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:

  • 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:

  • 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).
  • 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), Pearsondigits (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). 6As 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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:

  • 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:

  • 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 student-teacher 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 enVisionMATHis 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.