Content Specifications For The Summative Assessment Of The

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Content Specificationsfor the Summative Assessment of theCommon Core State Standards for MathematicsREVISED DRAFTJuly 2015Developed with input from content experts and Smarter Balanced AssessmentConsortium Staff, Work Group Members, andTechnical Advisory Committee1

AcknowledgementsAlan Schoenfeld, University of California at Berkeley and Hugh Burkhardt, Shell Centre, Universityof Nottingham served as principal authors of this paper. Sections of the document were also authored byJamal Abedi, University of California at Davis; Karin Hess, National Center for the Improvement ofEducational Assessment; Martha Thurlow, National Center on Educational Outcomes, University ofMinnesotaSignificant contributions and organization of the second draft were provided by Shelbi Cole,Connecticut State Department of Education, and Jason Zimba, Student Achievement Partners. Theproject was facilitated by Linda Darling-Hammond at Stanford University. The final polishing teamconsisted of Alan Schoenfeld, Shelbi Cole, Jason Zimba, and William McCallum of the University ofArizona.Content and assessment experts who offered advice, counsel, and feedback include:Rita Crust, Lead Designer, Mathematics Assessment Resource Service; Past President, Association ofState Supervisors of MathematicsBrad Findell, Former Mathematics Initiatives Administrator, Ohio Department of EducationDavid Foster, Director, Silicon Valley Mathematics InitiativeHenry Pollak, Adjunct Professor, Columbia University, Teachers College; Former Head ofMathematics and Statistics, Bell LaboratoriesW. James Popham, Emeritus Professor, University of California, Los AngelesCathy Seeley, Senior Fellow, Charles A. Dana Center, The University of Texas at AustinMalcolm Swan, Professor of Mathematics Education, Centre for Research in Mathematic Education,University of NottinghamThe principal authors acknowledge the contributions to this document by the 2010 “Report of theWorking Group on Assessment in the Service of Policy" of the International Society for Design andDevelopment in Education. In addition to the principal authors of this document, the Working Groupreport was contributed to by:Paul Black, Professor and Chair of the Task Group on Assessment and Testing, UK NationalCurriculumGlenda Lappan, Past President National Council of Teachers of MathematicsPhil Daro, Chair CCSSM Writing GroupA Smarter Balanced-focused version of the Working Group report may be foundat http://www.mathshell.org/papers/pdf/ISDDE SBAC Feb11.pdf2

More than 200 individuals and organizations offered feedback on one or more drafts of the contentspecifications. The organizations included the State Departments of Education from California,Colorado, Connecticut, Delaware, Hawaii, Idaho, Kansas, Maine, Michigan, Missouri, North Carolina,Oregon, Utah, Vermont, Washington, West Virginia, and Wisconsin, as well as:ACT, Inc.Addison Central Supervisory UnitAiea High SchoolAltus Network of Charter SchoolsAsheboro City SchoolsAsheville City SchoolsAsheville Middle SchoolAssociation of California School AdministratorsBeaufort County Public SchoolsBerlin Area School DistrictBridgeport Public SchoolsBrien McMahon HSCabarrus County SchoolsCalifornia Office to Reform EducationCalifornia Teachers AssociationCalifornians TogetherCamden Hills Regional High SchoolCascade MCSCatholic Diocese of Wichita, KansasCentral Connecticut State UniversityChippewa Falls Area SchoolsClinton City SchoolsCollege BoardConnecticut Education Resource CenterConnecticut Technical High SchoolCouncil of the Great City SchoolsCraven County SchoolsDelavan-Darien School DistrictDiscovery Charter SchoolEast Lyme Public SchoolsEast Oakland LeadershipEdith Bowen Laboratory SchoolElk Grove Unified School DistrictEnvision Schools/3CSFederal Way Public SchoolsFreedom Area School DistrictGolden Valley HSGranite School DistrictHayward High SchoolHeritage AcademiesHot Springs School District3

International Reading AssociationJordan Education AssociationJunction City High School, Geary Co. SchoolsLiberty Public SchoolsMetaMetrics, Inc.Milwaukee Public SchoolsMonterey County Office of EducationNational Council of La RazaNational Writing ProjectNebo School DistrictNew Hope Elementary School DistrictNewhall Middle SchoolNortheast Elementary SchoolNorthside High SchoolOdessa R-VII School DistrictOld Saybrook High SchoolOrange Unified School DistrictPartnership for 21st Century SkillsPearsonPewaukee School DistrictPymatuning Valley High SchoolRandolph School DistrictRiverside Unified School DistrictSan Bernardino City Unified School DistrictSan Bernardino County Superintendent of SchoolsSan Diego Unified School DistrictSan Luis Obispo County Office of EducationSanta Clara County Office of EducationSanta Monica–Malibu USDSERCSouthington High SchoolSpring Creek Middle School, Cache County School DistrictSundale Union Elementary School DistrictUC RiversideUniversity of BridgeportVallejo City USDWagner Community SchoolWashoe County School DistrictWestEdWesterly Public SchoolsWestern Connecticut State UniversityWinston-Salem Forsyth County SchoolsWiseburn School DistrictWoodburn School DistrictZanesville High School4

Table of ContentsPage6Introduction and Background Smarter Balanced Content Specifications Development Timelines andActivities6Part I – General Considerations for the Use of Items and Tasks to AssessMathematics Content and Practice16Part II – Overview of Claims and Evidence for CCSS Mathematics Assessment18 Claims for Mathematics Summative AssessmentPresentation of the Claims in Part IIIReporting Categories192020Part III – Detailed Rationale and Evidence for Each Claim23 Mathematics Claim #1: Concepts and Procedures “Students can explainand apply mathematical concepts and interpret and carry out mathematicalprocedures with precision and fluency.”Mathematics Claim #2: Problem Solving “Students can solve a range ofcomplex well-posed problems in pure and applied mathematics, makingproductive use of knowledge and problem solving strategies.”Mathematics Claim #3: Communicating Reasoning “Students can clearlyand precisely construct viable arguments to support their own reasoning andto critique the reasoning of others.”Mathematics Claim #4: Modeling and Data Analysis “Students cananalyze complex, real-world scenarios and can construct and usemathematical models to interpret and solve problems.”25414856References65Appendices Appendix A: CAT Sampling Proportions for Claim 1 Appendix B: Cognitive Rigor Matrix/Depth of Knowledge (DOK) Appendix C: Core Content from Grades 6-8 that Remains WidelyApplicable in High School6872735

Introduction and BackgroundUsing This Document: This version of the Smarter Balanced Assessment Consortium’s work onContent Specifications and Content Mapping consists of several sets of materials. It includes changesbased on the two rounds of extensive and productive feedback provided to the Consortium.Pages 1–68 represent the core of this document, and should be read carefully for comment and feedback.Appendices are intended to provide further elaboration of our work so far. All are embedded in thisdocument, as it might be most useful for a reader to have them ready at hand.This document follows an earlier release by the Consortium of a companion document coveringspecifications for English language arts and literacy. Both of these sets of documents have beendeveloped in collaboration with comments from Consortium members and other stakeholders. The tablebelow outlines the schedule that was used for the two rounds of public review for the contentspecifications of mathematics and English language arts/literacy when they were first developed.Smarter Balanced Content Specifications DevelopmentTimelines and ActivitiesReview StepsDateInternal Review Start: ELA/Literacy- ELA/Literacy content specifications distributed to specific Smarter Balanced work groups forinitial review and feedbackInternal Review Due: ELA/Literacy- Emailed to Smarter BalancedTechnical Advisory Committee (TAC) Review: ELA/Literacy- Draft submitted to TAC for review, comment, and feedbackWebinar: ELA/Literacy (including Evidence-Based Design Orientation)- Orientation for Smarter Balanced members to Evidence-Based Design and walkthrough ofdraft ELA/Literacy specifications documentRelease for Review: ELA/Literacy (Round 1)- ELA/Literacy specifications documents posted on Smarter Balanced website and emailed tostakeholder groupsInternal Review Start: Mathematics- Mathematics content specifications distributed to specific Smarter Balanced work groups forpreliminary review and feedbackTechnical Advisory Committee (TAC) Review: Mathematics- Draft submitted to TAC for review, comment, and feedbackInternal Review Due: Mathematics- Emailed to Smarter BalancedRelease to Item Specifications to Bidders: ELA/Literacy- Current drafts of ELA/Literacy content specifications posted to OSPI website to support ItemSpecifications RFP processWebinar: Mathematics- Walkthrough for Smarter Balanced members of the draft Mathematics specificationsdocumentRelease for Review: Mathematics (Round 1)- Mathematics content specifications posted on Smarter Balanced website and emailed tostakeholder 10/1108/10/1108/15/1108/15/1108/29/1108/29 /11

Release of Specifications to Bidders: Mathematics- Current drafts of Mathematics content specifications posted to OSPI website to support ItemSpecifications RFP processFeedback Surveys Due: ELA/Literacy (Round 1)- Emailed to Smarter BalancedFeedback Surveys Due: Mathematics (Round 1)- Emailed to Smarter BalancedRelease for Review: ELA/Literacy (Round 2)- ELA/Literacy content specifications posted on Smarter Balanced website and emailed tostakeholder groupsFeedback Surveys Due: ELA/Literacy (Round 2)- Emailed to Smarter BalancedRelease for Review: Mathematics (Round 2)- Mathematics content specifications posted on Smarter Balanced website; email notificationsent to stakeholder groupsFeedback Surveys Due: Mathematics (Round 2)- Emailed to Smarter BalancedELA/Literacy Claims Webinar Discussion- Summative assessment claims are discussed in preparation for subsequent vote by Governingstates. Voting will be open 1/22/12 through /09/1101/03/1201/29/12Mathematics Claims Webinar Discussion- Summative assessment claims are discussed in preparation for subsequent vote by Governingstates. Voting will be open 3/19/12 through 3/26/123/13/12ELA/Literacy Claims adopted by Governing States- Summative assessment claims are established as policy for the Consortium through emailvoting of Governing State leads03/01/12Final Content Specifications and Content Mapping Released: ELA/Literacy- Final ELA/Literacy content specifications posted to Smarter Balanced website; emailnotification sent to member states and partner organizationsEarly Apr 2012Mathematics Claims adopted by Governing States- Summative assessment claims are established as policy for the Consortium through emailvoting of Governing State leadsEarly Apr 2012Final Content Specifications and Content Mapping Released: Mathematics- Final Mathematics content specifications posted to Smarter Balanced website; emailnotification sent to member states and partner organizationsLate Apr 2012The contents of this document describe the Consortium’s specification of critically important claimsabout student learning in mathematics that are derived from the Common Core State Standards. Theseclaims will serve as the basis for the Consortium’s system of summative and interim assessments and itsformative assessment support for teachers. Open and transparent decision-making is one of theConsortium’s central principles. A series of draft of the mathematics content specifications has beenmade available for comment consistent with that principle, and all responses to this work have beenconsidered as the document has been refined.Purpose of the Content Specifications: The Smarter Balanced Assessment Consortium is developing acomprehensive assessment system for mathematics and English language arts/literacy— aligned to theCommon Core State Standards—with the goal of preparing all students for success in college and theworkforce. Developed in partnership with member states, leading researchers, content expert experts,7

and the authors of the Common Core, content specifications are intended to ensure that the assessmentsystem accurately assesses the full range the standards.This content specification of the Common Core mathematics standards provides clear and rigorousfocused assessment targets that will be used to translate the grade-level Common Core standards intocontent frameworks along a learning continuum, from which specifications for items, tasks, and testblueprints will be established. Assessment evidence at each grade level provides item and taskspecificity and clarifies the connections between instructional processes and assessment outcomes.The Consortium Theory of Action for Assessment Systems: As stated in the Smarter BalancedAssessment Consortium’s (Smarter Balanced) Race to the Top proposal, “the Consortium’s Theory ofAction calls for full integration of the learning and assessment systems, leading to more informeddecision-making and higher-quality instruction, and ultimately to increased numbers of students who arewell prepared for college and careers” (p. 31). To that end, the Smarter Balanced proposed systemfeatures rigorous content standards; common adaptive summative assessments that make use oftechnology-enhanced item types, extended performance tasks that provide students the opportunities todemonstrate proficiency both with content and in the mathematical practices described in the CommonCore State Standards; computer adaptive interim assessments that provide mid-course information aboutwhat students know and can do; instructionally sensitive formative tools, processes, and practices thatcan be accessed on-demand; focused ongoing support to teachers through professional developmentopportunities and exemplary instructional materials; and an online, tailored, reporting and trackingsystem that allows teachers, administrators, and students to access information about progress towardsachieving college- and career-readiness as well as to identify specific strengths and weaknesses alongthe way. Each of these components serve to support the Consortium’s overarching goal: to ensure that8

all students leave high school prepared for post-secondary success in college or a career throughincreased student learning and improved teaching. Meeting this goal will require the coordination ofmany elements across the educational system, including but not limited to a high quality assessmentsystem that strategically “balances” summative, interim, and formative components (Darling-Hammond& Pecheone, 2010; Smarter Balanced, 2010).The proposed Smarter Balanced mathematics assessments and the assessment system are shapedby a set of characteristics shared by the systems of high-achieving nations and states, and includethe following principles: 11) Assessments are grounded in a thoughtful, standards-based curriculum and are managedas part of an integrated system of standards, curriculum, assessment, instruction, and teacherdevelopment. Curriculum and assessments are organized around a set of learning progressions 2along multiple dimensions within subject areas. These guide teaching decisions, classroom-basedassessment, and external assessment.2) Assessments include evidence of student performance on challenging tasks that evaluateCommon Core standards of 21st century learning. Instruction and assessments seek to teach andevaluate knowledge and skills that generalize and can transfer to higher education and multiplework domains. They emphasize deep knowledge of core concepts and ideas within and acrossthe disciplines, along with analysis, synthesis, problem solving, communication, and criticalthinking. This kind of learning and teaching requires a focus on complex performances as well asthe testing of specific concepts, facts, and skills.3) Teachers are integrally involved in the development and scoring of assessments. Whilemany assessment components can and will be efficiently and effectively scored with computerassistance, teachers will also be involved in the interim/benchmark, formative, and summativeassessment systems so that they deeply understand and can teach to the standards.4) Assessments are structured to continuously improve teaching and learning. Assessment as,of, and for learning is designed to develop understanding of what learning standards are, whathigh-quality work looks like, what growth is occurring, and what is needed for student learning.This includes:1Darling-Hammond, L. (2010) Performance counts. Washington, DC: Council of Chief State School Officers.Empirically-based learning progressions visually and verbally articulate a hypothesis, or an anticipated path, of how studentlearning will typically move toward increased understanding over time with good instruction (Hess, Kurizaki, & Holt, 2009).The major concept of learning progressions is that students should progress through mathematics by building on what theyknow, moving toward some defined goals. While the structure of the mathematics shapes the pathways, there is not oneprescribed or optimal pathway through the content.29

developing assessments around learning progressions that allow teachers to see whatstudents know and can do on multiple dimensions of learning and to strategically supporttheir progress;using computer-based technologies to adapt assessments to student levels to moreeffectively measure what they know, so that teachers can target instruction more carefullyand can evaluate growth over time;creating opportunities for students and teachers to get feedback on student learningthroughout the school year, in forms that are actionable for improving success;providing curriculum-embedded assessments that offer models of good curriculum andassessment practice, enhance curriculum equity within and across schools, and allowteachers to see and evaluate student learning in ways that can feed back into instructionaland curriculum decisions; andallowing close examination of student work and moderated teacher scoring as sources ofongoing professional development.5) Assessment, reporting, and accountability systems provide useful information on multiplemeasures that is educative for all stakeholders. Reporting of assessment results is timely,specific, and vivid—offering specific information about areas of performance and examples ofstudent responses along with illustrative benchmarks, so that teachers and students can follow upwith targeted instruction. Multiple assessment opportunities (formative and interim/benchmark,as well as summative) offer ongoing information about learning and improvement. Reports tostakeholders beyond the school provide specific data, examples, and illustrations so thatadministrators and policymakers can more fully understand what students know in order to guidecurriculum and professional development decisions.Accessibility to Content Standards and Assessments: In addition to these five principles, SmarterBalanced is committed to ensuring that the content standards, summative assessments, teacherdeveloped performance tasks, and interim assessments adhere to the principles of accessibility forstudents with disabilities and English Language Learners. 3 It is important to understand that the purposeof accessibility is not to reduce the rigor of the Common Core State Standards, but rather to avoid thecreation of barriers for students who may need to demonstrate their knowledge and skills at the samelevel of rigor in different ways. Toward this end, each of the claims for the CCSS in Mathematics is3Accessibility in assessments refers to moving “beyond merely providing a way for students to participate in assessments

This content specification of the Common Core mathematics standards provides clear and rigorous focused assessment targets that will be used to translate the grade-level Common Core standards into content frameworks along a learning continuum, from which specifications for items, tasks, and test blueprints will be established.

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