2011 — 350 p. — (Anneli Lax New Mathematical Library, MAA Notes, 78) — ISBN 9780883851883, 0883851881There has been increased interest in recent years in the use of the history of mathematics in the teaching of mathematics. Many researchers around the world are now conducting empirical studies of the use of history in the mathematics classroom to get more insight into its educational implications. To make these new results available to a wider audience the editors of this book have collected articles stemming from presentations at recent meetings of the International Study Group on the Relations Between History and Pedagogy of Mathematics (the HPM Group), the European Summer University on the History and Epistemology in Mathematics Education (ESU), and the Congress of the European Society for Research in Mathematics Education (CERME). Some of the articles present theoretical perspectives on the use of history, while others give results of empirical studies on how the history of mathematics aided their students in understanding mathematical ideas.Teaching with Primary Historical Sources: Should it Go Mainstream? Can it?, David PengelleyA Personal Odyssey as an Illustration of Issues
Motivations: Why or Why Not?
Logistical Obstacles
A Sample Project: Pascal on Induction and Combinatorics
FinaleDialogism 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 ClassroomThe Process of Mathematical Agreement: Examples from Mathematics History and an Experimental
Sequence of Activities, Gustavo Martinez-Sierra and Roc´ıo Antonio-AntonioThe 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 ConclusionResearching the History of Algebraic Ideas from an Educational Point of View, Luis PuigBabylonian Cut and Paste Operations: A Tool for Analysis
Cut and Paste Operations in Al-Khw¯arizm¯ı’s Algebra
A Reading of Jordanus de Nemore’ De Numberis Datis
Didactical Comments
By Way of ConclusionEquations and Imaginary Numbers: A Contribution from Renaissance Algebra, Giorgio T. Bagni
Editors’ Introductory CommentsTheoretical Framework
History of Mathematics and Imaginary Numbers
Imaginary Numbers from History to Mathematics Education
The Semiosic Chain
Final ReflectionsThe Multiplicity of Viewpoints in Elementary Function Theory: Historical and Didactical Perspectives,Renaud ChorlayThe Interplay Between Four Viewpoints
A Historical Case-Study of f 0 and Variations of f According to Cauchy
Ways of World-Making: The Case of Functions
From Historical Research to Didactic Engineering and Research in DidacticsFrom History to Research in Mathematics Education: Socio-Epistemological Elements for Trigonometric Functions, Gabriela Buendia Abalos and Gisela Montiel EspinosaSocio-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
ReflectionHarmonies 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 TutorialsExposure 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 RemarksHistory, Figures and Narratives in Mathematics Teaching, Adriano Dematt`e and Fulvia FuringhettiUsing Pictures as a Special Case of Using Original Sources
The Experiment
Didactical Implications and ConclusionsPedagogy, History, and Mathematics: Measure as a Theme, Luis Casas and Ricardo LuengoThe Innovation Project
Evaluation of the Project and ConclusionsStudents’ Beliefs About the Evolution and Development of Mathematics, Uffe Thomas JankvistThe Danish Context
Students’ Beliefs About the ‘Identity’ of Mathematics
Evaluating Students’ Beliefs Against the ‘Goals’
Final Remarks and ReflectionsChanges in Student Understanding of Function Resulting from Studying Its History, Beverly M. ReedTheoretical Basis for the Study: APOS Theory
Procedure for the Study
The Research Instruments
The Worksheets and Readings
Findings
Discussion
Conclusion and SummaryIntegrating the History of Mathematics into Activities Introducing Undergraduates to Concepts of Calculus, Theodorus Paschos and Vassiliki FarmakiThe 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 Collected–ResultsHistory in a Competence Based Mathematics Education: A Means for the Learning of Differential Equations, Tinne Hoff KjeldsenMathematical 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 RemarksHistory of Statistics and Students’ Difficulties in Comprehending Variance, Michael Kourkoulos and Constantinos TzanakisClassroom Observations
Looking for Solutions: History Enters the Scene
An Important Predecessor
The Normal Distribution and the Central Limit TheoremDesigning 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 RanjanPedagogical Goals and Design Principles
Incorporating Pedagogical Design Goals: Two Sample Projects
ImplementationHistory of Mathematics for Primary School Teacher Education Or: Can You Do Something Even if You Can’t Do Much?, Bjørn SmestadBackground
Ways of Working with History of Mathematics
DiscussionReflections and Revision: Evolving Conceptions of a Using History Course, Kathleen ClarkCourse Context
The Capstone Project: The First Three Semesters
Reflections for Further Course RevisionMapping 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 ImagesTeachers’ Conceptions of History of Mathematics, Bjørn SmestadBackground—Norway
Background—International
The Research Question
Method
The Participants
DiscussionThe 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: 1876-1900
The Twentieth Century: The Consolidation and Growth of Research-Level Mathematics
The North American Mathematical Landscape by 1950The Transmission and Acquisition of Mathematics in Latin America, from Independence to the First Half of the Twentieth Century, Ubiratan D’AmbrosioIndependence
The 20th Century up to the End of World War II
After the End of the Second World War
Concluding Remarks on Contemporary DevelopmentsIn Search of Vanishing Subjects: The Astronomical Origins of Trigonometry, Glen Van BrummelenFalse Beginnings
Heavenly Foreshadowing
A Union of Opposites
Cultural Divergence: Trigonometry in IndiaAbout the Editors