Mathematics Instructional Materials Analysis:
Supporting TEKS Implementation
Overview
Mathematics Instructional Materials Analysis: Supporting TEKS Implementation
About The University of Texas at Austin Charles A. Dana Center
Copyright and terms of service
The Charles A. Dana Center supports education leaders and policymakers in
strengthening education. As a research unit of The University of Texas at Austin’s
College of Natural Sciences, the Dana Center maintains a special emphasis on
mathematics and science education. The Dana Center’s mission is to strengthen
the mathematics and science preparation and achievement of all students
through supporting alignment of all the key components of mathematics and
science education prekindergarten–16: the state standards, accountability system,
assessment, and teacher preparation.
This material is copyright Charles A. Dana Center, The University of Texas at Austin, 2006, 2007.
We focus our efforts on providing resources to help local communities meet
the demands of the education system—by working with leaders, teachers,
and students through our Instructional Support System; by strengthening
mathematics and science professional development; and by publishing and
disseminating mathematics and science education resources
About the development of this resource
The Charles A. Dana Center has developed this Mathematics Instructional
Materials Analysis resource for mathematics teachers and leaders to use in
selecting high-quality, TEKS-aligned materials for use in their schools and
districts.
The development and production of Mathematics Instructional Materials Analysis
was supported by the Charles A. Dana Center at The University of Texas at
Austin. Any opinions, findings, conclusions, or recommendations expressed in
this material are those of the author(s) and do not necessarily reflect the views of
The University of Texas at Austin.
The University of Texas at Austin
The Charles A. Dana Center
2901 North IH-35, Suite 2.200
Austin, Texas
78722-2348
Unless otherwise indicated, the materials found in this publication are the copyrighted property
of the Charles A. Dana Center at The University of Texas at Austin (the University). No part of
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to the owner of the copyright rather than to the University. The following specifically excludes
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2) Teachers and educational administrators may reproduce and use one printed copy of the material
for their personal use without obtaining further permission from the University, subject to the terms
and conditions listed below (A, B, and C).
3) Public school districts, charter schools, education service centers, and teachers may reproduce and
use printed copies of the materials for internal professional development or classroom instruction
without obtaining further permission from the University, subject to the terms and conditions listed
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Terms and conditions
A) Any portion reproduced must remain unedited from the original.
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reasonable fee for use, provided that the fees not exceed the cost of reproduction and distribution.
Otherwise, no monetary charge can be made for the reproduced materials or any document
containing them without prior written consent or license from the University.
C) The following copyright and attribution notice must be affixed to each copy produced:
Copyright 2006, 2007, Charles A. Dana Center at The University of Texas at Austin
www.utdanacenter.org
© 2006, 2007, Charles A. Dana Center at The University of Texas at Austin
Mathematics Instructional Materials Analysis: Overview
In keeping with our longstanding practice, we will use all royalties generated
through use of our materials to further our nonprofit educational mission.
Please send your permission requests or questions to this address:
Charles A. Dana Center
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DCshop@lists.cc.utexas.edu
Extensive efforts have been made to ensure the accuracy of the information in
this resource. The Charles A. Dana Center and The University of Texas at Austin,
as well as the authors and editors, assume no liability for any loss or damage
resulting from the use of this book/resource.
If you find an error, please email us at DCShop@lists.cc.utexas.edu.
Every effort has been made to provide proper acknowledgement of original
sources and to comply with copyright law. If cases are identified where this has
not been done, please contact the Charles A. Dana Center at DCShop@lists.
cc.utexas.edu to correct any omissions.
Credits
The TEKS for mathematics, as well as for other areas, can be downloaded in
printable format, free of charge, through the Texas Education Agency website,
www.tea.state.tx.us/teks, or from the Dana Center’s Mathematics TEKS Toolkit
website, www.mathtekstoolkit.org.
Acknowledgments
Unless otherwise noted, individuals listed here are affiliated with the Charles A.
Dana Center at The University of Texas at Austin.
Project director
Patti Bridwell, Senior Program Coordinator
Contributing authors
Patti Bridwell, Senior Program Coordinator;
Laurie Mathis, Ph.D., Program Director;
David Molina, Ph.D., Independent Consultant
Danielle Seabold, Senior Program Coordinator;
Charles A. Dana Center editorial and production team
Melissa Campos-Hernandez, Editor
Tom McVey, Senior Program Coordinator
Rachel Jenkins, Senior Editor
Resources
Resources for implementing the mathematics TEKS, including professional
development opportunities, are available through the Charles A. Dana
Center at The University of Texas at Austin. Many resources can be found in
the Mathematics TEKS Toolkit at www.mathtekstoolkit.org. Professional
development opportunities are listed in the Dana Center’s products catalog,
www.utdanacenter.org/catalog. You may also find out about professional
development opportunities by calling the Dana Center’s main line, at 512-4716190.
Perfect-bound and spiral-bound versions of the mathematics and science TEKS
booklets are available for a fee (to cover the costs of production) from the Charles
A. Dana Center at The University of Texas at Austin (www.utdanacenter.org/
catalog).
October 2006 release.
© 2006, 2007, Charles A. Dana Center at The University of Texas at Austin
Mathematics Instructional Materials Analysis: Overview
Introduction
Notes
Foreword
The selection of appropriate instructional materials is critical to the implementation
of high-quality mathematics instruction. High-quality materials and mathematics
programs can significantly improve student learning. The selected materials should
be consistent with the goals, objectives, and mathematical content of the Texas
Essential Knowledge and Skills (TEKS).
In its role of supporting the implementation of the Mathematics TEKS in
kindergarten–Grade 12, the Charles A. Dana Center has developed a process to help
districts and schools review materials with respect to the TEKS in a timely, efficient,
and comprehensive manner. The role of the Dana Center is not to influence the
selection of any particular set of materials, but rather to help schools and districts
make informed decisions based on their local needs and on the material’s alignment
with the TEKS.
It is no longer sufficient to think of instructional materials simply as textbooks.
Today, more than ever, a program of instruction must be examined in terms of
all its components. Instructional materials may include—but are not limited
to—textbooks, supplementary materials, computer software, calculators, internetbased services, videotapes, discs, manipulatives, curriculum guides, and trade books.
Educators will want to examine the complete set of materials to ensure they meet the
rigor and depth outlined in the appropriate grade level TEKS.
This document delineates a process for using the TEKS as the focal point for
analyzing instructional materials for K–12 mathematics. In the analysis process,
participants look in-depth at a broad range of materials. The Instructional Materials
Analysis instrument is best used in a facilitated process where the facilitator has
undergone the Instructional Materials Analysis professional development training.
© 2006, 2007 Charles A. Dana Center at The University of Texas at Austin
Mathematics Instructional Materials Analysis: Overview
Notes
Components of Quality Instructional Materials
Simply checking the instructional materials’ topics against a scope and sequence
chart is not sufficient for determining the quality of the materials. For materials to
earn a rating of high-quality in the Instructional Materials Analysis, they should:
• include the major goals of developing students’ problem-solving, reasoning,
and communication skills;
• emphasize the development of conceptual understanding and connections
among topics;
• allow ample opportunities for students to apply mathematics in realistic
and meaningful situations;
• reflect high expectations for all students;
• include appropriate student assignments;
• promote students’ active involvement in learning mathematics;
• reflect an appropriate developmental sequence;
• provide alternative assessment instruments and methods;
• integrate the use of technology;
• reflect current research in mathematics education; and, above all
• teach all the TEKS (including Basic Understandings or Introductory
Paragraphs, Strands, Knowledge and Skills, and Student Expectations)
© 2006, 2007 Charles A. Dana Center at The University of Texas at Austin
Mathematics Instructional Materials Analysis: Overview
Notes
The Role of Instructional Materials Analysis and Professional Development in a
Quality Mathematics Program
There is no single right answer to address which set of instructional materials is a
school’s or district’s best choice, since different sets of materials might be used in
different settings to form a quality instructional program.
However, it is teachers, not materials, who are key to successful instruction; they
are the most important element of an effective mathematics program. Treated
appropriately, the review and selection of instructional materials can be a rich
professional development opportunity for teachers. To help ensure the success of
their students, all teachers must be knowledgeable about the TEKS and engage in
continuous professional development activities. This Instructional Materials Analysis
affords them the opportunity to do both.
© 2006, 2007 Charles A. Dana Center at The University of Texas at Austin
Mathematics Instructional Materials Analysis: Overview
Notes and Next Steps
The Process: An Overview of the Four Phases
Phase 1:
Studying the TEKS
Before analyzing instructional materials, those involved should have a current and functional knowledge of the TEKS. Phase 1 of
the Instructional Materials Analysis involves a guided exploration of the TEKS. This guided exploration provides structures and
tools for developing a better understanding and working knowledge of the TEKS. Phase 1 materials are designed to promote the
study of the following attributes of the TEKS:
•
•
•
•
•
All portions of the TEKS
Knowledge and Skills and Student Expectations
Primary Focal Points
Underlying Processes
Balance between conceptual (knowledge) and behavioral (skills)
Although a study of the mathematics TEKS is an essential component of the Instructional Materials Analysis process, in a
broader sense all teachers and leaders should study the TEKS. As the TEKS are non-negotiable in Texas, an ongoing study of
them is the best way for districts and schools to improve the quality of their mathematics program and ensure the success of all
students.
Implementation
All persons influencing the selection of instructional materials—especially textbook selection committee members—should
be required to participate in the Phase 1 learning experience prior to examining instructional materials. Textbook committee
members, campus and district leaders, classroom teachers, and community members involved in selecting instructional materials
should all have Phase 1 experiences of studying the TEKS. Allow about 3 hours for conducting Phase 1 activities. Phase 1 must
occur prior to the review of any instructional materials.
Materials and Supplies
•
Phase 1: Studying the TEKS Blackline Master — 1 per participant
•
Phase 1: Studying the TEKS Format Packet Blackline Master — 1 per participant
•
K-12 Mathematics TEKS (available online at the Texas Education Agency website, www.tea.state.tx.us/teks, or from
the Dana Center’s Mathematics TEKS Toolkit, www.mathtekstoolkit.org)
•
Markers
•
Glue sticks
•
Half-sheets of paper
•
Sticky notes
© 2006, 2007 Charles A. Dana Center at The University of Texas at Austin
Mathematics Instructional Materials Analysis: Overview
Notes and Next Steps
Phase 2:
Narrowing the field of instructional materials
Phase 2 is designed to help the materials selection committee take a broad and holistic survey of the many instructional
materials under review to reduce the number of materials to a manageable size. This reduction is best accomplished by
engaging participants in small group discussions concerning the degree to which the materials align with the TEKS. As
part of this process, participants familiarize themselves with—and practice using—a scoring rubric and documentation
form designed to help determine the degree of correlation to the TEKS. The Phase 2 tool uses criteria directly based on the
TEKS and information from Phase 1. This phase should help narrow down the number of viable instructional materials
sets to two or three. These will be reviewed in greater depth in Phases 3 and 4.
Implementation
Selection committee members should practice applying the Phase 2 rubric to reach consensus on a single sample of
instructional materials. To make the analysis of up to 15 different resources manageable, determine a strand and/or big
idea to be analyzed across all resources. Determine a method for aggregating and analyzing the data to determine the 2-3
resources to be analyzed in greater depth in Phases 3 and 4. Establish the structure that small groups will follow in Phase 2
(i.e., elementary, middle school, high school, grade bands, courses, a grade).
Materials and Supplies
•
Phase 2: Narrowing the Field of Instructional Materials Blackline Master — multiple copies per person
•
The instructional materials for each grade/course that are under initial consideration (teacher edition and
student edition)
© 2006, 2007 Charles A. Dana Center at The University of Texas at Austin
Mathematics Instructional Materials Analysis: Overview
Notes and Next Steps
Phase 3:
Assessing mathematical content alignment
In Phase 3, participants now conduct in-depth reviews of the materials selected in Phase 2. This deeper analysis allows
for detailed documentation of the degree to which the materials are aligned with the TEKS. The Phase 3 process requires
selection committee members to use the outlined criteria to determine a rating and to cite examples to justify their score.
Additionally, this phase requires participants to document Knowledge and Skills statements and/or Student Expectations
that were underemphasized or missing.
Implementation
Selection committee members should practice applying the Phase 3 rubric and documentation form to reach consensus
on a single sample. Participants determine a starting point, such as a big idea within each strand, to be analyzed across the
remaining resources, and then determine a method for aggregating and analyzing the data collected. Next, determine how
individuals or small groups will be organized to carry out next steps; include a timeline.
Materials and Supplies
•
Phase 3: Assessing Mathematical Content Alignment Blackline Master — multiple copies per person
•
The 2 to 4 instructional materials selected in Phase 2
© 2006, 2007 Charles A. Dana Center at The University of Texas at Austin
Mathematics Instructional Materials Analysis: Overview
Notes and Next Steps
Phase 4:
Assessing vertical alignment of instructional materials
In Phase 4, participants determine which instructional materials to adopt, unless a final decision was reached in Phase 3.
Participants consider the vertical nature of the TEKS to determine how well the materials present concepts and develop
ideas across grade levels. During this last phase, participants continue to rely on their common understanding of the TEKS
across grade levels that they developed in prior phases. Phase 4 allows participants to document the degree to which the
materials address mathematics content, instruction, and content-depth across three or more grade levels.
Implementation
Selection committee members should practice applying the Phase 4 Instructional Alignment Chart and scoring rubric
and documentation form to reach consensus on a single sample. Determine a starting point for analysis, such as a big idea
within each strand across a three-grade/course span. Determine a method for aggregating and analyzing the data collected.
Determine how individuals or small groups will be organized to carry out next steps; include a timeline.
Materials and Supplies
•
Phase 4: Assessing Vertical Alignment of Instructional Materials Blackline Master — multiple copies per person
•
The 2 instructional materials finalists
© 2006, 2007 Charles A. Dana Center at The University of Texas at Austin
Mathematics Instructional Materials Analysis: Overview
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