Reflecting the World

Reflecting the World

Reflecting the World

A Guide to Incorporating Equity

in Mathematics Teacher Education

Mathew D. Felton-Koestler

Ohio University

Ksenija Simic-Muller

Pacific Lutheran University

José María Menéndez

Pima Community College

INFORMATION AGE PUBLISHING, INC.

Charlotte, NC • www.infoagepub.com

Copyright © 2017 Information Age Publishing Inc.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or

transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,

recording or otherwise, without written permission from the publisher.

Printed in the United States of America

Library of Congress Cataloging-in-Publication Data

Names: Felton-Koestler, Mathew D., author. | Simic-Muller, Ksenija, author.

| Menbendez, Josbe Marbia, author.

Title: Reflecting the world : a guide to incorporating equity in mathematics

teacher education / Mathew D. Felton-Koestler, Ohio University, Ksenija

Simic-Muller, Pacific Lutheran University, Josbe Marbia Menbendez, Pima

Community College.

Description: Charlotte, NC : Information Age Publishing, Inc., [2017] |

Includes bibliographical references.

Identifiers: LCCN 2016055065 (print) | LCCN 2017000027 (ebook) | ISBN

9781681237671 (paperback) | ISBN 9781681237688 (hardcover) | ISBN

9781681237695 (ebook) | ISBN 9781681237695 (EBook)

Subjects: LCSH: Mathematics--Study and teaching--United States. |

Mathematics--Study and teaching--Social aspects. | Educational

equalization--United States.

Classification: LCC QA13 .F45 2017 (print) | LCC QA13 (ebook) | DDC

510.71--dc23

LC record available at https://lccn.loc.gov/2016055065

Reflecting the World: A Guide to Incorporating Equity in Mathematics Teacher Education, pages v–viii

Copyright © 2017 by Information Age Publishing

All rights of reproduction in any form reserved. v

Contents

Preface ...............................................................................................................................................xix

PART I

Foundation

1 Introduction.......................................................................................................................................... 3

Why Real-World Problems?.........................................................................................................................3

What We Mean by “Real-World” Contexts ................................................................................................4

Our Settings, Philosophies, Successes, and Challenges............................................................................4

Simic-Muller’s Story.....................................................................................................................................5

Felton-Koestler’s Story..................................................................................................................................6

Menéndez’s Story.........................................................................................................................................6

References ............................................................................................................................................7

2 Frameworks........................................................................................................................................... 9

Types of Tasks ..............................................................................................................................................9

Type of Connection ......................................................................................................................................9

The Structure of the Inquiry....................................................................................................................... 11

Summary of Types of Tasks ........................................................................................................................ 12

Notes........................................................................................................................................................... 13

References.................................................................................................................................................. 13

3 Getting Started.................................................................................................................................... 15

Where Do I Start? Do I Have to Redesign My Entire Course? ............................................................... 15

How Does This Fit With What I Have to Teach? ..................................................................................... 16

How Do I Decide What Real-World Topics to Investigate?..................................................................... 16

Should I Only Investigate Issues My Students Know and Care About? ................................................. 16

Are There Any Topics to Avoid? ............................................................................................................... 17

Where Can I Get My Ideas? ...................................................................................................................... 17

How Do You Create the Lessons? ............................................................................................................. 17

How Do You Come Up With Projects? ..................................................................................................... 18

vi ◾ CONTENTS

What Are Some Challenges One Faces When Teaching in This Way? .................................................. 18

What Are Some Counter-Resistance Strategies Instructors Can Use? .................................................. 19

References..................................................................................................................................................20

PART II

Overview of Lessons

4 Whole Number Lessons ...................................................................................................................... 23

4.1 A Living Wage (Introduction) ..........................................................................................................23

A Living Wage (Task) ........................................................................................................................ 24

A Living Wage (Data) ........................................................................................................................25

4.2 Cost of Healthy Food (Introduction) ...............................................................................................26

Cost of Healthy Food (Task) .............................................................................................................26

4.3 Cost of the War on Terror (Introduction) .......................................................................................27

Cost of the War on Terror (Task) .....................................................................................................28

4.4 Culture Quiz (Introduction).............................................................................................................28

Culture Quiz (Bell Work)..................................................................................................................30

4.5 Poverty Problem Types (Introduction).............................................................................................30

Poverty Problem Types (Task)........................................................................................................... 31

Poverty Problem Types (Answers).....................................................................................................33

Notes...................................................................................................................................................33

5 Rational Number Lessons................................................................................................................... 35

5.1 A Representative Congress (Introduction) ......................................................................................35

A Representative Congress (Task)....................................................................................................36

5.2 Childhood Poverty and Hunger (Introduction)..............................................................................37

Childhood Poverty and Hunger (Task)............................................................................................38

5.3 Division of Income (Introduction) ...................................................................................................40

Division of Income (Task).................................................................................................................40

5.4 Renting to Own (Introduction)........................................................................................................42

Renting to Own (Task)......................................................................................................................43

5.5 The Gender Pay Gap (Introduction)................................................................................................44

The Gender Pay Gap (Task)..............................................................................................................45

5.6 The Gender Pay Gap: Equal Pay Day (Introduction)......................................................................47

The Gender Pay Gap: Equal Pay Day? (Task) ..................................................................................48

5.7 Two Sides to Every News Story (Introduction) ................................................................................49

Two Sides to Every (News) Story (Task) ...........................................................................................50

5.8 Who Gets More? (Introduction).......................................................................................................50

Who Gets More? (Task)..................................................................................................................... 51

CONTENTS ◾ vii

6 Algebra Lessons .................................................................................................................................. 53

6.1 Graphing Towards Social Justice (Introduction) ............................................................................53

Graphing Towards Social Justice (Task) ..........................................................................................54

Graphing Towards Social Justice (Example Contexts) ...................................................................55

6.2 Incarceration Rates (Introduction).................................................................................................. 57

Incarceration Rates (Task)................................................................................................................58

6.3 Juvenile Delinquency (Introduction) ...............................................................................................59

Juvenile Delinquency (Task) .............................................................................................................60

6.4 The Cost of Water (Introduction) .................................................................................................... 61

The Cost of Water (Task) ..................................................................................................................62

7 Geometry and Measurement Lessons ................................................................................................. 65

7.1 Congressional Redistricting (Introduction)....................................................................................65

Congressional Redistricting (Task)..................................................................................................66

Congressional Redistricting (Map) ..................................................................................................68

7.2 Displaced Persons (Introduction) ....................................................................................................68

Displaced Persons (Task) ..................................................................................................................69

7.3 Mountain Top Removal (Introduction) ...........................................................................................71

Mountain Top Removal (Task).........................................................................................................72

Mountain Top Removal (“Did You Know?” Fact Sheet).................................................................. 74

7.4 Native American Star Quilts (Introduction) ...................................................................................75

Native American Star Quilts (Task) .................................................................................................76

7.5 Plastic Floating in the Ocean (Introduction) ..................................................................................76

Plastic Floating in the Ocean (Task) ................................................................................................77

7.6 The Cost of Bottled Water (Introduction).......................................................................................78

The Cost of Bottled Water (Task).....................................................................................................79

7.7 Water Bottles for Detroit (Introduction)..........................................................................................80

Water Bottles for Detroit (Task) .......................................................................................................82

Water Bottles for Detroit (Nets)........................................................................................................84

8 Data Analysis Lessons ......................................................................................................................... 87

8.1 Historical Trends in Crime (Introduction) .....................................................................................87

Historical Trends in Crime (Task) ...................................................................................................88

8.2 Income Inequality (Introduction)....................................................................................................89

Income Inequality (Task)..................................................................................................................90

8.3 Income Then and Now (Introduction) ............................................................................................ 91

Income Then and Now (Task) ..........................................................................................................92

8.4 Income: Teacher Salaries (Introduction).........................................................................................93

Income: Teacher Salaries (Task).......................................................................................................94

Income: Teacher Salaries (Spreadsheet)..........................................................................................94

viii ◾ CONTENTS

8.5 Messages in Children’s Ads (Introduction) .....................................................................................95

Messages in Children’s Ads (Task) ...................................................................................................96

8.6 Mortality and Race (Introduction)...................................................................................................97

Mortality and Race (Task).................................................................................................................97

Mortality and Race (Handouts)........................................................................................................98

8.7 Youth Poverty and Homelessness (Introduction) ............................................................................99

Youth Poverty and Homelessness (Task) ........................................................................................ 101

9 Probability Lessons ........................................................................................................................... 103

9.1 Income Mobility (Introduction) ..................................................................................................... 103

Income Mobility (Task) ................................................................................................................... 104

9.2 Marijuana Arrests (Introduction) .................................................................................................. 105

Marijuana Arrests (Task) ................................................................................................................106

9.3 Money Cube (Introduction)............................................................................................................ 107

Money Cube (Task)..........................................................................................................................108

10 Projects ..............................................................................................................................................111

10.1 Paper Cup Use (Introduction)........................................................................................................ 111

Paper Cup Use (Task)...................................................................................................................... 112

10.2 Tunnel of Oppression (Introduction) ............................................................................................ 113

Tunnel of Oppression (Task).......................................................................................................... 114

11 Additional Materials ..........................................................................................................................117

Excerpts From Syllabus (Middle Childhood Methods) ........................................................................ 117

Excerpt From Syllabus (Modern Elementary Mathematics) ................................................................ 119

Readings (Various Content and Methods Courses)..............................................................................120

Readings and Reflections (Math for Social Analysis)........................................................................... 121

Funds of Knowledge Assignment (Introduction) ................................................................................. 123

Funds of Knowledge Assignment (Directions)...................................................................................... 124

Funds of Knowledge Assignment (Interview Questions) .....................................................................126

Funds of Knowledge Assignment (Reflection Prompts).......................................................................127

Reflecting the World: A Guide to Incorporating Equity in Mathematics Teacher Education, pages ix–x

Copyright © 2017 by Information Age Publishing

All rights of reproduction in any form reserved. ix

Preface

We have been working with prospective and practicing teachers in a variety of contexts, including content

and methods courses and professional development settings, for the past ten years. During this time, our

primary concern has been preparing teachers to teach mathematics for equity, diversity, and justice. While

we have addressed this goal in a variety of ways, this book is primarily concerned with the curriculum we have de￾veloped and implemented, primarily in our mathematics courses for prospective K–8 teachers. We believe, along

with others whose work precedes us, among those Gutstein (2006) and Frankenstein (2009), that mathematics is a

powerful and essential tool for understanding the world. We see an opportunity in the recent emphasis in the Com￾mon Core State Standards for Mathematics (CCSSM) (Common Core State Standards Initiative, 2010) on real-world

mathematics contexts and mathematical modeling. We argue that, to bring forth equity in mathematics education,

mathematics learning must go beyond “neutral” topics to include real-world contexts that may be deemed contro￾versial or political. Investigating controversial social issues—such as income inequality, racial justice, or disparity in

educational outcomes—helps us understand the world as it is and as it could be.

In our informal conversations with colleagues we have found that while many mathematics teacher edu￾cators are concerned with social justice and would like to see future teachers attend to these ideas in their

own teaching, many of them shy away from integrating these issues into their content or methods courses,

because they are unsure of how to do so and uncomfortable with how they may play out. We offer this book as

a response to these concerns: as a guide for those who wish to incorporate issues related to equity and social

justice into their courses for the first time, as a refresher for those who are already doing this work, and as a

resource for anyone else who is interested in the fruitful relationship between teaching mathematics and social

justice. In this book, we share stories of our own journeys, give some theoretical background to our work, offer

practical advice for getting started, and most importantly, share the lessons, activities, and projects we have de￾veloped. We also hope this book will foster new conversations about what we see as the central goal of teacher

education: preparing teachers to teach for a more just world.

This book is divided into two parts. Chapters 1–3 lay the foundation for our work, and Chapters 4–12 pro￾vide the actual lessons and materials we have used in our courses. In the first part, Chapter 1 provides some

theoretical background and rationale for our work: It describes our understanding of real-world problems and

argues for the importance of the use of authentic real-world mathematics problems in teaching and teacher

education. This chapter also includes our stories: the contexts in which we teach, our philosophies, experi￾ences, and journeys. Although many of our beliefs and practices are shared, our contexts and approaches

differ. By sharing them, we hope to engage teacher educators and teachers with a variety of backgrounds and

circumstances. Chapter 2 includes a framework for our work, including a categorization of different types

of problems that we have identified in our curriculum. Chapter 3 offers an introduction to the practicali￾ties of implementing a social justice-based mathematics curriculum especially in courses for prospective K–8

teachers. It gives practical advice for getting started with social justice contexts, and addresses some potential

questions and concerns. In this chapter we also share our experiences with implementation of social justice

contexts, though we offer much more detail about individual lessons in the second part.

The second part of the book contains the lessons and materials we have developed and used. We introduce

this second part by providing a tabular representation of all the lessons, organized by different criteria. The

lessons are divided according to strands of school mathematics, and Chapters 4–9 address each strand: whole

x ◾ PREFACE

number, rational number, algebra, geometry and measurement, data analysis, and probability. In Chapter 10

we include two projects that do not fit neatly into any one category and instead span a range of mathematical

content. Finally, Chapter 11 includes additional materials, such as recommended readings to assign, other as￾signments, and excerpts from our course syllabi. There is a website where supplemental materials, such as Excel

spreadsheets that accompany some lessons, can be downloaded (http://www.infoagepub.com/simic-muller).

References

Common Core State Standards Initiative. (2010). Common Core State Standards for mathematics. Washington, DC: National Gov￾ernors Association Center for Best Practices and the Council of Chief State School Officers. Retrieved from http://www.

corestandards.org/assets/CCSI_Math Standards.pdf

Frankenstein, M. (2009). Developing a critical mathematical numeracy through real real-life word problems. In L. Verschaffel, B.

Greer, W. Van Dooren, & S. Mukhopadhyay (Eds.), Words and worlds: Modelling verbal descriptions of situations (pp. 111–130).

Boston, MA: Sense.

Gutstein, E. (2006). Reading and writing the world with mathematics: Toward a pedagogy for social justice. New York, NY: Routledge.

PART

I

Foundation