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Moving Things Around

Bowen Kerins Education Development Center, Inc., Waltham, MA
Darryl Yong Harvey Mudd College, Claremont, CA
Al Cuoco Education Development Center, Inc., Waltham, MA
Glenn Stevens Boston University, MA
Mary Pilgrim Colorado State University, Fort Collins, CO
A co-publication of the AMS and IAS/Park City Mathematics Institute
Available Formats:
Softcover ISBN: 978-1-4704-2926-3
Product Code: SSTP/5
List Price: $29.00 MAA Member Price:$26.10
AMS Member Price: $23.20 Electronic ISBN: 978-1-4704-3536-3 Product Code: SSTP/5.E List Price:$29.00
MAA Member Price: $26.10 AMS Member Price:$23.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $43.50 MAA Member Price:$39.15
AMS Member Price: $34.80 Click above image for expanded view Moving Things Around Bowen Kerins Education Development Center, Inc., Waltham, MA Darryl Yong Harvey Mudd College, Claremont, CA Al Cuoco Education Development Center, Inc., Waltham, MA Glenn Stevens Boston University, MA Mary Pilgrim Colorado State University, Fort Collins, CO A co-publication of the AMS and IAS/Park City Mathematics Institute Available Formats:  Softcover ISBN: 978-1-4704-2926-3 Product Code: SSTP/5  List Price:$29.00 MAA Member Price: $26.10 AMS Member Price:$23.20
 Electronic ISBN: 978-1-4704-3536-3 Product Code: SSTP/5.E
 List Price: $29.00 MAA Member Price:$26.10 AMS Member Price: $23.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$43.50 MAA Member Price: $39.15 AMS Member Price:$34.80
• Book Details

IAS/PCMI--The Teacher Program Series
Volume: 52016; 134 pp
MSC: Primary 00;

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Moving Things Around is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute.

But this book isn't a “course” in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves.

The goal of Moving Things Around is to help participants make what might seem to be surprising connections among seemingly different areas: permutation groups, number theory, and expansions for rational numbers in various bases, all starting from the analysis of card shuffles. Another goal is to use these connections to bring some coherence to several ideas that run throughout school mathematics—rational number arithmetic, different representations for rational numbers, geometric transformations, and combinatorics. The theme of seeking structural similarities is developed slowly, leading, near the end of the course, to an informal treatment of isomorphism.

Moving Things Around is a volume of the book series “IAS/PCMI—The Teacher Program Series” published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest.

Teachers of middle and high school mathematics.

• Cover
• Title page
• Contents
• Preface
• Chapter 1: Problem Sets
• Chapter 2: Facilitator Notes
• Chapter 3: Solutions
• Back Cover

• Reviews

• Here, a sequenced and carefully curated collection of problem sets --- not a grab-bag problem bank --- guides students toward the awareness of connections between group and number theory. I feel that to realize the full potential for students to experience discovering these connections requires committing to a semester-length course; fourteen problem sets at roughly one per week. This would be more directed groupwork than lecture presentations, although strategic selections among this material could make for enlightening diversions in a traditional, lecture-based course.

Tom Schulte, MAA Reviews
• ...[T]hese problems were carefully and coherently sequenced to unfold an interesting mathematical story complete with plot twists and turns, ultimately building to a satisfying resolution of real mathematical substance. In other words, this was not a problem bank to be viewed as a companion resource for a course. Rather, these problem sets entirely define a complete mathematical course. To do justice to these problems and to allow students to experience the joys of discovering the beautiful and often unexpected connections the problems are designed to reveal, one needs to take the plunge and commit to making them the basis of the course. To me, that meant eschewing lecture presentations in favor of letting the problems tell the story. That would constitute my best advice to instructors using the materials: Let the problems tell the story. Go along for the ride, enjoy it yourself, and fight the urge to drive.

Thomas Dick, The College Mathematics Journal
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 52016; 134 pp
MSC: Primary 00;

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Moving Things Around is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute.

But this book isn't a “course” in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves.

The goal of Moving Things Around is to help participants make what might seem to be surprising connections among seemingly different areas: permutation groups, number theory, and expansions for rational numbers in various bases, all starting from the analysis of card shuffles. Another goal is to use these connections to bring some coherence to several ideas that run throughout school mathematics—rational number arithmetic, different representations for rational numbers, geometric transformations, and combinatorics. The theme of seeking structural similarities is developed slowly, leading, near the end of the course, to an informal treatment of isomorphism.

Moving Things Around is a volume of the book series “IAS/PCMI—The Teacher Program Series” published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest.

Teachers of middle and high school mathematics.

• Cover
• Title page
• Contents
• Preface
• Chapter 1: Problem Sets
• Chapter 2: Facilitator Notes
• Chapter 3: Solutions
• Back Cover
• Here, a sequenced and carefully curated collection of problem sets --- not a grab-bag problem bank --- guides students toward the awareness of connections between group and number theory. I feel that to realize the full potential for students to experience discovering these connections requires committing to a semester-length course; fourteen problem sets at roughly one per week. This would be more directed groupwork than lecture presentations, although strategic selections among this material could make for enlightening diversions in a traditional, lecture-based course.

Tom Schulte, MAA Reviews
• ...[T]hese problems were carefully and coherently sequenced to unfold an interesting mathematical story complete with plot twists and turns, ultimately building to a satisfying resolution of real mathematical substance. In other words, this was not a problem bank to be viewed as a companion resource for a course. Rather, these problem sets entirely define a complete mathematical course. To do justice to these problems and to allow students to experience the joys of discovering the beautiful and often unexpected connections the problems are designed to reveal, one needs to take the plunge and commit to making them the basis of the course. To me, that meant eschewing lecture presentations in favor of letting the problems tell the story. That would constitute my best advice to instructors using the materials: Let the problems tell the story. Go along for the ride, enjoy it yourself, and fight the urge to drive.

Thomas Dick, The College Mathematics Journal
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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