Pearson Instructional Programs
and the Common Core Standards for Mathematics
A timeline of concurrent development
Common Core Goals
The Common Core State Standards for Mathematics were developed under the
auspices of the Council of Chief State School Officers (CCSSO) and the National
Governors Association Center for Best Practices (NGA Center) in 2009 and 2010. The
stated goals of the standards are to (1) to bring about real and meaningful
transformation of our educational system to benefit all students 1 and (2) to bring
focus, coherence, and rigor (as evidence-based design principles) to K-12
mathematics instruction. 2
Across the nation, the adoption of the Common Core State Standards for
Mathematics (CCSSM) represents a significant foundational change in K-12
instruction. Standards by themselves cannot raise achievement. 3 The alignment of
instructional materials to the standards is one critical success factor. Two other
critical factors are professional development for teachers as they grapple with new
content and new expectations of students, and the creation of valid and reliable
testing instruments that track individual students’ progress against the standards.
Only success in these three areas will guarantee that all US students acquire the
critical concepts and skills necessary to succeed in college and in their careers;
regardless of the state or district they live in, or school they attend.
Three Key Pillars
These pillars form the foundation of a successful implementation of the Common
Core State Standards for Mathematics:
1) Research-based, Common Core
Standards-aligned, instructional
materials that are proven
effective;
2) Transitional support and
professional development,
including new teaching
strategies; and
3) Data-driven reporting and
progress monitoring tools to
assist with new summative
assessment requirements.
Individually, any one of these three pillars would be a challenge to implement.
Collectively, the task of simultaneous implementation is daunting to most school
districts.
Publishers’ Criteria
With respect to instructional materials, the recent release by the CCSSO and NGA
Center of the K-8 Publishers’ Criteria for the Common Core State Standards for
Mathematics represents a welcome guideline for both publishers and school districts.
It contains not only a comprehensive discussion of criteria for evaluating materials,
but begins to suggest expected classroom behaviors on the part of both teachers and
students, to wit:
Students and teachers using [instructional materials] as designed spend
the large majority of their time, approximately three-quarters, on the
major work of each grade. 4
Teachers and students using the materials as designed spend from a
quarter to a half of their classroom time communicating reasoning (by
constructing viable arguments and explanations and critiquing those of
others). 5
Over the coming months, we at Pearson look forward to the release of a full range of
assessment items from the Partnership for Assessment of Readiness for College and
Careers (PARCC) and the Smarter Balanced Assessment Consortium (SBAC). And we
continue to listen carefully to individual districts as they define the nature of
professional development they seek.
Documentation around the CCSS for Mathematics
Since the release of the first public draft of the CCSS for Mathematics, there have
been continuing and numerous releases of supporting and interpretive documents,
including progressions, content frameworks, and suggested review criteria.
Timeline of “official” and not-so-official Common Core documents already released:
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March 2010: Draft for review of Common Core State Standards for
Mathematics
June 2010: Common Core State Standards for Mathematics
August 2010: Appendix A: Designing High School Mathematics Courses (aka
Model Course Pathways in Mathematics, Achieve)
December 2010: Learning Progressions Frameworks Designed for Use with
the Common Core State Standards in Mathematics K-12 (Hess & Kerns,
National Center for the Improvement of Educational Assessment & National
Alternate Assessment Center)
January 2011: Expanded Learning Progressions Frameworks for K-12
Mathematics (Hess, National Center for the Improvement of Educational
Assessment)
January 2011: Preparation of Effective Teachers in Mathematics (National
Comprehensive Center for Teacher Quality)
April 2011: Draft Progressions Documents for the Common Core Math
Standards
April 2011: Learning Progressions for the Common Core State Standards
(Findell, Association of State Supervisors of Mathematics)
Sept 2011-July 2012: various Progressions Documents for the Common Core
Math Standards (McCallum, Tools for the Common Core Standards)
August 2011: Draft PARCC Model Content Frameworks for Mathematics
Fall 2011: PARCC Model Content Frameworks for Mathematics—Response to
public feedback
Summer 2012: Draft Model Content Frameworks for High School Mathematics
(PARCC)
July 2012: K-8 Publishers’ Criteria for the Common Core State Standards for
Mathematics (draft)
Each of these releases has generated vigorous discussion of the interpretations,
suggestions, and assumptions contained therein. All of this is healthy and necessary
to bring the country to a common understanding of the objectives of the Common
Core standards. There is no reason to expect that future releases of guidelines,
samples, etc., will be any different.
Expected future releases:
 Late summer 2012: final Model Content Frameworks for High School
Mathematics (PARCC)
 January 2013: final K-8 Publishers’ Criteria
 Fall 2012? Sample assessment items (PARCC)
 ? Sample assessment items (SBAC)
 ? Assessment blueprints (PARCC)
 ? Assessment blueprints (SBAC)
 2014? Released tests
Pearson’s Instructional Materials
Pearson provides K-12 mathematics instructional materials of two major types:
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National Science Foundation (NSF)-funded programs developed over the last
twenty years that have anticipated the call for focus, coherence, and rigor,
including an emphasis on conceptual understanding, fluency, applications,
and student reasoning. These include Investigations in Number, Data, and
Space (K-5), Connected Mathematics (6-8), and Center for Mathematics
Education Project Mathematics (9-12).
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Comprehensive, flexible programs designed for a variety of instructional
models, including whole class direct instruction, small group work, and
individually paced learning. These include Pearson enVisionMATH (K-6),
Pearson digits (6-8), and Pearson High School Mathematics (9-12). One of
these offerings (digits) has been built from “scratch” since the release of the
Common Core Standards.
Pearson Authors
The author teams for these programs include many thought leaders and contributors
to both the foundations and development of the Common Core State Standards for
Mathematics. Below is a partial description of their influential work.

Randall I. Charles, Professor Emeritus, Department of Mathematics, San Jose
State University, longtime researcher into effective ways to embed problem
solving in mathematics instruction. Dr. Charles was part of the writing team
for NCTM’s Curriculum Focal Points for Prekindergarten through Grade 8
Mathematics: A Quest for Coherence (2006). 6 As the title suggests, the
Curriculum Focal Points and the related Focus series of publications represent
a strong call for focus and coherence in math curricula across the country. As
the Publishers Criteria cites, “With the advent of the Common Core, a
decade’s worth of recommendations for greater focus and coherence finally
have a chance to bear fruit.” 7 Dr. Charles is an author of enVisionMATH and
Pearson High School Mathematics.
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Al Cuoco, Senior Scientist and Director of the Center for Mathematics
Education of the Education Development Center, Inc. Beginning in 1996, Dr.
Cuoco has been instrumental in articulating a description of mathematical
habits of mind that can serve as an organizing principle for a mathematics
curriculum. 8 In many ways, Dr. Cuoco’s work has permeated the Common
Core Standards for Mathematical Practice. The Publishers Criteria calls for
“Each mathematical practice standard [to be] meaningfully present in the
form of activities or problems that stimulate students to develop the habits of
mind described in the practice standards.” 9 Dr. Cuoco is an author of CME
Project Mathematics.
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Francis (Skip) Fennell, Bowlsbey Professor of Education and Professional
Studies at McDaniel College, past President of the National Council of
Teachers of Mathematics (2006-2008), and at that time a member of the
National Mathematics Advisory Panel. The Panel called for a research-based,
focused mathematics curriculum, with mathematically knowledgeable
teachers and improved assessments. Notably, as with the CCSSM, the Panel’s
report emphasized that “high-quality research does not support the
contention that instruction should be either entirely ‘student centered’ or
‘teacher directed’.” 10 Professor Fennell is an author of enVisionMATH and
digits.
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Glenda Lappan, University Distinguished Professor of Mathematics at Michigan
State University, past President of the National Council of Teachers of
Mathematics (1998-2000), at the time of the release of Principles and
Standards for School Mathematics. 11 This document is cited in the Common
Core Standards, especially for its Process Standards, as an important source
for the Common Core State Standards for Mathematical Practice. 12 Professor
Lappan is an author of Connected Mathematics.
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Stuart J. Murphy, a visual learning specialist and author of the award-winning
MathStart series for young children. Mr. Murphy has been instrumental in
helping Pearson to bring clarity and focus to the visual elements of our
programs—to better support student understanding, modeling of
mathematics, and connections to applications. As the Publishers Criteria
suggests, “The visual design isn’t distracting or chaotic, or aimed at adult
purchasers, but instead serves only to support young students in engaging
thoughtfully with the subject.” 13 Mr. Murphy is a consulting author for
enVisionMATH, digits, and Pearson High School Mathematics.
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Susan Jo Russell, Principal Scientist at the Education Research Collaborative at
TERC, and a principal investigator for Developing Mathematical Ideas, a
professional development curriculum series for elementary and middle grades
teachers. In 2004, Dr. Russell co-authored with Dr. William McCallum (one of
the three principal writers of the CCSSM) an article calling for “Educators [to]
provide –and parents [to] demand—a balanced, rigorous curriculum in which
all children, not just those in privileged communities, learn serious
mathematics in a serious way—with understanding.” 14 Further, “Schools must
commit to coherent plans that include establishing learning goals, providing
professional development to support teachers in learning more about
mathematics and how children learn it, and implementing good assessment
tools to evaluate progress.” 15 Dr. Russell is an author of Investigations in
Number, Data, and Space.
Details of Pearson Math Programs and Alignment with Common Core Goals
Each major Pearson program aligns to Common Core goals in important ways. All of
these programs will continue to be revised and extended as the goals move from
academic statements to real, shared expectations on the part of educators across the
country.
Investigations in Number, Data, and Space is a K-5 program designed to engage
students in making sense of mathematical ideas. Six major goals guided the
development of Investigations:
1. Support students to make sense of mathematics and learn that they can be
mathematical thinkers.
2. Focus on computational fluency with whole numbers.
3. Provide substantive work in important areas of mathematics—rational
numbers, geometry, measurement, data, and early algebra—and make
connections among them.
4. Emphasize reasoning about mathematical ideas.
5. Communicate mathematics content and pedagogy to teachers.
6. Engage the range of learners in understanding mathematics.
The program stresses student reasoning, conceptual understanding, and fluency with
procedures—all hallmarks of the Common Core Standards. Each curriculum unit
(about a month of instruction) focuses on an area of content in depth, providing time
for students to develop and practice ideas across a variety of activities and contexts
that build on each other. This program completely embraces the Common Core goals
of focus, coherence, and rigor, and the Standards for Mathematical Practice.
Common Core transition lessons are now available for current Investigations users. A
new edition of Investigations that aligns to the sequence of the Common Core State
Standards for Mathematical Content will be available for back-to-school 2015.
Connected Mathematics is a 6-8 program crafted around a single goal:
All students should be able to reason and communicate proficiently in
mathematics. They should have knowledge of and skill in the use of
the vocabulary, forms of representation, materials, tools, techniques,
and intellectual methods of the discipline of mathematics, including the
ability to define and solve problems with reason, insight,
inventiveness, and technical proficiency.
The curriculum is both problem-centered and research-based. First, what makes
good problems? Each problem in Connected Mathematics satisfies the following
criteria:
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The problem must have important, useful mathematics embedded in it.
Investigation of the problem should contribute to students; conceptual
development of important mathematics.
Work on the problem should promote skillful use of mathematics and
opportunities to practice important skills.
The problem should create opportunities for teachers to assess what students
are learning and where they are experiencing difficulty.
Further, each problem satisfies some or all of the following:
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The problem should engage students and encourage classroom discourse.
The problem should allow various solution strategies or lead to alternative
decisions that can be taken and defended.
Solution of the problem should require higher-level thinking and problem
solving.
The mathematical content of the problem should connect to other important
mathematical ideas.
Comparing these criteria to the Publishers Criteria discussion of the role of problems
in grade-level work, as a vehicle for making coherent connections, as an opportunity
to form arguments, and as an indicator of quality in a Common Core mathematics
curriculum reveals a remarkable alignment of Connected Mathematics to the view of
problems and problem-solving expressed in the Publishers Criteria.
The research base of Connected Mathematics includes research from the cognitive
sciences, mathematics education, and education policy and organization.
Cognitive sciences research base:
 Social constructivism—the role of discourse (student-student and studentteacher dialogue) in learning
 Conceptual and procedural knowledge—mathematical knowledge is
fundamentally a web of connections among ideas; sound conceptual
understanding is a important foundation for procedural skill
 Multiple representations—an important indication of students’ connected
mathematical knowledge is their ability to represent ideas in a variety of ways
 Cooperative learning—both individual and cooperative learning formats can
enhance mathematical learning
Mathematics education research base: Research in the areas of rational numbers and
proportional reasoning, probability and statistical reasoning, algebraic reasoning, and
geometric and measurement reasoning have informed the treatment of specific
topics in all the major strands of content in Connected Mathematics. These include
rates of change and representation, equivalence, graphic displays, functions,
variables, congruence, similarity, and transformations—all topics of central
importance in the Common Core standards for Grades 6–8.
 Research rational numbers/proportional reasoning
Education policy and organization research base: One of the fundamental challenges
in mathematics teaching is convincing students that serious effort in study of the
subject will be rewarding (and also enjoyable). Finding aspects of mathematics and
its applications that are effective in engaging students has been informed by
research on extrinsic and intrinsic motivation. Another challenge is supporting
teachers through effective professional development in implementing the program
successfully and with fidelity. Connected Mathematics continues to have a
comprehensive array of support for teacher and school change.
All the aspects of research cited above resonate with the expectations of the
Publishers Criteria, particularly with respect to rigor, the balance of conceptual
understanding, fluency, and application, the embedding of the standards for
mathematical practice, and the quality expected of teacher materials.
Common Core transition lessons are available for current CMP users. A new edition of
CMP that aligns to the sequence of the Common Core State Standards for
Mathematical Content will be available for back-to-school 2013.
Center for Mathematics Education Project Mathematics is a high school
program covering Algebra 1, Geometry, Algebra 2 and Pre-Calculus in either a
traditional or an integrated sequence. The following organizing principle is
fundamental to the CME Project materials:
The widespread utility and effectiveness of mathematics come not just
from mastering specific skills, topics, and techniques, but more
important, from developing the ways of thinking—the habits of mind—
used to create the results.
A curriculum organized around habits of mind tries to close the gap
between what the users and makers of mathematics say and what
they do.
CME Project is such a curriculum. It lets students in on the process of creating,
inventing, conjecturing, and experimenting. It lets them experience what goes on
behind the study door, before new results are polished and presented. It encourages
false starts, calculations, experiments, and explaining special cases. Students
develop the habit of reducing things to lemmas for which they have no proofs, and of
suspending work on these lemmas and on other details until they see if assuming the
lemmas are true will help. It helps students look for logical and heuristic connections
between new ideas and old ones.
The Common Core State Standards for Mathematics adopts a very similar view
towards school mathematics. In fact, the paper cited above is listed in the Common
Core as one of the works consulted by the writers. The influence of the ``habits of
mind approach’’ is especially prominent in Common Core’s Standards for
Mathematical Practice—some of the standards are almost identical to the habits of
mind that are used as CME’s fundamental organizing principle, and some of the
examples used in Common Core’s description of the standards for mathematical
practice are identical to examples used in CME.
Common Core transition lessons are now available for current CME users. New
editions of CME (traditional and integrated sequences) that embed all content called
for in the Common Core Standards will be available for back-to-school 2012.
Pearson enVisionMATH is a K–6 blended print and digital program first published
in 2008. enVisionMATH uses a research-based instructional model designed to make
mathematics more accessible to a wide range of students. Through interactive
learning and problem-based activities, students are able to build their own
understanding of concepts and skills before the formal representation of ideas
occurs. Visual representations drive concept and skill development and each lesson
contains a student “visual learning band” which incorporates a dynamic presentation
of the objective and essential understanding of the lesson. Timely, frequent
assessments assist teachers in individualizing instruction, which is supported by the
large range of differentiated instructional resources provided to teachers. Technology
alternatives allowed the print version to come alive through motion and sound.
Teacher explanations and Center Activities reinforce, deepen and extend learning.
Randomized control trial studies have shown that students using the program
achieved significant percentile gains year-over-year in concepts and problem solving,
computation, vocabulary, and math communication. Students also performed
significantly better than control students in these areas on three national math
assessments. Further, these gains held for multiple subgroups, including those of
gender, ethnicity, free/reduced lunch, special education, and math ability level.
Students using enVisionMATH showed significantly greater gains in math
communication and problem solving than those using inquiry-based materials, and
significantly greater gains in problem solving and computation than those using a
traditional program.
enVisionMATH teachers noted that they were more prepared to use various math
practices and strategies as compared to control teachers, including the following:
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Provide hands-on, concrete experience before introducing abstract concepts.
Help students develop communication skills related to math (e.g., have
students explain how they arrived at math solutions).
Engage students in applications of mathematics in a variety of contexts.
Use informal questioning to assess student understanding.
Help students with problem solving skills.
Teach different methods to solve mathematics problems.
Overall, teachers using enVisionMATH reported increased comfort with inquiry-based
teaching techniques. In light of the emphasis in the Publishers’ Criteria on discourse,
conceptual understanding, fluency, and learning mathematics by solving significant
problems, all of these results suggest that enVisionMATH is an effective program that
moves classroom practices in precisely the direction called for by the Common Core
Standards.
A Common Core Edition of enVisionMATH, currently available, maintains all of the
instructional design of the 2008 program, but increases the content coverage called
for in the Common Core Standards, while removing extraneous content.
Pearson digits is a 6–8 digitally delivered program first published in 2011. The
content and instructional design of digits were driven by the release of the Common
Core standards in early 2010.
digits combines a comprehensive math curriculum, powerful best practices in
teaching, and easy-to-use technology in order to meet these goals:
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Provide complete, rigorous, in-depth coverage of the Common Core
Standards for Mathematical Content.
Provide embedded, daily opportunities for students to engage in the
expectations of the Common Core Standards for Mathematical Practice.
Simplify preparation and management tasks for teachers by providing
prevention and enrichment paths along with individualized study plans,
reporting, and auto-scored homework.
Personalize learning for students by providing individualized learning paths, a
Companion notebook to support problem solving and formative assessment,
and self-guided exploration options.
As observed in field studies and first-year users of the program, the resulting
instructional design of digits has enabled higher achievement levels in students;
greater class time spent on problem solving, discourse, and instruction; more
engagement of students through the interactive, digitally-presented problems; and
greater completion rates and success with practice assignments.
Random control trial studies are underway for digits. An accelerated sequence of
instruction to support Algebra 1 in Grade 8 will be available in late 2012.
Pearson High School Mathematics is a 9-12 blended program first published in
2010. It incorporates several critical principles in its instructional design:
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Teaching through problem solving. New concepts and skills are introduced in
the context of solving problems that have important mathematical ideas
embedded. Then examples are used that extend understanding and promote
thinking and reasoning. Presenting examples as problems and modeling
effective thinking and reasoning habits promotes understanding and mastery.
Support learning through effective visual elements. Visual learning strategies
can make a profound difference in a student’s depth of understanding about
mathematics. Through the universal language of visuals, students are able to
understand and express mathematical concepts more quickly and easily than
they could when reliant on numbers and words alone. Effective visual
elements are a powerful teaching tool for those who are natural visual/spatial
learners, for those who are English language learners, and for all students.
Model “thinking mathematically” for students (and teachers). Promote
increasing student autonomy in directing their own learning by providing
observational questions about the mathematics (e.g., “How is this situation
the same or different as . . .”), and structuring the questions and answers to
support increasing maturity of thought. Learning is achieved not through
hoping that “teaching” the content yields understanding, but through carefully
designed instruction derived from the specific understandings and applications
sought.
Random control trials of Pearson High School Mathematics show that students of all
math ability levels using Algebra 1 showed significantly greater gains in open
response items than their comparison peers. Students using Algebra 1 showed
significant year-over-year gains of 38 percentile points in math achievement.
A Common Core Edition of Pearson High School Mathematics (© 2012) is currently
available. It maintains all of the instructional design of the 2010 program, but
increases the content coverage called for in the Common Core Standards while
removing some extraneous content. Because the association of assessed standards
with specific high school courses is still in flux, no date for a more complete revision
has been set.
Pearson’s Larger Response
Pearson is prepared to assist students, teachers, districts, and states by providing a
comprehensive and progressive approach to a Common Core Standards learning
environment. Specifically, Pearson is providing:
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Instructional materials that will continue to be revised to reflect the evolving
expectations of focus, coherence, and rigor. Research-based and proven
effective, Pearson’s programs already reflect state-of-the-art knowledge of
learning cognition and effective pedagogy.
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Tailored professional development offerings to support teachers through the
adoption and implementation of the Common Core Standards in their
classrooms. Through these resources, teachers will feel ready to lead their
students through this important change.
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Community outreach so that parents and families understand the importance
of adopting the Common Core Standards and the impact they will have on
children’s long term success. Pearson’s tools for ongoing home connections
provide a unique opportunity for school districts to engage all of their
stakeholders.
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Data management capabilities that integrate across our instructional
materials, professional development and community tools so that teachers,
parents, and administrators have a complete picture of student
improvement—including monitoring progress in advance of state testing.
Increasingly, all of Pearson’s programs are moving to digital delivery, including
digital support for teacher professional development, planning, and progress
monitoring of individual students. Such changes can assist teachers in gaining the
expertise demanded of them by the Common Core Standards, as well as making it
more feasible for them to track student performance and to individualize instruction
to meet each learner’s needs.
Summary
Pearson understands that the implementation of the Common Core State Standards
for Mathematics is not a single event for any school district or teacher, but rather a
series of actions to improve curricular materials, teacher knowledge, assessment
data, and, ultimately, student performance. We welcome the release of the
Publishers Criteria as an important step helping to define a shared expectation of
instructional materials. Without a growing agreement across the country around all
aspects of Common Core implementation, the dream of common standards that
foster a focused, coherent, and rigorous curriculum will remain elusive.
Notes
Common Core State Standards Initiative Frequently Asked Questions, NGA Center
& CCSSO; September 2009, 1.
1
K-8 Publishers’ Criteria for the Common Core State Standards for Mathematics,
NGA Center, CCSSO, Achieve, Council of Great City Schools, & National Association
of State Boards of Education; Summer 2012, 2.
2
3
Ibid., 1.
4
Ibid., 7.
5
Ibid., 15.
Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest
for Coherence. National Council of Teachers of Mathematics, 2006.
6
K-8 Publishers’ Criteria for the Common Core State Standards for Mathematics, op.
cit., 2.
7
Cuoco, A., Goldenberg, E. P., and Mark, J., “Habits of Mind: An Organizing Principle
for a Mathematics Curriculum,” Journal of Mathematical Behavior, 15(4), 375-402,
1996.
8
K-8 Publishers’ Criteria for the Common Core State Standards for Mathematics, op.
cit., 13.
9
Foundations for Success: The Final Report of the National Mathematics Advisory
Panel, U. S. Department of Education; 2008, xiii-xiv.
10
Principles and Standards for School Mathematics, National Council of Teachers of
Mathematics; 2000.
11
Common Core State Standards for Mathematics, NGA Center & CCSSO; June
2010, 6.
12
K-8 Publishers’ Criteria for the Common Core State Standards for Mathematics, op.
cit., 18.
13
McCallum, William & Russell, Susan Jo, We can do better at teaching kids math,
The Boston Globe, December 14, 2004.
14
15
Ibid.
The unfolding clarity of the goals of CC Standards: focus, coherence, and rigor
CC Standards and specific Pearson programs