**AMS/MAA Textbooks**

Volume: 69;
2022;
124 pp;
Softcover

MSC: Primary 97; 01;

**Print ISBN: 978-1-4704-6504-9
Product Code: TEXT/69**

List Price: $45.00

AMS Member Price: $33.75

MAA Member Price: $33.75

**Electronic ISBN: 978-1-4704-6799-9
Product Code: TEXT/69.E**

List Price: $45.00

AMS Member Price: $33.75

MAA Member Price: $33.75

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#### Supplemental Materials

# The Number Line through Guided Inquiry

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*David M. Clark; Xiao Xiao*

MAA Press: An Imprint of the American Mathematical Society

The Number Line through Guided Inquiry is
designed to give future secondary teachers a deep understanding of the
real numbers and functions on the reals. By presenting just that part
of the subject that underlies the high school curriculum, this book
offers an alternative to a standard real analysis sequence for
advanced undergraduate or beginning graduate students. It will give
any student a much deeper understanding of the mathematics that they
were taught in high school.

Written in a guided-inquiry format, this book consists of a
carefully scaffolded sequence of definitions, problems, and theorems
that guides students through each topic. Readers solve the problems
and prove the theorems on their own and present their results to their
peers with the instructor as a mentor and a guide. Students will learn
not only the mathematics, but also how to help others learn
mathematics. They will learn to think creatively and to make
compelling arguments to justify their conclusions. They will learn to
listen critically to others and give constructive feedback. Ultimately,
they will learn to work as a team to answer the bigger questions and
build a common understanding of the broader subject.

#### Readership

Graduate students interested in secondary school mathematics and general undergraduate mathematics majors.

#### Table of Contents

# Table of Contents

## The Number Line through Guided Inquiry

- Title page 44
- Copyright 55
- Contents 66
- Preface 88
- To the Student 1818
- Acknowledgement 2222
- Chapter 1. Rational Numbers and Missing Numbers 2424
- Chapter 2. Limit Points and Sequences 3636
- Chapter 3. Decimal Representations of Numbers 4444
- Chapter 4. Complete Number Lines 5858
- Chapter 5. Continuity 6464
- Chapter 6. Calculus 7676
- Chapter 7. Log and Exponential Functions 8888
- Chapter 8. The Real Number Line 9898
- Chapter 9. The Price of Completeness 116116
- Appendix A. Historical Summary 124124
- Appendix B. The Reals via Dedekind Cuts 128128
- Appendix C. Guidelines for the Instructor 138138
- Bibliography 144144
- Index 146146