Principles to Actions: Ensuring Mathematical Success for All

151 Pages·2014·9.9 MB·English

by  National Council of Teachers of Mathematics

Principles to Actions
Ensuring Mathematical Success for All
Principles to Actions
Ensuring Mathematical Success for All
Copyright © 2014 by the National Council of Teachers of Mathematics, Inc., www.nctm.org. All rights reserved.
This material may not be copied or distributed electronically or in other formats without written permission from NCTM.
Copyright © 2014 by
The National Council of Teachers of Mathematics, Inc.
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ISBN 978-0-87353-904-3
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 all students through vision, leadership, professional development, and research.
Principles to Actions: Ensuring Mathematical Success for All
the National Council of Teachers of Mathematics as approved by the
NCTM Board of Directors, February 2014.
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Contents
Principles to Actions Writing Team..................................................................................v
Preface ..............................................................................................................................vii
Acknowledgments ............................................................................................................ix
Progress and Challenge .....................................................................................................1
Effective Teaching and Learning .....................................................................................7
Establish Mathematics Goals to Focus Learning .................................................12
Implement Tasks That Promote Reasoning and Problem Solving .......................17
Use and Connect Mathematical Representations .................................................24
Facilitate Meaningful Mathematical Discourse ...................................................29
Pose Purposeful Questions ...................................................................................35
Build Procedural Fluency from Conceptual Understanding ...............................42
Support Productive Struggle in Learning Mathematics ......................................48
Elicit and Use Evidence of Student Thinking ......................................................53
Essential Elements ...........................................................................................................59
Access and Equity ................................................................................................59
Curriculum ...........................................................................................................70
Tools and Technology ...........................................................................................78
Assessment ...........................................................................................................89
Professionalism .....................................................................................................99
Taking Action .................................................................................................................109
Leaders and Policymakers in All Districts and States or Provinces ..................110
Principals, Coaches, Specialists, and Other School Leaders .............................112
Teachers ..............................................................................................................114
References .......................................................................................................................119

Principles to Actions
Writing Team
Steven Leinwand American Institutes for Research
Washington, D.C.
Daniel J. Brahier Bowling Green State University
Bowling Green, Ohio
DeAnn Huinker University of Wisconsin–Milwaukee
Milwaukee, Wisconsin
Robert Q. Berry III University of Virginia
Charlottesville, Virginia
Frederick L. Dillon Strongsville City Schools (retired)
Strongsville, Ohio
Matthew R. Larson Lincoln Public Schools
Lincoln, Nebraska
Miriam A. Leiva University of North Carolina at Charlotte
Charlotte, North Carolina
W. Gary Martin Auburn University
Auburn, Alabama
Margaret S. Smith University of Pittsburgh
Pittsburgh, Pennsylvania
NCTM Board of Directors
Linda M. Gojak, President John Carroll University
University Heights, Ohio
Diane J. Briars, President-Elect Pittsburgh, Pennsylvania
Bob Doucette, Executive Director Reston, Virginia
(cid:35)(cid:34)(cid:36)(cid:44) • • • v
PrinciPles to Actions
Robert Q. Berry III University of Virginia
Charlottesville, Virginia
Margaret (Peg) Cagle Vanderbilt University
Nashville, Tennessee
Dane R. Camp ‘Iolani School
Honolulu, Hawaii
Mark W. Ellis California State University, Fullerton
Fullerton, California
Florence Glanfield University of Alberta
Edmonton, Alberta, Canada
Karen J. Graham University of New Hampshire
Durham, New Hampshire
Gladis Kersaint University of South Florida
Tampa, Florida
Latrenda Knighten Polk Elementary School
Baton Rouge, Louisiana
Ruth Harbin Miles Falmouth Elementary School
Mary Baldwin College
Madison, Virginia
Jane Porath Traverse City Area Public Schools
Traverse City, Michigan
Jonathan (Jon) Wray Howard County Public Schools
Ellicott City, Maryland
Rose Mary Zbiek The Pennsylvania State University
University Park, Pennsylvania
vi • • •
Preface
The National Council of Teachers of Mathematics is proud to be the organization that
launched the education standards movement. Growing out of its visionary Agenda for
Action in 1980, NCTM’s 1989 publication of Curriculum and Evaluation Standards for
School Mathematics presented a comprehensive vision for mathematics teaching, learning,
and assessment in kindergarten–grade 4, grades 5–8, and grades 9–12. In 2000, NCTM’s
Principles and Standards for School Mathematics expanded on the 1989 Standards and
added underlying Principles for school mathematics for four grade bands: pre-K–grade 2,
grades 3–5, grades 6–8, and grades 9–12. In 2006, Curriculum Focal Points for Pre-
kindergarten through Grade 8 Mathematics: A Quest for Coherence extended this work
by identifying the most significant mathematical concepts and skills at each level from
prekindergarten through grade 8. NCTM addressed high school mathematics education in
2009 in Focus in High School Mathematics: Reasoning and Sense Making.
The next phase in the evolution of mathematics standards was the development of the
Common Core State Standards for Mathematics by the National Governors Association and
the Council of Chief State School Officers. The release of these standards in 2010, and their
adoption by forty-five states, has presented a historic opportunity for mathematics education
in the United States.
Over the past twenty-five years, we have learned that standards alone—no matter their
origins, authorship, or the process by which they are developed—will not realize the goal of
high levels of mathematical understanding by all students. More is needed than standards.
For that reason, NCTM has developed Principles to Actions: Ensuring Mathematical Success
for All, the next in its line of landmark publications guiding mathematics education into the
future. Principles to Actions describes the conditions, structures, and policies that must exist
for all students to learn. It addresses the essential elements of teaching and learning, access
and equity, curriculum, tools and technology, assessment, and professionalism. Finally, it
suggests specific actions that teachers and stakeholders need to take to realize our shared
goal of ensuring mathematical success for all.
Principles to Actions represents a significant step in articulating a unified vision of what
is needed to realize the potential of educating all students—under any standards or in any
educational setting. Most important, it describes the actions required to ensure that all
students learn to become mathematical thinkers and are prepared for any academic career or
professional path that they choose. Principles to Actions is for teachers, coaches, specialists,
principals, and other school leaders. It is for policymakers and leaders in districts and states,
(cid:35)(cid:34)(cid:36)(cid:44) • • • vii
Preface
including commissioners, superintendents, and other central office administrators. Moreover,
it will give families guidance about what to look for and expect in the system educating
their children. Principles to Actions spells out the part that we all must play in supporting
the success of today’s students to ensure a bright future for the world around us.
Linda M. Gojak
President, 2012–2014
National Council of Teachers of Mathematics
viii • • •
Acknowledgments
The Principles to Actions Writing Team received many comments as a result of sharing the
fi rst draft with all members of the National Council of Teachers of Mathematics. The team
also received and considered comments from a select group of invited reviewers. Some of
these invited reviewers also read and commented on a second draft, which then underwent
extensive further revisions before preparation of the fi nal manuscript. Included among the re-
viewers were mathematicians, mathematics educators, curriculum developers, policymakers,
and classroom practitioners. Several other individuals, committees, or groups committed to
improving pre-K–12 mathematics teaching and learning offered their perceptions and com-
ments less formally. The NCTM Board of Directors and the Principles to Actions Writing
Team are grateful to all the reviewers who shared their expertise.
We extend sincere thanks to the following individuals who offered particularly thorough re-
views or provided exceptional insights in sharing their perspectives on Principles to Actions
in its formative stages. Their thoughtful contributions do not constitute endorsement of the
fi nal publication, but they provided the writing team with fresh perspectives that ultimately
led to a better publication.
Cal Armstrong Mark Ellis Glenda Lappan
Don Balka Francis (Skip) Fennell Jim Lewis
Hyman Bass Shirley Frye Johnny Lott
Diane Briars Karen Fuson Susan Jo Russell
George Bright Sol Garfunkel Cathy Seeley
Margaret (Peg) Cagle Martin Gartzman J. Michael Shaughnessy
Gail Burrill Patrick Hopfensberger Linda Sheffi eld
Anne Collins Andy Isaacs Lee V. Stiff
Al Cuoco Diana Kasbaum Marilyn Strutchens
David Custer Cathy Kelso Denisse Thompson
Todd Davies Henry S. Kepner, Jr. Uri Treisman
Barbara Dougherty Gladis Kersaint Zalman Usiskin
Debbie Duvall Michael Lach Judith Zawojewski
(cid:35)(cid:34)(cid:36)(cid:44) (cid:127)(cid:127) (cid:127)(cid:127) (cid:127)(cid:127) iixx