Understanding Analysis and its Connections to Secondary Mathematics Teaching

A course in real analysis is typically required to become certified to teach high school mathematics, but most teachers report that it has little influence on their teaching. This textbook aims to change that by showing how real analysis can be a meaningful part of a teacher's mathematical education and preparation for teaching secondary mathematics. It focuses on how mathematical ideas are connected to the practice of teaching and uses particular situations in teaching to make explicit ways that the content of real analysis can be important for teaching secondary mathematics.

Format: Paperback / softback
Length: 215 pages
Publication date: 04 January 2022
Publisher: Springer Nature Switzerland AG

Getting certified to teach high school mathematics typically requires completing a course in real analysis. However, most teachers argue that real analysis content bears little resemblance to secondary mathematics and has no significant impact on their teaching. This textbook aims to challenge that narrative. We believe that analysis can be a valuable part of a teacher's mathematical education and preparation for teaching. This book serves as a companion text, intended to be 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 mathematics, rather than just the content of secondary mathematics itself. Discussions around pedagogy are grounded in the belief that the ways mathematicians do mathematics can be helpful in understanding how to teach mathematics. The book employs specific teaching scenarios to illustrate how the content of real analysis can be relevant to teaching secondary mathematics, and how mathematical practices prevalent in the study of real analysis can be incorporated as teaching practices. This textbook will be of particular interest to mathematics instructors and mathematics teacher educators considering how the mathematics of real analysis can be applied to secondary teaching, as well as to any prospective or current teacher who has wondered about the purpose of taking such courses.

Getting certified to teach high school mathematics typically requires completing a course in real analysis. However, most teachers argue that real analysis content bears little resemblance to secondary mathematics and has no significant impact on their teaching. This textbook aims to challenge that narrative. We believe that analysis can be a valuable part of a teacher's mathematical education and preparation for teaching. This book serves as a companion text, intended to be 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 mathematics, rather than just the content of secondary mathematics itself. Discussions around pedagogy are grounded in the belief that the ways mathematicians do mathematics can be helpful in understanding how to teach mathematics. The book employs specific teaching scenarios to illustrate how the content of real analysis can be relevant to teaching secondary mathematics, and how mathematical practices prevalent in the study of real analysis can be incorporated as teaching practices. This textbook will be of particular interest to mathematics instructors and mathematics teacher educators considering how the mathematics of real analysis can be applied to secondary teaching, as well as to any prospective or current teacher who has wondered about the purpose of taking such
such courses.

Weight: 367g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030891978
Edition number: 1st ed. 2022