Enhancing Classroom Practice with Research behind Principles to Actions

174 Pages·2017·116.095 MB·English

by  National Council of Teachers of Mathematics, Denise A. Spangler, Jeffrey J. Wanko

Enhancing
Classroom
Practice
with Research behind Principles to Actions
Edited by
Denise A. Spangler
and Jeffrey J. Wanko
CXl
NATIONAL COUNCIL OF
NCTM
TEACHERS OF MATHEMATICS
Copyright© 2017 by
The National Council of Teachers of Mathematics, Inc.
1906 Association Drive, Reston, VA 20191-1502
[phone]; [phone]; www.nctm.org
All rights reserved
ISBN 978-0-87353-978-4
Library of Congress Cataloging-in-Publication Data
Names: Spangler, Denise A., editor. I Wanko, Jeffrey J., editor. I National Council of Teachers of Mathematics.
Title: Enhancing classroom practice with research behind Principles to actions / edited by Denise A. Spangler,
University of Georgia, and Jeffrey J. Wanko, Miami University of Ohio.
Other titles: Principles to actions
Description: Reston, VA: National Council of Teachers of Mathematics,
[2017] I Includes bibliographical references.
Identifiers: LCCN 2017010676 (print) I LCCN 2016059785 (ebook) I ISBN 9781680540048 (pbk.) I
ISBN 781680540055 (ebook)
Subjects: LCSH: Mathematics--Study and teaching--United States. I Effective teaching. I Curriculum planning.
Classification: LCC QA13 .E49 2017 (ebook) I LCC QA13 (print) I DDC 510.71/073--dc23
LC record available at https://lccn.loc.gov/2017010676
The National Council of Teachers of Mathematics is the public voice of mathematics
education, supporting teachers to ensure equitable mathematics learning of the highest
quality for each and every student through vision, leadership, professional development,
and research.
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The publications of the National Council of Teachers of Mathematics present a variety of
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interpreted as official positions of the Council.
Printed in the United States of America
Contents
Acknowledgments .................................................................................................................................................. v
Introduction .......................................................................................................................................................... vii
Denise A. Spangler and Jeffrey J. Wanko
1. The Nature and Role of Goals in and for Mathematics Instruction ............................................................. 1
Mary Kay Stein and Erin Meikle
2. Implementing Tasks That Promote Reasoning and Problem Solving: Successes and Obstacles in
Making Day-to-Day Mathematics High Level ................................................................................................... 13
Melissa D. Boston, Kayla Madler, and Christopher Cutone
3. Representations as Tools for Mathematical Understanding ......................................................................... 27
Thomas E. Hodges and Malisa Johnson
4. Elicting, Supporting, and Guiding the Math: Three Key Functions of the Teacher's Role in
Facilitating Meaningful Mathematical Discourse ............................................................................................. 37
Megan Staples and Sherryl King
5. Repurposing Teacher Questions: Working toward Assessing and Advancing Student Mathematical
Understanding ....................................................................................................................................................... 49
Marcy B. Wood and Maggie Hackett
6. Teaching to Build Procedural Fluency ........................................................................................................... 61
Jennifer M. Bay-Williams and Amy Stokes-Levine
7. Key Questions to Guide Teachers in Supporting Productive Struggle in Learning Mathematics ........... 73
Blake E. Peterson and Rina Viramontes
8. Eliciting and Using Evidence of Student Thinking: Giving Students Voice ............................................... 89
Dana C. Cox, Judy Meicenheimer, and Danette Hickey
9. Providing Access to Equitable Mathematics Learning ................................................................................ 99
Anita A. Wager, Barbara Pietz, and Mary Klehr
10. "The Right Stuff": Curriculum to Support the Vision of NCTM and CCSSM ..................................... 113
Jill Newton and Yvonne Grant
11. What (Research on) Technology in the Mathematics Classroom Can and Cannot Do .......................... 129
Keith R. Leatham and D. Ray Barton
iii
Contents
12. Using Assessment to Enhance Mathematics Teaching and Learning ..................................................... 141
Christine Suurtamm and Ann Arden
13. Professionalism: Collaborating on Instruction .......................................................................................... 153
Robert Q. Berry III and Michelle P. Berry
iv
Acknowledgments
All chapters in this book were reviewed by at least two reviewers. We wish to thank the following mathematics
educators for their thorough, thoughtful, and timely reviews: Shelby Aaberg, Scottsbluff (Nebraska) High School;
Vickie Anderson, Rising Starr Middle School, Fayetteville, Georgia; Elizabeth Coyne, Heritage Academy, Atlanta,
Georgia; Natalie Crist, Baltimore (Maryland) County Public Schools; Liza Dallavalle, Hampstead Elementary
School, Westminster, Maryland; Sandra Hogan, Newnan, Georgia; DeAnn Huinker, University of Wisconsin
Milwaukee; Susie Katt, Lincoln (Nebraska) Public Schools; Steven Leinwand, American Institutes for Research,
Washington D.C.; LouAnn H. Lovin, James Madison University; Robyn L. B. Ovrick, University of Georgia,
Griffin; Ami N. Rivera, Rocky Branch Elementary School, Bogart, Georgia; Gregory P. Sand, Omaha (Nebraska)
Central High; Kyle T. Schultz, James Madison University; Karina S. Scott, Decatur (Georgia) High School;
Margaret Smith, University of Pittsburgh; Wendy M. Smith, University of Nebraska-Lincoln; Laura Steward,
Conyers (Georgia) Middle School; Christy Sutton, Lee County Primary School, Leesburg, Georgia; Matthew D.
Timm, Indian Hill Elementary School, Omaha, Nebraska; Andrew Tyminski, Clemson University; Cori Wilson,
Landmark Christian School, Peachtree City, Georgia; Kim Zeugner, Kingswood Elementary School, Cary, North
Carolina.
We were also assisted in the preparation of this book by graduate students at our universities, and we wish to
extend our appreciation to them for their diligent and thoughtful work on this book: Angel M. Carreras-Jusino,
University of Georgia; and Alex Trassare, Miami University.
V

Introduction
Denise A. Spangler, University ofG eorgia
Jeffrey J. Wanko, Miami University
In 2014 the National Council of Teachers of Mathemat Many of the chapters in this book were written
ics (NCTM) released Principles to Actions: Ensuring collaboratively by school-based mathematics educa-
Mathematical Success for All (PtA) to describe "the tors and university-based mathematics educators in a
conditions, structures, and policies that must exist for deliberate effort to exemplify NCTM's commitment
all students to learn" (p. vii). PtA articulates eight guid to linking research and practice. Working together in
ing principles and five essential elements that are neces teams allowed the authors to combine and integrate
sary for effective mathematics teaching and learning their expertise, to craft chapters that reflect a balance
regardless of the standards, curriculum, type of school, of research and practice examples in ways that meet the
age of students, or other circumstances. This book was needs of practitioners in both schools and universities.
commissioned as a companion to PtA to enact NCTM's To further ensure that the book would meet the needs of
longstanding commitment to linking research and prac practitioners at both levels, every chapter was reviewed
tice. In the remainder of this introduction we describe by both school-based and university-based mathematics
the purpose of the book, its intended audiences, and educators.
suggestions for how this book might be used by a range
of mathematics education professionals. Audience for and Uses of This
Book
Purpose of This Book
This book was designed to be useful to many audienc
The purpose of this book is to summarize and synthe es, including preservice teachers, in-service teachers,
size the research behind each of the guiding principles instructional coaches, administrators, professional
and essential elements and to offer examples of what developers, and mathematics teacher educators. For ex
they might look like in classroom practice. While each ample, preservice teachers might read the tasks chapter
of the principles and elements is backed by an extensive as part of a mathematics methods course to gain a sense
body of research, our goal was not to offer a compre of how tasks with high cognitive demand can be imple
hensive, exhaustive, or detailed review of the literature. mented on a daily basis in classrooms. Administrators
Rather, the goal was to give readers a sense of where might read the discourse chapter to gain a lens for
the field stands in its knowledge and its hypotheses thinking about what to expect when observing a teach
about the big ideas put forth in PtA. In addition, the er who is trying to create a discourse-rich classroom
goal was to make the principles and elements- as environment. A group of teachers in a school might use
well as the research-concrete for readers by offering the equity chapter as a springboard for ongoing critical
examples from classroom practice. Again, however, our conversations about the ways the practices they enact in
goal was not to be comprehensive and detailed, so the their classrooms, as well as school-wide practices relat
examples do not cover every grade level or every con ed to tracking, are or are not supportive of all students
tent area, nor do they contain full-fledged lesson plans. learning mathematics. Instructional coaches and pro
Rather, the illustrative examples are meant to give fessional developers might suggest particular chapters
readers a flavor of what a principle or element might to teachers who are trying to grow their practice in spe
look like in practice. It is up to the reader to tailor the cific areas or to gain ideas for how to support teachers.
examples to a particular context.
vii
Introduction
And some readers may wish to read the entire book in
order to gain a high-level overview of the professional
commitments of mathematics educators and how those
commitments play out in classrooms.
Whatever use is made of this book, readers might
wish to read the relevant section of PtA along with the
corresponding chapter in this book in order to gain a
full picture ofNCTM's recommendations, the research
that supports those recommendations, and the imple
mentation of the recommendations in classrooms. It is
important to note that chapter authors did not reproduce
PtA in its entirety in this book. In most cases, only a
very short summary of the principle or element from
PtA is included, so we encourage readers to visit the
PtA document for full details of the recommendations.
Conclusion
As noted in PtA, we all have a role to play in ensuring
that every student is engaged in mathematics learning
that is a vibrant, dynamic, enriching experience. This
book is but one small part in supporting mathematics
educators and other professionals in developing the
knowledge base, attitudes, beliefs, and skills to make
that vision a reality.
Reference
National Council of Teachers of '.viathematics (NCTM). Prin
ciples to Actions: Ensuring :vfathematica! Success for All.
Reston, Va.: NCTM. 2014.
viii