Lining Up: The Relationship between the Common Core State Standards and Five Sets of Comparison Standards

Are the Common Core State Standards aligned with the standards states and others have developed over many years? Do they cover the same topic areas with the same emphases? To help answer these questions, the Educational Policy Improvement Center (EPIC) designed and conducted a study to determine the extent of correspondence (alignment) between the exit level Common Core standards and each of five sets of existing standards. These five sets of standards were selected because they were either identified as exemplary, were explicitly written at the college readiness level, or represented a rigorous instructional program focused on college readiness. The study asked three questions: 1. To what extent are the knowledge and skills found in the comparison standards the same as or different from what is described in the Common Core standards? (match) 2. What is the cognitive complexity level of the Common Core standards and to what extent are the matched comparison standards at a higher or lower level of cognitive complexity? (depth) 3. How broadly do the matched comparison standards cover the content of the Common Core standards? (breadth)

Lining Up: The Relationship between the Common Core State Standards and Five Sets of Comparison Standards David T. Conley Kathryn V. Drummond Alicia de Gonzalez Mary Seburn Odile Stout Jennifer Rooseboom Acknowledgements 5IF TUVEZ DPVME OPU IBWF PDDVSSFE XJUIPVU UIF SBUJOHT GSPN UIF FYQFSUT XIP DPNQMFUFE UIF BMJHONFOU BDUJWJUJFT 5IF TUVEZT FYUFSOBM SFWJFXFST QSPWJEFE WBMVBCMF JOTJHIUT PO BO FBSMZ WFSTJPO PG UIF SFQPSU 8F UIBOL 3JDI #SPXO +PIO ,FOEBMM BOE"OESFB7FOF[JBGPSUIFJSIFMQGVMDPNNFOUTBOERVFTUJPOT3JDI#SPXO HBWF BEEJUJPOBM NFUIPEPMPHJDBM GFFECBDL BOE BEWJDF EVSJOH QMBOOJOH QIBTFT PG the project and data collection. Additional EPIC staff made contributions beyond those listed as authors of the SFQPSU $IBSJT .D(BVHIZ IFMQFE XPSL PO UIF JOJUJBM EFTJHO BOE QSPQPTBM GPS UIF TUVEZ,BSJO,MJOHFSBOE"MJTPO3JDIDPMMBCPSBUFEUPFEJUBOEQSFQBSFUIFEPDVNFOU The Authors 5IJTSFQPSUJTCBTFEPOSFTFBSDIGVOEFEJOQBSUCZUIF#JMM.FMJOEB(BUFT'PVOEBUJPO5IFmOEJOHTBOE DPODMVTJPOTDPOUBJOFEXJUIJOBSFUIPTFPGUIFBVUIPSTBOEEPOPUOFDFTTBSJMZSFnFDUQPTJUJPOTPSQPMJDJFT of the Bill & Melinda Gates Foundation. Prepared and published by the Educational Policy Improvement Center. &UI"WFOVF &VHFOF 0SFHPO XXXFQJDPOMJOFPSH $PQZSJHIUª&EVDBUJPOBM1PMJDZ*NQSPWFNFOU$FOUFS"MMSJHIUTSFTFSWFE Alignment Study •  Executive Summary In June , the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Ofﬁcers (CCSSO) released the Common Core State Standards. The stated aim of the Common Core standards is to deﬁne the knowledge *O+VOF UIF/BUJPOBM(PWFSOPST"TTPDJBUJPO$FOUFSGPS#FTU 1SBDUJDFT /("$FOUFS BOEUIF$PVODJMPG$IJFG4UBUF4DIPPM0GmDFST $$440 SFMFBTFEUIF$PNNPO$PSF4UBUF4UBOEBSET1 The stated aim PGUIF$PNNPO$PSFTUBOEBSETJTUPEFmOFUIFLOPXMFEHFBOETLJMMT TUVEFOUTTIPVMEBDIJFWFJOPSEFSUPHSBEVBUFGSPNIJHITDIPPMSFBEZ UPTVDDFFEJOBXJEFSBOHFPGQPTUTFDPOEBSZFEVDBUJPOBMTFUUJOHT $PNNPO$PSF4UBUF4UBOEBSET*OJUJBUJWF B "TPG0DUPCFS TUBUFTBOEUIF%JTUSJDUPG$PMVNCJBIBEPGmDJBMMZ adopted the standards. This widespread potential implementation of the Common Core standards has led to interest by states and national PSHBOJ[BUJPOTSFHBSEJOHUIFSFMBUJPOTIJQCFUXFFOUIFTFOFXTUBOEBSET BOEFYJTUJOHTZTUFNTPGTUBOEBSET"SFUIF$PNNPO$PSFTUBOEBSET BMJHOFEXJUIUIFTUBOEBSETTUBUFTBOEPUIFSTIBWFEFWFMPQFEPWFS NBOZZFBST "SFUIFZBTDIBMMFOHJOH %PUIFZDPWFSUIFTBNF topic areas with the same emphases? Alig n m e nt To help answer these questions, the Educational Policy *NQSPWFNFOU$FOUFS &1*$ EFTJHOFEBOEDPOEVDUFEUIJT t licy Improvemen Po al n o ti ca u Ed The this study and conducted ed n ig es d r te Cen pondence extent of corres e th e in m er et to d level ween the exit (alignment) bet and each ate Standards St re Co n o m Com s. The sets isting standard ex f o ts se ve ﬁ of se they e selected becau er w s d ar d an st of lary state tiﬁed as exemp en id er th ei e wer en at the explicitly writt e er w s, d ar d stan presented a ess level, or re in ad re e g lle co focused on ional program ct ru st in s u ro o rig ess. college readin TUVEZUPEFUFSNJOFUIFFYUFOUPGDPSSFTQPOEFODF BMJHONFOU CFUXFFOUIFFYJUMFWFM$PNNPO$PSFTUBOEBSETBOEFBDIPG mWFTFUTPGFYJTUJOHTUBOEBSET5IFTFUTPGTUBOEBSETXFSF TFMFDUFECFDBVTFUIFZXFSFFJUIFSJEFOUJmFEBTFYFNQMBSZTUBUF TUBOEBSET XFSFFYQMJDJUMZXSJUUFOBUUIFDPMMFHFSFBEJOFTTMFWFM PSSFQSFTFOUFEBSJHPSPVTJOTUSVDUJPOBMQSPHSBNGPDVTFEPO DPMMFHFSFBEJOFTT5IFQVSQPTFXBTUPTFFJGUIF$PNNPO Core standards cover similar content, how broadly they cover UIFDPNQBSJTPOTUBOEBSET BOEIPXUIFDPHOJUJWFDIBMMFOHF MFWFMPGBMJHOFEDPOUFOUNBUDIFTVQ 5IFTUVEZBTLTUISFFRVFTUJPOTBCPVUUIF$PNNPO$PSF TUBOEBSETJO&OHMJTIMBOHVBHFBSUTBOEMJUFSBDZ BOE mathematics: XIBUJTEFTDSJCFEJOUIF$PNNPO$PSF4UBUF4UBOEBSET NBUDI 1 3FGFSSFEUPIFSFBGUFSBTUIF$PNNPO$PSFTUBOEBSET Executive Summary •  Study Overview 5FYBT 5IF 5FYBT $PMMFHF BOE $BSFFS 3FBEJOFTT4UBOEBSETJO&OHMJTIMBOHVBHFBSUT mathematics, and cross-disciplinary standards SFMFBTFEJO ,4645IF,OPXMFEHFBOE4LJMMTGPS6OJWFSTJUZ 4VDDFTT ,464 TUBOEBSET JO &OHMJTI and mathematics,2 EFWFMPQFE BT DPMMFHF QSFQBSBUPSZ TUBOEBSET CZ 4UBOEBSET GPS 4VDDFTT SFMFBTFEJO *# 5IF *OUFSOBUJPOBM #BDDBMBVSFBUF %JQMPNB 1SPHSBNNF &OHMJTI MBOHVBHF BSUT BOE mathematics standards, developed by EPIC, GPS *#T 1SPHSBNT PG 4UVEZ GPS UIoUI HSBEFT3 SFMFBTFEJO Comparison Standards Methodology The comparison standards selected for the study come 8FBEPQUFEBOEBEBQUFE$PPLBOE8JMNFTT GSPNUXPTUBUFTUIBUIBWFCFFOSFHBSEFEBTIBWJOHIJHI TUBOEBSETUPTUBOEBSETBMJHONFOUNFUIPEPMPHZUIBUJODMVEFT quality educational standards: California and Massachusetts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nFDUTUIF VOJWFSTJUZGBDVMUZJOUIFFBSMZTBOESFQSFTFOUUIFmSTUTFU TUBOEBSETJOUFSNTPGDPOUFOUBOEDPHOJUJWFDIBMMFOHF 8FCC PGTVDITUBOEBSET $POMFZ 'JOBMMZ UPDBQUVSFBNPSF )FSNBO 8FCC 4UBOEBSETUPTUBOEBSETBMJHONFOU international perspective, the standards from the International $PPL $PPL8JMNFT QSPWJEFTBNFBOTUP #BDDBMBVSFBUF *# %JQMPNB1SPHSBNNFBSFBMTPFYBNJOFE RVBOUJGZBOEFWBMVBUFUIFFYUFOUPGPWFSMBQCFUXFFOEJGGFSFOU 5IF*#%JQMPNB1SPHSBNNFJTPGGFSFEJODPVOUSJFTBOEJT TFUTPGTUBOEBSETJOUFSNTPGLOPXMFEHF TLJMMT BOEDPOUFOU 5PXIBUFYUFOUBSFUIFLOPXMFEHFBOETLJMMTGPVOEJOUIF 1. comparison standards the same as or different from what JTEFTDSJCFEJOUIF$PNNPO$PSFTUBOEBSET NBUDI 2. 8IBUJTUIFDPHOJUJWFDPNQMFYJUZMFWFMPGUIF$PNNPO $PSFTUBOEBSETBOEUPXIBUFYUFOUBSFUIFNBUDIFE DPNQBSJTPOTUBOEBSETBUBIJHIFSPSMPXFSMFWFMPG DPHOJUJWFDPNQMFYJUZ EFQUI 3. How broadly do the matched comparison standards cover UIFDPOUFOUPGUIF$PNNPO$PSFTUBOEBSET CSFBEUI CFDPNJOHJODSFBTJOHMZQPQVMBSJOUIF64 5ISFFBMJHONFOUJOEJDFTQSPWJEFUIFEBUBUPBOTXFSUIF TUVEZTUISFFSFTFBSDIRVFTUJPOT 5IFTQFDJmDDPNQBSJTPOTUBOEBSETBSFBTGPMMPXT $BMJGPSOJB5IF$POUFOU4UBOEBSETGPS$BMJGPSOJB 1VCMJD4DIPPMT GPSUIFUIoUIHSBEFCBOE JO &OHMJTI MBOHVBHF BSUT BOE GPS UIoUI HSBEFCBOEJONBUIFNBUJDT SFMFBTFEJO Massachusetts: The Massachusetts Curriculum 'SBNFXPSLT GPS UIF UIoUI HSBEF CBOE JO &OHMJTI MBOHVBHF BSUT SFMFBTFE JO BOE NBUIFNBUJDT SFMFBTFEJO 1. Categorical Concurrence:UIFFYUFOUPGPWFSMBQPSNBUDI between the comparison standards and the Common Core standards. 5IFTFEJEOPUJODMVEFUIF,OPXMFEHFBOE4LJMMT'PVOEBUJPOTXJUIJOUIF&OHMJTI and mathematics sections. 3 /PUFUIBUUIFTUVEZEJEOPUJODMVEFBOZDPOUFOUGSPN*#iPQUJPOTw5IFTFBSF additional required components, which each IB school selects. The number of PQUJPOTWBSJFTCZDPVSTFBOECZTVCKFDU5IF*#PQUJPOTEPOPUIBWFTQFDJmD standards. 2 Executive Summary •  2. 3. Depth of Knowledge Consistency: a comparison of contained in the Common Core standards. For ELA and DPHOJUJWFEFNBOEPGNBUDIFEDPOUFOUCFUXFFOUIF MJUFSBDZ PGTUSBOEBOBMZTFTTIPXTUSPOHDPWFSBHF'PS sets of comparison standards and the Common Core NBUIFNBUJDT mOEJOHTTVHHFTUUIBUDPNQBSJTPOTFUTTIPX standards. TUSPOHDPWFSBHFPGBMMDPODFQUVBMDBUFHPSZBOBMZTFT8IJMF Breadth of Coverage: how broadly matched comparison standards cover content elements of the Common Core standards. /JOF&OHMJTIMBOHVBHFBSUTFYQFSUTBOETFWFONBUIFNBUJDT every standard in the Common Core standards may not have a match with each and every set of comparison standards, the topics around which the Common Core standards are PSHBOJ[FEBSFSFnFDUFEJOUIFDPNQBSJTPOTUBOEBSETXJUIB IJHIEFHSFFPGGSFRVFODZ FYQFSUTDPNQSJTJOHTFDPOEBSZBOEQPTUTFDPOEBSZFEVDBUPST DPNQMFUFEUXPUBTLT&BDISBUFEUIF%FQUIPG,OPXMFEHF Conclusion PGFBDITUBOEBSEBOEUIFOEFUFSNJOFEUIFEFHSFFUPXIJDI 5IFCVTJOFTTPGBOBMZ[JOHBMJHONFOU DPHOJUJWFDIBMMFOHF BOE each comparison standard matched content in the Common DPWFSBHFCFUXFFOTFUTPGTUBOEBSETSFNBJOTBOBQQSPYJNBUF $PSFTUBOEBSET8IFOEFUFSNJOJOHNBUDI UIFZJEFOUJmFE BSU FWFOXIFOBNQMFDBSFJTHJWFOUPDPOUSPMMJOHWBSJBUJPOBOE up to three Common Core standards that corresponded with FOTVSJOHSFMJBCMFBOEWBMJESFTVMUT5IJTJTPOFPGUIFSFBTPOT a standard in a comparison set. The limit of three standards XFPGGFSmOEJOHTBUBIJHIMFWFMPGBHHSFHBUJPO&EVDBUPST GPMMPXTUIF8FCCQSPUPDPMBOEQIJMPTPQIZUIBUBMJHONFOU TIPVMECFBSJONJOEUIFPWFSBMMHPBMTPGUIF$PNNPO$PSF should concentrate only on content central to the statements. TUBOEBSETXIFODPOTJEFSJOHUIFNFDIBOJDTPGBMJHONFOU 5IPTFHPBMTBSFUPSBJTFUIFDIBMMFOHFMFWFMGPS64TUVEFOUT Findings to enable all students to pursue successful futures beyond 5IFPWFSBMMSFTVMUTPGUIFTUVEZTVHHFTUTVCTUBOUJBM IJHITDIPPM BOEUPFRVJQTUVEFOUTXJUIBTFUPGDPSF concurrence between the Common Core standards and the LOPXMFEHFBOETLJMMTUIBUFOBCMFUIFNUPCFBEBQUJWFMFBSOFST DPNQBSJTPOTUBOEBSET XJUITPNFXIBUHSFBUFSBMJHONFOUJO UISPVHIPVUUIFJSMJWFT mathematics than in ELA and literacy. For ELA and literacy, PGBOBMZTFTBUUIFTUSBOEMFWFMNFFUUIF$BUFHPSJDBM Concurrence criterion. For mathematics, all 25 analyses at the DPODFQUVBMDBUFHPSZMFWFMNFFUUIF$BUFHPSJDBM$PODVSSFODF criterion. "MJHONFOUJTBQSFMJNJOBSZBOEmSTUTUFQUPBDIJFWJOHUIF HPBMPGTUBOEBSETJNQMFNFOUBUJPO5IJTTUVEZPGGFSTJOJUJBM mOEJOHTSFHBSEJOHmWFTFUTPGDPNQBSJTPOTUBOEBSETUIBU BSFDPOTJEFSFESJHPSPVTBOEHPPEJOEJDBUPSTPGDPMMFHFBOE DBSFFSSFBEJOFTT8IJMFBEEJUJPOBMBOBMZTFTBUUIFJOEJWJEVBM 5IFmOEJOHTTVHHFTUHFOFSBMDPOTJTUFODZCFUXFFOUIF TUBUFMFWFMBSFOFFEFE UIFPWFSBMMmOEJOHTGSPNUIJTTUVEZ DPHOJUJWFDIBMMFOHFMFWFMPGUIF$PNNPO$PSFTUBOEBSET TVHHFTUBHFOFSBMMFWFMPGBHSFFNFOUCFUXFFOUIF$PNNPO BOEUIFmWFDPNQBSJTPOTUBOEBSETFUT.BUIFNBUJDTTIPXT $PSFTUBOEBSETBOEUIFDPNQBSJTPOTUBOEBSETSFHBSEJOH TPNFXIBUNPSFDPOTJTUFODZPGDPHOJUJWFDIBMMFOHFUIBOEP XIBUJTJNQPSUBOUGPSIJHITDIPPMTUVEFOUTUPLOPXBOE UIF&-"BOEMJUFSBDZTUBOEBSET*O&-"BOEMJUFSBDZ PG CFBCMFUPEPBOEUIFDPHOJUJWFMFWFMBUXIJDIUIFZOFFE strand-level analyses indicate that the comparison standard UPEFNPOTUSBUFLFZTLJMMTJO&OHMJTIMBOHVBHFBSUTBOE sets are at or above the level of the Common Core standards. NBUIFNBUJDTJOPSEFSUPCFSFBEZGPSDPMMFHFBOEDBSFFST 'PSNBUIFNBUJDT PGDPODFQUVBMDBUFHPSZMFWFMBOBMZTFT indicate that the comparison standard sets are at or above the MFWFMPGUIF$PNNPO$PSFTUBOEBSET0WFSBMM UIFTUBOEBSET from the comparison sets tend to cover the breadth of topics Executive Summary •  Table of Contents Executive Summary ....................................................................&4 4UVEZ0WFSWJFX .............................................................................................&4 'JOEJOHT .........................................................................................................&4 Conclusion.....................................................................................................&4 Chapter 1: Introduction .................................................................... 1 Chapter 2: Methodology .................................................................. %BUB$PMMFDUJPO ................................................................................................... 3BUFST ........................................................................................................... 3BUFS0SJFOUBUJPO .......................................................................................... 5 3BUFS1SPDFTT ............................................................................................... 5 3BUJOHPG$PNNPO$PSF4UBOEBSET ................................................................... 5 &OHMJTI-BOHVBHF"SUTBOE-JUFSBDZ ............................................................ 5 Mathematics ................................................................................................. 7 3BUJOHPG$PNQBSJTPO4UBOEBSET ....................................................................... 3BUFS3FMJBCJMJUZ ............................................................................................ %BUB"OBMZTJT.................................................................................................... 10 $BUFHPSJDBM$PODVSSFODF ........................................................................... 10 %FQUIPG,OPXMFEHF$POTJTUFODZ.............................................................. 10 #SFBEUIPG$PWFSBHF .................................................................................. 11 Chapter 3: Results for English Language Arts and Literacy ............................................................................................ 12 Match................................................................................................................ 12 0WFSBMM.BUDIPG$PNQBSJTPO4UBOEBSETUPUIF$PNNPO $PSF4UBOEBSET .......................................................................................... 12 .BUDIGPS&BDI$PNQBSJTPO4FUUPUIF$PNNPO$PSF 4UBOEBSET$BUFHPSJDBM$PODVSSFODF4UBUJTUJD ............................................ 13 %FQUIPG,OPXMFEHF......................................................................................... 15 3BUJOHGPS$PNNPO$PSF4UBOEBSET .......................................................... 15 %0,$POTJTUFODZPG&BDI$PNQBSJTPO4FUUPUIF $PNNPO$PSF4UBOEBSET........................................................................... 15 #SFBEUIPG$PWFSBHF ........................................................................................ 17 Chapter 4: Results for Mathematics .................................................. Match................................................................................................................ 0WFSBMM.BUDIPG$PNQBSJTPO4UBOEBSETUPUIF$PNNPO $PSF4UBOEBSET .......................................................................................... .BUDIGPS&BDI$PNQBSJTPO4FUUPUIF$PNNPO$PSF4UBOEBSET ............ 21 $BUFHPSJDBM$PODVSSFODF4UBUJTUJD ............................................................. 21 %FQUIPG,OPXMFEHF......................................................................................... 21 3BUJOHTGPS$PNNPO$PSF4UBOEBSET ........................................................ 22 %0,$POTJTUFODZPG&BDI$PNQBSJTPO4FUUPUIF$PNNPO $PSF4UBOEBSET .......................................................................................... 23 #SFBEUIPG$PWFSBHF ........................................................................................ Table of Contents • i Table of Contents Chapter 5: Summary and Discussion ............................................... 25 $MPTJOH/PUFGSPNUIF"VUIPST ......................................................................... 27 References .............................................................................................. Appendix A: Description of the Depth of Knowledge Calculation .............................................................................................. 32 Appendix B: Common Core Standards ............................................ 33 Appendix C: Results by Individual Comparison Standards ................................................................................................ 52 $BMJGPSOJB4UBOEBSET ......................................................................................... 52 &OHMJTI-BOHVBHF"SUTBOE-JUFSBDZ'JOEJOHTGPSUIF$BMJGPSOJB 4UBOEBSET ......................................................................................................... 52 Match ......................................................................................................... 52 #SFBEUIPG$PWFSBHF .................................................................................. 53 %FQUIPG,OPXMFEHF .................................................................................. 53 .BUIFNBUJDT'JOEJOHTGPSUIF$BMJGPSOJB4UBOEBSET ......................................... Match ......................................................................................................... #SFBEUIPG$PWFSBHF .................................................................................. 55 %FQUIPG,OPXMFEHF .................................................................................. 55 .BTTBDIVTFUUT4UBOEBSET ................................................................................ &OHMJTI-BOHVBHF"SUTBOE-JUFSBDZ'JOEJOHTGPSUIF .BTTBDIVTFUUT4UBOEBSET ................................................................................ Match ......................................................................................................... #SFBEUIPG$PWFSBHF .................................................................................. 57 %FQUIPG,OPXMFEHF .................................................................................. 57 .BUIFNBUJDT'JOEJOHTGPSUIF.BTTBDIVTFUUT4UBOEBSET ................................ Match ......................................................................................................... #SFBEUIPG$PWFSBHF .................................................................................. %FQUIPG,OPXMFEHF .................................................................................. 5FYBT$PMMFHFBOE$BSFFS3FBEJOFTT4UBOEBSET ............................................ &OHMJTI-BOHVBHF"SUTBOE-JUFSBDZ'JOEJOHTGPSUIF 5FYBT$PMMFHFBOE$BSFFS3FBEJOFTT4UBOEBSET ............................................ Match ......................................................................................................... #SFBEUIPG$PWFSBHF .................................................................................. %FQUIPG,OPXMFEHF .................................................................................. .BUIFNBUJDT'JOEJOHTGPSUIF5FYBT$PMMFHFBOE$BSFFS 3FBEJOFTT4UBOEBSET ....................................................................................... Match ......................................................................................................... #SFBEUIPG$PWFSBHF .................................................................................. %FQUIPG,OPXMFEHF .................................................................................. ,OPXMFEHFBOE4LJMMTGPS6OJWFSTJUZ4VDDFTT4UBOEBSET ................................. &OHMJTI-BOHVBHF"SUTBOE-JUFSBDZ'JOEJOHTGPSUIF ,OPXMFEHFBOE4LJMMTGPS6OJWFSTJUZ4VDDFTT4UBOEBSET ................................. Match ......................................................................................................... Table of Contents • ii Table of Contents #SFBEUIPG$PWFSBHF .................................................................................. %FQUIPG,OPXMFEHF .................................................................................. .BUIFNBUJDT'JOEJOHTGPSUIF,OPXMFEHFBOE4LJMMTGPS 6OJWFSTJUZ4VDDFTT4UBOEBSET ......................................................................... Match ......................................................................................................... #SFBEUIPG$PWFSBHF .................................................................................. %FQUIPG,OPXMFEHF .................................................................................. *OUFSOBUJPOBM#BDDBMBVSFBUF4UBOEBSET ............................................................ &OHMJTI-BOHVBHF"SUTBOE-JUFSBDZ'JOEJOHTGPSUIF *OUFSOBUJPOBM#BDDBMBVSFBUF4UBOEBSET ............................................................ Match ......................................................................................................... #SFBEUIPG$PWFSBHF .................................................................................. %FQUIPG,OPXMFEHF .................................................................................. .BUIFNBUJDT'JOEJOHTGPSUIF*OUFSOBUJPOBM#BDDBMBVSFBUF4UBOEBSET ............ 70 Match ......................................................................................................... 70 #SFBEUIPG$PWFSBHF .................................................................................. 71 %FQUIPG,OPXMFEHF .................................................................................. 71 Appendix D: Alignment Matches for Common &RUH&RQWHQWVSHFLÀF$UHDV ............................................................... 72 /VNCFSPG"MJHONFOU.BUDIFTGPS$PNNPO$PSF&OHMJTI-BOHVBHF "SUTBOE-JUFSBDZ5PQJDT CZ$PNQBSJTPO4UBOEBSE4FU .................................. 72 /VNCFSPG"MJHONFOU.BUDIFTGPS$PNNPO$PSF$MVTUFST CZ $PNQBSJTPO4UBOEBSE4FUGPS.BUIFNBUJDT ..................................................... 75 Table of Contents • iii Chapter  4UBUFT BSF DPODFSOFE BCPVU UIF SJHPS PG UIF $PNNPO $PSF 4UBUF4UBOEBSETBOEUIFSFMBUJPOTIJQCFUXFFOUIJTOFXTZTUFN PGTUBOEBSETBOEFYJTUJOHTUBOEBSET QBSUJDVMBSMZBUUIFFYJU MFWFMGSPNIJHITDIPPM5IF&EVDBUJPOBM1PMJDZ*NQSPWFNFOU $FOUFS &1*$ UIFSFGPSF EFTJHOFE BOE DPOEVDUFE UIF DVSSFOU TUVEZ UP EFUFSNJOF UIF FYUFOU PG DPSSFTQPOEFODF BMJHONFOU CFUXFFO UIF FYJU MFWFM $PNNPO $PSF 4UBUF 4UBOEBSET BOE FBDI PG mWF TFUT PG FYJTUJOH TUBOEBSET 5IF sets of standards were selected because they were either JEFOUJmFE BT FYFNQMBSZ TUBUF TUBOEBSET XFSF FYQMJDJUMZ XSJUUFO BU UIF DPMMFHF SFBEJOFTT MFWFM PS SFQSFTFOUFE B SJHPSPVTJOTUSVDUJPOBMQSPHSBNGPDVTFEPODPMMFHFSFBEJOFTT 5IFQVSQPTFXBTUPTFFJGUIF$PNNPO$PSF4UBUF4UBOEBSET DPWFSFETJNJMBSDPOUFOUJGTP IPXCSPBEMZUIFZDPWFSFEUIF DPNQBSJTPOTUBOEBSETBOEXIFUIFSUIFDPHOJUJWFDIBMMFOHF MFWFMPGBMJHOFEDPOUFOUXBTDPNQBSBCMF The study addressed three research questions for each PG UIF UXP TVCKFDU BSFBT GPS XIJDI $PNNPO $PSF 4UBUF 4UBOEBSETIBWFCFFOEFWFMPQFEoOBNFMZ &OHMJTIMBOHVBHF arts and literacy, and mathematics. These three questions QSPWJEF JOGPSNBUJPO PO XIFUIFS UIF mWF TFUT PG DPNQBSJTPO TUBOEBSETSFnFDUTJNJMBSSFRVJSFNFOUTBTUIF$PNNPO$PSF 4UBUF4UBOEBSET DBMMFE$PNNPO$PSFTUBOEBSETUISPVHIPVU UIFSFTUPGUIJTSFQPSU Re se s n o i t s e u Q a rch stions rch que the a e s e r hether ee r w h t n e o h T mation dards e infor d i v o on stan r s i p r a p e m ts as th s of co t n e e s m e e v r i ﬁ requ rds. similar Standa e reﬂect t a t S e on Cor Comm | Introduction The research questions are as follows: 1. 5PXIBUFYUFOUBSFUIFLOPXMFEHFBOETLJMMTGPVOEJO the comparison standards the same as or different from what is described in the Common Core TUBOEBSET NBUDI 2. 8IBU JT UIF DPHOJUJWF DPNQMFYJUZ MFWFM PG UIF $PNNPO$PSFTUBOEBSETBOEUPXIBUFYUFOUBSFUIF NBUDIFEDPNQBSJTPOTUBOEBSETBUBIJHIFSPSMPXFS MFWFMPGDPHOJUJWFDPNQMFYJUZ EFQUI 3. How broadly do the matched comparison standards cover the content of the Common Core standards? CSFBEUI The comparison standards included sets of standards from UXPTUBUFTUIBUIBWFCFFOSFHBSEFEBTMFBEFSTJOFEVDBUJPOBM standards: California and Massachusetts (Achieve, Inc., 5IF 'PSEIBN 'PVOEBUJPO BXBSEFE UIF $BMJGPSOJB TUBOEBSET B SBSF " HSBEF GPS CPUI &OHMJTI MBOHVBHF BSUT and mathematics in its 2005 and 2010 analyses (Carmichael FU BM 'PS .BTTBDIVTFUUT UIF 'PSEIBN 'PVOEBUJPO HBWF UIF &OHMJTI MBOHVBHF BSUT TUBUF TUBOEBSET " HSBEFT JO JUT BOE BOBMZTFT BOE HBWF UIF NBUIFNBUJDT standards a B+ in 2005 and an A in 2010 (Carmichael et BM "EEJUJPOBMMZ TUVEFOUT GSPN .BTTBDIVTFUUT QFSGPSN BNPOH UIF UPQ TUBUFT PO UIF /BUJPOBM "TTFTTNFOU PG &EVDBUJPOBM 1FSGPSNBODF -FF (SJHH %JPO -FF (SJHH%POBIVF /BUJPOBM$FOUFSGPS&EVDBUJPO 4UBUJTUJDT B C 8FBMTPDPNQBSFEUIF$PNNPO$PSFTUBOEBSETUPUXPTFUT PGDPMMFHFBOEDBSFFSSFBEJOFTTTUBOEBSETPOFGSPNBTUBUF 5FYBT BOE BOPUIFS UIBU IBT CFFO VTFE CSPBEMZ EVSJOH UIF QBTU FJHIU ZFBST o UIF ,OPXMFEHF BOE 4LJMMT GPS 6OJWFSTJUZ 4VDDFTT5IF5FYBT$PMMFHFBOE$BSFFS3FBEJOFTT4UBOEBSET BSF B DPMMFDUJPO PG DPNQFUFODJFT BOE TLJMMT UIBU TFDPOEBSZ students must possess to succeed in postsecondary FEVDBUJPO 5IFZ BSF JOUFOEFE UP DPNQMFNFOU FYJTUJOH TUBUF IJHITDIPPMTUBOEBSET BOEDSFBUFBDVMUVSFPGDPMMFHFBOE DBSFFSSFBEJOFTT 5FYBT&EVDBUJPO"HFODZ 1VCMJTIFE JO UIF ,OPXMFEHF BOE 4LJMMT GPS 6OJWFSTJUZ 4VDDFTT ,464 TUBOEBSETSFnFDUUIFDPOUSJCVUJPOTPGNPSFUIBO GBDVMUZ BOE TUBGG GSPN MFBEJOH SFTFBSDI VOJWFSTJUJFT 5IF GBDVMUZJEFOUJmFELOPXMFEHFBOETLJMMTUIBUTUVEFOUTOFFEUP succeed in entry-level courses at their institutions. Multiple peer reviews were used to hone the standards and ensure Chapter One •  Chapter  | Introduction UIFJSWBMJEJUZ $POMFZ 5IF,464TUBOEBSETIBWFCFFO FOEPSTFECZSFTFBSDIVOJWFSTJUJFTBTSFnFDUJOHFYQFDUBUJPOT at the institutions for students in entry-level courses (Conley 8BSE BOE IBWF CFFO VTFE CZ UIF $PMMFHF #PBSE as a reference in the development of its assessments and TUBOEBSET #SPXO$POMFZ Finally, we included a set of international standards from UIF *OUFSOBUJPOBM #BDDBMBVSFBUF *# %JQMPNB 1SPHSBNNF %FTJHOFE UP CF BDBEFNJDBMMZ DIBMMFOHJOH QSFQBSBUJPO GPS DPMMFHF XPSL UIF *# QSPHSBN DPNQSJTFT TJY DPVSTFT UBLFO PWFS UIF mOBM UXP ZFBST PG IJHI TDIPPM *O JUT BOBMZTJT PG UIF *# UIF'PSEIBN'PVOEBUJPOHBWFUIF*#-BOHVBHF"&OHMJTI 4UBOEBSE-FWFM 4- DPVSTFBHSBEFPG# CBTFEPODPOUFOU SJHPS BOEDMBSJUZ #ZSE &MMJOHUPO (SPTT +BHP 4UFSO 3FWJFXFST EFFNFE UIBU UIF DPVSTF SFRVJSFT TUVEFOUT UP CF iXFMM HSPVOEFE JO MJUFSBSZ HFOSFTw Q 5IFZ HBWF UIF .BUI 4UBOEBSE -FWFM DPVSTF B # QSBJTJOH JO QBSUJDVMBS UIF GSFFSFTQPOTFFYBNTBTiFYDFMMFOU SFRVJSJOHXBZCFZPOEUIF OPSNBM IJHI TDIPPM GBSFw Q 5IF DPVSTFT BSF LOPXO UP FNQIBTJ[FUIFBQQMJDBUJPOPGTUVEFOUMFBSOJOHTPUIBUTUVEFOUT USBOTGFS UIFJS MFBSOJOH GSPN POF DPOUFYU UP BOPUIFS 1IJMMJQT 8POH )JTUPSJDBMMZ UIF *# %JQMPNB 1SPHSBNNF IBT SFMJFEPOUIFBJNTBOEHPBMTTQFDJmFEJODPVSTFEPDVNFOUTUP DPOWFZSFRVJSFEDPOUFOU3FMBUJWFMZSFDFOUMZ GPSNBMTUBOEBSET XFSF EFWFMPQFE $POMFZ 8BSE 5IFTF TUBOEBSET serve as the reference point for this analysis. In this study, the Common Core standards are the reference QPJOUUPXIJDIUIFPUIFSmWFTFUTPGTUBOEBSETBSFDPNQBSFE BOEXFUIFSFGPSFSFGFSUPUIFPUIFSmWFTFUTPGTUBOEBSETBTUIF DPNQBSJTPOTUBOEBSET 0VSQSJNBSZJOUFSFTUXBTUPBOBMZ[FUIF Common Core standards, particularly as a companion piece UP BOPUIFS &1*$ TUVEZ UIBU FYQMPSFE UIF FYUFOU UP XIJDI UIF $PNNPO$PSFTUBOEBSETBSFSFBTPOBCMFDPMMFHFBOEDBSFFS QSFQBSBUPSZTUBOEBSET TFF$POMFZ %SVNNPOE EF(PO[BMF[ 3PPTFCPPN 4UPVU XXXFQJDPOMJOFPSH 8FVTFEUIF $PNNPO$PSFTUBOEBSETBTUIFSFGFSFODFQPJOUGPSNBUDIJOH UP FYJTUJOH TUBOEBSET JO PSEFS UP JEFOUJGZ DPOTJTUFOU QBUUFSOT PGBMJHONFOUPSNJTBMJHONFOUBDSPTTTUBOEBSETFUT 'JOEJOHT GPSUIFJOEJWJEVBMTUVEJFTEPBQQFBSUISPVHIPVUUIFSFQPSUBOE JO UIF BQQFOEJDFT IPXFWFS UIF $PNNPO $PSF TUBOEBSET XFSFDPOTJTUFOUMZUIFSFGFSFODFQPJOU 8FEJEOPUDPOEVDUUIF SFWFSTF BOBMZTJT VTJOH FBDI TFU PG FYUFSOBM TUBOEBSET BT B SFGFSFODFGPSNBUDIJOHUPUIF$PNNPO$PSF5IFJOUFOUXBT OPU UP QSPWJEF JOEJWJEVBM BMJHONFOU QSPmMFT GPS B OVNCFS PG TUBOEBSET TFUT UP UIF $PNNPO $PSF 8F VOEFSTUBOE NBOZ TUBUFT BSF FOHBHJOH JO UIJT UZQF PG BOBMZTJT BOE XF EJE OPU want to duplicate such efforts. M et h od We used Cook and W () conception ilmes’s of standardsto-standards alignm ent – a combination of lin king (match between standard s) and correspondence (d epth and breadth). 8FVTFE$PPLBOE8JMNFTT DPODFQUJPOPGTUBOEBSET UPTUBOEBSET BMJHONFOU o B DPNCJOBUJPO PG MJOLJOH NBUDI CFUXFFO TUBOEBSET BOE DPSSFTQPOEFODF EFQUI BOE CSFBEUI CBTFE PO 8FCCT XJEFMZ FNQMPZFE UFTUJUFNUP TUBOEBSET NFUIPEPMPHZ B 8F VTFE UIF 8FC "MJHONFOU 5PPM 8"5 DSFBUFE CZ 8FCC GPS BOBMZTJT &YQFSUTSBUFEBMMUIFTUBOEBSETTFUTJOUFSNTPGUIFJSDPHOJUJWF DPNQMFYJUZ BOE UIFO GPMMPXJOH 8FCCT NFUIPEPMPHZ 8FCC C 3PBDI &MMJPU 8FCC $PPL NBUDIFE up to three standards from Common Core standards to each standard in the comparison standard sets. This method differs from other standards-to-standards methods in two important ways. First, the method we used MJNJUTSBUFSTUPTQFDJGZJOHUISFFNBUDIJOHTUBUFNFOUT XIFSFBT PUIFS NFUIPET BMMPX BO VOMJNJUFE OVNCFS PG NBUDIFT FH 3PMGVT %FDLFS #SJUF (SFHPSZ 5JNNT 4DIOFJEFS -FF 3PMGVT 8FCC PSJHJOBMMZ DSFBUFE UIJT MJNJUBUJPO so that reviewers would concentrate on only the central DPOUFOU LOPXMFEHF FYQSFTTFE JO B TUBUFNFOU 8FCC 4FDPOE UIF 8FCC NFUIPEPMPHZ BOE 8"5 UPPM BTTJHOT FRVBM JNQPSUBODF UP FWFSZ TFU PG NBUDIFT 5IFSFGPSF 8FCC FNQIBTJ[FTUIBUXIFONBLJOHBNBUDI SBUFSTTIPVMEFOTVSF UIBU UIF DPNQBSJTPO TUBUFNFOU UBSHFUT JO GVMM UIF SFGFSFODF TUBUFNFOU 8FCC "MU &MZ 7FTQFSNBO *OTIPSU UIF Chapter One 2 Chapter  | Introduction NFUIPEPMPHZEPFTOPUNBLFVTFPGQBSUJBMNBUDIFTUIFXBZ UIBUPUIFSBMJHONFOUTUVEJFTEP FH 3PMGIVT $PPL #SJUF )BSUNBO "T3PMGIVT $PPL #SJUF BOE)BSUNBO QPJOUPVU BXFBLOFTTPGUIFQBSUJBMNBUDINFUIPEPMPHZJTUIBU JOEJDBUJPOPGQBSUJBMNBUDIJOHDBONFBOUIBUUIFDPNQBSJTPO standard matches just one element of a multidimensional reference standard or that it matches all but one of the many FMFNFOUT5IVT XFEFDJEFEPOBMFTTBNCJHVPVTBOENPSF DPOTFSWBUJWFEFmOJUJPOPGNBUDIJOH 8FVTFUISFFNFUSJDTNBUDI EFQUI BOECSFBEUI UPBOTXFS UIF UISFF SFTFBSDI RVFTUJPOT 5P BOTXFS UIF mSTU SFTFBSDI RVFTUJPO XF MPPL BU UIF NFBTVSF PG NBUDI $BUFHPSJDBM $PODVSSFODF UP EFUFSNJOF UIF FYUFOU UP XIJDI DPOUFOU JT consistent across the Common Core standards and each set of comparison standards. To answer the second research RVFTUJPO XF mSTU EFUFSNJOF UIF DPHOJUJWF EFNBOE PG UIF Common Core standards and the comparison standards by NFBOTPGUIF%FQUIPG,OPXMFEHFSBUJOH5IFO XFDPNQBSF DPHOJUJWF EFNBOE UP HBVHF XIFSF DPHOJUJWF DIBMMFOHF JT IJHIFS MPXFS PS UIF TBNF VTJOH UIF %FQUI PG ,OPXMFEHF Consistency statistic for content areas that match with the $PNNPO $PSF TUBOEBSET 8F BEESFTT UIF UIJSE SFTFBSDI RVFTUJPOVTJOHUIF#SFBEUIPG$PWFSBHFNFUSJDUIBUBTDFSUBJOT UIF FYUFOU UP XIJDI UIF DPNQBSJTPO TUBOEBSET UIBU NBUDI Common Core standards cover a similar scope of content. M et rics Three metrics: match , depth, and breadth were used to answer the three rese arch questions. *O$IBQUFS XFEFTDSJCFUIFNFUIPEPMPHZBOEQSPWJEFBO overview of the standards that were used in the study. Chapter QSFTFOUT UIF SFTVMUT PG BMJHONFOU PG UIF $PNNPO $PSF TUBOEBSETGPS&OHMJTIMBOHVBHFBSUTBOEMJUFSBDZ BOE$IBQUFS QSFTFOUT SFTVMUT GPS NBUIFNBUJDT $IBQUFS EJTDVTTFT TUVEZmOEJOHTBOEJNQMJDBUJPOT"QQFOEJY"QSPWJEFTNPSF JOGPSNBUJPOBCPVUUIFNFUIPEPMPHZUIBUXBTVTFE"QQFOEJY B lists the Common Core standards and summary information BCPVUUIFFYQFSUSBUJOHT"QQFOEJDFT$BOE%QSPWJEFNPSF EFUBJMFEJOGPSNBUJPOPOUIFmOEJOHTGPSFBDITFUPGDPNQBSJTPO TUBOEBSET -FOHUIJFS BOE NPSF EFUBJMFE JOGPSNBUJPO BCPVU each set of comparison standards and precise matches with the Common Core standards is provided under separate DPWFS JO UIF 5FDIOJDBM 4VQQMFNFOU IUUQTXXXFQJDPOMJOF PSHmMFTQEG-JOJOH6Q5FDIOJDBM4VQQMFNFOUQEG Chapter One 3 Chapter  8F NFBTVSFE BMJHONFOU VTJOH B NPEJmFE WFSTJPO PG UIF 8FCC BMJHONFOU QSPUPDPM 5IF 8FCC NFUIPEPMPHZ B IBT CFFO XJEFMZ VTFE UP BTTFTT BMJHONFOU of assessments to standards. The approach relies on VTJOH QBOFMT PG FYQFSUT UP FYBNJOF DPOUFOU BOE DPHOJUJWF processes in assessments and standards and then, based POUIPTFFYQFSUTSBUJOHT DBMDVMBUJOHTUBUJTUJDTPGBMJHONFOU These statistics demonstrate how closely the assessment SFnFDUT UIF TUBOEBSET 8FCC )FSNBO 8FCC 0WFSUJNF SFTFBSDIFSTIBWFVTFENPEJmFEWFSTJPOTPGUIF 8FCC NFUIPE XJUI EJGGFSFOU WBSJBUJPOT PG BMJHONFOU JOEJDFT 3PUINBO 8JYTPO 'JTL %VUSP .D%BOJFM 5IF BQQSPBDI IBT BMTP CFFO NPEJmFE UP EFUFSNJOF TUBOEBSETUPTUBOEBSET BMJHONFOU $PPL $PPL 8JMNFT 4UBOEBSETUPTUBOEBSET BMJHONFOU QSPWJEFT B NFBOT UP RVBOUJGZ BOE FWBMVBUF UIF FYUFOU PG PWFSMBQ CFUXFFOEJGGFSFOUTFUTPGTUBOEBSETJOUFSNTPGLOPXMFEHF TLJMMT BOE DPOUFOU "MJHONFOU NFUIPEPMPHZ BMTP BMMPXT GPS DPNQBSJTPO CFUXFFO TUBOEBSET JO UFSNT PG UIF DPHOJUJWF demand of content and in terms of the breadth of overlap. In UIFDVSSFOUTUVEZ BMJHONFOUJODMVEFTUISFFJOEJDFT 1. Categorical Concurrence:UIFFYUFOUPGPWFSMBQPS match between the comparison standards and the Common Core standards. 2. Depth of Knowledge Consistency: a comparison PGDPHOJUJWFEFNBOEPGNBUDIFEDPOUFOUCFUXFFO the sets of comparison standards and the Common Core standards. 3. Breadth of Coverage: how broadly matched comparison standards cover content elements of the Common Core standards. #FMPX XF EJTDVTT UIF QSPDFTT GPS DPMMFDUJOH UIF SFRVJTJUF EBUBGPSBMJHONFOUBOEUIFOFYQMBJOUIFBMJHONFOUTUBUJTUJDT and data analysis. Data Collection 8FGPMMPXFEUIFUSBJOJOHBOEEBUBDPMMFDUJPOQSPDFTTFTMBJE PVUCZ8FCCFUBM Raters 3BUFST XFSF SFDSVJUFE GSPN B QPPM PG FYQFSUT XIP IBE FYQFSJFODF XJUI TUBOEBSET BMJHONFOU 3FQSFTFOUBUJPO GSPN OBUJPOBMFEVDBUJPOBMPSHBOJ[BUJPOTXBTBMTPTPVHIUJOWJUBUJPOT | Methodology XFSFFYUFOEFEUPUIF*OUFSOBUJPOBM3FBEJOH"TTPDJBUJPOBOE UIF/BUJPOBM$PVODJMPG5FBDIFSTPG.BUIFNBUJDT " UPUBM PG SBUFST QBSUJDJQBUFE JODMVEJOH OJOF &OHMJTI MBOHVBHF BSUT &-" FYQFSUT BOE TFWFO NBUIFNBUJDT FYQFSUT5IFSBUFSTDPNQSJTFEBNJYPGTFDPOEBSZBOEQPTU TFDPOEBSZFEVDBUPST&BDITVCKFDUBSFBIBEBHSPVQMFBEFS 5IJT JOEJWJEVBM IBE NPSF TUBOEBSET BMJHONFOU FYQFSJFODF than other raters in the subject area and helped facilitate the HSPVQ Rater Orientation &BDI HSPVQ MFBEFS QBSUJDJQBUFE JO B XFC DPOGFSFODF PSJFOUBUJPO TFTTJPO QSJPS UP UIF GVMM HSPVQ TFTTJPOT &1*$ SFTFBSDIFST FYQMBJOFE UIF PWFSBMM BMJHONFOU QSPDFTT BOE TQFDJmDMFBEFSSFTQPOTJCJMJUJFT5IFOEVSJOHHSPVQTFTTJPOT UIF MFBEFST FYQMBJOFE UIF %FQUI PG ,OPXMFEHF %0, SBUJOHTBOEDPEJOHQSPDFTTBOEHVJEFEPUIFSSBUFSTUISPVHI BMJHONFOU FYBNQMFT VOEFS UIF PWFSBMM TVQFSWJTJPO PG &1*$ researchers. &BDIHSPVQ &-"BOENBUIFNBUJDT QBSUJDJQBUFEJOUXPXFC DPOGFSFODFT %VSJOH UIF mSTU TFTTJPO &1*$ SFTFBSDIFST FYQMBJOFE UIF TUBOEBSETUPTUBOEBSET BMJHONFOU QSPDFTT BOE EFmOFE UFSNJOPMPHZ 6OEFS HVJEBODF GSPN UIF HSPVQ MFBEFS UIF SBUFST EFWFMPQFE BO JOJUJBM VOEFSTUBOEJOH PG %0,DBUFHPSJFT FYQMBJOFECFMPX BOEFOHBHFEJOQSBDUJDF SBUJOHT"UUIFFOEPGUIFmSTUUSBJOJOH FBDIHSPVQXBTHJWFO UIF UBTL PG BTTJHOJOH B %0, SBUJOH UP FBDI $PNNPO $PSF IJHI TDIPPM NBUIFNBUJDT TUBOEBSE PS FBDI $PNNPO $PSF TUBOEBSEGPS&-"BOEMJUFSBDZGPSHSBEFTo %VSJOH UIF TFDPOE TFTTJPO SBUFST BHSFFE VQPO B TJOHMF %0, SBUJOH GPS FBDI $PNNPO $PSF TUBOEBSE 5IJT XBT BDDPNQMJTIFE CZ QSFTFOUJOH BMM SBUFST %0, MFWFMT GPS FBDI$PNNPO$PSFTUBOEBSEUPUIFFOUJSFHSPVQPGSBUFST 4UBOEBSET XJUIPVU B DMFBS NBKPSJUZ SBUJOH XFSF EJTDVTTFE until consensus was reached. In the second part of the call, SBUFSTEJTDVTTFEBOEDPNQMFUFEQSBDUJDFFYBNQMFTPGIPX to determine whether to match comparison standards and Common Core standards. They developed decision rules EFTJHOFE UP QSPWJEF DMBSJUZ JO TJUVBUJPOT XIFSF BNCJHVJUZ PS DPOGVTJPO DPVME BSJTF JO UIF SBUJOHT QSPDFTT "T 8FCC C QPJOUT PVU BMUIPVHI UIF USBJOJOH QSPDFTT JOWPMWFT DBMJCSBUJPO JU JT OPU EFTJHOFE GPS SBUFST UP SFBDI FYBDU BHSFFNFOU3FWJFXFSTSFTQPOTFTBSFBWFSBHFE XIJDIIFMQT BDDPVOUGPSEJGGFSFODFTJODPEJOH 8FCC "EEJUJPOBMMZ Chapter Two •  Chapter  | Methodology WBSJBODFBNPOHSFWJFXFSTSFnFDUTWBMJEEJGGFSFODFTPGPQJOJPO SFTVMUJOH GSPN MBDL PG DMBSJUZ JO TUBOEBSET TUBUFNFOUT 8FCC C standards refer to this level as a cluster 3BUJOH EBUB XFSF FOUFSFEJOUPUIF8FC"MJHONFOU5PPM 8"5 GPSBOBMZTJT/FYU XF QSFTFOU NPSF TQFDJmD JOGPSNBUJPO BCPVU UIF OVNCFS PG statements that were rated for each set of standards. Rating Process 'PS FBDI PG UIF mWF TFUT PG DPNQBSJTPO TUBOEBSET SBUFST JOEFQFOEFOUMZ DPNQMFUFE UXP UBTLT 5IFZ SBUFE UIF %0, PG FBDI DPNQBSJTPO TUBOEBSE BOE UIFO EFUFSNJOFE UIF EFHSFF to which each comparison standard matched content in UIF $PNNPO $PSF TUBOEBSET 8IFO EFUFSNJOJOH NBUDI UIFZ JEFOUJmFE VQ UP UISFF $PNNPO $PSF TUBOEBSET UIBU corresponded with a standard in a comparison set. The limit PGUISFFTUBOEBSETGPMMPXTUIF8FCCQSPUPDPMBOEQIJMPTPQIZ UIBU BMJHONFOU TIPVME DPODFOUSBUF POMZ PO DPOUFOU DFOUSBM UP the statements. If raters found more than three statements that DPVME NBUDI UIFZ VTFE QSPGFTTJPOBM KVEHNFOU UP TFMFDU UIF UISFF CFTU NBUDIFT 3BUFST XFSF OPU BMMPXFE UP NBLF QBSUJBM NBUDIFTUIBUJT UIFDPNQBSJTPOTUBOEBSEIBEUPNBUDIUIFGVMM Common Core standard. This meant that a broader comparison standard could be matched to a more narrow Common Core standard, but the reverse could not occur because the content in the Common Core standard would not be fully addressed. If raters found that every standard within a particular Common Core subarea corresponded with comparison standards, then they rated at the superordinate level. This was the only time that more than three standards could be matched. For ease of reference, we call this level a topic for the Common Core ELA and literacy standards. The Common Core mathematics Rating of Common Core Standards English Language Arts and Literacy 5IF $PNNPO $PSF &OHMJTI MBOHVBHF BSUT &-" BOE MJUFSBDZ TUBOEBSET GPS HSBEFT o BSF PSHBOJ[FE JOUP strands, anchor standards, and standards8FVTFUIFUFSNstrand to SFGFS UP FBDI PG UIF FJHIU HSPVQT PG SFMBUFE TUBOEBSET &BDI TUSBOE JT CBTFE PO TJY UP UFO TUBUFNFOUT DBMMFE $PMMFHF BOE $BSFFS 3FBEJOFTT $$3 "ODIPS 4UBOEBSET 5IF $$3 "ODIPS 4UBOEBSET BJN UP EFTDSJCF DSPTTEJTDJQMJOBSZ MJUFSBDZ FYQFDUBUJPOT UIBU TIPVME CF NFU JO PSEFS GPS TUVEFOUT UP CF QSFQBSFE GPS TVDDFTT JO DPMMFHF BOE XPSLGPSDF USBJOJOH QSPHSBNT $PNNPO $PSF 4UBUF 4UBOEBSET *OJUJBUJWF C 'PSFBDITUSBOE UIF$$3TUBOEBSETQSFTFOUCSPBEDPODFQUT UIBU BSF BQQMJFE UP BMM HSBEF MFWFMT 4QFDJmD TUBOEBSET UIFO TQFMMPVUIPXUIF$$3"ODIPS4UBOEBSETBSFBQQSPBDIFEGPS EJGGFSFOUHSBEFCBOET1 For this study, we used the Common $PSF&-"BOEMJUFSBDZTUBOEBSETGPSUIFIJHIFTUHSBEFCBOE HSBEFT o 5BCMF TVNNBSJ[FT UIF PSHBOJ[BUJPO PG UIF $PNNPO$PSF&-"BOEMJUFSBDZTUBOEBSETGPSIJHITDIPPM &BDIPGUIFTUSBOETDPOUBJOTUXPUPGPVSPSHBOJ[JOHDBUFHPSJFT *OTPNFDBTFTUIFIJHITDIPPMHSBEFTQFDJmDTUBOEBSEJTJEFOUJDBMUPUIF $PMMFHFBOE$BSFFS3FBEJOFTTBODIPSTUBOEBSE 1 Table . Organization of the Common Core English Language Arts and Literacy Standards Standards for English Language Arts a CCR Anchor Standards for Reading Standards for Literacy CCR Anchor Standards for Readinga . Reading in History/Social Studies . Reading for Literature . Reading in Science and Technical Subjects . Reading for Informational Texts b CCR Anchor Standards for Writing . Writing CCR Anchor Standards for Writingb . Writing in History/Social Studies, Science, and Technical Subjects CCR Anchor Standards for Speaking and Listening . Speaking and Listening CCR Anchor Standards for Language . Language a The  reading CCR anchor standards are the same for the English language arts and literacy strands. The  writing CCR anchor standards are the same for English language arts and literacy strands. b Chapter Two 5 Chapter  | Methodology XIJDIXFSFGFSUPBTUPQJDT"EEJUJPOBMMZ IBMGPGUIF$PNNPO$PSF&-"TUSBOETDPOUBJOTUBUFNFOUTUIBUBSFPSHBOJ[FECFMPX UIFTUBOEBSEMFWFM BTTVCTUBOEBSET'PSUIFQVSQPTFTPGUIFTUVEZ UIFTFXFSFSBUFEBTUIPVHIUIFZXFSFPOUIFTBNFMFWFMBT TUBOEBSET5IVTUIF$PNNPO$PSFTUBOEBSETGPS&-"BOEMJUFSBDZDPNQSJTFESBUBCMFTUBUFNFOUT TFF'JHVSF 2 'PSUIFQVSQPTFTPGBOBMZTJTJOUIF8"5UPPM FMFNFOUTJOUIF$PNNPO$PSFTUBOEBSETXFSFPSHBOJ[FEUPmUUIF8FCCMBCFMJOHTUSVDUVSF XIJDIVTFTPOMZUISFF MFWFMT$PNNPO$PSFTUSBOETXFSFMBCFMFEBTTUBOEBSET UIF$PNNPO$PSFUPQJDTXFSFMBCFMFEBTHPBMT BOE$PNNPO$PSFTUBOEBSETBOETVCTUBOEBSETXFSF both labeled as objectives. 2 Figure . Common Core English Language Arts and Literacy Standards for Grades  and : Number of Rated Statements Common Core standard statements rated for ELA and literacy (113) Reading for Literature (9) 4 topics = 9 standards Reading for Informational Texts (10) 4 topics = 10 standards Writing (28) 4 topics = 10 standards + 18 substandards Speaking and Listening (10) 2 topics = 6 standards + 4 substandards Language (17) 3 topics = 6 standards + 11 substandards Reading for Literacy in History/Social Studies (10) 4 topics = 10 standards Reading for Literacy in Science and Technical Subjects (10) 4 topics = 10 standards Writing for Literacy in History/Social Studies, Science and Technical Subjects (19) 4 topics = 9 standards + 10 substandards Chapter Two 6 Chapter  | Methodology Mathematics 'PSUIF$PNNPO$PSFNBUIFNBUJDTTUBOEBSETGPSIJHITDIPPM conceptual categoriesBSFUIFIJHIFTUMFWFMPGSFMBUFEDPOUFOU5IFSF BSF TJY DPODFQUVBM DBUFHPSJFT /VNCFS BOE 2VBOUJUZ "MHFCSB 'VODUJPOT .PEFMJOH (FPNFUSZ BOE 4UBUJTUJDT BOE 1SPCBCJMJUZ 5IFSFJTKVTUPOFHSBEFCBOEGPSIJHITDIPPM JOUFOEFEGPSHSBEFTo5IFNBUIFNBUJDTTUBOEBSETEPOPUIBWFBODIPSTUBOEBSET BTEP&-"BOEMJUFSBDZ.BUIFNBUJDTJTPSHBOJ[FEJOUPHSPVQJOHTCFOFBUIUIFDPODFQUVBMDBUFHPSZMFWFMMBCFMFEdomains and clusters #FDBVTF NBOZ NBUIFNBUJDT UPQJDT BOE TLJMMT BSF JOUFSDPOOFDUFE BDSPTT EPNBJOT TUBOEBSET GSPN UIFTF HSPVQJOHT NBZTPNFUJNFTCFDMPTFMZSFMBUFE0OFPGUIFDPODFQUVBMDBUFHPSJFTo.PEFMJOHoIBTTUBOEBSETUIBUBSFJOUFHSBUFEJOUPPUIFS DPODFQUVBM DBUFHPSJFT BOE UIFSFGPSF BOBMZTFT GPS UIF DBUFHPSZ XFSF OPU DPOEVDUFE TFQBSBUFMZ 5IF NPEFMJOH TUBOEBSET BSF indicated in the Common Core document with a star symbol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mUUIF8FCCMBCFMJOHTUSVDUVSF XIJDIVTFTUISFFMFWFMT$PNNPO$PSFDPODFQUVBM DBUFHPSJFTXFSFMBCFMFEBTTUBOEBSET $PNNPO$PSFDMVTUFSTXFSFMBCFMFEBTHPBMT BOE$PNNPO$PSFTUBOEBSETBOETVCTUBOEBSETXFSFMBCFMFEBTPCKFDUJWFT 5IF$PNNPO$PSFEPNBJOMBCFMXBTOPUVTFEJOUIF8FCCTUSVDUVSF BTJUJTBCSPBEEFTDSJQUJPOPGUIFNPSFEFUBJMFEMFWFMTUIBUGPMMPX 3 Figure . Common Core Mathematics Standards for High School: Number of Rated Statements Common Core standard statements rated for mathematics (192) Number and Quantity (32) 9 clusters = 27 standards + 5 substandards Algebra (34) 11 clusters = 27 standards + 7 substandards Functions (45) 10 clusters = 28 standards + 17 substandards Geometry (45) 15 clusters = 43 standards + 2 substandards Statistics and Probability (36) 9 clusters = 31 standards + 5 substandards Chapter Two 7 Chapter  | Methodology Table . Descriptive Information About the Five Comparison Standards Sets for English Language Arts (ELA) and Literacy ELA comparison standards sets California ELA standards for grades – Massachusetts ELA standards for grades – Texas ELA and cross-disciplinary college and career readiness standards Number of comparison standards    ( are cross-disciplinary) Knowledge and Skills for University Success ELA college and career readiness standards  International Baccalaureate ELA standards for grades –  5IF $PNNPO $PSF NBUIFNBUJDT TUBOEBSET JODMVEF FJHIU 4UBOEBSET GPS .BUIFNBUJDBM 1SBDUJDF 5IFTF IPOF JO PO iQSPDFTTFT BOE QSPmDJFODJFTw XJUI MPOHTUBOEJOH JNQPSUBODF JO NBUIFNBUJDT FEVDBUJPO $PNNPO $PSF 4UBUF 4UBOEBSET *OJUJBUJWF D TVDI BT QSPCMFN TPMWJOH SFBTPOJOH BOE QSPPG DPNNVOJDBUJPO SFQSFTFOUBUJPO BEBQUJWF SFBTPOJOH TUSBUFHJDDPNQFUFODF DPODFQUVBMVOEFSTUBOEJOH QSPDFEVSBM nVFODZ BOEUIFJODMJOBUJPOUPTFFNBUIFNBUJDTBTTFOTJCMFBOE VTFGVM5IF4UBOEBSETGPS.BUIFNBUJDBM1SBDUJDFBSFFYQMBJOFE BU UIF CFHJOOJOH PG UIF $PNNPO $PSF TUBOEBSET EPDVNFOU BOE UIFO QSFTFOUFE BHBJO PO FBDI DPODFQUVBM DBUFHPSZ PWFSWJFX QBHF *O HFOFSBM CFDBVTF UIFZ BSF OPU MBJE PVU BT TQFDJmDTUBOEBSET UIFQSBDUJDFTXFSFOPUSBUFEJOUIJTTUVEZ )PXFWFS POFPGUIFQSBDUJDFTJTNBLJOHNBUIFNBUJDBMNPEFMT BOETQFDJmDNPEFMJOHTUBOEBSETBQQFBSJOUIF$PNNPO$PSF document. Table . Descriptive Information About the Five Comparison Standards Sets for Mathematics Mathematics comparison standards sets Number of comparison standards California mathematics standards for grades –  Massachusetts mathematics standards for grades –  Texas mathematics and cross-disciplinary college and career readiness standards Rating of Comparison Standards 5IFmWFTFUTPGDPNQBSJTPOTUBOEBSETBSFBTGPMMPXT 5IF $POUFOU 4UBOEBSET GPS $BMJGPSOJB 1VCMJD 4DIPPMT GPSUIFthothHSBEFCBOEJO&OHMJTI MBOHVBHFBSUTBOEGPSUIFthothHSBEFCBOE JONBUIFNBUJDT 5IF .BTTBDIVTFUUT $VSSJDVMVN 'SBNFXPSLT for the 11thothHSBEF CBOE JO &OHMJTI MBOHVBHFBSUT BOENBUIFNBUJDT 5IF 5FYBT $PMMFHF BOE $BSFFS 3FBEJOFTT 4UBOEBSET JO &OHMJTI MBOHVBHF BSUT mathematics, and cross-disciplinary standards 5IF ,OPXMFEHF BOE 4LJMMT GPS 6OJWFSTJUZ 4VDDFTT ,464 TUBOEBSET JO &OHMJTI BOE mathematics, EFWFMPQFE BT DPMMFHF QSFQBSBUPSZ TUBOEBSET CZ 4UBOEBSET GPS 4VDDFTT 5IF *OUFSOBUJPOBM #BDDBMBVSFBUF *# %JQMPNB 1SPHSBNNF &OHMJTI MBOHVBHF BSUT BOE mathematics standards, developed by EPIC, GPS*#T1SPHSBNTPG4UVEZGPSthothHSBEFT5 "NPOH UIF mWF TFUT UIF OVNCFS PG DPNQBSJTPO TUBOEBSET JO &-" BOE MJUFSBDZ SBOHFE CFUXFFO BOE 5IF OVNCFS PG DPNQBSJTPO NBUIFNBUJDT TUBOEBSET SBOHFE CFUXFFO BOE *O TPNF JOTUBODFT UIFMPXFTUMFWFMGPSSBUJOHXBTOPUUIFWFSZ TNBMMFTU HSBJO TJ[F XJUIJO UIF TFUT PG DPNQBSJTPO standards but rather the level that had consistent EFUBJMGPSUIFQVSQPTFPGBMJHONFOU5BCMFTBOE CSFBL EPXO UIF OVNCFS PG SBUBCMF TUBUFNFOUT GPS each of the comparison standards sets for ELA and literacy and mathematics. 5IFTFEJEOPUJODMVEFUIF,OPXMFEHFBOE4LJMMT'PVOEBUJPOT XJUIJOUIF&OHMJTIBOENBUIFNBUJDTTFDUJPOT /PUFUIBUUIFTUVEZEJEOPUJODMVEFBOZDPOUFOUGSPN*#iPQUJPOTw These are additional required components, which each IB school selects. The number of options varies by course and by subject. 5IF*#PQUJPOTEPOPUIBWFTQFDJmDTUBOEBSET 5  ( are cross-disciplinary) Knowledge and Skills for University Success mathematics college and career readiness standards  International Baccalaureate mathematics standards for grades –  Chapter Two 8 Chapter  | Methodology Rater Reliability 3FMJBCJMJUZTUBUJTUJDTXFSFJOUIFBDDFQUBCMFSBOHFGPSBMM%FQUIPG ,OPXMFEHFSBUJOHT'PSFBDITFUPGDPNQBSJTPOTXFFYBNJOFE UIF JOUSBDMBTT DPSSFMBUJPO XIJDI DBMDVMBUFT BHSFFNFOU BDDPVOUJOH GPS UIF QPTTJCJMJUZ PG BHSFFNFOU CZ DIBODF BOE SBUJOHT UIBU BSF DMPTF CVU OPU BO FYBDU NBUDI 4ISPVU BOE 'MFJTT *O UIJT DPOUFYU WBMVFT PG PS MBSHFS JOEJDBUF SFBTPOBCMF MFWFM PG BHSFFNFOU BOE WBMVFT PG PS MBSHFS JOEJDBUFBHPPEMFWFMPGSFMJBCJMJUZ $PPL8JMNFT 'PS ELA and literacy, the intraclass correlation was close to .70 for POFDPNQBSJTPOBOEBCPWFGPSUIFPUIFSGPVSDPNQBSJTPOT 5IFDPSSFMBUJPOTSBOHFGSPNUP TFF5BCMF For mathematics, the intraclass correlations were close to or BCPWFGPSFBDITFU SBOHJOHGSPNUP TFF5BCMF 3BUFSDPOTJTUFODZEBUBXFSFFYBNJOFEGPSWBSJBODFBOEFSSBOU DPEJOHUPEFUFSNJOFJGBOZTJOHMFSBUFSXBTTLFXJOHSFMJBCJMJUZ and therefore warranted removal from the analysis data. /P TVDI QBUUFSO XBT GPVOE BOE BMM EBUB GSPN BMM SBUFST XFSF retained. Table . Consistency of Depth of Knowledge Ratings Across Nine Raters for English Language Arts and Literacy Number of standards Intraclass correlation California  . Massachusetts  . Texas and College and Career Readiness  . Knowledge and Skills for University Success  . International Baccalaureate  . Comparison standard set Table . Consistency of Depth of Knowledge Ratings Across Seven Raters for Mathematics Number of standards Intraclass correlation California  . Massachusetts  . Texas and College and Career Readiness  . Knowledge and Skills for University Success  . International Baccalaureate  . Comparison standard set Chapter Two 9 Chapter  | Methodology Figure . Illustration of Categorical Concurrence Statistic IF Total number of matches THEN 1.0 Categorical Concurrence criterion met Number of raters Data Analysis Categorical Concurrence 8FCCT $BUFHPSJDBM $PODVSSFODF TUBUJTUJD NFBTVSFT UIF BWFSBHF OVNCFS PG DPNQBSJTPO TUBOEBSET GSPN POF TFU PG TUBOEBSET UIBU SBUFST NBUDI UP TQFDJmD TUBOEBSET GSPN UIF SFGFSFODF TFU PG TUBOEBSET *O UIF DVSSFOU TUVEZ $BUFHPSJDBM Concurrence is the mean number of matches between each set of comparison standards and the Common Core standards. It is NFBTVSFEGPSFBDIDPOUFOUTQFDJmDBSFBPGUIF$PNNPO$PSF TUBOEBSET OBNFMZUIFFJHIUTUSBOETJO&OHMJTIMBOHVBHFBSUT BOEMJUFSBDZBOEUIFmWFDPODFQUVBMDBUFHPSJFTJONBUIFNBUJDT *G PO BWFSBHF BDSPTT BMM SBUFST BU MFBTU POF TUBOEBSE JO UIF DPOUFOUTQFDJmD BSFB PG UIF $PNNPO $PSF XBT NBUDIFE UP a standard in the comparison standard set, the criterion for UIBU DPOUFOUTQFDJmD BSFB JT NFU *O UFTU JUFNTUPTUBOEBSET BMJHONFOU BUMFBTUTJYUFTUJUFNTNVTUNBUDIJOPSEFSUPNFFU UIF DSJUFSJPO 8FCC FU BM 5IJT OVNCFS JT OFDFTTBSZ EVF UP UIF TQFDJmDJUZ PG UFTU JUFNT JO UIBU OP TJOHMF UFTU JUFN JTFYQFDUFEUPDPNQSFIFOTJWFMZBTTFTTBOFOUJSFTUBOEBSE*O TUBOEBSETUPTUBOEBSET BMJHONFOU IPXFWFS TUBOEBSET UFOE UPCFCSPBETUBUFNFOUTEFTDSJCJOHTLJMMTBOELOPXMFEHF BOE B TJOHMF DPSSFTQPOEFODF CFUXFFO UXP TFUT PG TUBOEBSET GPS B DPOUFOU BSFB JT DPOTJEFSFE TVGmDJFOU UP NFFU UIF DSJUFSJPO $PPL 'JHVSFJMMVTUSBUFTUIJTDSJUFSJPOHSBQIJDBMMZ Depth of Knowledge Consistency %FQUIPG,OPXMFEHF %0, JTEFUFSNJOFECZIBWJOHBMMSBUFST BTTJHOPOFPGGPVSMFWFMTPGDPHOJUJWFDPNQMFYJUZ 8FCC UPFBDI$PNNPO$PSFTUBOEBSEBOEFBDITUBOEBSEJOUIFmWF DPNQBSJTPOTUBOEBSETTFUT8FCCPVUMJOFEUIFGPMMPXJOHMFWFMT Level 1:3FDBMMBOESFQSPEVDUJPO Level 2:4LJMMTBOEDPODFQUT Level 3:4USBUFHJDUIJOLJOH Level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hapter Two 10 Chapter  | Methodology Figure . Illustration of Depth of Knowledge Consistency Statistic At Above THEN IF > Depth of Knowledge Consistency criterion met 75% 0ODF SBUFST HBWF BMM TUBOEBSET B %0, SBUJOH XF DBMDVMBUFE UIF%0,$POTJTUFODZTUBUJTUJDGPSFBDI$PNNPO$PSFDPOUFOU TQFDJmD BSFB 5IF TUBUJTUJD JOWPMWFT DPNQBSJOH UIF %0, SBUJOHTPG$PNNPO$PSFTUBOEBSETUIBUIBECFFONBUDIFEUP DPNQBSJTPO TUBOEBSET BOE UIF %0, SBUJOHT PG UIF TUBOEBSET UIBU IBE CFFO NBUDIFE 8F TFU BO B QSJPSJ UISFTIPME PG GPS UIF %0, $POTJTUFODZ DSJUFSJPO 5IJT NFBOT UIBU GPS FBDI $PNNPO$PSFDPOUFOUTQFDJmDBSFB JGNPSFUIBOPGUIF NBUDIFEDPNQBSJTPOTUBOEBSETXFSFBUPSBCPWFUIF%0,PG UIFDPSSFTQPOEJOH$PNNPO$PSFTUBOEBSE UIFOUIFDSJUFSJPO JT NFU 'PS UFTU JUFNTUPTUBOEBSET BMJHONFOU SFTFBSDIFST UZQJDBMMZ VTF B %0, DSJUFSJPO 8FCC CBTFE PO the fact that a substantial number of test items are supposed UP SFnFDU UIF TUBOEBSET BOE HSFBUFS NBUDI JT SFRVJSFE GPS DBUFHPSJDBM DPODVSSFODF $PPL 'PS TUBOEBSETUP standards comparisons, since the match requirement is less, UIFDSJUFSJPOJTJOTVGmDJFOU5IFSFGPSF B%0,DSJUFSJPO has typically been adopted for standards-to-standards BMJHONFOU $PPL 'JHVSF TIPXT UIJT HSBQIJDBMMZ 'PS JOGPSNBUJPO PO UIF TQFDJmD EFUBJMT PG UIJT DBMDVMBUJPO TFF "QQFOEJY" Breadth of Coverage #SFBEUIPG$PWFSBHFJTBNFBTVSFPGEJTQFSTJPOUIBUTIPXTUIF FYUFOUUPXIJDINBUDIFEDPNQBSJTPOTUBOEBSETDPWFSBTJNJMBS scope of content as that found in the reference standards. 4QFDJmDBMMZ JO UIJT TUVEZ UIF TUBUJTUJD XBT VTFE UP DBMDVMBUF UIF OVNCFS PG DPOUFOU FMFNFOUT TVCBSFBT JO UIF $PNNPO Core standards that are covered by matched standards in the comparison standard set. For ELA and literacy, we refer to the subareas as topics. For mathematics, the subareas are referred UP BT DMVTUFST JO UIF $PNNPO $PSF TUBOEBSET 8IFO NPSF subareasIBWFNBUDIJOHTUBOEBSET UIFOHSFBUFSCSFBEUIPG DPWFSBHF FYJTUT 4QFDJmDBMMZ UIF DPWFSBHF TUBUJTUJD VTFT UIF OVNCFS PG TVCBSFBT XJUIJO B $PNNPO $PSF DPOUFOUTQFDJmD area that have standards matched with comparison standards. "TUSPOHDPWFSBHFTDPSFGPSBDPOUFOUTQFDJmDBSFBNFBOTB NBKPSJUZPGUIFTVCBSFBTJOUIBU$PNNPO$PSFDPOUFOUTQFDJmD area match with the comparison standard set. Moderate DPWFSBHFNFBOTUIBUNPSFUIBOPOFTVCBSFBNBUDIFTGPSUIF DPOUFOUTQFDJmD BSFB -JNJUFE DPWFSBHF NFBOT UIBU XJUIJO B DPOUFOUTQFDJmD BSFB POF PS OP TVCBSFB NBUDIFT UP UIF $PNNPO$PSFTUBOEBSET'JHVSFJMMVTUSBUFTUIJTDSJUFSJPO Figure . Illustration of Coverage Statistic Strong (all or majority) Number of subareas with matches Under 0 1 2 3 4 0 1 2 3 4 Moderate (less than majority, more than 1) 0 1 2 3 4 Limited (0 or 1) 0 1 2 3 4 0 1 2 3 4 8FCCVTFTUIFUFSNiHPBMwIFSFBTBHFOFSJDUFSN5PSFEVDFDPOGVTJPO XFVTFUFSNTTQFDJmDBMMZSFMBUFEUPUIFPSHBOJ[BUJPOPGUIF$PNNPO$PSF standards. Chapter Two 11 Chapter  | Results for English Language Arts and Literacy 3FTVMUTCFMPXEFTDSJCFUIFNBUDICFUXFFOUIF$PNNPO$PSF&OHMJTIMBOHVBHFBSUT &-" BOEMJUFSBDZTUBOEBSETBOEUIFmWF TFUTPGDPNQBSJTPOTUBOEBSET#FDBVTFUIF8FCCNFUIPEPMPHZDBMDVMBUFTBMJHONFOUBUUIFIJHIFTUMFWFM SFTVMUTBSFHFOFSBMMZ presented at the strand level. Match Overall Match of Comparison Standards to the Common Core Standards 'JHVSFT BOE TIPX UIF BWFSBHF OVNCFS PG NBUDIFT QFS $PNNPO $PSF TUBOEBSE JO FBDI UPQJD BDSPTT BMM DPNQBSJTPO TUBOEBSET#PUIUIFTUSBOETBOEUPQJDTXJUIJOBTUSBOEBSFTPSUFEJOEFTDFOEJOHPSEFSBDDPSEJOHUPGSFRVFODZ'JHVSFTIPXT UIFmSTUGPVSTUSBOETBOE'JHVSFTIPXTUIFTFDPOEGPVSTUSBOET5IFHSBQITSFWFBMDFSUBJOUFOEFODJFTCFUXFFOTUSBOET FH NPSF DPNQBSJTPO TUBOEBSET NBUDIFE GPS 3FBEJOH GPS -JUFSBUVSF UIBO GPS 3FBEJOH GPS *OGPSNBUJPOBM 5FYUT 5IFZ BMTP TIPX USFOETXJUIJOTUSBOET FH POFPGUIFUPQJDTJO4QFBLJOHBOE-JTUFOJOHIBTNBOZNPSFNBUDIJOHTUBOEBSETUIBOUIFPUIFS UPQJD Figure . Average Number of Matches per Standard Across All Comparison Standards, by Topic 0 10 20 30 40 50 60 70 Speaking and Listening Reading for Literature Integration of Knowledge and Ideas (2) Range of Reading and Level of Text Complexity (1) Craft and Structure (3) Key Ideas and Details (3) Presentation of Knowledge and Ideas (3) Comprehension and Collaboration (7) Production and Distribution of Writing (3) Writing Research to Build and Present Knowledge (5) Range of Writing (1) Reading for Informational Texts Text Types and Purposes (19) Craft and Structure (3) Key Ideas and Details (3) Integration of Knowledge and Ideas (3) Range of Reading and Level of Text Complexity (1) Note/VNCFSTJOQBSFOUIFTFTJOEJDBUFIPXNBOZTUBOEBSETTUBUFNFOUTBQQFBSXJUIJOUIFUPQJD Chapter Three •  Chapter  | Results for English Language Arts and Literacy Figure . Average Number of Matches per Standard Across All Comparison Standards, by Topic 0 10 20 30 40 50 60 70 Reading in Science and Technical Subjects Reading in History/Social Studies Writing in History/Social Studies, Science, and Technical Subjects Language Conventions of Standard English (6) Vocabulary Acquisition and Use (9) Knowledge of Language (2) Research to Build and Present Knowledge (3) Production and Distribution of Writing (3) Range of Writing (1) Text Types and Purposes (12) Integration of Knowledge and Ideas (3) Key Ideas and Details (3) Craft and Structure (3) Range of Reading and Level of Text Complexity (1) Craft and Structure (3) Integration of Knowledge and Ideas (3) Key Ideas and Details (3) Range of Reading and Level of Text Complexity (1) Note/VNCFSTJOQBSFOUIFTFTJOEJDBUFIPXNBOZTUBOEBSETTUBUFNFOUTBQQFBSXJUIJOUIFUPQJD Match for Each Comparison Set to the Common Core Standards 5BCMFQSFTFOUTUIFBWFSBHFOVNCFSPGNBUDIFTQFSTUSBOECFUXFFOUIF$PNNPO$PSFTUBOEBSETGPSFBDITFUPGDPNQBSJTPO TUBOEBSET5IFEBUBJMMVTUSBUFUIBUUIFSFJTBXJEFSBOHFJOUIFOVNCFSPGBWFSBHFNBUDIFTBOEUIBUTPNFTUSBOETIBWFIJHI TUBOEBSEEFWJBUJPOT JOEJDBUJOHUIBUSBUFSTWBSJFEXJEFMZJOUIFOVNCFSPGNBUDIFTUIFZJEFOUJmFE Chapter Three 13 Chapter  | Results for English Language Arts and Literacy Table . Average Number of Matches for English Language Arts (ELA) and Literacy Common Core Strands Across All Comparison Standards Average number of matches Common Core ELA and literacy strands CA MA TCCRS KSUS IB M SD M SD M SD M SD M SD Reading for Literature . . . . . . . . . . Reading for Informational Texts . . . . . . . . . . Writing . . . . . . . . . . Speaking and Listening . . . . . . . . . . Language . . . . . . . . . . Reading in History/Social Studies . . . . . . . . . . Reading in Science and Technical Subjects . . . . . . . . . . Writing in History/Social Studies, Science, and Technical Subjects . . . . . . . . . . Total . . . . . . . . . . CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate. Categorical Concurrence Statistic 3FDBMMUIBUBTJOHMFDPSSFTQPOEFODFJOBDPOUFOUBSFBCFUXFFO UXP TFUT PG TUBOEBSET JT DPOTJEFSFE TVGmDJFOU UP NFFU UIF TUBOEBSETUPTUBOEBSETBMJHONFOUDSJUFSJPO $PPL 5IVT PWFSBMMUIFDSJUFSJPOGPS$BUFHPSJDBM$PODVSSFODFCFUXFFOUIF $PNNPO $PSF BOE UIF mWF TFUT PG DPNQBSJTPO TUBOEBSET JT NFUGSFRVFOUMZ0OBWFSBHFBDSPTTSBUFST BUMFBTUPOFTUBOEBSE GSPNFWFSZTFUPGUIFmWFDPNQBSJTPOTUBOEBSETJTNBUDIFEUP BTUBOEBSEJOBMM$PNNPO$PSFTUSBOET XJUIGFXFYDFQUJPOT 5IJT JOEJDBUFT PWFSMBQ CFUXFFO UIF LOPXMFEHF BOE TLJMMT TQFDJmFE JO UIF $PNNPO $PSF TUBOEBSET BOE UIF DPOUFOU PG the comparison standards. Table 7 shows the Common Core TUSBOETGPSXIJDIUIF$BUFHPSJDBM$PODVSSFODFDSJUFSJPOJTNFU BDSPTTUIFmWFTFUTPGDPNQBSJTPOTUBOEBSET Table . Categorical Concurrence for English Language Arts (ELA) and Literacy Common Core ELA and literacy strands CA MA TCCRS KSUS IB Reading for Literature Reading for Informational Texts Writing Speaking and Listening Language − Reading in History/Social Studies − Reading in Science and Technical Subjects − − Writing in History/Social Studies, Science, and Technical Subjects CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate. Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of standards); Does not meet the criterion for Categorical Concurrence. Chapter Three 14 Chapter  | Results for English Language Arts and Literacy 5IFDSJUFSJPOJTNFUGPSBMM FJHIUPGFJHIU $PNNPO$PSF&-" BOEMJUFSBDZTUSBOETGPSUIF$BMJGPSOJBTUBOEBSET 5FYBT$PMMFHF BOE $BSFFS 3FBEJOFTT 4UBOEBSET BOE UIF ,OPXMFEHF BOE 4LJMMTGPS6OJWFSTJUZ4VDDFTT5IFDSJUFSJPOJTNFUGPSTJYPGFJHIU Common Core ELA and literacy strands for the Massachusetts and International Baccalaureate standards. TFF 5BCMF "T BO FYBNQMF GPS UIF $BMJGPSOJB TUBOEBSET SBUFST JEFOUJmFE BO BWFSBHF PG TUBOEBSE SD UIBU NBUDIFTXJUIUIF$PNNPO$PSF3FBEJOH4UBOEBSETJO4DJFODF BOE5FDIOJDBM4VCKFDUTBOEBOBWFSBHFPGTUBOEBSET SD UIBUNBUDIXJUIUIF8SJUJOH4UBOEBSET#PUIPGUIFTF meet the criterion. For the Massachusetts standards, the criterion is not met for UIF$PNNPO$PSF3FBEJOH4UBOEBSETJO)JTUPSZ4PDJBM4UVEJFT BOEUIF3FBEJOH4UBOEBSETJO4DJFODFBOE5FDIOJDBM4VCKFDUT 5BCMFTIPXTXIZUIFDSJUFSJPOJTOPUNFUGPSFBDIPGUIFTFUXP BSFBT'PSUIF.BTTBDIVTFUUTTUBOEBSET UIFSFJTBOBWFSBHF PG TUBOEBSET SD UIBU NBUDI XJUI UIF 3FBEJOH 4UBOEBSETJO)JTUPSZ4PDJBM4UVEJFT5IFSFJTBOBWFSBHFPG standards (SD UIBUNBUDIXJUIUIF3FBEJOH4UBOEBSETJO 4DJFODFBOE5FDIOJDBM4VCKFDUT *O"QQFOEJY$ UIFSFJTNPSFEFUBJMFEEJTDVTTJPOBCPVUFBDI TFUPGDPNQBSJTPOTUBOEBSETBOEIPXJUBMJHOTUPUIF$PNNPO Core. The precise correspondence of matches between the Common Core standards and individual comparison sets of TUBOEBSETJTQSPWJEFEJOUIF5FDIOJDBM4VQQMFNFOU For the International Baccalaureate standards, the criterion JT OPU NFU GPS UIF $PNNPO $PSF -BOHVBHF 4UBOEBSET BOE 3FBEJOH4UBOEBSETJO4DJFODFBOE5FDIOJDBM4VCKFDUT5IFSF JTBOBWFSBHFPGTUBOEBSET SD UIBUNBUDIXJUIUIF $PNNPO $PSF -BOHVBHF 4UBOEBSET BOE BO BWFSBHF PG standards (SD UIBUNBUDIXJUI3FBEJOH4UBOEBSETJO 4DJFODFBOE5FDIOJDBM4VCKFDUT 5BCMFTIPXTUIFNPEBM%FQUIPG,OPXMFEHF %0, SBUJOHGPS FBDI PG UIF $PNNPO $PSF &OHMJTI MBOHVBHF BSUT &-" BOE MJUFSBDZTUSBOET.PTUSFQSFTFOUUIFTUSBUFHJDUIJOLJOHMFWFMPG DPHOJUJWFEFNBOE MFWFM "TUIFUBCMFTIPXT UIF-BOHVBHF 4UBOEBSETIBWFMPXFSSBUJOHTUIBOUIFPUIFSTUSBOET NPEFPG MFWFM 5IJTNJHIUCFCFDBVTFUIFTUSBOEDPOUBJOTFMFNFOUT PG HSBNNBS DPOWFOUJPOT BOE VTBHF XIJDI EP OPU UFOE UP JOWPMWFBCTUSBDUBOEDPNQMFYUIJOLJOH "NPOHUIFTFUTPGDPNQBSJTPOTUBOEBSETGPSXIJDIBMMDSJUFSJB BSFNFU UIFSFJTBXJEFSBOHFJOUIFOVNCFSPGBWFSBHFNBUDIFT Depth of Knowledge Ratings for Common Core Standards Table . Depth of Knowledge (DOK) Modal Ratings for English Language Arts and Literacy Common Core Strands Common Core ELA and literacy strand DOK mode Reading for Literature  Reading for Informational Texts  Writing  Speaking and Listening  Language  Reading in History/Social Studies  Reading in Science and Technical Subjects  Writing in History/Social Studies, Science, and Technical Subjects  Chapter Three 15 Chapter  | Results for English Language Arts and Literacy "UUIFTUBOEBSEMFWFM UIF$PNNPO$PSFTUBOEBSETGBMMBDSPTTUIFGVMMSBOHFPGUIF%0,TDBMF CVUMFTTGSFRVFOUMZBUUIFMPXFS MFWFMTPGUIFTDBMF0WFSBMM POMZPGUIFTUBOEBSETBSFBUBMFWFM SFDBMMBOESFQSPEVDUJPO BSFBUBMFWFM TLJMMTBOE DPODFQUT BSFBUBMFWFM TUSBUFHJDUIJOLJOH BOEBSFBUMFWFM FYUFOEFEUIJOLJOH 5IJTTVNNBSZJOGPSNBUJPOJT QSFTFOUFEHSBQIJDBMMZJO'JHVSF%0,SBUJOHTGPSBMMTUBOEBSETBSFQSPWJEFEJO"QQFOEJY# Figure . Percent of Common Core ELA and Literacy Standards at each Depth of Knowledge Level Level 1 Recall and Reproduction 7% Level 4 Extended Thinking 26% Level 2 Skills and Concepts 12% Level 3 Strategic Thinking 55% DOK Consistency of Each Comparison Set to the Common Core Standards %0, $POTJTUFODZ EFTDSJCFT UIF FYUFOU UP XIJDI UIF &-" BOE MJUFSBDZ TUBOEBSET UIBU FYQFSUT NBUDIFE CFUXFFO UIF comparison sets and the Common Core are consistent in level PGDPHOJUJWFEFNBOE.FFUJOHUIJTDSJUFSJPOSFRVJSFTNPSFUIBO PGUIFDPNQBSJTPOTUBOEBSETNBUDIJOHGPSUIFDPOUFOUBSFB UPCFBUPSBCPWFUIFMFWFMPGDPHOJUJWFEFNBOEPGUIF$PNNPO Core standards. Consistency is only computed for those DPOUFOUTQFDJmDBSFBTGPSXIJDIUIF$BUFHPSJDBM$PODVSSFODF criterion is met. 'JHVSF TIPXT GPS FBDI DPNQBSJTPO TFU UIF QFSDFOU PG TUBOEBSET BWFSBHFE BDSPTT SBUFST TFF "QQFOEJY " UIBU GFMM BCPWF BU BOE VOEFS UIF DPHOJUJWF EFNBOE MFWFM PG UIF $PNNPO$PSFTUBOEBSET*OUIFmHVSF BMJOFJTESBXOBU XIJDIJTUIFDSJUFSJPOGPSUIFQFSDFOUPGTUBOEBSETGBMMJOHBCPWF PSBUUIFDPHOJUJWFEFNBOEMFWFMPGUIF$PNNPO$PSFJOPSEFS UP NFFU UIF %0, $POTJTUFODZ TUBUJTUJD 'JOEJOHT GPS UIF %0, Consistency statistic are inconsistent across the different DPNQBSJTPO TFUT BOE EJGGFSFOU TUSBOET 0WFSBMM UIF $PNNPO $PSF TUSBOE GPS XIJDI UIF %0, DSJUFSJPO JT NPTU PGUFO NFU JT UIF -BOHVBHF 4UBOEBSET TUSBOE JOEJDBUJOH UIBU UIF NBUDIFE DPNQBSJTPOTUBOEBSETBSFBUPSBCPWFUIF%0,PGUIF$PNNPO $PSF-BOHVBHF4UBOEBSET5IFTUSBOETGPSXIJDIUIFDSJUFSJPO is met for less than half of the comparison standards sets are UIF 3FBEJOH 4UBOEBSET GPS *OGPSNBUJPOBM 5FYUT UIF 8SJUJOH 4UBOEBSET UIF4QFBLJOHBOE-JTUFOJOH4UBOEBSET UIF3FBEJOH 4UBOEBSETJO)JTUPSZ4PDJBM4UVEJFT UIF3FBEJOH4UBOEBSETJO 4DJFODF BOE 5FDIOJDBM 4VCKFDUT BOE UIF 8SJUJOH 4UBOEBSET JO )JTUPSZ4PDJBM 4UVEJFT 4DJFODF BOE 5FDIOJDBM 4VCKFDUT For these strands, there are more comparisons for which the $PNNPO $PSF TUBOEBSET BSF SBUFE BU B IJHIFS MFWFM JO UFSNT PGDPHOJUJWFEFNBOE"T'JHVSFTIPXT TPNFTUBOEBSETTFUT GBMMKVTUBCPWFPSKVTUCFMPXGPSTPNFTUSBOETBOESFTVMUT would be different if an alternative criterion had been selected. -PPLJOH BU %0, $POTJTUFODZ BDSPTT UIF DPNQBSJTPO TFUT PG standards, the criterion is met most often for the Massachusetts TUBOEBSET GPSmWFPVUPGTJYTUSBOETUIBUGVMmMMUIF$BUFHPSJDBM $PODVSSFODFDSJUFSJPO 5IJTTVHHFTUTUIBUGPS&-"BOEMJUFSBDZ UIF DPHOJUJWF EFNBOE PG UIF .BTTBDIVTFUUT TUBOEBSET JT TJNJMBSUPPSNPSFDPHOJUJWFMZDPNQMFYUIBOUIF$PNNPO$PSF standards. The International Baccalaureate standards meet UIFDSJUFSJPOGPSGPVSPVUPGTJYTUSBOETUIBUGVMmMMUIF$BUFHPSJDBM $PODVSSFODFDSJUFSJPO'PSUIFPUIFSUISFFTFUT $BMJGPSOJB 5FYBT $PMMFHFBOE$BSFFS3FBEJOFTT BOE,OPXMFEHFBOE4LJMMTGPS 6OJWFSTJUZ4VDDFTT UIFDSJUFSJPOJTNFUGPSUXPPSUISFFPGFJHIU TUSBOETUIBUGVMmMMUIF$BUFHPSJDBM$PODVSSFODFDSJUFSJPO Chapter Three 16 Chapter  | Results for English Language Arts and Literacy Figure . Depth of Knowledge Level Comparisons of the Five Sets of Comparison Standards to Common Core ELA and Literacy Standards Reading for Literature CA MA TCCRS KSUS IB 25 50 75 CA MA TCCRS KSUS IB CA MA TCCRS KSUS IB Reading in Science and Technical Subjects CA MA TCCRS KSUS IB CA MA TCCRS KSUS IB CA MA TCCRS KSUS IB 100 Average Percent Above At Under CA MA TCCRS KSUS IB Writing in History/Social Studies, Science, and Technical Subjects Reading in History/Social Studies Language Speaking and Listening Writing Reading for Informational Texts 0 CA MA TCCRS KSUS IB NA NA NA NA Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH Breadth of Coverage #SFBEUI PG $PWFSBHF HJWFT JOGPSNBUJPO PO UIF CSFBEUI PS EJTQFSTJPOPGDPSSFTQPOEJOHTUBOEBSETBDSPTTTUBOEBSETTFUT " DPNQBSJTPO TFU PG TUBOEBSET DPVME IBWF B IJHI EFHSFF PG concurrence with reference standards but still not cover the entire scope or breadth of content of the reference standards. In this study, the criterion is related to the number of Common Core topics within a strand for which a set of comparison standards has matches to the Common Core standards. 4USPOHDPWFSBHFNFBOTUIBUBNBKPSJUZPGUPQJDTJOUIFTUSBOE IBWFNBUDIFT.PEFSBUFDPWFSBHFNFBOTUIBUNPSFUIBOPOF UPQJD JO UIF TUSBOE IBT NBUDIFT -JNJUFE DPWFSBHF NFBOT that one or fewer than one topic in the strand has matches. *G DPWFSBHF JT MJNJUFE UIJT JOEJDBUFT UIBU DPNQBSJTPO DPOUFOU tends to concentrate in particular topics of the Common Core TUSBOE BDDPSEJOH UP UIF XBZ UIF $PNNPO $PSF TUBOEBSET BSF PSHBOJ[FE 5IFSFGPSF PUIFS DBUFHPSJFT PG DPOUFOU BSF OPU covered by the comparison standards. 'PS UIF NPTU QBSU DPWFSBHF CFUXFFO UIF $PNNPO $PSF standards and the comparison standards was consistently TUSPOHPSCSPBE TFF5BCMF .PTUTFUTPGDPNQBSJTPOTUBOEBSET cover a majority of Common Core topics for each strand. There Chapter Three 17 Chapter  | Results for English Language Arts and Literacy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a necessary relationship because there are also two strands for XIJDIUIF$BUFHPSJDBM$PODVSSFODFDSJUFSJPOJTOPUNFUCVUUIBU TUJMMIBWFTUSPOHDPWFSBHF 3FBEJOH4UBOEBSETJO)JTUPSZ4PDJBM 4UVEJFTGPS.BTTBDIVTFUUTBOE3FBEJOH4UBOEBSETJO4DJFODF BOE5FDIOJDBM4VCKFDUTGPS*OUFSOBUJPOBM#BDDBMBVSFBUF "QQFOEJY % QSFTFOUT NPSF JOGPSNBUJPO BCPVU UIF EJTUSJCVUJPO PGTUBOEBSENBUDIFTXJUIJOFBDIPGUIFFJHIU&-"BOEMJUFSBDZ strands. Table . Breadth of Coverage Criterion for English Language Arts and Literacy Common Core ELA and literacy strand CA MA TCCRS KSUS IB Reading for Literature Reading for Informational Texts Writing Speaking and Listening Language Standards Reading in History/Social Studies Reading in Science and Technical Subjects Writing in History/Social Studies, Science, and Technical Subjects CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate. means that a majority of topics in the Common Core strand have at least one matched comparison standard; means that one topic in the Common Core strand have at least one matched comparison standard; means that one or fewer than one topic in the Common Core strand have at least one matched comparison standard. Chapter Three 18 Chapter  | Results for Mathematics 3FTVMUT CFMPX EFTDSJCF UIF NBUDI CFUXFFO UIF $PNNPO $PSF NBUIFNBUJDT TUBOEBSET BOE UIF mWF TFUT PG DPNQBSJTPO TUBOEBSET3FTVMUTBSFHFOFSBMMZQSFTFOUFEBUUIFDPODFQUVBMDBUFHPSZMFWFM Match Overall Match of Comparison Standards to the Common Core Standards 'JHVSFTBOETIPXUIFBWFSBHFOVNCFSPGNBUDIFTQFS$PNNPO$PSFTUBOEBSEJOFBDIDMVTUFSBDSPTTBMMDPNQBSJTPO TUBOEBSET #PUI UIF DPODFQUVBM DBUFHPSJFT BOE DMVTUFST XJUIJO B DBUFHPSZ BSF TPSUFE JO EFTDFOEJOH PSEFS BDDPSEJOH UP GSFRVFODZ'JHVSFQSPWJEFTUIFJOGPSNBUJPOGPS4UBUJTUJDTBOE1SPCBCJMJUZ BOE(FPNFUSZ'JHVSFQSPWJEFTUIFJOGPSNBUJPO GPS'VODUJPOT "MHFCSB BOE/VNCFSBOE2VBOUJUZ5IFHSBQITTIPXUFOEFODJFTCFUXFFOBOEXJUIJODPODFQUVBMDBUFHPSJFT Figure . Average Number of Matches per Standard Across All Comparison Standards, by Cluster 0 10 20 30 40 50 Summarize, represent, and interpret data on a single count or measurement variable (4) Summarize, represent, and interpret data on two categorical and quantitative variables (5) Statistics and Probability Understand and evaluate random processes underlying statistical experiments (2) Understand independence and conditional probability and use them to interpret data (5) Make inferences and justify conclusions from sample surveys, experiments, and observational studies (4) Use the rules of probability to compute probabilities of compound events in a uniform probability model (4) Interpret linear models (3) Calculate expected values and use them to solve problems (4) Use probability to evaluate outcomes of decisions (5) 4'-+" ('(&-+"+-"(,',(%/)+(%&,"'/(%/"' +" !- triangles (3) Use coordinates to prove simple geometric theorems algebraically (4) Prove theorems involving similarity (2) Explain volume formulas and use them to solve problems (3) Translate between the geometric description and the equation for a conic section (3) Geometry Visualize relationships between two-dimensional and threedimensional objects (1) Apply trigonometry to general triangles (3) Prove geometric theorems (3) Make geometric constructions (2) Apply geometric concepts in modeling situations (3) Understand and apply theorems about circles (4) Understand congruence in terms of rigid motions (3) Experiment with transformations in the plane (5) Find arc lengths and areas of sectors of circles (1) Understand similarity in terms of similarity transformations (5) Note/VNCFSTJOQBSFOUIFTFTJOEJDBUFIPXNBOZTUBOEBSETTUBUFNFOUTBQQFBSXJUIJOUIFDMVTUFS Chapter Four •  Figure . Average Number of Matches per Standard Across All Comparison Standards, by Cluster 0 10 20 30 40 50 Understand the concept of a function and use function notation (3) Interpret functions that arise in applications in terms of the context (3) Prove and apply trigonometric identities (2) Functions Build a function that models a relationship between two quantities (5) Analyze functions using different representations (10) Model periodic phenomena with trigonometric functions (3) Extend the domain of trigonometric functions using the unit circle (4) Construct and compare linear and exponential models and solve problems (7) Build new functions from existing functions (7) Interpret expressions for functions in terms of the situation they model (1) Solve equations and inequalities in one variable (4) Perform arithmetic operations on polynomials(1) Represent and solve equations and inequalities graphically (3) Write expressions in equivalent forms to solve problems (5) Algebra Understand solving equations as a process of reasoning and explain the reasoning (2) Solve systems of equations (5) Rewrite rational expressions (2) Create equations that describe numbers or relationships (4) Understand the relationship between zeros and factors of polynomials (2) Interpret the structure of expressions (4) Use polynomial identities to solve problems (2) Extend the properties of exponents to rational exponents (2) Reason quantitatively and use units to solve problems (3) Number and Quanitiy Perform arithmetic operations with complex numbers (3) Represent complex numbers and their operations on the complex plane (3) Use properties of rational and irrational numbers (1) Represent and model with vector quantities (3) Perform operations on matrices and use matrices in applications (7) Perform operations on vectors (7) Use complex numbers in polynomial identities and equations (3) Note/VNCFSTJOQBSFOUIFTFTJOEJDBUFIPXNBOZTUBOEBSETTUBUFNFOUTBQQFBSXJUIJOUIFDMVTUFS Chapter Four 20 Chapter  | Results for Mathematics Match for Each Comparison Set to the Common Core Standards Categorical Concurrence Statistic 5BCMFTIPXTUIFBWFSBHFOVNCFSPGNBUDIFTQFSDPODFQUVBM DBUFHPSZ CFUXFFO UIF $PNNPO $PSF TUBOEBSET BOE FBDI set of comparison standards for mathematics. Generally, all DBUFHPSJFTGPSBMMTUBOEBSETTFUTIBWFBSFMBUJWFMZIJHIOVNCFS PGNBUDIFT"TXJUI&OHMJTIMBOHVBHFBSUTBOEMJUFSBDZ TPNF DBUFHPSJFTIBWFWFSZIJHITUBOEBSEEFWJBUJPOT JOEJDBUJOHUIBU SBUFSTWBSJFEXJEFMZJOUIFOVNCFSPGNBUDIFTUIFZJEFOUJmFE #FDBVTFBTJOHMFDPSSFTQPOEFODFJOBDPOUFOUBSFBCFUXFFO UXP TFUT PG TUBOEBSET JT DPOTJEFSFE TVGmDJFOU UP NFFU UIF TUBOEBSETUPTUBOEBSET BMJHONFOU DSJUFSJPO $PPL UIF DSJUFSJPO GPS $BUFHPSJDBM $PODVSSFODF JT NFU GPS FWFSZ DPODFQUVBM DBUFHPSZ GPS FWFSZ DPNQBSJTPO TUBOEBSE TFU "DSPTTSBUFST NPSFUIBOPOFTUBOEBSEGSPNFWFSZTFUPGUIFmWF DPNQBSJTPO TUBOEBSET PO BWFSBHF JT NBUDIFE UP B $PNNPO $PSFTUBOEBSE TFF5BCMF *O"QQFOEJY$ UIFSFJTNPSFEFUBJMFEEJTDVTTJPOGPSFBDITFUPG DPNQBSJTPOTUBOEBSETBOEIPXJUBMJHOTUPUIF$PNNPO$PSF The precise correspondence of matches between the Common Core standards and individual comparison sets of standards is QSPWJEFEJOUIF5FDIOJDBM4VQQMFNFOU Table . Average Number of Matches for Mathematics Common Core Standards Across Five Sets of Standards Common Core mathematics conceptual category Average number of matches CA MA TCCRS KSUS IB M SD M SD M SD M SD M SD Number and Quantity . . . . . . . . . . Algebra . . . . . . . . . . Functions . . . . . . . . . . Geometry . . . . . . . . . . Statistics and Probability . . . . . . . . . . Total . . . . . . . . . . CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate. Table . Categorical Concurrence for Mathematics Common Core mathematics conceptual category CA MA TCCRS KSUS IB Number and Quantity Algebra Functions Geometry Statistics and Probability CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate. Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of standards); Does not meet the criterion for Categorical Concurrence. Chapter Four 21 Chapter  | Results for Mathematics Depth of Knowledge Ratings for Common Core Standards 5BCMFTIPXTUIFNPEBM%FQUIPG,OPXMFEHF %0, SBUJOH for each of the Common Core mathematics conceptual DBUFHPSJFT5ISFFDBUFHPSJFTSFQSFTFOUUIFTLJMMTBOEDPODFQUT MFWFMPGDPHOJUJWFEFNBOE MFWFM *OUIF/VNCFSBOE2VBOUJUZ DBUFHPSZ XIJDIIBTBNPEFPGMFWFM SFDBMMBOESFQSPEVDUJPO UIF TUBOEBSET JOWPMWF TVDI TLJMMT BT FYQMBJOJOH QSPQFSUJFT PG JSSBUJPOBM FYQPOFOUT SBUJPOBM BOE JSSBUJPOBM OVNCFST BOE QFSGPSNJOH BSJUINFUJD PQFSBUJPOT XJUI DPNQMFY OVNCFST WFDUPST BOE NBUSJDFT 5IFTF TLJMMT NBZ CF NPSF PSJFOUFE UPXBSE POFTUFQ SFDBMM PS QSPCMFN TPMWJOH *O UIF (FPNFUSZ DBUFHPSZ UIFTUBOEBSETJOWPMWFTVDITLJMMTBTQSPWJOHUIFPSFNT EFSJWJOH FRVBUJPOT BOE VTJOH FYQFSJNFOUBUJPO UP WFSJGZ DPODFQUT TVDI BT TJNJMBSJUZ 4VDI TLJMMT NBZ MFOE UIFNTFMWFT NPSF UPXBSE TUSBUFHJD BOE FYUFOEFE UIJOLJOH XIJDI DPVME FYQMBJOXIZUIFNPEFSBUJOHGPSUIBUDPOUFOUTQFDJmDBSFBXBT BUMFWFM TUSBUFHJDUIJOLJOH Figure . Percent of Common Core Mathematics Standards at each Depth of Knowledge Level Level 4 Extended Thinking 5% Level 3 Strategic Thinking 20% Level 1 Recall and Reproduction 21% Table . Depth of Knowledge (DOK) Modal Ratings for Mathematics Common Core Conceptual Categories Common Core mathematics conceptual category DOK mode Number and Quantity  Algebra  Functions  Geometry  Statistics and Probability  At the standard level, the Common Core mathematics standards DPWFSBTPNFXIBUCSPBEFSSBOHFPGDPHOJUJWFDPNQMFYJUZUIBO the ELA and literacy Common Core standards with fewer at the IJHIFTUMFWFM5IFNBKPSJUZPGUIF$PNNPO$PSFNBUIFNBUJDT TUBOEBSET BSF SBUFE BT TLJMMT BOE DPODFQUT MFWFM 0WFSBMM BSF BU B MFWFM SFDBMM BOE SFQSPEVDUJPO BSF BU B MFWFM TLJMMT BOE DPODFQUT BSF BU B MFWFM TUSBUFHJD UIJOLJOH BOEBSFBUMFWFM FYUFOEFEUIJOLJOH 'JHVSF TVNNBSJ[FTUIJTJOGPSNBUJPO%0,SBUJOHTGPSBMMTUBOEBSETBSF QSPWJEFEJO"QQFOEJY# Level 2 Skills and Concepts 54% Chapter Four 22 Chapter  | Results for Mathematics "T NFOUJPOFE FBSMJFS UIF 4UBOEBSET GPS .BUIFNBUJDBM Practice within the Common Core standards were not rated for the purposes of this study. The Mathematical Practices BSF EFTJHOFE GPS FEVDBUPST UP BQQMZ BDSPTT BMM $PNNPO $PSF NBUIFNBUJDT TUBOEBSET 5IVT VTJOH UIF NBUIFNBUJDT practices in the application and use of the other Common Core mathematics standards could conceivably lead to different MFWFMTPGDPHOJUJWFEFNBOEUIBOUIPTFQSFTFOUFEIFSF DOK Consistency of Each Comparison Set to the Common Core Standards 'JHVSF TIPXT GPS FBDI DPNQBSJTPO TFU UIF QFSDFOU PG TUBOEBSET BWFSBHFE BDSPTT SBUFST TFF "QQFOEJY " UIBU GFMM BCPWF BU BOEVOEFSUIFDPHOJUJWFEFNBOEMFWFMPGUIF$PNNPO $PSFTUBOEBSET*OUIFmHVSF BMJOFJTESBXOBU XIJDIJT UIFDSJUFSJPOGPSUIFOVNCFSPGTUBOEBSETGBMMJOHBCPWFPSBUUIF DPHOJUJWFEFNBOEMFWFMPGUIF$PNNPO$PSFJOPSEFSUPNFFU UIF%0,$POTJTUFODZTUBUJTUJD'PSUIF/VNCFSBOE2VBOUJUZ "MHFCSB BOE4UBUJTUJDTBOE1SPCBCJMJUZDPODFQUVBMDBUFHPSJFT BMM TFUT PG TUBOEBSET NFFUJOH UIF $BUFHPSJDBM $PODVSSFODF DSJUFSJPO BMTP NFFU UIF %0, DSJUFSJPO 'PS (FPNFUSZ POMZ UIF 5FYBT $PMMFHF BOE $BSFFS 3FBEJOFTT TUBOEBSET XFSF BU PS BCPWFUIFDPHOJUJWFEFNBOEPGUIF$PNNPO$PSFTUBOEBSET 'PS 'VODUJPOT UISFF PG mWF TFUT PG TUBOEBSET UIBU NFFU UIF $BUFHPSJDBM $PODVSSFODF DSJUFSJPO NFFU UIF %0, DSJUFSJPO 5IFTFSFTVMUTTVHHFTUUIBUGPSFWFSZNBUIFNBUJDTDPODFQUVBM DBUFHPSZ UIF5FYBT$PMMFHFBOE$BSFFS3FBEJOFTTTUBOEBSET UFOE UP CF TJNJMBS UP PS NPSF DPHOJUJWFMZ DPNQMFY UIBO UIF Common Core standards. The California state standards and the Massachusetts state standards are similar to or more DPHOJUJWFMZ DPNQMFY UIBO UIF $PNNPO $PSF TUBOEBSET GPS GPVS PVU PG mWF DPODFQUVBM DBUFHPSJFT UIBU TIPX DBUFHPSJDBM DPODVSSFODF 'JHVSF JMMVTUSBUFT UIFTF mOEJOHT 5IF mHVSF also shows that some standards sets fall just above or just CFMPXGPSTPNFDBUFHPSJFTBOESFTVMUTXPVMECFEJGGFSFOU if an alternative criterion had been selected. Figure . Depth of Knowledge Level Comparisons of the Five Sets of Comparison Standards to Common Core Mathematics Standards 25 50 CA MA TCCRS KSUS IB Functions CA MA TCCRS KSUS IB Geometry CA MA TCCRS KSUS IB CA MA TCCRS KSUS IB Statistics and Probability Algebra Number and Quantity 0 CA MA TCCRS KSUS IB 75 100 Average Percent % Above % At % Under Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH Chapter Four 23 Chapter  | Results for Mathematics Breadth of Coverage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able . Breadth of Coverage Criterion for Mathematics Common Core mathematics conceptual category CA MA TCCRS KSUS IB Number and Quantity Algebra Functions Geometry Statistics and Probability CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate. means that a majority of clusters in the Common Core conceptual category have at least one matched comparison standard; means that more than one cluster in the Common Core conceptual category have at least one matched comparison standard; means that one or fewer than one cluster in the Common Core conceptual category have at least one matched comparison standard. "QQFOEJY % QSFTFOUT NPSF JOGPSNBUJPO BCPVU UIF EJTUSJCVUJPO PG TUBOEBSE NBUDIFT XJUIJO FBDI PG UIF mWF $PNNPO $PSF NBUIFNBUJDTDPODFQUVBMDBUFHPSJFT Chapter Four 24 Chapter  | Summary and Discussion In this chapter we review the purpose of the study, discuss the method chosen to obtain data necessary to answer the three SFTFBSDI RVFTUJPOT JOUSPEVDF JNQMJDBUJPOT PG UIF mOEJOHT BOEPGGFSTVHHFTUJPOTGPSGVUVSFSFTFBSDI The study addresses three research questions: 1. 5PXIBUFYUFOUBSFUIFLOPXMFEHFBOETLJMMTGPVOEJO the comparison standards the same as or different from what is described in the Common Core TUBOEBSET NBUDI 2. 8IBUJTUIFDPHOJUJWFDPNQMFYJUZMFWFMPGUIF$PNNPO $PSFTUBOEBSETBOEUPXIBUFYUFOUBSFUIFNBUDIFE DPNQBSJTPO TUBOEBSET BU B IJHIFS PS MPXFS MFWFM PG DPHOJUJWFDPNQMFYJUZ EFQUI 3. How broadly do the matched comparison standards cover the content of the Common Core standards? CSFBEUI 5IF SFBTPO GPS BTLJOH UIFTF RVFTUJPOT JT UIBU TUBUFT BSF DPODFSOFE BCPVU UIF SJHPS PG UIF $PNNPO $PSF TUBOEBSET and the comparison of the Common Core standards to FYJTUJOH TUBOEBSET #FDBVTF UIF $PNNPO $PSF TUBOEBSET TQPOTPST FYQMJDJUMZ JOUFOEFE UIF TUBOEBSET UP CF BU UIF MFWFM PG SFBEJOFTT GPS DPMMFHF BOE DBSFFST XF DPNQBSFE UIF $PNNPO $PSF TUBOEBSET UP mWF TFUT PG DPNQBSJTPO TUBOEBSET UIBU BSF DPOTJEFSFE SJHPSPVT BOE JO UXP DBTFT BSF FYQMJDJUMZ EFTJHOBUFE BT DPMMFHF BOE DBSFFS SFBEJOFTT standards. The two states deemed to have standards that IBWF CFFO SFDPHOJ[FE BT SJHPSPVT PS PUIFSXJTF FYFNQMBSZ BSF $BMJGPSOJB BOE .BTTBDIVTFUUT 5IF UXP TFUT PG DPMMFHF BOE DBSFFS SFBEJOFTT TUBOEBSET BSF UIF 5FYBT $PMMFHF BOE $BSFFS 3FBEJOFTT 4UBOEBSET BOE UIF ,OPXMFEHF BOE 4LJMMT GPS6OJWFSTJUZ4VDDFTT'JOBMMZ XFJODMVEFEBOJOUFSOBUJPOBMMZ HSPVOEFETFUPGTUBOEBSETGSPNUIF*OUFSOBUJPOBM#BDDBMBVSFBUF *# %JQMPNB1SPHSBNNF 8FNFBTVSFEBMJHONFOUVTJOHUISFFNFUSJDTGSPNBNPEJmFE WFSTJPO PG UIF 8FCC B NFUIPE EFTJHOFE UPEFUFSNJOFTUBOEBSETUPTUBOEBSETBMJHONFOU $PPL $PPL8JMNFT 5IFNFUSJDTQSPWJEFBNFBOTUPRVBOUJGZ BOE FWBMVBUF UIF FYUFOU PG PWFSMBQ CFUXFFO EJGGFSFOU TFUT PG TUBOEBSETJOUFSNTPGLOPXMFEHF TLJMMT BOEDPOUFOU8IFSF PWFSMBQ FYJTUT UIF NBUDIJOH TUBOEBSET BSF UIFO DPNQBSFE UP EFUFSNJOF SFMBUJWF DPHOJUJWF EFNBOE 5IF UIJSE NFUSJD EFUFSNJOFT CSFBEUI PG PWFSMBQ PS DPWFSBHF GPS NBUDIJOH TUBOEBSET"MMUISFFNFUSJDTBSFDBMDVMBUFEBUUIFIJHIFTUMFWFM PGPSHBOJ[BUJPOGPSUIF$PNNPO$PSF FJHIUTUSBOETGPS&OHMJTI -BOHVBHF"SUT &-" BOEMJUFSBDZmWFDPODFQUVBMDBUFHPSJFT GPS NBUIFNBUJDT CFDBVTF UIF TUVEZT HPBM JT UP QSPWJEF BO JOJUJBMIJHIMFWFMWJFXPGUIFSFMBUJPOTIJQCFUXFFOUIF$PNNPO $PSFTUBOEBSETBOEPUIFSTUBOEBSETZTUFNT OPUUPFOHBHFJO mOFHSBJOFEDPNQBSJTPOT The overall results of the study, as summarized in Table 20, TVHHFTUTVCTUBOUJBMDPODVSSFODFCFUXFFOUIF$PNNPO$PSF standards and the comparison standards, with somewhat HSFBUFSPWFSMBQJONBUIFNBUJDTUIBOJO&-"BOEMJUFSBDZ'PS &-"BOEMJUFSBDZ PGBOBMZTFTBUUIFTUSBOEMFWFMNFFU UIF $BUFHPSJDBM $PODVSSFODF DSJUFSJPO 5IF iNFFUTw DSJUFSJPO is relatively modest, namely, one or more correspondences CFUXFFOUXPTFUTPGTUBOEBSET $PPL )PXFWFS GPSPG UIFTFDPNQBSJTPOT UIFNFBOOVNCFSPGNBUDIJOHTUBOEBSET JTBCPWFTJY TJYNBUDIFTJTBDPNNPODSJUFSJPOGPSBMJHONFOU TUVEJFT UIBU FYBNJOF DPODVSSFODF CFUXFFO UFTU JUFNT BOE TUBOEBSET *OQMBDFT UIFOVNCFSPGNBUDIFTFYDFFET'PS NBUIFNBUJDT PG BOBMZTFT BU UIF DPODFQUVBM DBUFHPSZ MFWFM NFFU UIF $BUFHPSJDBM $PODVSSFODF DSJUFSJPO 'PS PG UIFTFDPNQBSJTPOT UIFNFBOOVNCFSPGNBUDIJOHTUBOEBSET JTBCPWFTJY JOQMBDFTFYDFFEJOHNBUDIFT Chapter Five •  Chapter  | Summary and Discussion Table . Summary of Alignment Findings for Five Sets of Standards Compared to the Common Core Standards Common Core FRQWHQWVSHFLÀFDUHDV Comparison standards CA MA TCCRS KSUS IB English language arts and literacy Reading for Literature Reading for Informational Texts Writing Speaking and Listening Language NA Reading in History/Social Studies NA Reading in Science and Technical Subjects NA NA Writing in History/Social Studies, Science, and Technical Subjects Mathematics Number & Quantity Algebra Functions Geometry Statistics & Probability CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate. Key Categorical Concurrence met Strong coverage Depth of Knowledge met Moderate coverage Limited or no coverage *OUFSNTPGUIFDPHOJUJWFEFNBOEPGUIFTUBOEBSET UIFmOEJOHT TVHHFTU HFOFSBM DPOTJTUFODZ CFUXFFO UIF $PNNPO $PSF TUBOEBSET BOE UIF mWF DPNQBSJTPO TUBOEBSE TFUT 5IFSF JT TPNFXIBU HSFBUFS DPSSFTQPOEFODF JO DPHOJUJWF EFQUI XJUI the mathematics standards comparisons than the ELA and MJUFSBDZTUBOEBSETDPNQBSJTPOT BmOEJOHDPOTJTUFOUXJUIPUIFS $PNNPO $PSF BMJHONFOU XPSL 1PSUFS .D.BLFO )XBOH :BOH 'PSDPHOJUJWFDPNQMFYJUZJO&-"BOEMJUFSBDZ PGTUSBOE level analyses indicated that the comparison standard sets XFSFBUPSBCPWFUIFMFWFMPGUIF$PNNPO$PSFTUBOEBSET*O cases, the comparison standard sets tended to be rated lower JO DPHOJUJWF DPNQMFYJUZ UIBO UIF $PNNPO $PSF TUBOEBSET 5IJT TVHHFTUT UIBU BT TUBUFT USBOTJUJPO UP UIF $PNNPO $PSF TUBOEBSET JU XJMM CF XPSUIXIJMF UP MPPL DMPTFMZ BU UIF MFWFM PG DPHOJUJWFDPNQMFYJUZJOUIFJSDVSSFOUTUBOEBSETJOSFMBUJPOUPUIF $PNNPO$PSFTUBOEBSET4UBUFTTIPVMEDBSFGVMMZJOUFSQSFUUIF DPNQMFYJUZPGUIF$PNNPO$PSFTUBOEBSETBTUIFZJNQMFNFOU DVSSJDVMVN GSBNFXPSLT BOE EFWFMPQ FYBNQMF NBUFSJBMT UP QVUUIFTUBOEBSETJOUPQMBDF5IFDPHOJUJWFDPNQMFYJUZPGUIF Common Core ELA and literacy standards in particular will be EFmOFECZUIFBDUVBMBTTJHONFOUTBOEBTTFTTNFOUTHJWFOUP TUVEFOUT TFF #FBDI 4UBUFT BOE HSPVQT EFWFMPQJOH curriculum materials for the Common Core standards need to QBZ DMPTF BUUFOUJPO UP UIF DPHOJUJWF DIBMMFOHF MFWFM PG UIFTF NBUFSJBMTUPFOTVSFUIFZBSFTVGmDJFOUMZDIBMMFOHJOH5IJTJTUSVF Chapter Five 26 Chapter  | Summary and Discussion GPSNBOZPGUIFTUSBOET BMUIPVHIUIF-BOHVBHF4UBOEBSETBSF BOPUBCMFFYDFQUJPO JOQBSUCFDBVTFUIJTBSFBUFOETUPSFRVJSF MFTTDPHOJUJWFEFQUI CVUJTQBSUJDVMBSMZJNQPSUBOUUPDPOTJEFS XIFO EFWFMPQJOH NBUFSJBMT UP UFBDI BOE BTTFTT SFBEJOH PG JOGPSNBUJPOBM UFYUT BOE SFBEJOH BOE XSJUJOH GPS MJUFSBDZ JO UIF content areas. 'PSNBUIFNBUJDT PGDPODFQUVBMDBUFHPSZMFWFMBOBMZTFT indicate that the comparison standard sets are at or above the MFWFMPGUIF$PNNPO$PSFTUBOEBSET$POWFSTFMZ TJYBOBMZTFT found comparison standard sets to be below the level of the Common Core standards. The Common Core content areas UIBU UFOEFE UP CF IJHIFS BSF UIF NPSF DPODFQUVBMMZPSJFOUFE DPODFQUVBM DBUFHPSZ PG (FPNFUSZ BOE UP B MFTTFS EFHSFF Functions. 0WFSBMM UIFTUBOEBSETGSPNUIFDPNQBSJTPOTFUTUFOEUPDPWFS the breadth of topics set forth in the Common Core standards. 'PS &-" BOE MJUFSBDZ PG TUSBOE BOBMZTFT TIPX TUSPOH DPWFSBHF "OPUIFS UXP TUSBOE BOBMZTFT TIPXFE NPEFSBUF DPWFSBHFBOEPOFTIPXFEMJNJUFEDPWFSBHF'PSNBUIFNBUJDT mOEJOHTTVHHFTUUIBUDPNQBSJTPOTFUTTIPXTUSPOHDPWFSBHF JOBMMDPODFQUVBMDBUFHPSZBOBMZTFT8IJMFFWFSZTUBOEBSEJO the Common Core standards may not have a match, the topics BSPVOEXIJDIUIF$PNNPO$PSFTUBOEBSETBSFPSHBOJ[FEBSF SFnFDUFEJOUIFDPNQBSJTPOTUBOEBSET 5IFmWFTFUTPGDPNQBSJTPOTUBOEBSETBSFOPUGVMMZBEFRVBUFUP BDDPVOUGPSUIFDPOUFOUUIBUNJHIUCFJODMVEFEJOFWFSZTQFDJmD TUBUFT TUBOEBSET "NPOH UIF DPNQBSJTPO TUBOEBSET JO UIJT TUVEZ UIBU BSF DPOTJEFSFE SJHPSPVT BOE DPMMFHF BOE DBSFFS QSFQBSBUPSZ IPXFWFS UIF PWFSBMM mOEJOHT TVHHFTU B HFOFSBM MFWFMPGBHSFFNFOUCFUXFFOUIF$PNNPO$PSFTUBOEBSETBOE UIF DPNQBSJTPO TUBOEBSET SFHBSEJOH XIBU JT JNQPSUBOU GPS IJHI TDIPPM TUVEFOUT UP LOPX JO &OHMJTI MBOHVBHF BSUT BOE NBUIFNBUJDT JO PSEFS UP CF IJHIMZ DIBMMFOHFE BOE SFBEZ GPS DPMMFHFBOEDBSFFST 5IF QVSQPTF PG UIJT TUVEZ XBT UP BTDFSUBJO BMJHONFOU OPU UP KVEHF UIF RVBMJUZ PG BOZ TFU PG TUBOEBSET JO SFMBUJPO UP BOZ other set of standards. There is no absolute reason that every set of comparison standards must match the Common Core TUBOEBSETJOFWFSZBSFBJOPSEFSUPCFDPOTJEFSFEIJHIRVBMJUZ TUBOEBSET4JNQMZCFDBVTFBTFUPGTUBOEBSETMBDLTBNBUDI to the Common Core standards in one or more areas does not mean the comparison standards are inferior or need to CFDIBOHFEUPNBUDIUIF$PNNPO$PSFTUBOEBSET,OPXJOH TPNFUIJOHBCPVUBMJHONFOUDBOIFMQJOQSPHSBNQMBOOJOH CVU is not necessarily the best or only measure of standards quality. Closing Note From The Authors 5IFCVTJOFTTPGBOBMZ[JOHBMJHONFOU DPHOJUJWFDIBMMFOHF BOE DPWFSBHFCFUXFFOTFUTPGTUBOEBSETSFNBJOTBOBQQSPYJNBUF BSU FWFO XIFO BNQMF DBSF JT HJWFO UP DPOUSPM WBSJBUJPO BOE ensure reliable and valid results. This is one of the reasons we PGGFSmOEJOHTBUBIJHIMFWFMPGBHHSFHBUJPO 8FOPUFUIBUBOPUIFSSFDFOUTUVEZ 1PSUFSFUBM VTFEB different method and reached a different conclusion. This study BMJHOFEBMMHSBEFMFWFMTPGBMMTUBUFTUBOEBSETUPUIF$PNNPO $PSFVTJOHUIF4VSWFZPG&OBDUFE$VSSJDVMVN 4&$ BNFUIPE UIBU JOWPMWFT DPNQBSJOH TFUT PG TUBOEBSET UP B DPNNPO GSBNFXPSL UIBU JOUFSTFDUT QBSUJDVMBS UPQJDT XJUI DPHOJUJWF EFNBOE%BUBBSFDPOWFSUFEJOUPQSPQPSUJPOTBOEBOBMJHONFOU JOEFYDBMDVMBUFEUPBTTFTTDPNNPOBMJUZJODPOUFOUBDSPTTUIF UXPTUBOEBSETFUT-PPLJOHBU4&$SFTVMUTBDSPTTBMMTUBUFT UIF authors conclude that the Common Core standard represent DPOTJEFSBCMFDIBOHFGSPNDVSSFOUTUBUFTUBOEBSET In our opinion, it is possible for both studies to be correct in their DPODMVTJPOT0VSTUVEZGPDVTFTPOUIFNBDSPMFWFMUPJEFOUJGZ HFOFSBMSFMBUJPOTIJQTXIJMFUIF1PSUFSFUBMTUVEZ[FSPFTJOBU B NVDI NPSF EFUBJMFE MFWFM "T TUVEJFT PG DPOUFOU BMJHONFOU NPWFUPmOFSHSBJOTJ[F UIFQSPCBCJMJUZPGBDIJFWJOHVOJWFSTBM QSFDJTFNBUDIFTCFHJOTUPEFDSFBTF5IJTNBZCFQBSUJDVMBSMZ true in the case of the Common Core standards, which were JOUFOEFEUPCFBUBNPSFHFOFSBMMFWFMBOEOPUUPTQFDJGZFBDI BOEFWFSZFMFNFOUTUVEFOUTBSFFYQFDUFEUPMFBSO 8FXPVMEBMTPOPUFUIBUJOBQSFWJPVTTUVEZ $POMFZ %SVNNPOE EF(PO[BMF[ 3PPTFCPPN 4UPVU XFGPVOEUIF$PNNPO $PSF TUBOEBSET UP CF XFMM BMJHOFE XJUI B DSPTTTFDUJPO PG entry-level postsecondary course areas. At the same time, EJGGFSFOUNBKPSPSmFMETPGTUVEZSFRVJSFEJGGFSFOUDPNCJOBUJPOT of Common Core standards. In other words, it does not appear UIBU UIFSF JT B NBHJD TFU PG TUBOEBSET UIBU SFnFDU XIBU FWFSZ TUVEFOUOFFETUPTVDDFFEJOFWFSZQPTUTFDPOEBSZTFUUJOH5IF GBDUUIBUUIF$PNNPO$PSFTUBOEBSETEPOPUBMJHOQSFDJTFMZXJUI FBDITUBUFTFYJTUJOHTUBOEBSETTIPVMEOPUCFDBVTFGPSVOEVF BMBSNJGTUBUFTQBZBUUFOUJPOUPBOPUIFSmOEJOHGSPNPVSQSFWJPVT XPSL $POMFZ $POMFZ FU BM UIBU QPTUTFDPOEBSZ JOTUSVDUPSTJOEJDBUFUIBUTUVEFOUUIJOLJOHTLJMMTBSFBTJNQPSUBOU BTBOZQBSUJDVMBSCJUPGDPOUFOULOPXMFEHF8IJMFBMMTUVEFOUT OFFE B TPVOE BDBEFNJD GPVOEBUJPO UIF TQFDJmD LOPXMFEHF BOETLJMMTSFRVJSFEGPSQPTUIJHITDIPPMTVDDFTTXJMMWBSZ5IF UIJOLJOHTLJMMTBOEMFBSOJOHTUSBUFHJFTUIBUCBDDBMBVSFBUFBOE DBSFFSPSJFOUFEQSPHSBNTSFRVJSFEPBQQFBSUPCFNPSFVOJGPSN BOEDPOTJTUFOU5IFDPHOJUJWFDIBMMFOHFMFWFMPGTUBOEBSETBOE UIF XBZT JO XIJDI UIFZ BSF UBVHIU JO DMBTTSPPNT XJMM CF BT Chapter Five 27 Chapter  | Summary and Discussion important as the content covered in most cases. 3FTVMUTGSPNHFOFSBMBMJHONFOUTUVEJFTDBOCFJOGPSNBUJWFBU BCSPBEMFWFM4UBUFTTUJMMNVTUOFDFTTBSJMZFOHBHFJOBNVDI NPSFmOFHSBJOFEUZQFPGBOBMZTJTJGUIFZXBOUUPBTDFSUBJOUIF QSFDJTFSFMBUJPOTIJQCFUXFFOBOEBNPOHFBDITUBOEBSEJOUXP TZTUFNT UIF FYJTUJOH TUBUF TUBOEBSET BOE UIF $PNNPO $PSF standards. 0VSBEWJDFUPTUBUFTJTOPUUPMPTFTJHIUPGUIFGPSFTUGPSUIFUSFFT 4UBUFTXJMMCFXFMMTFSWFEUPMPPLGPSQBUUFSOTBMPOHXJUITQFDJmD NBUDITUBUJTUJDTBOEBEESFTTJTTVFTPGDPHOJUJWFDIBMMFOHFJO QBSUJDVMBSCZUIFMJCFSBMVTFPGFYBNQMFNBUFSJBMTBOEFYFNQMBS TUVEFOU XPSL JO BOZ TUBOEBSET DSPTTXBML BOE XIFO UIF Common Core standards are rolled out statewide. This is true and necessary for both ELA and mathematics. It is perhaps more obvious that the ELA standards will be operationalized OPUUISPVHIUIFMJUFSBMUFBDIJOHPGUIFTUBOEBSETTUBUFNFOUTCVU UISPVHIUIFNBUFSJBMTTFMFDUFEUPUFBDIUIFTUBOEBSETBUFBDI HSBEFMFWFM"T#FBDI QPJOUTPVU TUBOEBSETMBOHVBHF DBO CF JOUFSQSFUFE WBSJBCMZ SFTVMUJOH JO EJGGFSFOU USBOTMBUJPOT JOEJGGFSFOUDPOUFYUT&EVDBUPSTNVTUNBLFJOUFMMJHFOUDIPJDFT about how students should learn the standards. As we note in UIF mOEJOHT TFDUJPO TQFDJBM BUUFOUJPO XJMM OFFE UP CF QBJE UP JOGPSNBUJPOBMUFYUTJOQBSUJDVMBSUPFOTVSFUIFZSFnFDUBCSPBE SBOHFPGDIBMMFOHJOHNBUFSJBMBOEUPQJDT *ONBUIFNBUJDT FWFOUIPVHIUIFDBUFHPSJDBMNBUDIFTCFUXFFO state standards and the Common Core standards may be WFSZ IJHI JU JT TUJMM XPSUI OPUJOH UIBU UIF DPHOJUJWF DIBMMFOHF MFWFM PG UIFTF TUBOEBSET XJMM CF EFUFSNJOFE JO MBSHF NFBTVSF CZUIFQSPCMFNTTUVEFOUTBSFHJWFOUPUFTUUIFJSLOPXMFEHFPG UIF NBOZ mOFHSBJOFE BOE EFUBJMFE TUBOEBSET 5IF XBZ UIF Mathematical Practices standards factor into the Common $PSF TUBOEBSET QPTFT B DIBMMFOHF UP USBEJUJPOBM BMJHONFOU NFUIPEPMPHZ TFF $PCC +BDLTPO "MUIPVHI UIF Mathematical Practices did not lend themselves to inclusion JOUIFDVSSFOUTUVEZ UIFZBSFRVJUFJNQPSUBOUUPLFFQJONJOE XIFO DPOTJEFSJOH UIF JOUFOEFE DPHOJUJWF DIBMMFOHF MFWFM PG each of the mathematical standards. The standards authors note the importance of the Mathematical Practice standards BOEUIFJOUFOUUIBUUIFZCFBQQMJFEUPUIFMFBSOJOHPGBMMPGUIF PUIFS NBUIFNBUJDT TUBOEBSET 5IF JOUFOUJPO JT UIBU JO EPJOH TP NBUIFNBUJDTXJMMCFUBVHIUXJUINPSFSPCVTUBOEDPNQMFY applications of mathematical processes and principles. *OTIPSU FEVDBUPSTTIPVMECFBSJONJOEUIFHPBMPGUIF$PNNPO $PSFTUBOEBSETXIFODPOTJEFSJOHUIFNFDIBOJDTPGBMJHONFOU 5IBU HPBM JT UP SBJTF UIF DIBMMFOHF MFWFM GPS 64 TUVEFOUT UP FOBCMFBMMTUVEFOUTUPQVSTVFTVDDFTTGVMGVUVSFTCFZPOEIJHI school, futures that include additional postsecondary study for most students, and to equip students with a set of core LOPXMFEHFBOETLJMMTUIBUFOBCMFUIFNUPCFBEBQUJWFMFBSOFST UISPVHIPVU UIFJS MJWFT "MJHONFOU JT POMZ B QSFMJNJOBSZ TUFQ JO BDIJFWJOHUIJTHPBM Chapter Five 28 | References "DIJFWF *OD $PNQBSJOHUIF$PNNPO$PSF4UBUF4UBOEBSETJONBUIFNBUJDTUP$BMJGPSOJBBOE.BTTBDIVTFUUT TUBOEBSET3FUSJFWFEGSPNIUUQXXXBDIJFWFPSHDPNQBSJOHDPNNPODPSFTUBUFTUBOEBSETNBUIFNBUJDTDBMJGPSOJBBOE massachusetts-standards #FBDI 38 *TTVFTJO"OBMZ[JOH"MJHONFOUPG-BOHVBHF"SUT$PNNPO$PSF4UBOEBSET8JUI4UBUF4UBOEBSET Educational Researcher, o #SPXO 34 $POMFZ %5 $PNQBSJOHTUBUFIJHITDIPPMBTTFTTNFOUTUP4UBOEBSETGPS4VDDFTTJOFOUSZMFWFM university courses. Educational Assessment o #ZSE 4 &MMJOHUPO - (SPTT 1 +BHP $ 4UFSO 4 Advanced Placement and International Baccalaureate: Do they deserve gold star status?8BTIJOHUPO %$5IPNBT#'PSEIBN*OTUJUVUF $BMJGPSOJB%FQBSUNFOUPG&EVDBUJPO B English–Language arts content standards kindergarten through grade twelve. 3FUSJFWFEGSPNIUUQXXXDEFDBHPWCFTUTTEPDVNFOUTFMBDPOUFOUTUOETQEG $BMJGPSOJB%FQBSUNFOUPG&EVDBUJPO C Mathematics content standards kindergarten through grade twelve3FUSJFWFE GSPNIUUQXXXDEFDBHPWCFTUTTEPDVNFOUTNBUITUBOEBSETQEG $BSNJDIBFM 4# .BSUJOP ( 1PSUFS.BHFF , 8JMTPO 84 'BJSDIJME % )BZEFM & 4FOFDIBM % 8JOLMFS ". +VMZ The state of state standards and the Common Core in 20108BTIJOHUPO %$5IPNBT#'PSEIBN*OTUJUVUF $PCC 1 +BDLTPO , "TTFTTJOHUIF2VBMJUZPGUIF$PNNPO$PSF4UBUF4UBOEBSETGPS.BUIFNBUJDTEducational Researcher o $PNNPO$PSF4UBUF4UBOEBSET*OJUJBUJWF B About the Standards3FUSJFWFEGSPNIUUQXXXDPSFTUBOEBSETPSHBCPVU the-standards $PNNPO$PSF4UBUF4UBOEBSET*OJUJBUJWF C Common Core State Standards for English language arts and literacy in history/social studies, science, and technical subjects3FUSJFWFEGSPNIUUQXXXDPSFTUBOEBSETPSHBTTFUT$$44*@ &-"4UBOEBSETQEG $PNNPO$PSF4UBUF4UBOEBSET*OJUJBUJWF D Common Core State Standards for mathematics3FUSJFWFEGSPNIUUQXXX DPSFTUBOEBSETPSHBTTFUT$$44*@.BUI4UBOEBSETQEG $POMFZ %5 Understanding university success: A report from Standards for Success, a project of the Association of American Universities and The Pew Charitable Trusts&VHFOF 03$FOUFSGPS&EVDBUJPOBM1PMJDZ3FTFBSDI $POMFZ %5 %SVNNPOE ,7 EF(PO[BMF[ " 3PPTFCPPN + 4UPVU 0 Reaching the goal: The applicability and importance of the Common Core State Standards to college and career readiness&VHFOF 03&EVDBUJPOBM1PMJDZ Improvement Center. $POMFZ % .D(BVHIZ $ $BEJHBO , 'MZOO , 7FBDI % 'PSCFT + Validation Study I: Alignment of the Texas College and Career Readiness Standards with Entry-Level General Education Courses at Texas Postsecondary Institutions&VHFOF 0SFHPO5IF&EVDBUJPOBM1PMJDZ*NQSPWFNFOU$FOUFS $POMFZ %5 8BSE 5 International Baccalaureate Standards Development and Alignment Project&VHFOF 0SFHPO Educational Policy Improvement Center. $PPL )( Research Report #0504: Milwaukee Public Schools alignment study of Milwaukee Public Schools’ Learning Targets in reading and math to Wisconsin student assessment system criterion-referenced test frameworks in reading and math.JMXBVLFF 8*.JMXBVLFF1VCMJD4DIPPMT0GmDFPG"TTFTTNFOUBOE"DDPVOUBCJMJUZ $PPL )( 4PNFUIPVHIUTPO&OHMJTIMBOHVBHFQSPmDJFODZTUBOEBSETUPBDBEFNJDDPOUFOUTUBOEBSETBMJHONFOU. 6OQVCMJTIFENBOVTDSJQU .BEJTPO 8*6OJWFSTJUZPG8JTDPOTJO 8JTDPOTJO$FOUFSGPS&EVDBUJPO3FTFBSDI $PPL )( 8JMNFT , Alignment between the Kentucky Core Content for assessment and the WIDA Consortium &OHMJTI-BOHVBHF1SPmDJFODZ4UBOEBSET.BEJTPO 8*8JTDPOTJO$FOUFSGPS&EVDBUJPO3FTFBSDI -FF + (SJHH 8 BOE%JPO ( The Nation’s Report Card: Mathematics 2007 /$&4o 8BTIJOHUPO %$ /BUJPOBM$FOUFSGPS&EVDBUJPO4UBUJTUJDT *OTUJUVUFPG&EVDBUJPO4DJFODFT 64%FQBSUNFOUPG&EVDBUJPO -FF + (SJHH 8 BOE%POBIVF 1 The Nation’s Report Card: Reading 2007 /$&4o 8BTIJOHUPO %$ /BUJPOBM$FOUFSGPS&EVDBUJPO4UBUJTUJDT *OTUJUVUFPG&EVDBUJPO4DJFODFT 64%FQBSUNFOUPG&EVDBUJPO .BTTBDIVTFUUT%FQBSUNFOUPG&MFNFOUBSZBOE4FDPOEBSZ&EVDBUJPO Massachusetts mathematics curriculum framework3FUSJFWFEGSPNIUUQXXXEPFNBTTFEVGSBNFXPSLTNBUImOBMQEG .BTTBDIVTFUUT%FQBSUNFOUPG&MFNFOUBSZBOE4FDPOEBSZ&EVDBUJPO Massachusetts English language arts curriculum framework3FUSJFWFEGSPNIUUQXXXEPFNBTTFEVGSBNFXPSLTFMBQEG References •  | References /BUJPOBM$FOUFSGPS&EVDBUJPO4UBUJTUJDT B The Nation’s Report Card: Mathematics 2009 /$&4o 8BTIJOHUPO %$*OTUJUVUFPG&EVDBUJPO4DJFODFT 64%FQBSUNFOUPG&EVDBUJPO /BUJPOBM$FOUFSGPS&EVDBUJPO4UBUJTUJDT C The Nation’s Report Card: Reading 2009 /$&4o 8BTIJOHUPO %$ *OTUJUVUFPG&EVDBUJPO4DJFODFT 64%FQBSUNFOUPG&EVDBUJPO 1IJMMJQT 7 8POH $ 5ZJOHUPHFUIFSUIF$PNNPO$PSFPG4UBOEBSET JOTUSVDUJPO BOEBTTFTTNFOUTPhi Delta Kappan, 1PSUFS " .D.BLFO + )XBOH + :BOH 3 $PNNPO$PSFTUBOEBSET5IFOFX64JOUFOEFEDVSSJDVMVN Educational Researcher o 3PBDI "5 &MMJPU 4/ 8FCC /- "MJHONFOUPGBOBMUFSOBUJWFBTTFTTNFOUXJUITUBUFBDBEFNJDTUBOEBSET &WJEFODFGPSUIFDPOUFOUWBMJEJUZPGUIF8JTDPOTJO"MUFSOBUJWF"TTFTTNFOUJournal of Special Education 3PMGIVT & $PPL )( #SJUF +- BOE)BSUNBO + Are Texas English language arts and reading standards college ready? *TTVFT"OTXFST3FQPSU 3&-/P 8BTIJOHUPO %$64%FQBSUNFOUPG&EVDBUJPO *OTUJUVUFPG &EVDBUJPO4DJFODFT /BUJPOBM$FOUFSGPS&EVDBUJPO&WBMVBUJPOBOE3FHJPOBM"TTJTUBODF 3FHJPOBM&EVDBUJPOBM-BCPSBUPSZ 4PVUIXFTU3FUSJFWFEGSPNIUUQJFTFEHPWODFFFEMBCT 3PMGIVT & %FDLFS -& #SJUF +- (SFHPSZ - A systematic comparison of the American Diploma Project English language arts college readiness standards with those of the ACT, College Board, and Standards for Success. (Issues & "OTXFST3FQPSU 3&-/P 8BTIJOHUPO %$64%FQBSUNFOUPG&EVDBUJPO *OTUJUVUFPG&EVDBUJPO4DJFODFT /BUJPOBM$FOUFSGPS&EVDBUJPO&WBMVBUJPOBOE3FHJPOBM"TTJTUBODF 3FHJPOBM&EVDBUJPOBM-BCPSBUPSZ4PVUIXFTU3FUSJFWFE GSPNIUUQJFTFEHPWODFFFEMBCT 3PUINBO 3 Imperfect matches: The alignment of standards and tests. (Paper commissioned by the Committee on 5FTU%FTJHOGPS,4DJFODF"DIJFWFNFOU $POUFSGPS&EVDBUJPO /BUJPOBM3FTFBSDI$PVODJM 8BTIJOHUPO %$/BUJPOBM 3FTFBSDI$PVODJM 4ISPVU 1& 'MFJTT +- *OUSBDMBTTDPSSFMBUJPOT6TFTJOBTTFTTJOHSBUFSSFMJBCJMJUZPsychological Bulletin o 5FYBT)JHIFS&EVDBUJPO$PPSEJOBUJOH#PBSE5FYBT&EVDBUJPO"HFODZ Texas College and Career Readiness Standards3FUSJFWFEGSPNIUUQTFQJDPOMJOFPSHmMFTQEG$$34UBOEBSETQEG 5FYBT&EVDBUJPO"HFODZ 5FYBTDPMMFHFBOEDBSFFSSFBEJOFTTQSPHSBN3FUSJFWFEGSPNIUUQXXXUYDDSTPSH 5JNNT . 4DIOFJEFS 4 -FF $ 3PMGIVT & Aligning science assessment standards: Texas and the 2009 National Assessment of Educational Progress (NAEP) *TTVFT"OTXFST3FQPSU 3&-o/P 8BTIJOHUPO %$64 %FQBSUNFOUPG&EVDBUJPO *OTUJUVUFPG&EVDBUJPO4DJFODFT /BUJPOBM$FOUFSGPS&EVDBUJPO&WBMVBUJPOBOE3FHJPOBM "TTJTUBODF 3FHJPOBM&EVDBUJPOBM-BCPSBUPSZ4PVUIXFTU3FUSJFWFEGSPNIUUQJFTFEHPWODFFFEMBCT 8FCC /- Criteria for alignment of expectations and assessments in mathematics and science education. Council of $IJFG4UBUF4DIPPM0GmDFSTBOE/BUJPOBM*OTUJUVUFGPS4DJFODF&EVDBUJPO3FTFBSDI.POPHSBQI/P.BEJTPO 8* 6OJWFSTJUZPG8JTDPOTJO 8JTDPOTJO$FOUFSGPS&EVDBUJPO3FTFBSDI 8FCC /- Alignment of science and mathematics standards and assessments in four states 3FTFBSDI.POPHSBQI .BEJTPO 8*/BUJPOBM*OTUJUVUFGPS4DJFODF&EVDBUJPOBOE$PVODJMPG$IJFG4UBUF4DIPPM0GmDFST 8FCC /- B Alignment study in language arts, mathematics, science, and social studies of state standards and assessments for four states. A study of the State Collaborative on Assessment & Student Standards (SCASS) Technical Issues in Large-Scale Assessment (TILSA)8BTIJOHUPO %$$PVODJMPG$IJFG4UBUF4DIPPM0GmDFST 8FCC /- C "QSJM "OBOBMZTJTPGUIFBMJHONFOUCFUXFFONBUIFNBUJDTTUBOEBSETBOEBTTFTTNFOUTGPSUISFFTUBUFT Paper presented at the Annual Conference of the American Educational Research Association /FX0SMFBOT -" 8FCC /- "MU . &MZ 3 7FTQFSNBO # 8FCBMJHONFOUUPPM 8"5 5SBJOJOHNBOVBMESBGU3FUSJFWFE+VOF GSPNIUUQXXXXDFSXJTDFEV8"55SBJOJOH.BOVBM%SBGUEPD 8FCC /. )FSNBO +- 8FCC /- "MJHONFOUPGNBUIFNBUJDTTUBUFMFWFMTUBOEBSETBOEBTTFTTNFOUT5IFSPMF PGSFWJFXFSBHSFFNFOUEducational Measurement: Issues and Practice o 8JYTPO ,, .$'JTL &%VUSP +.D%BOJFM The Alignment of State Standards and Assessments in Elementary Reading$*&3"3FQPSU"OO"SCPS .*6OJWFSTJUZPG.JDIJHBO4DIPPMPG&EVDBUJPO $FOUFSGPSUIF*NQSPWFNFOUPG &BSMZ3FBEJOH"DIJFWFNFOU References 30 Appendices to Lining Up: The Relationship between the Common Core State Standards and Five Sets of Comparison Standards Appendix A | Description of the Depth of Knowledge Calculation 3FDBMM UIBU BMM SBUFST DPVME NBUDI VQ UP UISFF $PNNPO $PSF TUBOEBSET UIBU UIFZ KVEHFE UP CF BMJHOFE XJUI B DPNQBSJTPO TUBOEBSE5IF%FQUIPG,OPXMFEHF %0, $POTJTUFODZDBMDVMBUJPOGPSFBDI$PNNPO$PSFDPOUFOUTQFDJmDBSFBVTFTPOMZ SBUFST XIP IBE BU MFBTU POF NBUDI XJUI B $PNNPO $PSF TUBOEBSE GPS UIBU DPOUFOUTQFDJmD BSFB 'PS UIF QVSQPTFT PG UIJT FYQMBOBUJPO XFDBMMUIFTFiSFMFWBOUSBUFSTw5IPTFBSFUIFSBUFSTXIPJEFOUJmFEBUMFBTUPOFNBUDIJOB$PNNPO$PSFDPOUFOU TQFDJmDBSFBoTQFDJmDBMMZBTUSBOEGPS&OHMJTIMBOHVBHFBSUTBOEMJUFSBDZBOEBDPODFQUVBMDBUFHPSZJONBUIFNBUJDT 'PSFBDISFMFWBOUSBUFS UIF8"5mSTUDBMDVMBUFTUIFQSPQPSUJPOPGDPNQBSJTPOTUBOEBSETUIBUBSFVOEFS BU PSBCPWFUIF%0, MFWFM PG UIF NBUDIFE $PNNPO $PSF TUBOEBSE 5IFO UIF TUBUJTUJD JOWPMWFT DBMDVMBUJOH BO PWFSBMM BWFSBHF GPS FBDI DBUFHPSZ VOEFS BU BCPWF BDSPTTUIPTFSFMFWBOUSBUFST*GUIFTVNPGUIFBUBOEBCPWFDBUFHPSJFTJTPWFS UIFOUIFDSJUFSJBGPSUIF %0,$POTJTUFODZJTNFU Appendix A •  Appendix B | Common Core Standards 5IF$PNNPO$PSFTUBOEBSETCFMPXXFSFSFMFBTFEJO+VOFBOENBZDPOUBJONJOPSEJGGFSFODFTGSPNUIFDVSSFOUWFSTJPO EVFUPTMJHIUFEJUTBGUFSPSJHJOBMSFMFBTF5BCMF#DPOUBJOT&OHMJTIMBOHVBHFBSUTBOEMJUFSBDZTUBOEBSETBOE5BCMF#DPOUBJOT mathematics standards. Table B. English Language Arts and Literacy Common Core Standards Content, with Depth of Knowledge Consensus Ratings Reference standard numbera  Standard DOK rating Reading Standards for Literature  . Key Ideas and Details  .a . Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain.  .b . Determine two or more themes or central ideas of a text and analyze their development over the course of the text, including how they interact and build on one another to produce a complex account; provide an objective summary of the text.  . Analyze the impact of the author’s choices regarding how to develop and relate elements of a story or drama (e.g., where a story is set, how the action is ordered, how the characters are introduced and developed).  . Craft and Structure  .a . Determine the meaning of words and phrases as they are used in the text, including ﬁgurative and connotative meanings; analyze the impact of speciﬁc word choices on meaning and tone, including words with multiple meanings or language that is particularly fresh, engaging, or beautiful. (Include Shakespeare as well as other authors.)  . Analyze how an author’s choices concerning how to structure speciﬁc parts of a text (e.g., the choice of where to begin or end a story, the choice to provide a comedic or tragic resolution) contribute to its overall structure and meaning as well as its aesthetic impact.  . Analyze a case in which grasping point of view requires distinguishing what is directly stated in a text from what is really meant (e.g., satire, sarcasm, irony, or understatement).  . Integration of Knowledge and Ideas  .a . Analyze multiple interpretations of a story, drama, or poem (e.g., recorded or live production of a play or recorded novel or poetry), evaluating how each version interprets the source text. (Include at least one play by Shakespeare and one play by an American dramatist.)  . Demonstrate knowledge of eighteenth-, nineteenth-, and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics.  . Range of Reading and Level of Text Complexity  .a . By the end of grade , read and comprehend literature, including stories, dramas, and poems, in the grades –CCR text complexity band proﬁciently, with scaffolding as needed at the high end of the range. By the end of grade , read and comprehend literature, including stories, dramas, and poems, at the high end of the grades –CCR text complexity band independently and proﬁciently.   Reading Standards for Informational Texts  . Key Ideas and Details  .a . Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain.  .b . Determine two or more central ideas of a text and analyze their development over the course of the text, including how they interact and build on one another to provide a complex analysis; provide an objective summary of the text.  .c .b .c .b a The reference standard number refers to the numbering system that was used for the purposes of organizing ratings for this study. Appendix B •  Common Core Standards Table B. continued Reference standard numbera .c Standard DOK rating . Analyze a complex set of ideas or sequence of events and explain how speciﬁc individuals, ideas, or events interact and develop over the course of the text.  . Craft and Structure  .a . Determine the meaning of words and phrases as they are used in a text, including ﬁgurative, connotative, and technical meanings; analyze how an author uses and reﬁnes the meaning of a key term or terms over the course of a text (e.g., how Madison deﬁnes faction in Federalist No. ).  .b . Analyze and evaluate the effectiveness of the structure an author uses in his or her exposition or argument, including whether the structure makes points clear, convincing, and engaging.  .c . Determine an author’s point of view or purpose in a text in which the rhetoric is particularly effective, analyzing how style and content contribute to the power, persuasiveness, or beauty of the text.  . Integration of Knowledge and Ideas  .a . Integrate and evaluate multiple sources of information presented in different media or formats (e.g., visually, quantitatively) as well as in words in order to address a question or solve a problem.  .b . Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning (e.g., in U.S. Supreme Court majority opinions and dissents) and the premises, purposes, and arguments in works of public advocacy (e.g., The Federalist, presidential addresses).  . Analyze seventeenth-, eighteenth-, and nineteenth-century foundational U.S. documents of historical and literary signiﬁcance (including The Declaration of Independence, the Preamble to the Constitution, the Bill of Rights, and Lincoln’s Second Inaugural Address) for their themes, purposes, and rhetorical features.  . Range of Reading and Level of Text Complexity  .a . By the end of grade , read and comprehend literary nonﬁction in the grades –CCR text complexity band proﬁciently, with scaffolding as needed at the high end of the range. By the end of grade , read and comprehend literary nonﬁction at the high end of the grades –CCR text complexity band independently and proﬁciently.  Writing Standards  . Text Types and Purposes  .a . Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufﬁcient evidence.  .b a. Introduce precise, knowledgeable claim(s), establish the signiﬁcance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences claim(s), counterclaims, reasons, and evidence.  b. Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level, concerns, values, and possible biases.  c. Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.  .e d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.  .f e. Provide a concluding statement or section that follows from and supports the argument presented.  .g . Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content.  .h a. Introduce a topic; organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a uniﬁed whole; include formatting (e.g., headings), graphics (e.g., ﬁgures, tables), and multimedia when useful to aiding comprehension.  .c  .c .d Appendix B 34 Common Core Standards Table B. continued Reference standard numbera Standard DOK rating b. Develop the topic thoroughly by selecting the most signiﬁcant and relevant facts, extended deﬁnitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic.  .j c. Use appropriate and varied transitions and syntax to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts.  .k d. Use precise language, domain-speciﬁc vocabulary, and techniques such as metaphor, simile, and analogy to manage the complexity of the topic.  .l e. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.  .m f. Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the signiﬁcance of the topic).  .n . Write narratives to develop real or imagined experiences or events using effective technique, wellchosen details, and well-structured event sequences.  .o a. Engage and orient the reader by setting out a problem, situation, or observation and its signiﬁcance, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events.  .p b. Use narrative techniques, such as dialogue, pacing, description, reﬂection, and multiple plot lines, to develop experiences, events, and/or characters.  .q c. Use a variety of techniques to sequence events so that they build on one another to create a coherent whole and build toward a particular tone and outcome (e.g., a sense of mystery, suspense, growth, or resolution).  .r d. Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters.  .s e. Provide a conclusion that follows from and reﬂects on what is experienced, observed, or resolved over the course of the narrative.  . Production and Distribution of Writing  .a . Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-speciﬁc expectations for writing types are deﬁned in standards – above.)  . Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most signiﬁcant for a speciﬁc purpose and audience. (Editing for conventions should demonstrate command of Language standards –, up to and including grades – on page .)  .c . Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback, including new arguments or information.  . Research to Build and Present Knowledge  .a . Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation.  . Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations of each source in terms of the task, purpose, and audience; integrate information into the text selectively to maintain the ﬂow of ideas, avoiding plagiarism and overreliance on any one source and following a standard format for citation.  .c . Draw evidence from literary or informational texts to support analysis, reﬂection, and research.  .d a. Apply grades – Reading standards to literature (e.g., “Demonstrate knowledge of eighteenth-, nineteenth-, and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics”).  b. Apply grades – Reading standards to literary nonﬁction (e.g., “Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning [e.g., in U.S. Supreme Court Case majority opinions and dissents] and the premises, purposes, and arguments in works of public advocacy [e.g., The Federalist, presidential addresses]”).  .i .b .b .e Appendix B 35 Common Core Standards Table B. continued Reference standard numbera Standard DOK rating . Range of Writing  .a . Write routinely over extended time frames (time for research, reﬂection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.   Speaking and Listening Standards  . Comprehension and Collaboration  .a . Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades - topics, texts, and issues, building on others’ ideas and expressing their own ideas clearly and persuasively.  a. Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas.  .c b. Work with peers to promote civil, democratic discussions and decision-making, set clear goals and deadlines, and establish individual roles as needed.  .d c. Propel conversations by posing and responding to questions that probe reasoning and evidence; ensure a hearing for a full range of positions on a topic or issue; clarify, verify, or challenge ideas and conclusions; and promote divergent and creative perspectives.  d. Respond thoughtfully to diverse perspectives; synthesize comments, claims, and evidence made on all sides of an issue; resolve contradictions when possible; and determine what additional information or research is required to deepen the investigation or complete the task.  . Integrate multiple sources of information presented in diverse formats and media (e.g., visually, quantitatively, orally) in order to make informed decisions and solve problems, evaluating the credibility and accuracy of each source and noting any discrepancies among the data.  .g . Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, assessing the stance, premises, links among ideas, word choice, points of emphasis, and tone used.  . Presentation of Knowledge and Ideas  .a . Present information, ﬁndings, and supporting evidence, conveying a clear and distinct perspective, such that listeners can follow the line of reasoning, alternative or opposing perspectives are addressed, and the organization, development, substance, and style are appropriate to purpose, audience, and a range or formal and informal tasks.  .b . Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of ﬁndings, reasoning, and evidence and to add interest.  .c . Adapt speech to a variety of contexts and tasks, demonstrating a command of formal English when indicated or appropriate. (See grades – Language standards  and  on page  for speciﬁc expectations.)   Language Standards  . Conventions of Standard English  .a . Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.  .b a. Apply the understanding that usage is a matter of convention, can change over time, and is sometimes contested.  .c b. Resolve issues of complex or contested usage, consulting references (e.g., Merriam-Webster’s Dictionary of English Usage, Garner’s Modern American Usage) as needed.  .d . Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.  .e a. Observe hyphenation conventions.  .f b. Spell correctly.  . Knowledge of Language  .a . Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening.  .b .e .f Appendix B 36 Common Core Standards Table B. continued Reference standard numbera Standard DOK rating .b a. Vary syntax for effect, consulting references (e.g., Tufte’s Artful Sentences) for guidance as needed; apply an understanding of syntax to the study of complex texts when reading.  . Vocabulary Acquisition and Use  .a . Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades - reading and content, choosing ﬂexibly from a range of strategies.  .b a. Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase.  .c b. Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., conceive, conception, conceivable).  .d c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to ﬁnd the pronunciation of a word or determine or clarify its precise meaning, its part of speech, its etymology, or its standard usage.  .e d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).  .f . Demonstrate understanding of ﬁgurative language, word relationships, and nuances in word meanings.  .g a. Interpret ﬁgures of speech (e.g., hyperbole, paradox) in context and analyze their role in the text.  .h b. Analyze nuances in the meaning of words with similar denotations.  .i . Acquire and use accurately general academic and domain-speciﬁc words and phrases, sufﬁcient for reading, writing, speaking, and listening at the college- and career-readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.  Reading Standards for Literacy in History/Social Studies  . Key Ideas and Details  .a . Cite speciﬁc textual evidence to support analysis of primary and secondary sources, connecting insights gained from speciﬁc details to an understanding of the text as a whole.  .b . Determine the central ideas or information of a primary or secondary source; provide an accurate summary that makes clear the relationships among the key details and ideas.  .c . Evaluate various explanations for actions or events and determine which explanation best accords with textual evidence, acknowledging where the text leaves matters uncertain.  . Craft and Structure  .a . Determine the meaning of words and phrases as they are used in a text, including analyzing how an author uses and reﬁnes the meaning of a key term over the course of a text (e.g., how Madison deﬁnes faction in Federalist No. ).  .b . Analyze in detail how a complex primary source is structured, including how key sentences, paragraphs, and larger portions of the text contribute to the whole.  .c . Evaluate authors’ differing points of view on the same historical event or issue by assessing the authors’ claims, reasoning, and evidence.  . Integration of Knowledge and Ideas  .a . Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., visually, quantitatively, as well as in words) in order to address a question or solve a problem.  .b . Evaluate an author’s premises, claims, and evidence by corroborating or challenging them with other information.  .c . Integrate information from diverse sources, both primary and secondary, into a coherent understanding of an idea or event, noting discrepancies among sources.  . Range of Reading and Level of Text Complexity  .a . By the end of grade , read and comprehend history/social studies texts in the grades – text complexity band independently and proﬁciently.   Appendix B 37 Common Core Standards Table B. continued Reference standard numbera Standard DOK rating Reading Standards for Literacy in Science and Technical Subjects  . Key Ideas and Details  .a . Cite speciﬁc textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account.  .b . Determine the central ideas or conclusions of a text; summarize complex concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms.  .c . Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the speciﬁc results based on explanations in the text.  . Craft and Structure  .a . Determine the meaning of symbols, key terms, and other domain-speciﬁc words and phrases as they are used in a speciﬁc scientiﬁc or technical context relevant to grades - texts and topics.  .b . Analyze how the text structures information or ideas into categories or hierarchies, demonstrating understanding of the information or ideas.  .c . Analyze the author’s purpose in providing an explanation, describing a procedure, or discussing an experiment in a text, identifying important issues that remain unresolved.  . Integration of Knowledge and Ideas  .a . Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem.  .b . Evaluate the hypotheses, data, analysis, and conclusions in a science or technical text, verifying data when possible and corroborating or challenging conclusions with other sources of information.  .c . Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conﬂicting information when possible.  . Range of Reading and Level of Text Complexity  .a . By the end of Grade , read and comprehend science/technical texts in the grades – text complexity band independently and proﬁciently.   Writing Standards for Literacy in History/Social Studies, Science, and Technical Subjects  . Text Types and Purposes  .a . Write arguments focused on discipline-speciﬁc content.  .b a. Introduce precise, knowledgeable claim(s), establish the signiﬁcance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences the claim(s), counterclaims, reasons, and evidence.  b. Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline-appropriate form that anticipates the audience’s knowledge level, concerns, values, and possible biases.  c. Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.  .e d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.  .f e. Provide a concluding statement or section that follows from or supports the argument presented.  .g . Write informative/explanatory texts, including the narration of historical events, scientiﬁc procedures/ experiments, or technical processes.  .h a. Introduce a topic and organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a uniﬁed whole; include formatting (e.g., headings), graphics (e.g., ﬁgures, tables), and multimedia when useful to aiding comprehension.   .c .d Appendix B 38 Common Core Standards Table B. continued Reference standard numbera Standard DOK rating b. Develop the topic thoroughly by selecting the most signiﬁcant and relevant facts, extended deﬁnitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic.  .j c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts.  .k d. Use precise language, domain-speciﬁc vocabulary and techniques such as metaphor, simile, and analogy to manage the complexity of the topic; convey a knowledgeable stance in a style that responds to the discipline and context as well as to the expertise of likely readers.  .l e. Provide a concluding statement or section that follows from and supports the information or explanation provided (e.g., articulating implications or the signiﬁcance of the topic).  . Production and Distribution of Writing  .a . Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.  .b . Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most signiﬁcant for a speciﬁc purpose and audience.  .c . Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback, including new arguments or information.  . Research to Build and Present Knowledge  .a . Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation.  . Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations of each source in terms of the speciﬁc task, purpose, and audience; integrate information into the text selectively to maintain the ﬂow of ideas, avoiding plagiarism and overreliance on any one source and following a standard format for citation.  . Draw evidence from informational texts to support analysis, reﬂection, and research.  . Range of Writing  .a . Write routinely over extended time frames (time for reﬂection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-speciﬁc tasks, purposes, and audiences.  .i .b .c a The reference standard number refers to the numbering system that was used for the purposes of organizing ratings for this study. Appendix B 39 Common Core Standards Table B. Mathematics Common Core Standards Content, with Depth of Knowledge (DOK) Consensus Ratings Reference standard numbera  Standard DOK rating Number and Quantity  The Real Number System . Extend the properties of exponents to rational exponents.  .a . Explain how the deﬁnition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we deﬁne / to be the cube root of  because we want (/) = (/) to hold, so (/) must equal .  .b . Rewrite expressions involving radicals and rational exponents using the properties of exponents.  . Use properties of rational and irrational numbers.  .a . Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.  Quantities . Reason quantitatively and use units to solve problems.  .a . Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.  .b . Deﬁne appropriate quantities for the purpose of descriptive modeling.  .c . Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.  The Complex Number System . Perform arithmetic operations with complex numbers.   .a . Know there is a complex number i such that i = –, and every complex number has the form a + bi with a and b being real.  .b . Use the relation i = – and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.  .c . (+) Find the conjugate of a complex number; use conjugates to ﬁnd moduli and quotients of complex numbers.  . Represent complex numbers and their operations on the complex plane.  .a . (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.  .b . (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, ( – √i) =  because ( – √i) has modulus  and argument °.  .c . (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.  . Use complex numbers in polynomial identities and equations.  .a . Solve quadratic equations with real coefﬁcients that have complex solutions.  .b . (+) Extend polynomial identities to the complex numbers. For example, rewrite x +  as (x + i)(x – i).  .c . (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.  a The reference standard number refers to the numbering system that was used for the purposes of organizing ratings for this study. (+) is an indication in the Common Core mathematics standards document to show that some mathematics standards represent advanced content and are intended to prepare students for advanced courses (see Chapter  for description). + is an indication in the Common Core mathematics standards document to show a modeling standard (see Chapter  for description). Appendix B 40 Common Core Standards Table B. continued Reference standard numbera DOK rating Standard Vector and Matrix Quantities . Represent and model with vector quantities.  .a . (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).  .b . (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.  .c . (+) Solve problems involving velocity and other quantities that can be represented by vectors.  . Perform operations on vectors.  .a . (+) Add and subtract vectors.  .b a. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.  .c b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.  .d c. Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.  .e . (+) Multiply a vector by a scalar.  .f a. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).  .g b. Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ , the direction of cv is either along v (for c > ) or against v (for c < ).  . Perform operations on matrices and use matrices in applications.  .a . (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.  .b . (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.  .c . (+) Add, subtract, and multiply matrices of appropriate dimensions.  .d . (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisﬁes the associative and distributive properties.  .e . (+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of  and  in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.  .f . (+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.  .g . (+) Work with  ×  matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.   Algebra  Seeing Structure in Expressions . .a Interpret the structure of expressions  + . Interpret expressions that represent a quantity in terms of its context.  .b a. Interpret parts of an expression, such as terms, factors, and coefﬁcients.  .c b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(+r)n as the product of P and a factor not depending on P.  Appendix B 41 Common Core Standards Table B. continued Reference standard numbera Standard DOK rating . Use the structure of an expression to identify ways to rewrite it. For example, see x – y as (x) – (y), thus recognizing it as a difference of squares that can be factored as (x – y)(x + y).  . Write expressions in equivalent forms to solve problems  .a . Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.  .d .b a. Factor a quadratic expression to reveal the zeros of the function it deﬁnes.  .c b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it deﬁnes.  .d c. Use the properties of exponents to transform expressions for exponential functions. For example the expression .t can be rewritten as (./)t ≈ .t to reveal the approximate equivalent monthly interest rate if the annual rate is %.  . Derive the formula for the sum of a ﬁnite geometric series (when the common ratio is not ), and use the formula to solve problems. For example, calculate mortgage payments.  .e Arithmetic with Polynomials and Rational Functions . Perform arithmetic operations on polynomials  .a . Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.  . Understand the relationship between zeros and factors of polynomials  .a . Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) =  if and only if (x – a) is a factor of p(x).  .b . Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function deﬁned by the polynomial.  . Use polynomial identities to solve problems  .a . Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x + y) = (x – y) + (xy) can be used to generate Pythagorean triples.  .b . (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefﬁcients determined for example by Pascal’s Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.)  . Rewrite rational expressions  .a . Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.  . (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.  .b Creating Equations . Create equations that describe numbers or relationships  .a . Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.  .b . Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.  .c . Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.  . Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V =IR to highlight resistance R.  .d Appendix B 42 Common Core Standards Table B. continued Reference standard numbera Standard DOK rating Reasoning with Equations and Inequalities . Understand solving equations as a process of reasoning and explain the reasoning  .a . Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.  .b . Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.  . Solve equations and inequalities in one variable  .a . Solve linear equations and inequalities in one variable, including equations with coefﬁcients represented by letters.  .b . Solve quadratic equations in one variable.  .c .d a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p) = q that has the same solutions. Derive the quadratic formula from this form.  b. Solve quadratic equations by inspection (e.g., for x = ), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.  . Solve systems of equations  .a . Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.  .b . Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.  .c . Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, ﬁnd the points of intersection between the line y = -x and the circle x +y = .  .d . (+) Represent a system of linear equations as a single matrix equation in a vector variable.  .e . (+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension  ×  or greater).  . Represent and solve equations and inequalities graphically  .a . Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).  .b . Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); ﬁnd the solutions approximately, e.g., using technology to graph the functions, make tables of values, or ﬁnd successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.+  . Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.  Functions  .c  Interpreting Functions . Understand the concept of a function and use function notation  .a . Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).  Appendix B 43 Common Core Standards Table B. continued Reference standard numbera Standard DOK rating .b . Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.  .c . Recognize that sequences are functions, sometimes deﬁned recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is deﬁned recursively by f() = f() = , f(n+) = f(n) + f(n) for n ≥ .  . Interpret functions that arise in applications in terms of the context  .a . For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.+  . Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.+  .c . Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a speciﬁed interval. Estimate the rate of change from a graph.+  . Analyze functions using different representations  .a . Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.+  .b .b a. Graph linear and quadratic functions and show intercepts, maxima, and minima.  .c b. Graph square root, cube root, and piecewise-deﬁned functions, including step functions and absolute value functions.  .d c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.  .e d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.  .f e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.  .g . Write a function deﬁned by an expression in different but equivalent forms to reveal and explain different properties of the function.  .h a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.  .i b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (.)t, y = (.)t, y = (.)t, y = (.)t/, and classify them as representing exponential growth or decay.  . Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.  .j Building Functions . .a Build a function that models a relationship between two quantities  + . Write a function that describes a relationship between two quantities.  .b a. Determine an explicit expression, a recursive process, or steps for calculation from a context.  .c b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.  Appendix B 44 Common Core Standards Table B. continued Reference standard numbera .d Standard c. (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. DOK rating  .e . Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.+  . Build new functions from existing functions  .a . Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for speciﬁc values of k (both positive and negative); ﬁnd the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.  . Find inverse functions.  .b .c a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = x for x >  or f(x) = (x+)/(x–) for x ≠ .  .d b. (+) Verify by composition that one function is the inverse of another.  .e c. (+) Read values of an inverse function from a graph or a table, given that the function has an inverse.  .f d. (+) Produce an invertible function from a non-invertible function by restricting the domain.  .g . (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.  Linear and Exponential Models . Construct and compare linear and exponential models and solve problems  .a . Distinguish between situations that can be modeled with linear functions and with exponential functions.  .b a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.  .c b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.  .d c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.  .e . Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).  .f . Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.  .g . For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is , , or e; evaluate the logarithm using technology.  . Interpret expressions for functions in terms of the situation they model  .a . Interpret the parameters in a linear or exponential function in terms of a context.  Trigonometric Functions . Extend the domain of trigonometric functions using the unit circle  .a . Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.  .b . Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.  Appendix B 45 Common Core Standards Table B. continued Reference standard numbera .c Standard DOK rating . (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/, π/ and p/, and use the unit circle to express the values of sine, cosine, and tangent for x, π+x, and π–x in terms of their values for x, where x is any real number.  .d . (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.  . Model periodic phenomena with trigonometric functions  .a . Choose trigonometric functions to model periodic phenomena with speciﬁed amplitude, frequency, and midline.+  .b . (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.  .c . (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.+  . Prove and apply trigonometric identities .a . Prove the Pythagorean identity sin (ș) + cos (ș) =  and use it to calculate trigonometric ratios.  .b . (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.   Geometry     Congruence . Experiment with transformations in the plane  .a . Know precise deﬁnitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undeﬁned notions of point, line, distance along a line, and distance around a circular arc.  .b . Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).  .c . Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reﬂections that carry it onto itself.  .d . Develop deﬁnitions of rotations, reﬂections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.  .e . Given a geometric ﬁgure and a rotation, reﬂection, or translation, draw the transformed ﬁgure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given ﬁgure onto another.  . Understand congruence in terms of rigid motions  .a . Use geometric descriptions of rigid motions to transform ﬁgures and to predict the effect of a given rigid motion on a given ﬁgure; given two ﬁgures, use the deﬁnition of congruence in terms of rigid motions to decide if they are congruent.  .b . Use the deﬁnition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.  .c . Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the deﬁnition of congruence in terms of rigid motions.  . Prove geometric theorems  .a . Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; and points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.  Appendix B 46 Common Core Standards Table B. continued Reference standard numbera .b Standard DOK rating . Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to °; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; and the medians of a triangle meet at a point.  . Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.  . Make geometric constructions  .a . Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reﬂective devices, paper folding, dynamic geometric software, etc.). Examples include: copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.  . Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.  .c .b Similarity, Right Triangles, and Trigonometry . Understand similarity in terms of similarity transformations  .a . Verify experimentally the properties of dilations given by a center and a scale factor:  .b a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.  .c b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.  .d . Given two ﬁgures, use the deﬁnition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.  .e . Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.  . Prove theorems involving similarity  .a . Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.  .b . Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric ﬁgures.  . Deﬁne trigonometric ratios and solve problems involving right triangles  .a . Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to deﬁnitions of trigonometric ratios for acute angles.  .b . Explain and use the relationship between the sine and cosine of complementary angles.  .c . Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.  . Apply trigonometry to general triangles  .a . (+) Derive the formula A = / ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.  .b . (+) Prove the Laws of Sines and Cosines and use them to solve problems.  .c . (+) Understand and apply the Law of Sines and the Law of Cosines to ﬁnd unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).  Circles . Understand and apply theorems about circles  .a . Prove that all circles are similar.  Appendix B 47 Common Core Standards Table B. continued Reference standard numbera .b Standard DOK rating . Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; and the radius of a circle is perpendicular to the tangent where the radius intersects the circle.  .c . Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.  .d . (+) Construct a tangent line from a point outside a given circle to the circle.  . Find arc lengths and areas of sectors of circles  .a . Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and deﬁne the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.  Expressing Geometric Properties with Equations . Translate between the geometric description and the equation for a conic section  .a . Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to ﬁnd the center and radius of a circle given by an equation.  .b . Derive the equation of a parabola given a focus and directrix.  .c . (+) Derive the equations of ellipses and hyperbolas given foci and directrices.  . Use coordinates to prove simple geometric theorems algebraically  .a . Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a ﬁgure deﬁned by four given points in the coordinate plane is a rectangle; prove or disprove that the point (, √) lies on the circle centered at the origin and containing the point (, ).  . Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., ﬁnd the equation of a line parallel or perpendicular to a given line that passes through a given point).  .c . Find the point on a directed line segment between two given points that partitions the segment in a given ratio.  .d . Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.+  .b Geometric Measurement and Dimension . Explain volume formulas and use them to solve problems  .a . Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.  .b . (+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid ﬁgures.  .c . Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.+  . Visualize relationships between two-dimensional and three-dimensional objects  .a . Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify threedimensional objects generated by rotations of two-dimensional objects.  Modeling with Geometry . Apply geometric concepts in modeling situations  .a . Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).+  .b . Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).+  .c . Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).+  Appendix B 48 Common Core Standards Table B. continued Reference standard numbera  DOK rating Standard Statistics and Probability+  Interpreting Categorical and Quantitative Data . Summarize, represent, and interpret data on a single count or measurement variable  + .a . Represent data with plots on the real number line (dot plots, histograms, and box plots).  .b . Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.+  .c . Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).+  .d . Use the mean and standard deviation of a data set to ﬁt it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.+  . Summarize, represent, and interpret data on two categorical and quantitative variables  .a . Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.+  . Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.+  .b .c .d .e a. Fit a function to the data; use functions ﬁtted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.  b. Informally assess the ﬁt of a function by plotting and analyzing residuals.  c. Fit a linear function for a scatter plot that suggests a linear association.  . Interpret linear models  .a . Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.+  . Compute (using technology) and interpret the correlation coefﬁcient of a linear ﬁt.+  .b .c + . Distinguish between correlation and causation.  Making Inferences and Justifying Conclusions . Understand and evaluate random processes underlying statistical experiments  .a . Understand statistics as a process for making inferences about population parameters based on a random sample from that population.+  .b . Decide if a speciﬁed model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability .. Would a result of  tails in a row cause you to question the model?+  . Make inferences and justify conclusions from sample surveys, experiments, and observational studies  .a . Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.+  .b . Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.+  .c . Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are signiﬁcant.+  . Evaluate reports based on data.+  .d Appendix B 49 Common Core Standards Table B. continued Reference standard numbera Standard DOK rating Conditional Probability and the Rules of Probability . Understand independence and conditional probability and use them to interpret data  .a . Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).+  .b . Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.+  .c . Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.+  . Construct and interpret two-way frequency tables of data when two categories are associated with each object being classiﬁed. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among mathematics, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.+  . Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.+  . Use the rules of probability to compute probabilities of compound events in a uniform probability model  .a . Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.+  .b . Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.+  .c . (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B) P(A|B), and interpret the answer in terms of the model.+  .d . (+) Use permutations and combinations to compute probabilities of compound events and solve problems.+  .d .e Using Probability to Make Decisions . Calculate expected values and use them to solve problems  .a . (+) Deﬁne a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.+  .b . (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.+  .c . (+) Develop a probability distribution for a random variable deﬁned for a sample space in which theoretical probabilities can be calculated; ﬁnd the expected value. For example, ﬁnd the theoretical probability distribution for the number of correct answers obtained by guessing on all ﬁve questions of a multiple-choice test where each question has four choices, and ﬁnd the expected grade under various grading schemes.+  . (+) Develop a probability distribution for a random variable deﬁned for a sample space in which probabilities are assigned empirically; ﬁnd the expected value. For example, ﬁnd a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to ﬁnd in  randomly selected households?+  . Use probability to evaluate outcomes of decisions  .a . (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and ﬁnding expected values.+  .d Appendix B 50 Common Core Standards Table B. continued Reference standard numbera Standard DOK .b a. Find the expected payoff for a game of chance. For example, ﬁnd the expected winnings from a state lottery ticket or a game at a fast-food restaurant.  .c b. Evaluate and compare strategies on the basis of expected values. For example, compare a highdeductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.  . (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).+  . (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).+  .d .e a The reference standard number refers to the numbering system that was used for the purposes of organizing ratings for this study. (+) is an indication in the Common Core mathematics standards document to show that some mathematics standards represent advanced content and are intended to prepare students for advanced courses (see Chapter  for description). + is an indication in the Common Core mathematics standards document to show a modeling standard (see Chapter  for description). Appendix B 51 Appendix C | Results by Individual Comparison Standards *OUIFTFDUJPOTUIBUGPMMPX XFQSFTFOUUIFBMJHONFOUmOEJOHT between each set of individual comparison standards and the $PNNPO$PSFTUBOEBSET5IFTFJODMVEF UIFTUBUFTUBOEBSET GPS $BMJGPSOJB UIF TUBUF TUBOEBSET GPS .BTTBDIVTFUUT UIF 5FYBT $BSFFS BOE $PMMFHF 3FBEJOFTT 4UBOEBSET UIF,OPXMFEHFBOE4LJMMTGPS6OJWFSTJUZ4VDDFTTBOE UIF *OUFSOBUJPOBM #BDDBMBVSFBUF %JQMPNB 1SPHSBNNF TUBOEBSET $IBQUFST BOE QSFTFOUFE CBTJD mOEJOHT 5IF UFYU JO UIJT BQQFOEJY TVNNBSJ[FT BEEJUJPOBM mOEJOHT BOE UIF 5FDIOJDBM 4VQQMFNFOU DPOUBJOT FWFO NPSF EFUBJMFE JOGPSNBUJPO PO UIF statistics and raw data. California Standards The 11thothHSBEF &OHMJTI MBOHVBHF BSUT TUBOEBSET BOE UIFthothHSBEFTUBOEBSETJONBUIFNBUJDTPGUIF$BMJGPSOJB $POUFOU 4UBOEBSET XFSF DPNQBSFE UP UIF $PNNPO $PSF standards. Figure C. Percentage of Common Core Standards that Match California Standards for ELA and Literacy Percent 100 Matched Not matched 78 75 50 22 25 0 Common Core Standards (113 statements) English Language Arts and Literacy Findings for the California Standards Match 3FDBMM UIBU SBUFST JEFOUJmFE VQ UP UISFF $PNNPO $PSF TUBOEBSET BT NBUDIJOH FBDI $BMJGPSOJB TUBOEBSE 'JHVSF $ shows the percent of Common Core statements (n that any of the nine ELA raters matched to one or more of the California standards (n 5IF mHVSF DPMMBQTFT mOEJOHT BDSPTT BMM FJHIU &OHMJTI MBOHVBHF BSUT &-" BOE MJUFSBDZ TUSBOET *O 'JHVSF $ XF EJWJEF mOEJOHT CZ TUSBOE "T UIF CBS HSBQIT JOEJDBUF UIF $BMJGPSOJB TUBOEBSET IBWF NBUDIFT GPS PG UIF $PNNPO $PSF TUBOEBSET JO UISFF TUSBOET 3FBEJOH GPS -JUFSBUVSF 3FBEJOH GPS *OGPSNBUJPOBM 5FYU BOE3FBEJOH4UBOEBSETJO)JTUPSZ4PDJBM4UVEJFT5IF $BMJGPSOJBTUBOEBSETIBWFNBUDIFTUPPGUIF$PNNPO $PSF TUBOEBSET JO UIF 8SJUJOH 4QFBLJOH BOE -JTUFOJOH BOE -BOHVBHFTUSBOET5IFZIBWFNBUDIFTUPPGUIF$PNNPO $PSF TUBOEBSET JO UIF 3FBEJOH 4UBOEBSET JO 4DJFODF BOE 5FDIOJDBM4VCKFDUTTUSBOEBOEJOUIF8SJUJOH4UBOEBSET JO )JTUPSZ4PDJBM 4UVEJFT 4DJFODF BOE 5FDIOJDBM 4VCKFDUT strand. The data presented here is based on at least one SBUFS NBUDIJOH BU MFBTU POF TUBOEBSE IPXFWFS UIF OVNCFS PGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFTXJEFMZ$IBQUFS provides the mean and standard deviation for the number of DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJO FBDI TUSBOE 5IF 5FDIOJDBM 4VQQMFNFOU EJTQMBZT UIF FYBDU standards from the Common Core and the comparison sets that were matched. &WFSZ TUSBOE NFFUT UIF DSJUFSJPO GPS UIF $BUFHPSJDBM $PODVSSFODFTUBUJTUJD XIJDITQFDJmFTUIBU BDSPTTSBUFST BO BWFSBHFPGPOFDPSSFTQPOEFODFJOBDPOUFOUBSFBJTTVGmDJFOU Figure C. Percentage of Common Core Standards that Match California Standards for ELA and Literacy Strand Percent Matched 100 100 100 100 Not matched 89 80 76 75 60 50 40 20 25 47 53 24 11 0 0 0 0 Reading for Literature (9) Reading for Informational Texts (10) Writing (28) Speaking and Listening (10) Language (17) Reading in History/Social Studies (10) Reading in Science and Technical Subjects (10) Writing in History/Social Studies, Science, and Technical Subjects (19) Common Core strand (number of statements) Appendix C •  Results by Individual Comparison Standards Table C. Summary for Alignment Between the California Standards and Common Core Standards for English Language Arts and Literacy Common Core ELA and literacy strand Categorical Concurrence Coverage Reading for Literature Reading for Informational Texts Writing Speaking and Listening Language Reading in History/Social Studies Reading in Science and Technical Subjects Writing in History/Social Studies, Science, and Technical Subjects Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of standards); Does not meet the criterion for Categorical Concurrence; means that a majority of topics in the Common Core category have at least one matched comparison standard; means that in more than one topic in the Common Core category have at least one matched comparison standard; means that in one or less than one topic in the Common Core category have at least one matched comparison standard. Breadth of Coverage #SFBEUI PG $PWFSBHF JT TUSPOH GPS BMM UIF &-" BOE Figure C. California Standards Depth of Knowledge Levels Under, literacy strands (the majority of Common Core topics At, and Above the Common Core for ELA and Literacy IBWFNBUDIJOHDPNQBSJTPOTUBOEBSETXJUIJOUIFN This means that the California standards that match to Common Core standards are distributed across content topics within each Common Core strand. 5BCMF $ QSFTFOUT UIF BMJHONFOU TVNNBSZ GPS UIF 8FCC BOE $PPL BMJHONFOU TUBUJTUJDT $PPL $PPL8JMNFT 8FCC B Depth of Knowledge Across all matched standards for ELA and literacy, BOBWFSBHFPG SD PG$BMJGPSOJBTUBOEBSET BSF BU UIF TBNF %FQUI PG ,OPXMFEHF %0, MFWFM BT UIF $PNNPO $PSF TUBOEBSET XJUI BO BWFSBHF PG SD PGUIF$BMJGPSOJBTUBOEBSETSBUFE MPXFS JO DPHOJUJWF EFNBOE BOE BO BWFSBHF PG (SD SBUFE IJHIFS 5ISFF PG UIF FJHIU TUSBOET TIPXO JO 'JHVSF $ NFFU UIF %0, $POTJTUFODZ DSJUFSJPO XIJDI JT CBTFE PO BU MFBTU PG UIF NBUDIJOHDPNQBSJTPOTUBOEBSETCFJOHBUPSBCPWF UIF %0, PG UIF DPSSFTQPOEJOH $PNNPO $PSF TUBOEBSE "T 'JHVSF $ TIPXT TPNF TUSBOET GBMM DMPTF UP BOE SFTVMUT XPVME CF EJGGFSFOU JG BO alternative criterion had been selected. Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH Appendix C 53 Results by Individual Comparison Standards Mathematics Findings for the California Standards Match 'JHVSF$TIPXTUIFQFSDFOUPG$PNNPO$PSFTUBUFNFOUT n = UIBUBOZPGUIFTFWFONBUIFNBUJDTSBUFSTNBUDIFEUPPOFPS more of the California standards (n 5IFmHVSFDPMMBQTFT mOEJOHT BDSPTT UIF mWF DPODFQUVBM DBUFHPSJFT *O 'JHVSF $ XFEJWJEFmOEJOHTCZDPODFQUVBMDBUFHPSZ"TUIFCBSHSBQIT JOEJDBUF BIJHIQFSDFOUPGUIF$PNNPO$PSFTUBOEBSETNBUDI $BMJGPSOJBTUBOEBSETJOFBDIDPODFQUVBMDBUFHPSZ SBOHJOHGSPN o "HBJO UIFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTU POFSBUFSNBUDIJOHBUMFBTUPOFTUBOEBSE IPXFWFSUIFOVNCFS PG NBUDIFT GPS BOZ HJWFO TUBOEBSE WBSJFT XJEFMZ $IBQUFS provides the mean and standard deviation for the number of DPNQBSJTPO TUBOEBSET NBUDIJOH $PNNPO $PSF TUBOEBSET JO FBDIDPODFQUVBMDBUFHPSZ5IF5FDIOJDBM4VQQMFNFOUEJTQMBZT UIFFYBDUTUBOEBSETGSPNUIF$PNNPO$PSFBOEUIFDPNQBSJTPO TFUTUIBUXFSFNBUDIFE&WFSZDPODFQUVBMDBUFHPSZNFFUTUIF DSJUFSJPOGPSUIF$BUFHPSJDBM$PODVSSFODFTUBUJTUJD Figure C. Percentage of Common Core Standards that Match California Standards, for Mathematics Percent 100 87 Matched Not matched 75 50 13 25 0 Common Core Standards (192 statements) Figure C. Percentage of Common Core Standards that Match California Standards, by Mathematics Conceptual Category Matched Percent 100 91 88 Not matched 86 89 82 75 50 25 9 12 18 14 11 0 Number and Quantity (32) Algebra (34) Functions (45) Geometry (45) Statistics and Probability (36) Common Core conceptual category (number of statements) Appendix C 54 Results by Individual Comparison Standards Table C. Summary for Alignment Between the California Standards and Common Core Standards for Mathematics Common Core mathematics conceptual category Categorical Concurrence Coverage Number and Quantity Algebra Functions Geometry Statistics and Probability Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of standards); Does not meet the criterion for Categorical Concurrence; means that a majority of topics in the Common Core category have at least one matched comparison standard; means that in more than one topic in the Common Core category have at least one matched comparison standard; means that Common Core standards in one or less than one topic in the strand have at least one matched comparison standard. Breadth of Coverage #SFBEUI PG $PWFSBHF JT TUSPOH GPS BMM UIF NBUIFNBUJDT DPODFQUVBMDBUFHPSJFT UIFNBKPSJUZPG$PNNPO$PSFDMVTUFST IBWF NBUDIJOH DPNQBSJTPO TUBOEBSET XJUIJO UIFN 5BCMF $ QSFTFOUTUIFTVNNBSJ[FEBMJHONFOUSFTVMUTGPSNBUIFNBUJDT Depth of Knowledge For California mathematics standards that match to Common $PSFTUBOEBSET BOBWFSBHFPG SD GBMMBUUIFTBNF MFWFMBTUIF$PNNPO$PSFTUBOEBSETXJUIBOBWFSBHFPG (SD MPXFSJODPHOJUJWFEFNBOEBOE SD IJHIFS JODPHOJUJWFEFNBOE'PVSPGUIFmWF$PNNPO$PSFDPODFQUVBM DBUFHPSJFT TIPXO JO 'JHVSF $ NFFU UIF %0, $POTJTUFODZ DSJUFSJPO XJUI(FPNFUSZCFJOHUIFPOFDBUFHPSZUIBUEPFTOPU NFFU UIF DSJUFSJPO "T 'JHVSF $ TIPXT TPNF DBUFHPSJFT GBMM DMPTF UP BOE SFTVMUT XPVME CF EJGGFSFOU JG BO BMUFSOBUJWF criterion had been selected. 'JHVre%$BMJGPSOJB4UBOEBSET%FQUIPG,OPXMFEHF Figure C. Percentage of California Standards Under, At, or -FWFMT6OEFS, At, and Above, the Common Core Above the Depth of Knowledge Level of the Common Core Standards, for Mathematics 0 /VNCFS and 2VBOUJUZ "MHFCSB Functions 25 50 75 100 AWFSBHF Percent "CPWF "U 6OEFS Geometry 4UBUJTUJDT and Probability Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH Appendix C 55 Results by Individual Comparison Standards Massachusetts Standards The study compared the 11thothHSBEF TUBOEBSET GSPN UIF .BTTBDIVTFUUT $VSSJDVMVN 'SBNFXPSLT UP UIF $PNNPO $PSF standards. English Language Arts and Literacy Findings for the Massachusetts Standards Match 3FDBMM UIBU SBUFST JEFOUJmFE VQ UP UISFF $PNNPO $PSF standards that correspond with each Massachusetts standard. 'JHVSF$TIPXTUIFQFSDFOUPG$PNNPO$PSFTUBUFNFOUT n UIBUBOZPGUIFOJOF&-"SBUFSTNBUDIFEUPPOFPSNPSF of the Massachusetts standards (n 5IFmHVSFDPMMBQTFT mOEJOHT BDSPTT BMM FJHIU &OHMJTI MBOHVBHF BSUT &-" BOE MJUFSBDZTUSBOET*O'JHVSF$ XFEJWJEFmOEJOHTCZTUSBOE"T UIF CBS HSBQIT JOEJDBUF UIF .BTTBDIVTFUUT TUBOEBSET IBWF NBUDIFTGPSPGUIF$PNNPO$PSFTUBOEBSETJO3FBEJOH GPS-JUFSBUVSF BOE4QFBLJOHBOE-JTUFOJOH5IF.BTTBDIVTFUUT TUBOEBSET IBWF NBUDIFT UP o PG UIF $PNNPO $PSF TUBOEBSET JO UIF 3FBEJOH GPS *OGPSNBUJPOBM 5FYU 8SJUJOH BOE -BOHVBHF TUSBOET 'PS UIF 3FBEJOH 4UBOEBSET JO )JTUPSZ 4PDJBM 4UVEJFT TUSBOE 3FBEJOH 4UBOEBSET JO 4DJFODF BOE 5FDIOJDBM 4VCKFDUT TUSBOE BOE 8SJUJOH 4UBOEBSET JO )JTUPSZ 4PDJBM 4UVEJFT 4DJFODF BOE 5FDIOJDBM 4VCKFDUT TUSBOE UIF .BTTBDIVTFUUT TUBOEBSET IBWF NBUDIFT UP o PG UIF Common Core standards.14JYPGFJHIUTUSBOETNFFUUIFDSJUFSJPO GPSUIF$BUFHPSJDBM$PODVSSFODFTUBUJTUJD XIJDITQFDJmFTUIBU BDSPTTSBUFST BOBWFSBHFPGPOFDPSSFTQPOEFODFJOBDPOUFOU BSFB JT TVGmDJFOU 5IF UXP 3FBEJOH GPS -JUFSBDZ JO )JTUPSZ 4PDJBM4UVEJFTBOEJO4DJFODFBOE5FDIOJDBM4VCKFDUT EPOPU meet the criterion. 5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT widely. Chapter 3 provides the mean and standard deviation for the number of DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDITUSBOE5IF 5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF$PNNPO$PSFBOE the comparison sets that were matched. 1 Figure C. Percentage of Common Core Standards that Match Massachusetts Standards, for ELA and Literacy Percent 100 Matched Not matched 68 75 50 32 25 0 Common Core Standards (113 statements) Figure C. Percentage of Common Core Standards that Match Massachusetts Standards, by ELA and Literacy Strand Percent Matched 100 100 100 Not matched 94 90 80 71 75 63 60 50 40 37 29 20 25 10 0 0 6 0 Reading for Literature (9) Reading for Informational Texts (10) Writing (28) Speaking and Listening (10) Language (17) Reading in History/Social Studies (10) Reading in Science and Technical Subjects (10) Writing in History/Social Studies, Science, and Technical Subjects (19) Common Core strand (number of statements) Appendix C 56 Results by Individual Comparison Standards Table C. Summary for Alignment Between the Massachusetts Standards and the Common Core Standards for English Language Arts and Literacy Categorical Concurrence Common Core ELA and literacy strand Coverage Reading for Literature Reading for Informational Texts Writing Speaking and Listening Language Reading in History/Social Studies Reading in Science and Technical Subjects Writing in History/Social Studies, Science, and Technical Subjects Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of standards); Does not meet the criterion for Categorical Concurrence; means that a majority of topics in the Common Core category have at least one matched comparison standard; means that in more than one topic in the Common Core category have at least one matched comparison standard; means that in one or less than one topic in the Common Core category have at least one matched comparison standard. Breadth of Coverage Figure C. Percentage of Massachusetts Standards Under, At, or Above #SFBEUI PG $PWFSBHF JT TUSPOH GPS TFWFO TUSBOET GPS the Depth of Knowledge Level of the Common Core Standards, for ELA these, the majority of Common Core topics have and Literacy NBUDIJOH DPNQBSJTPO TUBOEBSET XJUIJO UIFN 5IF 3FBEJOH 4UBOEBSET JO )JTUPSZ4PDJBM 4UVEJFT TUSBOE JT NPEFSBUF JO UFSNT PG DPWFSBHF 5IJT NFBOT UIBU Common Core standards match to Massachusetts standards in more than one topic but not a majority of UPQJDTXJUIJOUIFTUSBOE"TVNNBSZUBCMF 5BCMF$ QSFTFOUT UIF &-" BOE MJUFSBDZ BMJHONFOU SFTVMUT GPS UIF8FCCBOE$PPLBMJHONFOUTUBUJTUJDT $PPL $PPL8JMNFT 8FCC B Depth of Knowledge Across all matched standards for ELA and literacy, BO BWFSBHF PG SD PG .BTTBDIVTFUUT TUBOEBSETBSFBUUIFTBNF%FQUIPG,OPXMFEHF %0, MFWFM BT UIF $PNNPO $PSF TUBOEBSET "DDPSEJOH UP TUVEZSBUJOHT BOBWFSBHFPG SD BSFMFTT DPHOJUJWFMZEFNBOEJOHBOEBOBWFSBHFPG SD = BSFNPSFDPHOJUJWFMZEFNBOEJOH NA NA Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH 0GUIFTJYTUSBOETNFFUJOHUIF$BUFHPSJDBM$PODVSSFODF DSJUFSJPO mWF NFFU UIF %0, $POTJTUFODZ DSJUFSJPO XIJDI JT CBTFE PO BU MFBTU PG UIF NBUDIJOH .BTTBDIVTFUUT TUBOEBSET CFJOH BU PS BCPWF UIF %0, PG UIF DPSSFTQPOEJOH$PNNPO$PSFTUBOEBSE TFF'JHVSF$ 0OF TUSBOEEJEOPUNFFUUIFDSJUFSJPO8SJUJOH4UBOEBSETGPS-JUFSBDZ JO)JTUPSZ4PDJBM4UVEJFT 4DJFODF BOE5FDIOJDBM4VCKFDUT"T 'JHVSF$TIPXT TPNFTUSBOETGBMMDMPTFUPBOESFTVMUT would be different if an alternative criterion had been selected. Appendix C 57 Results by Individual Comparison Standards Mathematics Findings for the Massachusetts Standards Match 'JHVSF$TIPXTUIFQFSDFOUPG$PNNPO$PSFTUBUFNFOUT n UIBUIBWFNBUDIFTJOUIF.BTTBDIVTFUUTTUBOEBSET n = 5IFmHVSFDPMMBQTFTmOEJOHTBDSPTTUIFmWFDPODFQUVBM DBUFHPSJFT *O 'JHVSF $ XF EJWJEF mOEJOHT CZ DPODFQUVBM DBUFHPSZ "T UIF CBS HSBQIT JOEJDBUF B IJHI QFSDFOU PG UIF Common Core standards cover the Massachusetts standards JOFBDIDPODFQUVBMDBUFHPSZ SBOHJOHGSPNo 2 Every DPODFQUVBM DBUFHPSZ NFFUT UIF DSJUFSJPO GPS UIF $BUFHPSJDBM Concurrence statistic. Figure C. Percentage of Common Core Standards that Match Massachusetts Standards, for Mathematics Percent 88 100 Matched Not matched 75 50 5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT XJEFMZ$IBQUFSQSPWJEFTUIFNFBOBOETUBOEBSEEFWJBUJPOGPSUIFOVNCFSPG DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDIDPODFQUVBM DBUFHPSZ5IF5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF Common Core and the comparison sets that were matched. 2 25 12 0 Common Core Standards (192 statements) Figure C. Percentage of Common Core Standards that Match Massachusetts Standards, by Mathematics Conceptual Category Matched Percent Not matched 100 91 100 89 89 72 75 50 28 25 0 9 11 11 0 Number and Quantity (32) Algebra (34) Functions (45) Geometry (45) Statistics and Probability (36) Common Core conceptual category (number of statements) Appendix C 58 Results by Individual Comparison Standards Table C. Summary for Alignment Between the Massachusetts Standards and Common Core Standards in Mathematics Common Core mathematics conceptual category Categorical Concurrence Coverage Number and Quantity Algebra Functions Geometry Statistics and Probability Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of standards); Does not meet the criterion for Categorical Concurrence; means that a majority of topics in the Common Core category have at least one matched comparison standard; means that in more than one topic in the Common Core category have at least one matched comparison standard; means that in one or less than one topic in the Common Core category have at least one matched comparison standard. Breadth of Coverage #SFBEUI PG $PWFSBHF JT TUSPOH GPS BMM UIF NBUIFNBUJDT DPODFQUVBMDBUFHPSJFT UIFNBKPSJUZPG$PNNPO$PSFDMVTUFST IBWF NBUDIJOH DPNQBSJTPO TUBOEBSET XJUIJO UIFN 5BCMF $ QSFTFOUTUIFTVNNBSJ[FEBMJHONFOUSFTVMUTGPSNBUIFNBUJDT 'JHVre%.BTTBDIVTFUUT4UBOEBSET%FQUIPG Figure C. Percentage ofAt, Massachusetts Under, At, ,OPXMFEHF-FWFMT6OEFS, and Above,Standards the or Above the Depth of Knowledge Level of the Common Core For the Massachusetts standards that match to Common Core for Mathematics Standards, for Mathematics Depth of Knowledge $PNNPO $PSF TUBOEBSET BO BWFSBHF PG SD = GBMM BU UIF TBNF MFWFM PG DPHOJUJWF EFNBOE BT UIF $PNNPO $PSF TUBOEBSET "O BWFSBHF PG SD PG UIF .BTTBDIVTFUUT TUBOEBSET BSF MPXFS JO DPHOJUJWF EFNBOE UIBO UIF $PNNPO $PSF TUBOEBSET BOEBOBWFSBHFPG SD BSFSBUFEBCPWFUIF $PNNPO $PSF TUBOEBSET 'PVS PG UIF mWF $PNNPO $PSFDPODFQUVBMDBUFHPSJFTNFFUUIF%0,$POTJTUFODZ DSJUFSJPO TFF 'JHVSF $ "DDPSEJOH UP SBUJOHT UIF (FPNFUSZDBUFHPSZEJEOPUNFFUUIFDSJUFSJPO"T'JHVSF $TIPXT TPNFDBUFHPSJFTGBMMDMPTFUPPSBUBOE results would be different if an alternative criterion had been selected. 0 /VNCFS and 2VBOUJUZ "MHFCSB Functions a 25 50 75 100 AWFSBHF Percent "CPWF "U 6OEFS Geometry 4UBUJTUJDT and Probability Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH a 5IF'VODUJPOTDPODFQUVBMDBUFHPSZNFFUTUIF%0,DSJUFSJPO CVUEVFUPSPVOEJOH UIF WBMVFBQQFBSTBUFYBDUMZ Appendix C 59 Results by Individual Comparison Standards Texas College and Career Readiness Standards 5IFTUVEZDPNQBSFEUIF&OHMJTIMBOHVBHFBSUT NBUIFNBUJDT BOE DSPTTEJTDJQMJOBSZ TUBOEBSET GSPN UIF 5FYBT $PMMFHF BOE $BSFFS 3FBEJOFTT 4UBOEBSET 5$$34 UP UIF $PNNPO $PSF standards. English Language Arts Findings for the TCCRS Standards Match 3BUFSTJEFOUJmFEVQUPUISFF$PNNPO$PSFTUBOEBSETXJUIFBDI 5$$34 TUBOEBSE 'JHVSF $ TIPXT UIF QFSDFOU PG $PNNPO Core statements (n UIBU BOZ PG UIF OJOF &-" SBUFST NBUDIFEUPPOFPSNPSFPGUIF5$$34TUBOEBSET n 5IF mHVSFDPMMBQTFTmOEJOHTBDSPTTBMMFJHIU&OHMJTIMBOHVBHFBSUT &-" BOE MJUFSBDZ TUSBOET *O 'JHVSF $ XF EJWJEF mOEJOHT CZ TUSBOE "T UIF CBS HSBQIT JOEJDBUF JO mWF TUSBOET UIF 5$$34TUBOEBSETIBWFNBUDIFTUPPGUIF$PNNPO$PSF TUBOEBSET 5XP BEEJUJPOBM TUSBOET IBWF NBUDIFT UP o PG UIF $PNNPO $PSF TUBOEBSET -BOHVBHF BOE 3FBEJOH 4UBOEBSET JO )JTUPSZ4PDJBM 4UVEJFT 5IF 5$$34 TUBOEBSET IBWF NBUDIFT UP PG UIF $PNNPO $PSF TUBOEBSET JO UIF 8SJUJOH 4UBOEBSET JO )JTUPSZ4PDJBM 4UVEJFT 4DJFODF BOE 5FDIOJDBM 4VCKFDUT TUSBOE3 Every strand meets the criterion GPSUIF$BUFHPSJDBM$PODVSSFODFTUBUJTUJD XIJDITQFDJmFTUIBU BDSPTTSBUFST BOBWFSBHFPGPOFDPSSFTQPOEFODFJOBDPOUFOU BSFBJTTVGmDJFOU 5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT widely. Chapter 3 provides the mean and standard deviation for the number of DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDITUSBOE5IF 5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF$PNNPO$PSFBOE the comparison sets that were matched. 3 Figure C. Percentage of Common Core Standards that Match Texas College and Career Readiness Standards, for ELA and Literacy Percent 92 100 Matched Not matched 75 50 25 8 0 Common Core Standards (113 statements) Figure C. Percentage of Common Core Standards that Match Texas College and Career Readiness Standards, by ELA and Literacy Strand Percent Matched 100 100 100 100 100 Not matched 100 90 88 68 75 50 32 25 12 0 0 0 10 0 0 0 Reading for Literature (9) Reading for Informational Texts (10) Writing (28) Speaking and Listening (10) Language (17) Reading in History/Social Studies (10) Reading in Science and Technical Subjects (10) Writing in History/Social Studies, Science, and Technical Subjects (19) Common Core strand (number of statements) Appendix C 60 Results by Individual Comparison Standards Table C. Summary of Alignment Between the Texas College and Career Readiness Standards and Common Core for English Language Arts and Literacy Common Core ELA and literacy strand Categorical Concurrence Coverage Reading for Literature Reading for Informational Texts Writing Speaking and Listening Language Reading in History/Social Studies Reading in Science and Technical Subjects Writing in History/Social Studies, Science, and Technical Subjects Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of standards); Does not meet the criterion for Categorical Concurrence; means that in a majority of topics in the Common Core category have at least one matched comparison standard; means that in more than one topic in the Common Core category have at least one matched comparison standard; means that in one or less than one topic in the Common Core category have at least one matched comparison standard. Breadth of Coverage #SFBEUIPG$PWFSBHFJTSBUFEBTTUSPOHGPSBMM&-"BOE literacy strands (the majority of Common Core topics IBWFNBUDIJOHDPNQBSJTPOTUBOEBSETXJUIJOUIFN This means that the Massachusetts standards that match to Common Core standards are distributed Figure C. Percent of Texas College and Career Readiness Standards across content topics within each Common Core Under, At, or Above the Depth of Knowledge Level of the Common Core Standards, for ELA and Literacy TUSBOE 5BCMF $ QSFTFOUT UIF BMJHONFOU TVNNBSZ GPSUIF8FCCBOE$PPLTUBUJTUJDT $PPL $PPL 8JMNFT 8FCC B Depth of Knowledge Across all matched standards for ELA and literacy, BO BWFSBHF PG SD BSF BU UIF TBNF MFWFM BT UIF $PNNPO $PSF TUBOEBSET "DDPSEJOH UP SBUJOHT BO BWFSBHF PG SD PG UIF TUBOEBSETBSFMPXFS BOE SD BSFIJHIFS JO DPHOJUJWF EFNBOE 5IF %FQUI PG ,OPXMFEHF %0, $POTJTUFODZDSJUFSJPOJTNFUGPSUXPPGFJHIU TUSBOET UIF -BOHVBHF 4UBOEBSET BOE UIF 8SJUJOH 4UBOEBSET JO )JTUPSZ4PDJBM 4UVEJFT 4DJFODF BOE 5FDIOJDBM4VCKFDUT'PSUIFPUIFSTJY$PNNPO$PSF TUSBOET UIFDSJUFSJPOJTOPUNFU'JHVSF$EJTQMBZT UIF SFTVMUT HSBQIJDBMMZ "T UIF mHVSF TIPXT TPNF TUSBOET GBMM DMPTF UP BOE SFTVMUT XPVME CF different if an alternative criterion had been selected. Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH Appendix C 61 Results by Individual Comparison Standards Mathematics Findings for the TCCRS Standards Match Figure C. Percentage of Common Core Standards that Match Texas College and Career Readiness Standards, for Mathematics 'JHVSF $ TIPXT UIF QFSDFOU PG $PNNPO $PSF TUBUFNFOUT (n UIBU IBWF NBUDIFT JO UIF 5$$34 NBUIFNBUJDT standards (n 5IFmHVSFDPMMBQTFTmOEJOHTBDSPTTUIF mWFDPODFQUVBMDBUFHPSJFT*O'JHVSF$ XFEJWJEFmOEJOHT CZ DPODFQUVBM DBUFHPSZ "T UIF CBS HSBQIT JOEJDBUF UIF 5$$34 TUBOEBSET IBWF NBUDIFT UP B IJHI QFSDFOU SBOHJOH GSPN o PG UIF $PNNPO $PSF TUBOEBSET JO GPVS PG mWF DPODFQUVBMDBUFHPSJFT'PS/VNCFSBOE2VBOUJUZ UIF5$$34 TUBOEBSET IBWF NBUDIFT UP POMZ PG UIF $PNNPO $PSF standards.&WFSZDPODFQUVBMDBUFHPSZNFFUTUIFDSJUFSJPOGPS UIF$BUFHPSJDBM$PODVSSFODFTUBUJTUJD Percent 100 Matched Not matched 75 75 50 25 25 0 Common Core Standards (192 statements) 5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT XJEFMZ$IBQUFSQSPWJEFTUIFNFBOBOETUBOEBSEEFWJBUJPOGPSUIFOVNCFSPG DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDIDPODFQUVBM DBUFHPSZ5IF5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF Common Core and the comparison sets that were matched. Figure C. Percentage of Common Core Standards that Match Texas College and Career Readiness Standards, by Mathematics Conceptual Category Matched Not matched 94 Not matched 94 Percent 100 66 75 50 84 78 76 34 24 25 22 16 6 0 Number and Quantity (32) Algebra (34) Functions (45) Geometry (45) Statistics and Probability (36) Common Core conceptual category (number of statements) Appendix C 62 Results by Individual Comparison Standards Table C. Summary for Alignment Between the Texas College and Career Readiness Standards and Common Core Standards in Mathematics Common Core mathematics conceptual category Categorical Concurrence Coverage Number and Quantity Algebra Functions Geometry Statistics and Probability Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of standards); Does not meet the criterion for Categorical Concurrence; means that in a majority of topics in the Common Core category have at least one matched comparison standard; means that in more than one topic in the Common Core category have at least one matched comparison standard; means that in one or less than one topic in the Common Core category have at least one matched comparison standard. Breadth of Coverage #SFBEUI PG $PWFSBHF JT TUSPOH GPS BMM NBUIFNBUJDT DPODFQUVBM DBUFHPSJFT JOEJDBUJOH UIBU UIF NBUDIJOH standards are distributed across a majority of Common Core mathematics clusters within each conceptual DBUFHPSZ5BCMF$TVNNBSJ[FTUIFmOEJOHT 'JHVre%5FYBT$PMMFHFBOE$BSFFS3FBEJOFTT Figure C. Percent of Texas College and Career Readiness Standards At, Across all matched standards in mathematics, an 4UBOEBSET%FQUIPG,OPXMFEHF-FWFMT6OEFS, Under, At, or Above the Depth of Knowledge Level of the Common and Above, the Common Core For Mathematics BWFSBHF PG SD GBMM BU UIF TBNF MFWFM BT Core Standards, for Mathematics Depth of Knowledge UIF$PNNPO$PSFTUBOEBSET XJUIBOBWFSBHFPG (SD PGUIF5FYBT$$34TUBOEBSETSBUFEMPXFSJO DPHOJUJWF EFNBOE BOE BO BWFSBHF PG SD SBUFE IJHIFS "MM mWF DPODFQUVBM DBUFHPSJFT NFFU UIF %0,$POTJTUFODZDSJUFSJPO 0 25 50 75 100 /VNCFS and 2VBOUJUZ "MHFCSB Functions AWFSBHF Percent "CPWF "U 6OEFS Geometry 4UBUJTUJDT and Probability Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH Appendix C 63 Results by Individual Comparison Standards Knowledge and Skills for University Success &OHMJTI TUBOEBSET BOE NBUIFNBUJDT TUBOEBSET TFDUJPOT GSPN UIF ,OPXMFEHF BOE 4LJMMT GPS 6OJWFSTJUZ 4VDDFTT ,464 4UBOEBSETXFSFDPNQBSFEUPUIF$PNNPO$PSFTUBOEBSET English Language Arts and Literacy Findings for the KSUS Standards Match 'JHVSF$TIPXTUIFQFSDFOUPG$PNNPO$PSFTUBUFNFOUT n UIBUBOZPGUIFOJOF&-"SBUFSTNBUDIFEUPPOFPSNPSF PGUIF,464TUBOEBSET n 5IFmHVSFDPMMBQTFTmOEJOHT BDSPTT BMM FJHIU &OHMJTI MBOHVBHF BSUT &-" BOE MJUFSBDZ TUSBOET*O'JHVSF$ XFEJWJEFmOEJOHTCZTUSBOE"TUIFCBS HSBQITJOEJDBUF UIF,464TUBOEBSETIBWFNBUDIFTGPS PGUIF$PNNPO$PSFTUBOEBSETGPSUIF3FBEJOHGPS-JUFSBUVSF TUSBOE5IF,464TUBOEBSETIBWFNBUDIFTUPoPGUIF $PNNPO$PSFTUBOEBSETGPSTJYTUSBOET5IFZIBWFNBUDIFTUP PGUIF$PNNPO$PSFTUBOEBSETJOUIF3FBEJOH4UBOEBSET JO4DJFODFBOE5FDIOJDBM4VCKFDUTTUSBOE5 Every strand meets UIF DSJUFSJPO GPS UIF $BUFHPSJDBM $PODVSSFODF TUBUJTUJD XIJDI TQFDJmFTUIBU BDSPTTSBUFST BOBWFSBHFPGPOFDPSSFTQPOEFODF JOBDPOUFOUBSFBJTTVGmDJFOU 5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT widely. Chapter 3 provides the mean and standard deviation for the number of DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDITUSBOE5IF 5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF$PNNPO$PSFBOE the comparison sets that were matched. 5 Figure C. Percentage of Common Core Standards that Match Knowledge and Skills for University Success Standards, for ELA and Literacy Percent 88 100 Matched Not matched 75 50 25 12 0 Common Core Standards (113 statements) Figure C. Percentage of Common Core Standards that Match Knowledge and Skills for University Success Standards, by ELA and Literacy Strand Percent Matched 100 100 96 90 94 90 Not matched 90 79 75 60 50 40 21 25 10 0 4 10 10 6 0 Reading for Literature (9) Reading for Informational Texts (10) Writing (28) Speaking and Listening (10) Language (17) Reading in History/Social Studies (10) Reading in Science and Technical Subjects (10) Writing in History/Social Studies, Science, and Technical Subjects (19) Common Core strand (number of statements) Appendix C 64 Results by Individual Comparison Standards Table C. Summary for Alignment Between the Knowledge and Skills for University Success Standards and the Common Core Standards in English Language Arts and Literacy Categorical Concurrence Common Core ELA and literacy strand Coverage Reading for Literature Reading for Informational Texts Writing Speaking and Listening Language Reading in History/Social Studies Reading in Science and Technical Subjects Writing in History/Social Studies, Science, and Technical Subjects Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of standards); Does not meet the criterion for Categorical Concurrence; means that in a majority of topics in the Common Core category have at least one matched comparison standard; means that in more than one topic in the Common Core category have at least one matched comparison standard; means that in one or less than one topic in the Common Core category have at least one matched comparison standard. Breadth of Coverage #SFBEUI PG $PWFSBHF JT SBUFE BT TUSPOH GPS BMM UIF ELA and literacy strands (the majority of Common $PSF UPQJDT IBWF NBUDIJOH DPNQBSJTPO TUBOEBSET XJUIJO UIFN 5IJT NFBOT UIBU UIF ,464 TUBOEBSET that match Common Core standards are distributed across content topics within each Common Core Figure C. Percent of Knowledge and Skills for University Success Standards Under, At, or Above the Depth of Knowledge Level of the TUSBOE5BCMF$QSFTFOUTUIFBMJHONFOUTVNNBSZGPS Common Core Standards, for ELA and Literacy UIF8FCCBOE$PPLBMJHONFOUTUBUJTUJDT $PPL $PPL8JMNFT 8FCC B Depth of Knowledge "DSPTTBMMNBUDIFETUBOEBSETGPS,464JO&-"BOE MJUFSBDZ BOBWFSBHFPG SD GBMMBUUIFTBNF %0,MFWFMBTUIF$PNNPO$PSFTUBOEBSET XJUIBO BWFSBHF PG SD SBUFE MPXFS JO DPHOJUJWF EFNBOEBOEBOBWFSBHFPG SD SBUFEIJHIFS 5ISFF TUSBOET 3FBEJOH 4UBOEBSET GPS -JUFSBUVSF -BOHVBHF 4UBOEBSET BOE 3FBEJOH 4UBOEBSET GPS -JUFSBDZJO4DJFODFBOE5FDIOJDBM4VCKFDUT NFFUUIF %0,$POTJTUFODZDSJUFSJPO 5ISFF TUSBOET 3FBEJOH 4UBOEBSET GPS -JUFSBUVSF -BOHVBHF 4UBOEBSET BOE 3FBEJOH 4UBOEBSET GPS -JUFSBDZ JO 4DJFODF BOE 5FDIOJDBM 4VCKFDUT NFFU UIF %0, $POTJTUFODZ DSJUFSJPO XIJDI JT CBTFE PO BUMFBTUPGUIFNBUDIJOH,464TUBOEBSETCFJOH BUPSBCPWFUIF%0,PGUIFDPSSFTQPOEJOH$PNNPO $PSFTUBOEBSE"T'JHVSF$TIPXT TPNFTUSBOET GBMMDMPTFUPBOESFTVMUTXPVMECFEJGGFSFOUJGBO alternative criterion had been selected. Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH Appendix C 65 Results by Individual Comparison Standards Mathematics Findings for the KSUS Standards Match Figure C. Percentage of Common Core Standards that Match Knowledge and Skills for University Success Standards, for Mathematics 'JHVSF $ TIPXT UIF QFSDFOU PG $PNNPO $PSF TUBUFNFOUT (n UIBU BOZ PG UIF TFWFO NBUIFNBUJDT SBUFST NBUDIFE UP POF PS NPSF PG UIF ,464 TUBOEBSET n 5IF mHVSF DPMMBQTFT mOEJOHT BDSPTT UIF mWF DPODFQUVBM DBUFHPSJFT *O 'JHVSF $ XF EJWJEF mOEJOHT CZ DPODFQUVBM DBUFHPSZ "T UIF CBS HSBQIT JOEJDBUF UIF ,464 IBWF NBUDIFT UP o PGUIF$PNNPO$PSFTUBOEBSETJOUIF"MHFCSB 'VODUJPOT BOE (FPNFUSZDPODFQUVBMDBUFHPSJFT5IFZIBWFNBUDIFTUP PG UIF $PNNPO $PSF TUBOEBSET JO UIF /VNCFS BOE 2VBOUJUZ DPODFQUVBMDBUFHPSZBOEJOUIF4UBUJTUJDTBOE1SPCBCJMJUZ DBUFHPSZ &WFSZ DPODFQUVBM DBUFHPSZ NFFUT UIF DSJUFSJPO GPS UIF$BUFHPSJDBM$PODVSSFODFTUBUJTUJD Percent 100 Matched Not matched 70 75 50 30 25 0 Common Core Standards (192 statements) 5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT XJEFMZ$IBQUFSQSPWJEFTUIFNFBOBOETUBOEBSEEFWJBUJPOGPSUIFOVNCFSPG DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDIDPODFQUVBM DBUFHPSZ5IF5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF Common Core and the comparison sets that were matched. Figure C. Percentage of Common Core Standards that Match Knowledge and Skills for University Success Standards, by Mathematics Conceptual Category Matched Percent Not matched 100 88 89 82 69 75 53 50 47 31 25 12 18 11 0 Number and Quantity (32) Algebra (34) Functions (45) Geometry (45) Statistics and Probability (36) Common Core conceptual category (number of statements) Appendix C 66 Results by Individual Comparison Standards Table C. Summary for Alignment Between the Knowledge and Skills for University Success Standards and Common Core Standards in Mathematics Common Core mathematics conceptual category Categorical Concurrence Coverage Number and Quantity Algebra Functions Geometry Statistics and Probability Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of standards); Does not meet the criterion for Categorical Concurrence; means that in a majority of topics in the Common Core category have at least one matched comparison standard; means that in more than one topic in the Common Core category have at least one matched comparison standard; means that in one or less than one topic in the Common Core category have at least one matched comparison standard. Breadth of Coverage #SFBEUI PG $PWFSBHF JT TUSPOH GPS BMM UIF NBUIFNBUJDT DPODFQUVBM DBUFHPSJFT UIF NBKPSJUZ PG $PNNPO $PSF DMVTUFSTIBWFNBUDIJOHDPNQBSJTPOTUBOEBSETXJUIJOUIFN 5BCMF$QSFTFOUTUIFTVNNBSJ[FESFTVMUTGPSNBUIFNBUJDT Depth of Knowledge "DSPTT DPODFQUVBM DBUFHPSJFT JO NBUIFNBUJDT GPS UIPTF ,464 TUBOEBSET UIBU NBUDI $PNNPO $PSF TUBOEBSET BO BWFSBHF PG SD GBMM BU UIF TBNF MFWFM BO BWFSBHF PG SD BSF MPXFS BOE BO BWFSBHF PG SD BSFIJHIFSJODPHOJUJWFEFNBOE5ISFFPGUIF mWF $PNNPO $PSF DPODFQUVBM DBUFHPSJFT NFFU UIF %0, $POTJTUFODZ DSJUFSJPO TFF 'JHVSF $ XJUI 'VODUJPOT BOE (FPNFUSZ CFJOH UIF UXP DBUFHPSJFT UIBU EP OPU NFFU UIF DSJUFSJPO "T 'JHVSF $ TIPXT TPNF DBUFHPSJFT GBMM DMPTFUPBOESFTVMUTXPVMECFEJGGFSFOUJGBOBMUFSOBUJWF criterion had been selected. 'JHVre%,OPXMFEHFBOE4LJMMTGPS6OJWFSTJUZ Figure C. Percent of Knowledge and Skills for University 4VDDFTT4UBOEBSET%FQUIPG,OPXMFEHF-FWFMT Success Standards Under, At, or Above the Depth of Knowledge 6OEFS, At, and Above, the Common Core for Level of the Common Core Standards, for Mathematics Mathematics 0 /VNCFS and 2VBOUJUZ "MHFCSB 25 50 75 100 AWFSBHF Percent "CPWF "U 6OEFS Functions Geometry 4UBUJTUJDT and Probability Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH Appendix C 67 Results by Individual Comparison Standards English Language Arts and Literacy Findings for 8FDPNQBSFEUIF*OUFSOBUJPOBM#BDDBMBVSFBUF *# 4UBOEBSET the IB Standards International Baccalaureate Standards GPS UIF %JQMPNB 1SPHSBNNF UP UIF $PNNPO $PSF TUBOEBSET 'PS &OHMJTI MBOHVBHF BSUT XF VTFE UIF DPVSTF TUBOEBSET GPS "-BOHVBHF &YUFOEFE&TTBZ BOE5IFPSZPG,OPXMFEHF'PS NBUIFNBUJDTXFVTFE.BUIFNBUJDBM4UVEJFT 4UBOEBSE-FWFM )JHIFS -FWFM DPVSTF TUBOEBSET 5IF TUVEZ EJE OPU JODMVEF BOZ DPOUFOU GSPN *# iPQUJPOTw 5IFTF BSF BEEJUJPOBM SFRVJSFE components that each IB school selects. The number of options varies by course and by subject. The IB options do not IBWFTQFDJmDTUBOEBSET Figure C. Percentage of Common Core Standards that Match International Baccalaureate Standards, for ELA and Literacy Percent 100 Matched Not matched 66 75 50 34 Match 3FDBMMUIBUSBUFSTJEFOUJmFEVQUPUISFF$PNNPO$PSFTUBOEBSET UIBUDPSSFTQPOEXJUIFBDI*#TUBOEBSE'JHVSF$TIPXTUIF percent of Common Core statements (n UIBUBOZPGUIF OJOF &OHMJTI -BOHVBHF "SUT &-" SBUFST NBUDIFE UP POF PS more of the IB standards (n 5IFmHVSFDPMMBQTFTmOEJOHT BDSPTT BMM FJHIU &-" BOE MJUFSBDZ TUSBOET *O 'JHVSF $ XF EJWJEF mOEJOHT CZ TUSBOE "T UIF CBS HSBQIT JOEJDBUF UIF *# TUBOEBSET IBWF NBUDIFT GPS PG UIF $PNNPO $PSF TUBOEBSETJOUIF3FBEJOHGPS-JUFSBUVSFTUSBOE5IF*#TUBOEBSET IBWF NBUDIFT UP o PG UIF $PNNPO $PSF TUBOEBSET JO UIF8SJUJOH 4QFBLJOHBOE-JTUFOJOH BOE3FBEJOH4UBOEBSETJO )JTUPSZ4PDJBM4UVEJFTTUSBOET5IFZIBWFNBUDIFTUPo PGUIF$PNNPO$PSFTUBOEBSETJOUIFSFNBJOJOHGPVSTUSBOET7 4JY PG UIF FJHIU TUSBOET NFFU UIF DSJUFSJPO GPS UIF $BUFHPSJDBM $PODVSSFODF TUBUJTUJD UIF -BOHVBHF TUSBOE BOE UIF 3FBEJOH 4UBOEBSETJO4DJFODFBOE5FDIOJDBM4VCKFDUTTUSBOEEPOPU 5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT widely. Chapter 3 provides the mean and standard deviation for the number of DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDITUSBOE5IF 5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF$PNNPO$PSFBOE the comparison sets that were matched. 7 25 0 Common Core Standards (113 statements) Figure C. Percentage of Common Core Standards that Match International Baccalaureate Standards, by ELA and Literacy Strand Percent Matched 100 93 100 Not matched 90 70 75 53 50 47 47 30 30 25 7 0 70 70 53 30 10 0 Reading for Literature (9) Reading for Informational Texts (10) Writing (28) Speaking and Listening (10) Language (17) Reading in History/Social Studies (10) Reading in Science and Technical Subjects (10) Writing in History/Social Studies, Science, and Technical Subjects (19) Common Core strand (number of statements) Appendix C 68 Results by Individual Comparison Standards Depth of Knowledge 0WFSBMM GPSUIPTF*#&-"BOEMJUFSBDZ standards that match the Common $PSF BOBWFSBHFPG SD of the IB standards fall at the same %FQUI PG ,OPXMFEHF %0, BT UIF Common Core standards across all TUSBOET "O BWFSBHF PG SD = PG UIF *# TUBOEBSET BSF SBUFE MPXFS BOE BO BWFSBHF PG SD BSF SBUFE IJHIFS JO DPHOJUJWF EFNBOE 0G UIF TJY TUSBOET UIBU NFFUUIFDSJUFSJPOGPSUIF$BUFHPSJDBM Concurrence statistic, four strands NFFU UIF DSJUFSJPO GPS UIF %0, $POTJTUFODZ TUBUJTUJD 'JHVSF $ EFQJDUT UIF SFTVMUT HSBQIJDBMMZ "T UIF mHVSF TIPXT TPNF TUSBOET GBMMDMPTFUPBOESFTVMUTXPVME therefore be different if an alternative criterion had been selected. Table C. Summary for Alignment Between the International Baccalaureate Standards and Common Core Standards in English Language Arts and Literacy Common Core ELA and literacy strand Categorical Concurrence Coverage Reading for Literature Reading for Informational Texts Writing Speaking and Listening Language Reading in History/Social Studies Reading in Science and Technical Subjects Writing in History/Social Studies, Science, and Technical Subjects Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of standards); Does not meet the criterion for Categorical Concurrence; means that in a majority of topics in the Common Core category have at least one matched comparison standard; means that in more than one topic in the Common Core category have at least one matched comparison standard; means that in one or less than one topic in the Common Core category have at least one matched comparison standard. Breadth of Coverage #SFBEUIPG$PWFSBHFJTTUSPOHGPSmWFPGUIF&-"BOE Figure C. Percent of International Baccalaureate Standards Under, literacy strands (for these, the majority of Common At, or Above the Depth of Knowledge Level of the Common Core $PSF UPQJDT IBWF NBUDIJOH DPNQBSJTPO TUBOEBSET Standards, for ELA and Literacy XJUIJO UIFN 5IJT NFBOT UIBU UIF *# TUBOEBSET UIBU match to Common Core standards are distributed BDSPTTDPOUFOUUPQJDTXJUIJOUIPTFmWF$PNNPO$PSF TUSBOET0OFTUSBOE 3FBEJOHGPS*OGPSNBUJPOBM5FYUT IBT NPEFSBUF DPWFSBHF 5IJT NFBOT UIBU $PNNPO Core standards match to IB standards in more than one topic but not a majority of topics within the strand. 0OF TUSBOE -BOHVBHF IBT MJNJUFE DPWFSBHF UIFSF is one topic that has Common Core standards with NA NBUDIFT UP UIF *# TUBOEBSET 5BCMF $ QSFTFOUT UIF TVNNBSZPGUIFBMJHONFOUTUBUJTUJDTGPSUIF8FCCBOE $PPLBMJHONFOUTUBUJTUJDT $PPL $PPL8JMNFT 8FCC NA Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH Appendix C 69 Results by Individual Comparison Standards Mathematics Findings for the IB Standards Match Figure C. Percentage of Common Core Standards that Match International Baccalaureate Standards, for Mathematics 'JHVSF$TIPXTUIFQFSDFOUPG$PNNPO$PSFTUBUFNFOUT n UIBU BOZ PG UIF TFWFO NBUIFNBUJDT SBUFST NBUDIFE UP one or more of the IB standards (n 5IFmHVSFDPMMBQTFT mOEJOHTBDSPTTUIFmWFDPODFQUVBMDBUFHPSJFT*O'JHVSF$ XFEJWJEFmOEJOHTCZDPODFQUVBMDBUFHPSZ"TUIFCBSHSBQIT JOEJDBUF UIF *# TUBOEBSET IBWF NBUDIFT UP o PG UIF $PNNPO$PSFTUBOEBSETJOGPVSPGUIFDPODFQUVBMDBUFHPSJFT 5IFZ IBWF NBUDIFT UP PG UIF $PNNPO $PSF TUBOEBSET JO UIF (FPNFUSZ DPODFQUVBM DBUFHPSZ Every conceptual DBUFHPSZNFFUTUIFDSJUFSJPOGPSUIF$BUFHPSJDBM$PODVSSFODF statistic. Percent 100 Matched Not matched 77 75 50 23 25 0 Common Core Standards (192 statements) 5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT XJEFMZ$IBQUFSQSPWJEFTUIFNFBOBOETUBOEBSEEFWJBUJPOGPSUIFOVNCFSPG DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDIDPODFQUVBM DBUFHPSZ5IF5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF Common Core and the comparison sets that were matched. Figure C. Percentage of Common Core Standards that Match International Baccalaureate Standards, by Mathematics Conceptual Category Matched Percent 97 100 Not matched 89 86 76 75 56 44 50 24 25 14 11 3 0 Number and Quantity (32) Algebra (34) Functions (45) Geometry (45) Statistics and Probability (36) Common Core conceptual category (number of statements) Appendix C 70 Results by Individual Comparison Standards Table C. Summary of Alignment for the International Baccalaureate Standards and Common Core Standards in Mathematics Common Core mathematics conceptual category Categorical Concurrence Coverage Number and Quantity Algebra Functions Geometry Statistics and Probability Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of standards); Does not meet the criterion for Categorical Concurrence; means that in a majority of topics in the Common Core category have at least one matched comparison standard; means that in more than one topic in the Common Core category have at least one matched comparison standard; means that in one or less than one topic in the Common Core category have at least one matched comparison standard. Breadth of Coverage #SFBEUI PG $PWFSBHF JT TUSPOH GPS BMM UIF NBUIFNBUJDT DPODFQUVBMDBUFHPSJFT UIFNBKPSJUZPG$PNNPO$PSFDMVTUFST IBWFNBUDIJOHDPNQBSJTPOTUBOEBSETXJUIJOUIFN 5BCMF$ QSFTFOUTUIFTVNNBSJ[FEBMJHONFOUSFTVMUTGPSNBUIFNBUJDT Depth of Knowledge Figure Percent of International Baccalaureate 30.C. International BaccalaurFBUF4UBOEBSds For those IB mathematics standards that match Common 'JHVre Standards Under, At, or Above the of Knowledge %FQUIPG,OPXMFEHF-FWFMT6OEFS, At,Depth and Above, $PSFDPOUFOU BOBWFSBHFPG SD PGTUBOEBSETGBMM of the Common Core Standards, for Mathematics theLevel Common Core BUUIFTBNFMFWFMPGDPHOJUJWFEFNBOEBTUIF$PNNPO$PSF 0 25 50 75 100 TUBOEBSET BDSPTT BMM NBUIFNBUJDT DPODFQUVBM DBUFHPSJFT AWFSBHF /VNCFS "OBWFSBHFPG SD PGUIF*#TUBOEBSETGBMMMPXFS Percent and JO DPHOJUJWF EFNBOE UIBO UIF $PNNPO $PSF TUBOEBSET 2VBOUJUZ BOE BO BWFSBHF PG SD GBMM BCPWF UIF $PNNPO "CPWF "MHFCSB $PSFTUBOEBSET5ISFFPGUIFmWF$PNNPO$PSFDPODFQUVBM "U DBUFHPSJFTNFFUUIF%0,$POTJTUFODZDSJUFSJPO TFF'JHVSF 6OEFS a XJUI'VODUJPOTBOE(FPNFUSZCFJOHUIFUXPDBUFHPSJFT Functions UIBU EP OPU NFFU UIF DSJUFSJPO "T 'JHVSF $ TIPXT TPNF DBUFHPSJFT GBMM DMPTF UP PS BU BOE SFTVMUT XPVME CF Geometry different if an alternative criterion had been selected. 4UBUJTUJDT and Probability Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH a 5IF'VODUJPOTDPODFQUVBMDBUFHPSZEPFTOPUNFFUUIF%0,DSJUFSJPO CVUEVFUP SPVOEJOH UIFWBMVFBQQFBSTBUFYBDUMZ Appendix C 71 Appendix D| Alignment Matches for Common Core Content-speciﬁc Areas NBEF GPS FBDI UPQJD UIF TVCBSFBT XJUIJO B TUSBOE 5IF tables illustrate that there is certain content within a strand that tends to have more concentration of matches than other DBUFHPSJFT XJUIJO UIF TBNF TUSBOE /PUF UIBU UIF OVNCFS PG SBUFE TUBUFNFOUT TIPXO JO QBSFOUIFTFT BMTP WBSJFT BDSPTT UPQJD$IBQUFSQSFTFOUFEUIFBWFSBHFOVNCFSPGNBUDIFT per standard for each topic across all comparison sets. Number of Alignment Matches for Common Core English Language Arts and Literacy Topics, by Comparison Standard Set The tables that follow present more information about the EJTUSJCVUJPO PG TUBOEBSE NBUDIFT XJUIJO FBDI PG UIF FJHIU &OHMJTIMBOHVBHFBSUT &-" BOEMJUFSBDZTUSBOET4QFDJmDBMMZ the tables show the total number of matches that all raters Table D. Number of Matches Within Each Common Core Topic in the Reading for Literature Strand Cumulative number of matchesa Topic (number of statements) CA MA TCCRS KSUS IB All standards Key Ideas and Details ()       Craft and Structure ()       Integration of Knowledge and Ideas ()       Range of Reading and Level of Text Complexity ()       CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate a These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times within one comparison set of standards and across multiple comparison sets of standards. Table D. Number of Matches Within Each Common Core Topic in the Reading for Informational Texts Strand Cumulative number of matchesa Topic (number of statements) CA MA TCCRS KSUS IB All standards Key Ideas and Details ()       Craft and Structure ()       Integration of Knowledge and Ideas ()       Range of Reading and Level of Text Complexity ()       CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate a These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times within one comparison set of standards and across multiple comparison sets of standards. Table D. Number of Matches Within Each Common Core Topic in the Writing Strand Topic (number of statements) Cumulative number of matchesa CA MA TCCRS KSUS IB All standards Text Types and Purposes ()       Production and Distribution of Writing ()       Research to Build and Present Knowledge ()       Range of Writing ()       CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate a These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times within one comparison set of standards and across multiple comparison sets of standards. Appendix D •  Alignment Matches for Specific Common Core Content-specific areas Table D. Number of Matches Within Each Common Core Topic in the Speaking and Listening Strand Cumulative number of matchesa Topic (number of statements) CA MA TCCRS KSUS IB All standards Comprehension and Collaboration ()       Presentation of Knowledge and Ideas ()       CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate a These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times within one comparison set of standards and across multiple comparison sets of standards. Table D. Number of Matches Within Each Common Core Topic in the Language Strand Cumulative number of matchesa Topic (number of statements) CA MA TCCRS KSUS IB All standards Conventions of Standard English ()       Knowledge of Language ()       Vocabulary Acquisition and Use ()       CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate a These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times within one comparison set of standards and across multiple comparison sets of standards. Table D. Number of Matches Within Each Common Core Topic in the Reading for Literacy in History/ Social Studies Strand Topic (number of statements) Cumulative number of matchesa CA MA TCCRS KSUS IB All standards Key Ideas and Details ()       Craft and Structure ()       Integration of Knowledge and Ideas ()       Range of Reading and Level of Text Complexity ()       CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate a These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times within one comparison set of standards and across multiple comparison sets of standards. Table D. Number of Matches Within Each Common Core Topic in the Reading for Literacy in Science and Technical Subjects Strand Topic (number of statements) Cumulative number of matchesa CA MA TCCRS KSUS IB All standards Key Ideas and Details ()       Craft and Structure ()       Integration of Knowledge and Ideas ()       Range of Reading and Level of Text Complexity ()       CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate a These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times within one comparison set of standards and across multiple comparison sets of standards. Appendix D 73 Alignment Matches for Specific Common Core Content-specific areas Table D. Number of Matches Within Each Common Core Topic in the Writing for Literacy in History/ Social Studies, Science, and Technical Subjects Strand Cumulative number of matchesa Topic (number of statements) CA MA TCCRS KSUS IB All standards Text Types and Purposes ()       Production and Distribution of Writing ()       Research to Build and Present Knowledge ()       Range of Writing ()       CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate a These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times within one comparison set of standards and across multiple comparison sets of standards. Appendix D 74 Alignment Matches for Specific Common Core Content-specific areas GPSFBDIDMVTUFS UIFTVCBSFBTXJUIJOBDPODFQUVBMDBUFHPSZ The tables illustrate that there are certain clusters within a DBUFHPSZUIBUUFOEUPIBWFNPSFDPODFOUSBUJPOPGNBUDIFTUIBO PUIFSDMVTUFSTXJUIJOUIFTBNFDBUFHPSZ/PUFUIBUUIFOVNCFS PGSBUFETUBUFNFOUT TIPXOJOQBSFOUIFTFT BMTPWBSJFTBDSPTT DMVTUFS$IBQUFSQSFTFOUFEUIFBWFSBHFOVNCFSPGNBUDIFT per standard for each cluster across all comparison sets. Number of Alignment Matches for Common Core Clusters, by Comparison Standard Set for Mathematics The tables that follow present more information about the EJTUSJCVUJPOPGTUBOEBSENBUDIFTXJUIJOFBDIPGUIFmWF$PNNPO $PSF NBUIFNBUJDT DPODFQUVBM DBUFHPSJFT 4QFDJmDBMMZ UIF tables show the total number of matches that all raters made Table D. Number of Matches Within Each Common Core Cluster in the Number and Quantity Conceptual Category Cluster (number of statements) Cumulative number of matchesa CA MA TCCRS KSUS IB All standards Extend the properties of exponents to rational exponents ()       Use properties of rational and irrational numbers ()       Reason quantitatively and use units to solve problems ()       Perform arithmetic operations with complex numbers ()       Represent complex numbers and their operations on the complex plane ()       Use complex numbers in polynomial identities and equations ()       Represent and model with vector quantities ()       Perform operations on vectors ()       Perform operations on matrices and use matrices in applications ()       CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate a These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times within one comparison set of standards and across multiple comparison sets of standards. Appendix D 75 Alignment Matches for Specific Common Core Content-specific areas Table D. Number of Matches Within Each Common Core Cluster in the Algebra Conceptual Category Cluster (number of statements) Cumulative number of matchesa CA MA TCCRS KSUS IB All standards Interpret the structure of expressions ()       Write expressions in equivalent forms to solve problems ()       Perform arithmetic operations on polynomials()       Understand the relationship between zeros and factors of polynomials ()       Use polynomial identities to solve problems ()       Rewrite rational expressions ()       Create equations that describe numbers or relationships ()       Understand solving equations as a process of reasoning and explain the reasoning ()       Solve equations and inequalities in one variable ()       Solve systems of equations ()       Represent and solve equations and inequalities graphically ()       CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate a These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times within one comparison set of standards and across multiple comparison sets of standards. Table D. Number of Matches Within Each Common Core Cluster in the Functions Conceptual Category Cluster (number of statements) Cumulative number of matchesa CA MA TCCRS KSUS IB All standards Understand the concept of a function and use function notation ()       Interpret functions that arise in applications in terms of the context ()       Analyze functions using different representations ()       Build a function that models a relationship between two quantities ()       Build new functions from existing functions ()       Construct and compare linear and exponential models and solve problems ()       Interpret expressions for functions in terms of the situation they model ()       Extend the domain of trigonometric functions using the unit circle ()       Model periodic phenomena with trigonometric functions ()       Prove and apply trigonometric identities ()       CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate a These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times within one comparison set of standards and across multiple comparison sets of standards. Appendix D 76 Alignment Matches for Specific Common Core Content-specific areas Table D. Number of Matches Within Each Common Core Cluster in the Geometry Conceptual Category Cluster (number of statements) Cumulative number of matchesa CA MA TCCRS KSUS IB All standards Experiment with transformations in the plane ()       Understand congruence in terms of rigid motions ()       Prove geometric theorems ()       Make geometric constructions ()       Understand similarity in terms of similarity transformations ()       Prove theorems involving similarity ()       Deﬁne trigonometric ratios and solve problems involving right triangles ()       Apply trigonometry to general triangles ()       Understand and apply theorems about circles ()       Find arc lengths and areas of sectors of circles ()       Translate between the geometric description and the equation for a conic section ()       Use coordinates to prove simple geometric theorems algebraically ()       Explain volume formulas and use them to solve problems ()       Visualize relationships between two-dimensional and three-dimensional objects ()       Apply geometric concepts in modeling situations ()       CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate a These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times within one comparison set of standards and across multiple comparison sets of standards. Appendix D 77 Alignment Matches for Specific Common Core Content-specific areas Table D. Number of Matches Within Each Common Core Cluster in the Statistics and Probability Conceptual Category Cluster (number of statements) Cumulative number of matchesa CA MA TCCRS KSUS IB All standards Summarize, represent, and interpret data on a single count or measurement variable ()       Summarize, represent, and interpret data on two categorical and quantitative variables ()       Interpret linear models ()       Understand and evaluate random processes underlying statistical experiments ()       Make inferences and justify conclusions from sample surveys, experiments, and observational studies ()       Understand independence and conditional probability and use them to interpret data ()       Use the rules of probability to compute probabilities of compound events in a uniform probability model ()       Calculate expected values and use them to solve problems ()       Use probability to evaluate outcomes of decisions ()       CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International Baccalaureate a These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times within one comparison set of standards and across multiple comparison sets of standards. Appendix D 78

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