Understanding analysis and its connections to secondary mathematics teaching / Nicholas H. Wasserman, Timothy Fukawa-Connelly, Keith Weber, Juan Pablo Mejía Ramos, Stephen Abbott.
Wasserman, Nicholas, author.; Fukawa-Connelly, Timothy, author.; Weber, Keith, author.; Mejía Ramos, Juan Pablo, author.; Abbott, Stephen, 1964- author.
2022
QA300 .W37 2022
Available Online

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Title
Understanding analysis and its connections to secondary mathematics teaching / Nicholas H. Wasserman, Timothy Fukawa-Connelly, Keith Weber, Juan Pablo Mejía Ramos, Stephen Abbott.
Author
Wasserman, Nicholas, author.
ISBN
9783030891985 (electronic bk.)
3030891984 (electronic bk.)
9783030891978
3030891976
DOI
https://doi.org/10.1007/978-3-030-89198-5
Published
Cham : Springer, [2022]
Copyright
©2022
Language
English
Description
1 online resource : illustrations.
Item Number
10.1007/978-3-030-89198-5 doi
Call Number
QA300 .W37 2022
Dewey Decimal Classification
515
Summary
Getting certified to teach high school mathematics typically requires completing a course in real analysis. Yet most teachers point out real analysis content bears little resemblance to secondary mathematics and report it does not influence their teaching in any significant way. This textbook is our attempt to change the narrative. It is our belief that analysis can be a meaningful part of a teacher's mathematical education and preparation for teaching. This book is a companion text. It is intended to be a supplemental resource, used in conjunction with a more traditional real analysis book.The textbook is based on our efforts to identify ways that studying real analysis can provide future teachers with genuine opportunities to think about teaching secondary mathematics. It focuses on how mathematical ideas are connected to the practice of teaching secondary mathematicsand not just the content of secondary mathematics itself. Discussions around pedagogy are premised on the belief that the way mathematicians do mathematics can be useful for how we think about teaching mathematics. The book uses particular situations in teaching to make explicit ways that the content of real analysis might be important for teaching secondary mathematics, and how mathematical practices prevalent in the study of real analysis can be incorporated as practices for teaching. This textbook will be of particular interest to mathematics instructorsand mathematics teacher educatorsthinking about how the mathematics of real analysis might be applicable to secondary teaching, as well as to any prospective (or current) teacher who has wondered about what the purpose of taking such courses could be.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed January 21, 2022).
Added Author
Fukawa-Connelly, Timothy, author.
Weber, Keith, author.
Mejía Ramos, Juan Pablo, author.
Abbott, Stephen, 1964- author.
Series
Springer texts in education.
Available in Other Form
Print version: 9783030891978
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Chapter 1: Teaching Principles
Chapter 2: Equivalent Real Numbers and Infinite Decimals
Chapter 3: Sequence Convergence and Irrational Decimal Approximations
Chapter 4: Algebraic Limit Theorem and Error Accumulation
Chapter 5: Divergence Description and Criteria and Logic in Communication
Chapter 6: Continuity and Definitions
Chapter 7: Intermediate Value Theorem and Implicit Assumptions
Chapter 8: Continuity, Monotonicity, Inverse Functions and Solving Equations
Chapter 9: Differentiability and the Secant Slope Function
Chapter 10: Differentiation Rules and Attending to Scope
Chapter 11: Taylors Theorem and Modeling Complex with Simple
Chapter 12: The Riemann Integral and Area-Preserving Transformations
Chapter 13: The Fundamental Theorem of Calculus and Conceptual Explanation.

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