“This magnificent book is a must for all mathematics teachers! Its practical value is derived from the fact that the authors are both seasoned and high‐quality mathematics teachers who have experienced and have explored every aspect of teaching they discuss in their book. It is comprehensive and challenges the reader to consider the pros and cons of the different strategies described, which go beyond a ‘toolbox’ of great ideas for teaching!”
Alice F. Artzt
Queens College of the City University of New York
“This resource is a must for all mathematics teachers! New and veteran teachers will find the practical strategies and explicit examples easy to implement in the classroom and helpful in enhancing one's own pedagogy. Authors Bobson Wong and Larisa Bukalov have crafted a fantastic student‐focused resource dedicated to ensuring high‐quality instruction. Highly recommended!”
Christine DeBono
K‐5 Math Instructional Coach, Higley Unified School District, Arizona
“This comprehensive book is an incredible resource for math teachers at any stage of their career. Master Teachers Bobson Wong and Larisa Bukalov do an excellent job describing practical strategies, justifying them with research, and bringing them to life with concrete examples. I highly recommend it.”
Michael Driskill
Chief Operating Officer, Math for America
“As someone who has been teaching for 30 years, I find The Math Teacher's Toolbox to be a very rich reference of teaching strategies and resources for practitioners, especially mentors and mentees. I plan to use this book in my lessons and my professional development.”
Irene Espiritu
Middle School Teacher, Math for America Master Teacher, New York State Master Teacher
“The Math Teacher's Toolbox provides the reader with a summation of research‐supported current best practices in mathematics teaching. The layout of this book masterfully helps move the reader from understanding through application of the central ideas most essential to teaching mathematics effectively. Practical ideas for the classroom, as well as discussion about what could possibly go wrong, combine to make this a useful guide for teachers of all experience levels.”
Tabetha Finchum
2014 Presidential Awardee for Excellence in Mathematics Teaching
“The Math Teacher's Toolbox provides concrete, innovative strategies for adapting often intangible pedagogical theories across a wide range of math content areas and grade levels. Larisa Bukalov and Bobson Wong draw extensively from current research as well as their own years of classroom experience to explore the benefits and possible limitations of each strategy. Having already sought to implement a number of their ideas into my own classroom, I cannot recommend this book enough.”
Nasriah Morrison
Math Teacher, Institute for Collaborative Education and Math for America Master Teacher
“This book is truly a ‘toolbox’ for math instruction. It offers great technology tools and resources for teachers and their students, free online resources for student learning, and practical ideas that every math teacher can use. I will use this book for years to come.”
Jendayi Nunn
Mathematics Virtual Instructional Specialist, Atlanta Public Schools
“The Math Teacher Toolbox provides a map that can guide new teachers as they begin their journey and help veterans navigate the shifting terrain. The authors summarize current research from many areas of teaching and connect it to structured classroom practices. The experienced writing team organizes complex parts of the profession into a structure that makes it easy for practitioners to put the ideas to use in their classroom.”
Carl Oliver
Assistant Principal, City‐As‐School, New York
“Both new and experienced teachers will have cause to reach into this box of tools and return time and again to dig deeper—and each time you return, you'll find the box just as organized as the last! You'll keep this book nearby throughout your career for its practical, detailed tips, copious references, and teacher‐to‐teacher tone.”
Ralph Pantozzi, Ed.D.
2014 MoMath Rosenthal Prize winner, 2017 Presidential Awardee for Excellence in Mathematics Teaching
A winning educational formula of engaging lessons and powerful strategies for math teachers in numerous classroom settings
The Teacher's Toolbox series is an innovative, research-based resource providing teachers with instructional strategies for students of all levels and abilities. Each book in the collection focuses on a specific content area. Clear, concise guidance enables teachers to quickly integrate low-prep, high-value lessons and strategies in their middle school and high school classrooms. Every strategy follows a practical, how-to format established by the series editors.
The Math Teacher's Toolbox is a classroom-tested resource offering hundreds of accessible, student-friendly lessons and strategies that can be implemented in a variety of educational settings. Concise chapters fully explain the research basis, necessary technology, standards correlation, and implementation of each lesson and strategy.
Favoring a hands-on approach, this book provides step-by-step instructions that help teachers to apply their new skills and knowledge in their classrooms immediately. Lessons cover topics such as setting up games, conducting group work, using graphs, incorporating technology, assessing student learning, teaching all-ability students, and much more. This book enables math teachers to:
Written by respected authors and educators, The Math Teacher's Toolbox: Hundreds of Practical Ideas to Support Your Students is an invaluable aid for upper elementary, middle school, and high school math educators as well as those in teacher education programs and staff development professionals.
Books in the Teacher's Toolbox series, published by Jossey-Bass:
The Teacher's Toolbox Series
Copyright © 2020 by John Wiley & Sons, Inc. All rights reserved.
Published by Jossey‐Bass
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Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Readers should be aware that websites offered as citations and/or sources for further information may have changed or disappeared between the time this was written and when it is read.
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Library of Congress Cataloging‐in‐Publication Data:
Names: Wong, Bobson, 1971- author. | Bukalov, Larisa, 1973- author.
Title: The math teacher's toolbox : hundreds of practical ideas to support your students / Bobson Wong, Larisa Bukalov.
Description: Hoboken, NJ: Jossey-Bass, [2020] | Series: Teacher's toolbox | Includes bibliographical references and index.
Identifiers: LCCN 2019051973 (print) | LCCN 2019051974 (ebook) | ISBN 9781119573296 (paperback) | ISBN 9781119573203 (adobe pdf) | ISBN 9781119573241 (epub)
Subjects: LCSH: Mathematics—Study and teaching (Middle school)—Handbooks, manuals, etc. | Mathematics—Study and teaching (Secondary)—Handbooks, manuals, etc.
Classification: LCC QA11.2 .W663 2020 (print) | LCC QA11.2 (ebook) | DDC 510.71/2—dc23
LC record available at https://lccn.loc.gov/2019051973
LC ebook record available at https://lccn.loc.gov/2019051974
Cover Design: Wiley
Cover Image: © malerapaso/Getty Images
FIRST EDITION
| Table 3.1 | Vocabulary Chart |
| Table 3.2 | Geometry Vocabulary Chart |
| Table 3.3 | Visual and Verbal Aids |
| Table 4.1 | Class Discussion |
| Table 4.2 | Low‐Floor, High‐Ceiling Problems |
| Table 4.3 | Problem‐Solving Chart |
| Table 4.4 | Scaffolded Lesson Summary |
| Table 4.5 | Scoring Guidelines for Lesson Summaries |
| Table 4.6 | Scoring Guidelines for Quick Writes |
| Table 5.1 | Table for Vehicle Word Problem |
| Table 7.1 | Summary Questions |
| Table 9.1 | Confidence Level Scoring Guidelines |
| Table 9.2 | Comparing Scoring Guidelines |
| Table 9.3 | Two Test Questions with Unequal Difficulty |
| Table 9.4 | Two Test Questions with Similar Difficulty |
| Table 10.1 | Standards‐Based Grading |
| Table 10.2 | Sample Report Card Grades for a Student with 20% Content Mastery |
| Table 12.1 | Parent Communication Outline |
| Table 14.1 | Levels of Complexity for Tiered Lessons |
| Table 14.2 | Ratio Word Problem Table |
| Table 14.3 | Rubric |
| Table 15.1 | US and Latin American Prime Factorization Methods |
| Table 16.1 | Project Ideas |
| Table 16.2 | Basic Project Rubric |
| Table 16.3 | Oral Presentation Rubric |
| Table 17.1 | Self‐Assessment Rubric |
| Table 17.2 | Notice and Wonder |
| Table 17.3 | Task Cards |
| Table 18.1 | Formative Assessment Questions |
| Table 20.1 | Using Technology for Multiple‐Choice Questions |
Bobson Wong has taught math at New York City public high schools since 2005. He is a three‐time recipient of the Math for America Master Teacher Fellowship, a New York State Master Teacher, and a 2014–2015 recipient of the New York Educator Voice Fellowship. He is a member of the Advisory Council of the National Museum of Mathematics.
He has also worked to improve the quality of high school mathematics standards and assessment in New York. He has served on several committees, including the state's Common Core standards review committee, the state's workgroup to reexamine teacher evaluations, and the United Federation of Teachers' Common Core Standards Task Force. As an educational specialist for the New York State Education Department, he writes and edits questions for high school math Regents exams.
He graduated from the Bronx High School of Science, Princeton University (B.A., history), the University of Wisconsin–Madison (M.A., history), and St. John's University (M.S.Ed., adolescent education, mathematics), where he received his teacher training through the New York City Teaching Fellows program.
He lives in New York City with his wife and children.
Larisa Bukalov has been teaching at Bayside High School since 1998. She has won several awards for excellence in classroom teaching. She is a four‐time recipient of the Math for America Master Teacher fellowship, a 2009 recipient of Queens College's Mary Fellicetti Memorial Award for excellence in mentoring and supervising student teachers, and a 2017 recipient of Queens College's Excellence in Mathematics Award for promoting mathematics teaching as a profession. A fourth‐generation math teacher, she simultaneously earned degrees from a specialized math high school in Ukraine and a distance learning high school at Moscow State University. After emigrating to the United States, she learned English while earning both her bachelor's degree in math and her master's degree in math education from Queens College, City University of New York.
Over the past 20 years at Bayside, Larisa has taught all levels of math from pre‐algebra to calculus, coached the school's math team, and created a math research program in which students wrote papers for the Greater New York City Math Fair, City College Engineering Expo, and the Intel Science and Talent Search.
Larisa has extensive experience providing professional development to pre‐service and in‐service teachers. She has mentored 16 student teachers. From 2007 to 2009 she provided professional development to early career teachers and math supervisors in New York City on Geometry, Probability, and Problem Solving. As part of her work with Math for America, Larisa has run several professional development sessions for teachers.
She lives in New York City with her husband and children.
Larry Ferlazzo and Katie Hull Sypnieski wrote The ELL Teacher's Toolbox and conceived of a series replicating the format of their popular book. They identified authors of all the books in the series and worked closely with them during their writing and publication.
Larry Ferlazzo teaches English, Social Studies, and International Baccalaureate classes to English Language Learners and others at Luther Burbank High School in Sacramento, California.
He's written nine books: The ELL Teacher's Toolbox (with co‐author Katie Hull Sypnieski); Navigating the Common Core with English Language Learners (with coauthor Katie Hull Sypnieski); The ESL/ELL Teacher's Survival Guide (with coauthor Katie Hull Sypnieski); Building a Community of Self‐Motivated Learners: Strategies to Help Students Thrive in School and Beyond; Classroom Management Q&As: Expert Strategies for Teaching; Self‐Driven Learning: Teaching Strategies for Student Motivation; Helping Students Motivate Themselves: Practical Answers to Classroom Challenges; English Language Learners: Teaching Strategies That Work; and Building Parent Engagement in Schools (with coauthor Lorie Hammond).
He has won several awards, including the Leadership for a Changing World Award from the Ford Foundation, and was the Grand Prize Winner of the International Reading Association Award for Technology and Reading.
He writes a popular education blog at http://larryferlazzo.edublogs.org/, a weekly teacher advice column for Education Week Teacher, and posts for The New York Times and The Washington Post.
He also hosts a weekly radio show on BAM! Education Radio.
He was a community organizer for 19 years prior to becoming a public school teacher.
Larry is married and has three children and two grandchildren.
A basketball team he played for came in last place every year from 2012 to 2017. He retired from league play after that year, and the team then played for the championship. These results might indicate that Larry made a wise career choice in not pursuing a basketball career.
Katie Hull Sypnieski has taught English Language Learners and others at the secondary level for over 20 years. She currently teaches middle school English Language Arts and Social Studies at Fern Bacon Middle School in Sacramento, California.
She leads professional development for educators as a teaching consultant with the Area 3 Writing Project at the University of California, Davis.
She is coauthor (with Larry Ferlazzo) of The ESL/ELL Teacher's Survival Guide, Navigating the Common Core with English Language Learners, and The ELL Teacher's Toolbox. She has written articles for the Washington Post, ASCD Educational Leadership, and Edutopia. She and Larry have developed two video series with Education Week on differentiation and student motivation.
Katie lives in Sacramento with her husband and their three children.
Teaching is a collaborative endeavor. We would never have accomplished everything that we've done – including writing this book – without the help of many individuals. We thank all of the people mentioned here. They've made us not just into better teachers but also into better people.
Several current and former administrators at Bayside High School have provided coaching and professional growth opportunities over the years: Michael Athy, Madeline Belfi‐Galvin, Harris Sarney, Susan Sladowski, and Judith Tarlo. Our colleagues in Bayside's Math Department have been a constant source of camaraderie, laughter, and valuable (if sometimes heated) pedagogical discussions. The thousands of students that we've taught at Bayside inspire and challenge us, giving us something to look forward to every day we go to work.
Math for America has created an active, supportive community that trusts and celebrates educators' expertise. Many of our ideas were refined in Math for America's professional development sessions.
Larry Ferlazzo and Katie Hull Sypnieski have been meticulous editors whose frequent questions about our thinking have improved our writing and teaching. Their timely and thought‐provoking edits have made this book much better than it would have been without them. David Powell has done an amazing job of formatting our manuscript. His attention to detail is amazing. Pete Gaughan at Wiley and Amy Fandrei at Jossey‐Bass patiently guided us through the stressful process of producing this book.
Bayside High School students Safi Ansari, Stefany Flores, Emily Hermida, Hana Ho, Anna Ling, Anyu Loh, Camila Palmada, Hardeep Singh, Navneet Sohal, Jason Sun, Ariana Verbanac, Richard Xing, and Joy Zou contributed their work for this book. Susie Xu and Justin Zhuo helped us proofread the figures and tables in this book.
Finally, our spouses and children deserve special mention for tolerating our many early‐morning and late‐night conversations about this book and helping us keep things in perspective.
Bobson Wong: Larisa Bukalov has been a mentor, colleague, and friend for 13 years. Prof. Charles Cohen, Sherrill Mirsky, Dr. Carol Nash, Barbara Rockow, and Prof. Robert C.‐H. Shell were some of the many educators that I've met over the years that taught me the patience and attention to detail that I needed to write this book. The people that I've met online at #MTBoS and #ITeachMath have influenced and encouraged me. Robert Lebowitz has been a source of mathematical and philosophical conversation for decades; without him, this book would not be possible.
Larisa Bukalov: Bobson Wong has been a colleague and a friend. Thank you for putting my ideas about teaching mathematics in writing and always motivating me to do more. Mary Chiesi hasn't just been my co‐teacher but also a mentor and best friend. We developed and practiced many of the strategies in this book together. Dr. Alice Artzt and the faculty at the mathematics education program at Queens College provided countless hours of debates on constructivism, hands‐on approach, teaching mathematics as a language, group work, as well as advice on this book's structure and organization. Twenty years after graduation, I know that I can always count on her help and advice. Dr. Nick Metas at Queens College was famous for his attention to detail. A history buff, he shared stories about mathematicians and helped introduce to me the idea of culturally relevant mathematics. My husband, Boris Bukalov, a math and science teacher, checked the math in the book. My late grandfather, Izaya Vayzman, taught me to love mathematics and teaching. Many of the ideas described in this book came from my watching his everyday interactions with students back in the Soviet Union.
We don't teach math, and we don't know much math, either.
We do, however, know pedagogy.
And there's more great pedagogy in Bobson's and Larisa's book than you can shake a stick at.
In fact, there's so much exceptional teaching advice in this book that any teacher – no matter what subject he/she teaches – can learn a great deal of information from this book about effective instructional strategies that can be used in any classroom.
We sure did!
And, because we have so much confidence in Bobson and Larisa, we're sure all the math is great, too.
If you don't believe us, just check out all the math people who have said so many terrific things about The Math Teacher's Toolbox – their endorsements can be found in the front of the book.
We're thrilled and honored that Bobson and Larisa's book follows our The ELL Teacher's Toolbox in the Toolbox series.
It was a pleasure working with them during the 12 months they spent writing it, and we'd wager this won't be the last book you see written by them.
Larry Ferlazzo and Katie Hull Sypnieski
Editors of the Toolbox series
When people find out what we do for a living, they often admit to us that they hate math or they're not good at it. After repeated negative experiences, many develop math anxiety—feelings of fear and tension when doing math (Namkung, Peng, & Lin, 2019, p. 482; Shields, 2007, p. 56). Math anxiety is not simply a set of emotions but a physiological response that affects heart rate and neural activity (Ramirez, Shaw, & Maloney, 2018, p. 145). It can be even more problematic when teachers or parents have it, since they can pass it on to students, which can negatively affect academic achievement (Beilock, Gunderson, Ramirez, & Levine, 2010, p. 1,862; Maloney, Ramirez, Gunderson, Levine, & Beilock, 2015, p. 1,485; Ramirez, Hooper, Kersting, Ferguson, & Yeager, 2018, p. 8).
Unfortunately, math anxiety is common among students, their parents, and teachers. We wrote this book not just to help people overcome math anxiety but also to help them appreciate and use math in the real world. The strategies described in this book reflect techniques and methods that we've used during our combined 35 years of teaching 26,000 lessons to over 5,000 students (including English Language Learners and students with learning differences) from around the world. Many of these strategies rely on social‐emotional learning (SEL, sometimes called social and emotional learning), the process by which people develop the skills necessary to manage their emotions, show empathy for others, and maintain positive relationships with others (Collaborative for Academic, Social, and Emotional Learning [CASEL], n.d.). SEL is a critical part of effective teaching because students' mindsets can affect their cognitive processing. People who experience success in an activity may be motivated and able to learn, while those who experience failure may tend to withdraw, rendering even the most engaging and well‐planned lesson useless (Sousa, 2017, p. 61).
What we write in this book reflects four of our core beliefs about math, pedagogy, and students:
This book is divided into four parts. Part I: Basic Strategies expands on what we believe to be the central ideas necessary to teach math effectively: motivating students, culturally responsive teaching, teaching math as a language, promoting mathematical communication, and making mathematical connections. Part II: How to Plan discusses strategies for units, lessons, homework, tests and quizzes, and grades. Part III: Building Relationships talks about how to build relationships with students, parents, and co‐teachers. Finally, Part IV: Enhancing Lessons contains other important strategies—differentiation, project‐based learning, cooperative learning, formative assessment, and technology.
This book is part of a series in The ELL Teacher's Toolbox (2018a) by Larry Ferlazzo and Katie Hull Sypnieski. All chapters in the books in this series have the following sections:
The bottom line is that in today's changing world, we need better thinkers and problem‐solvers. We believe that as teachers, we have to do more than just convey mathematical ideas. We also need to be role models for self‐confidence, self‐reflection, critical thinking, and conceptual understanding. What we say and do affects not only the way in which our students learn math but also their beliefs. We hope that this book can inspire you to do more for your students, your communities, and yourselves.