eBook ISBN:  9781470458287 
Product Code:  CLRM/3.E 
List Price:  $45.00 
MAA Member Price:  $33.75 
AMS Member Price:  $33.75 
eBook ISBN:  9781470458287 
Product Code:  CLRM/3.E 
List Price:  $45.00 
MAA Member Price:  $33.75 
AMS Member Price:  $33.75 

Book DetailsClassroom Resource MaterialsVolume: 3; 1995; 303 pp
This book is for high school and college teachers who want to know how they can use the history of mathematics as a pedagogical tool to help their students construct their own knowledge of mathematics. Often, a historical development of a particular topic is the best way to present a mathematical topic, but teachers may not have the time to do the research needed to present the material.
This book provides its readers with historical ideas and insights which can be immediately applied in the classroom. The book is divided into two sections: the first on the use of history in high school mathematics, and the second on its use in university mathematics. The articles are diverse, covering fields such as trigonometry, mathematical modeling, calculus, linear algebra, vector analysis, and celestial mechanics. Also included are articles of a somewhat philosophical nature, which give general ideas on why history should be used in teaching and how it can be used in various special kinds of courses. Each article contains a bibliography to guide the reader to further reading on the subject. 
Table of Contents

Articles

Part I: History in School Mathematics

Shmuel Avital  History of Mathematics Can Help Improve Instruction and Learning

Phillip S. Jones  The Role in the History of Mathematics of Algorithms and Analogies

Frank J. Swetz  Using Problems from the History of Mathematics in Classroom Instruction

John Fauvel  Revisiting the History of Logarithms

Victor J. Katz  Napier’s Logarithms Adapted for Today’s Classroom

Frank J. Swetz  Trigonometry Comes Out of the Shadows

Jan A. van Maanen  Alluvial Deposits, Conic Sections, and Improper Glasses, or History of Mathematics Applied in the Classroom

Frank J. Swetz  An Historical Example of Mathematical Modeling: The Trajectory of a Cannonball

Part II: History in Higher Mathematics

ManKeung Siu  Concept of Function—Its History and Teaching

V. Frederick Rickey  My Favorite Ways of Using History in Teachng Calculus

Michel Helfgott  Improved Teaching of the Calculus Through the Use of Historical Materials

ManKeung Siu  Euler and Heuristic Reasoning

Joel P. Lehmann  Converging Concepts of Series: Learning from History

Lars Mejlbo  Historical Thoughts on Infinite Numbers

Victor J. Katz  Historical Ideas in Teaching Linear Algebra

Otto B. Bekken  Wessel on Vectors

Karen Reich  Who Needs Vectors?

Israel Kleiner  The Teaching of Abstract Algebra: An Historical Perspective

David M. Burton and Donovan H. Van Osdol  Toward the Definition of an Abstract Ring

Anthony D. Gardiner  In Hilbert’s Shadow: Notes Toward a Redefinition of Introductory Group Theory

Eric J. Aiton  An Episode in the History of Celestial Mechanics and Its Utility in the Teaching of Applied Mathematics

ManKeung Siu  Mathematical Thinking and History of Mathematics

Abe Shenitzer  A Topics Course in Mathematics

Niels Henrik Abel (1802–1829): A Tribute

About the Authors


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This book is for high school and college teachers who want to know how they can use the history of mathematics as a pedagogical tool to help their students construct their own knowledge of mathematics. Often, a historical development of a particular topic is the best way to present a mathematical topic, but teachers may not have the time to do the research needed to present the material.
This book provides its readers with historical ideas and insights which can be immediately applied in the classroom. The book is divided into two sections: the first on the use of history in high school mathematics, and the second on its use in university mathematics. The articles are diverse, covering fields such as trigonometry, mathematical modeling, calculus, linear algebra, vector analysis, and celestial mechanics. Also included are articles of a somewhat philosophical nature, which give general ideas on why history should be used in teaching and how it can be used in various special kinds of courses. Each article contains a bibliography to guide the reader to further reading on the subject.

Articles

Part I: History in School Mathematics

Shmuel Avital  History of Mathematics Can Help Improve Instruction and Learning

Phillip S. Jones  The Role in the History of Mathematics of Algorithms and Analogies

Frank J. Swetz  Using Problems from the History of Mathematics in Classroom Instruction

John Fauvel  Revisiting the History of Logarithms

Victor J. Katz  Napier’s Logarithms Adapted for Today’s Classroom

Frank J. Swetz  Trigonometry Comes Out of the Shadows

Jan A. van Maanen  Alluvial Deposits, Conic Sections, and Improper Glasses, or History of Mathematics Applied in the Classroom

Frank J. Swetz  An Historical Example of Mathematical Modeling: The Trajectory of a Cannonball

Part II: History in Higher Mathematics

ManKeung Siu  Concept of Function—Its History and Teaching

V. Frederick Rickey  My Favorite Ways of Using History in Teachng Calculus

Michel Helfgott  Improved Teaching of the Calculus Through the Use of Historical Materials

ManKeung Siu  Euler and Heuristic Reasoning

Joel P. Lehmann  Converging Concepts of Series: Learning from History

Lars Mejlbo  Historical Thoughts on Infinite Numbers

Victor J. Katz  Historical Ideas in Teaching Linear Algebra

Otto B. Bekken  Wessel on Vectors

Karen Reich  Who Needs Vectors?

Israel Kleiner  The Teaching of Abstract Algebra: An Historical Perspective

David M. Burton and Donovan H. Van Osdol  Toward the Definition of an Abstract Ring

Anthony D. Gardiner  In Hilbert’s Shadow: Notes Toward a Redefinition of Introductory Group Theory

Eric J. Aiton  An Episode in the History of Celestial Mechanics and Its Utility in the Teaching of Applied Mathematics

ManKeung Siu  Mathematical Thinking and History of Mathematics

Abe Shenitzer  A Topics Course in Mathematics

Niels Henrik Abel (1802–1829): A Tribute

About the Authors