Understanding analysis and its connections to secondary mathematics teaching / Nicholas H. Wasserman, Timothy Fukawa-Connelly, Keith Weber, Juan Pablo Mejía Ramos, Stephen Abbott.

Format:

Book

Author/Creator:

Wasserman, Nicholas, author.

Fukawa-Connelly, Timothy, author.

Weber, Keith, author.

Mejía Ramos, Juan Pablo, author.

Abbott, Stephen, 1964- author.

Series:

Springer texts in education

Language:

English

Subjects (All):

Mathematical analysis.

Mathematics--Study and teaching (Secondary).

Mathematics.

Genre:

Electronic books.

Physical Description:

1 online resource : illustrations.

Place of Publication:

Cham : Springer, [2022]

System Details:

text file PDF

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.

Contents:

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.

Notes:

Includes bibliographical references and index.

Online resource; title from PDF title page (SpringerLink, viewed January 21, 2022).

ISBN:

9783030891985

3030891984

OCLC:

1290841782

Access Restriction:

Restricted for use by site license.