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Table of ContentsStyle Guides, Usage Guides, and Dictionaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
NCTM-Specific Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Governance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 OngoingProgramsandEvents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 WebsiteandOnlinePresence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 MissionStatementandOfficialPositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 OtherTerminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Electronic Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Education Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8 GeneralTerms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8 MathematicsEducation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 MaterialsintheMathematicsClassroom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Guidelines for Style and Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 ActiveVoice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 CampusesofUniversities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Capitalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Contractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Dates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 EllipsisPoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 HyphensandRelatedMatters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20 Closed-upWords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20 HyphenatedWords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20 OpenPhrases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Horizontal,Run-inLists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 VerticalLists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 MathematicsandSymbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22 Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 Parallelism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24 Parentheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24 Possessives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25 PunctuationandGrammar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25 QuotationMarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 ReferencesandCitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 SexismandRacism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 SoftwarePrograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 Subject-VerbAgreement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28 SubstitutesforOverusedWordsandPhrases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28 TablesandFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 TelephoneNumbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29
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TitlesofGames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 TitlesofProblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 TitlesofWorks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30 WordUsageandTerminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30
Appendix A: Style for References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
Appendix B: Chicago Style vs. APA Style at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Appendix C: Trademarked Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42
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Style Guides, Usage Guides, and DictionariesNCTMrecommendsandusesthefollowingsourcesasstyleguidesandauthoritiesinwritingandeditingforNCTM:
• TheChicagoManualofStyle,17thedition
• PublicationManualoftheAmericanPsychologicalAssociation,6thed .,2009
• TheAssociatedPressStylebook,2019
• Merriam-WebsterCollegiateDictionary,11thedition
Mathematics Teacher: Learning and Teaching PK–12(MTLT)andmostNCTMbooksfollowChicagostyle .TheJournal for Research in Mathematics Education(JRME)andMathematics Teacher Educator(MTE)followAPAstyle(asdosomebooksthatpresentoranalyzeresearchresults) .NewsreleasesandSumming UpfollowacombinationofAPandChicagostyles .Allowancesshouldbemadeforappropriatedifferencesinlanguage,tone,andstyleforthedifferentformatsandaudiences .Althoughnolessgrammaticallycorrect,marketingcopymayadoptamoreinformalandconversationaltonewhendeemedappropriateornecessaryforaprojectorinitiative .Thismaybeaccomplishedbytheuseofsuchthingsascontractionsandellipsesaswellasvaryingsentencelengthstoassistinconveyingbothmessageandtoneandhelpingremainwithinstrictwordorcharacterlimits .
AllNCTMpublicationswiththeexceptionofnewsreleasesusetheOxford(serial)comma .ChicagoandAPAbothusetheserialcomma;APdoesnot .
NCTM-Specific TerminologyIngeneral,NCTMrecommendscapitalizingtermsthatreferspecificallytoNCTMoritsorganizationalstructure,programs,events,andpublications,forthepurposeofhighlightingNCTMinallCouncilcommunications .
DonotusethebeforeNCTMunlesstheabbreviationisfollowedbyanothernoun .
Incorrect: Ingeneral,theNCTMrecommendscapitalizingtermsthatreferspecificallytotheCouncil .
Correct: Ingeneral,NCTMrecommendscapitalizingtermsthatreferspecificallytotheCouncil .
But: TheNCTMBoardofDirectorswillmeetinIndianapolisthismonth .
Or: NCTM’sBoardofDirectorswillmeetinIndianapolisthismonth .
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Governance
Council:CapitalizeinallinstancesreferringtoNCTMtodistinguishtheNationalCouncilofTeachersofMathematicsfromothercouncils .
Board of Directors; Board:CapitalizeinallcasesreferringtoNCTM’sBoardofDirectorstosetitapartfromotherboards:“theNCTMBoardofDirectors”;“theBoardofDirectors”;“theBoard .”
Affiliate; Affiliates:CapitalizewhenreferringtothecollegeanduniversitygroupsofficiallyaffiliatedwithNCTM .Suchgroupsarecalledsimply“Affiliates”ratherthan“affiliatedgroups .”NCTMhasPartnerAffiliates,AssociateAffiliates,andStudentAffiliates .
Delegate Assembly:Alwayscapitalize;referstotheregularlyscheduledgatheringsoftheofficersandrepresentativesofNCTM’sAffiliatesattheannualmeetingsforthepurposeofsharingcommonconcernsandproposingresolutionsforactionbytheBoardofDirectors .
President; President-Elect; Past President; Member of the Board; Committee Chair:NCTMstyleregardingtitlesofNCTMofficersessentiallyfollowsChicagostyle .Thatis,capitalizeofficialNCTMtitles(suchaspresident, president-elect,andcommittee chair)whentheyappearbefore specificofficeholders’names .
Examples: NCTMPresidentGeorgePrime;President-ElectAngelaAvogadro;PresidentArchieArchimedes;PCChairHollyHilbert .
UselowercaseforofficialNCTMtitleswhentheyappearafter currentorformerofficeholders’names .
Examples: JoséRacineservedasNCTMpresidentfortwoyears;BennyRiemannisamemberofNCTM’sBoardofDirectors;TabithaGaussisthechairoftheNCTMPublishingCommittee .
UselowercaseforNCTMdesignationsthattheCouncildoesnotconsiderasofficialtitles .SuchdesignationsareconvenienttouseatNCTM,butdonothavethestatusofofficialtitles .
Past presidentisanofficialtitleonlywhenitdesignatesanoutgoingNCTMpresidentinthefirstyearafterhisorhertermasNCTMpresident .ItissimplyadescriptivelabelwhenitdesignatesallotherformerNCTMpresidents .Inthelattercase,itislowercasebothbeforeandafterthename:“NCTMpastpresidentLoisDolciani”;“LoisDolciani,pastpresidentofNCTM .”
NCTMdoesnotuseBoard memberasanofficialtitleformembersoftheNCTMBoardofDirectors,soitisnotcappedbeforeaname:“BoardmemberAndyFibonacci .”NCTMdoesnotgenerallyusethetermDirectorforaBoardmember .
LowercaseNCTMofficialtitleswhentheyappearontheirown,unattachedtoanyone’sname:“NCTMelectsanewpresidenteverytwoyearsandseveralnewBoardmemberseachyear .”
Insertingamodifier(suchasnewly elected)infrontofanofficialtitlethatappearsbeforeanameusuallycausesthetitletoloseitsofficialstatus(“newlyelectedNCTMpresidentDesmondFermat”) .
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Examplesoftheseguidelinesinuse:
• DuringheryearasNCTMpresident-elect,AngelaAvogadrocloselyshadowedFelixFraction,thecurrentNCTMpresident .
• Duringthepastyear,NCTMPresident-ElectAngelaAvogadrocloselyshadowedNCTMPresidentFelixFraction .
• NCTMPresidentMaryDedekindandBoardmemberAndyFibonaccitestifiedonSTEMeducationbeforetheHouseCommitteeonEducationandLabor .
Committees and Panels:UseinitialcapswiththenamesofspecificcommitteesestablishedbytheNCTMBoardofDirectors—forexample,PublicationsCommittee .Insubsequentreferences,useeither“thecommittee”(lowercase)orthecommittee’sinitials(inallcaps) .Showtheinitialsinparenthesesafterthefirstappearanceofthecommitteenameinfullbeforeusingtheinitialsinsubsequentreferences:“thePublicationsCommittee(PC)… .ThePC… .”
Likewise,useinitialcapswiththenamesofeditorialpanelsservingtheNCTMBoard .Italicizenamesofspecificpublicationsinthepanels’names:“Mathematics Teacher Educator EditorialPanel;Journal for Research in Mathematics Education”(afterthefirstreference:“MTE EditorialPanel,”“JRME EditorialPanel,”“theEditorialPanel,”“thepanel”) .NotethatMTLT hasaneditorialboardnotapanel,aneditor-in-chief,andassociateeditors .
Chairispreferredtochairman,chairwoman,orchairperson .
OngoingProgramsandEvents
NCTM Annual Meeting & Exposition:CapitalizedesignationsofparticularNCTMannualmeetings .
Examples: 2019AnnualMeetinginSanDiego;2019AnnualMeeting&ExpositioninSanDiego
Lowercaseannual meeting ininstancesthatdonotrefertoaspecificmeeting .ThesameguidelinesapplyinthecaseofNCTMregionalmeetingsandexpositions .
Themesofmeetingsandconferencesshouldappearinromantype,inquotationmarks .
Example: ThethemeofNCTM’s2019AnnualMeetinginSanDiegois“EmpoweringtheMathematicsCommunity .”
NCTM Regional Meeting & Exposition:SeeNCTM Annual Meeting & Expositionabove .Thesameguidelinesapply .
Mathematics Education Trust (MET):Throughgiftsandendowments,METoffersfinancialsupportintheformofscholarshipsandotherawardstoqualifiedpreserviceandin-serviceteachersofmathematics .Capitalizethenamesofparticulargrantsandawards .
E-Seminars Anytime:OnlineprofessionaldevelopmentsessionsofferedbyNCTM.ThecapitalE isanexceptiontoNCTM’sgeneraltreatmentofe-tomeanelectronic .
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Illuminations:NCTM’sextensiveIlluminationswebsitefeaturesStandards-basedresourcestoimprovetheteachingandlearningofmathematics .
WebsiteandOnlinePresence
www.nctm.org:NCTM’sWebaddressshouldinclude“www”butinmostinstancesdoesnotneed“http:// .”
Illuminations website; http://illuminations.nctm.org:OffersmaterialstoilluminatethevisionforschoolmathematicssetoutinPrinciples and Standards for School Mathematics,Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics,andFocus in High School Mathematics: Reasoning and Sense Making .
more4u; www.nctm.org/more4u:Offerssupplementalmaterials(activitypages,videos,etc .)forNCTMbooks,availabletopurchaserswhogotothesiteandenteranaccesscodeforaparticulartitle .Writtenintextas“more4U .”
Headquarters; Headquarters office:CapitalizeHeadquarters todesignateNCTM’sHeadquarters .
Headquarters staff:Collectivenoun;treatassingular .
Intranet:CapitalizetoindicateNCTM’snetworktodisseminateinformationin-housetostaff .
MissionStatementandOfficialPositions
NCTM’sMissionStatementistheofficialstatementoftheCouncil’spurpose,craftedandperi-odicallyreviewedandupdatedbytheBoard .
NCTM’sMissionStatementappearsonthecopyrightpageofallNCTMbooksandonthemast-headofallNCTMjournals .Thecurrentwordingofthestatement,asupdatedin2018,follows:
TheNationalCouncilofTeachersofMathematicsadvocatesforhigh-qualitymathematicsteachingandlearningforeachandeverystudent .
Useinitialcaps inallreferencestoNCTM’sMissionStatement .
TheBoardalsoregularlyconsidersanddevelopsofficialpositionstosupportteachersinsecur-ingresourcestoprovidehigh-qualitymathematicseducationforallstudents .
Inaddition,theBoardoccasionallydeterminestheneedforbook-lengthpresentationsoftheCouncil’sofficialpositionsincertainareasofmathematicseducation,usuallyrelatedtoNCTM’sStandards .TheBoardappointswritinggroupsandchargesthemwithproducingthesesignaturepublications .
NCTMpositionstatementsarepostedontheNCTMwebsite .EachofficialpositionoftheCouncilappearsinabriefform,titledNCTM Position,andinacompleteform,titledNCTM Position Statement.
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Showthenameofaparticularpositionstatementinquotationmarks,withinitialcaps;identifyitasanNCTMPositionStatement;andgivethedate .
Example “AccessandEquityinMathematicsEducation,”NCTMPositionStatement,April2014 .
UselowercasewhenreferringtoNCTMpositionstatementsingeneral .
OtherTerminology
Standard; Standards:CapitalizetheSinareferencetoanindividualStandardoragroupofStandardsarticulatedbyNCTMformathematicslearning .Usealowercasesinareferencetoastandardorstandardsestablishedbyotherorganizations .
NCTM Standards publications; Standards publications:Useoneofthesephrases,withthecapitalizationsshown,torefertoallorseveralofNCTM’sStandards-relatedpublications .DonotitalicizeStandardsanduseitasacatchallshortenedtitleforNCTM’sStandardspublica-tions, asrecommendedpreviously .
Electronic TermsThefollowinglistshowscommontermsassociatedwithelectronictechnologyandindicateshowtotreattheminNCTMmaterial .
Calculator and computer commands:Designerswillshowinadifferentfont(e .g .,asansserififthebodytextisaseriffont),willusesmallcaps,andwilluseaninitialcap .Copyeditorsshouldnotstylebutshouldmakeanotetothedesigner .Thatis,usebodytext,nocaps,nobold,butindicateinsomewaythatdesignershouldapplythestyle .
Example: PressEntEr.
e- or e: Lowercasecombiningformmeaningelectronic. Withcommonnouns,ahyphenfollowsetoensurereadability:e-book, e-commerce, e-zine, e-publication (sometimesshortenedtoe-pub).Withmostpropernouns,includingmanyproductnames,eiscloseduptoacapitallet-ter,asinNCTM’seBooksandeChapters .Notethatasanexceptiontothelowercasee,NCTM’sprofessionaldevelopmentseriesE-SeminarsAnytimeusesacapitalE .Intitlesofmorethanoneword,eisfollowedbyahypheninsteadofbeingclosedup .Atthebeginningofasen-tence,eisuppercaseonlywhenitisfollowedbyahyphen .Anexceptiontothisruleistheterm“email .”
e-Standards:ReferstotheelectronicversionofPrinciples and Standards for School Mathematics,theCouncil’smostfullydevelopedformulationofNCTM’sStandards.
e-Examples:Thee-Standardsaresupportedbyagroupofe-ExamplesthatuseinteractiveappletstoillustratelearningandteachingalignedwiththeStandards .
internet isnowlowercase;donotrefertoitas“theNet .”
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web, website
World Wide Web:Webaddressesshouldbecheckedforaccuracyincopyeditingandrecheckedinproofing .
Education TermsThefollowinglisthasthreesections .Thefirstisa general section,showinghowtotreattermsthatareusedacrossdisciplinesineducation .Thesecondgivesguidanceontermsthatareparticulartomathematics education.Thethirdshowshowtotreatasamplingoftermsforspecificequipmentormaterialsthatareusedinmathematics classrooms.
NCTMjournalsandbooksshowthesymbol®orthesymbol™afterthefirstmentionofaproductthatis,respectively,aregisteredtrademarkoranunregisteredtrademark .Avoiduseofbrandnamesasmuchaspossible .Ifusingabrandname,usetheregisteredorunregisteredtrademarksymbolonlyatthefirstmentionoftheproduct .Subsequentbrandedproductmentionsdonotusethetrademarksymbols .AppendixIlistssuchproductsandidentifiestheappropriatesymbolforeachentryinthelist .
GeneralTerms
achievement gap
activity sheet:Pagesuppliedforstudents’useinworkingonatask;useinsteadofworksheet.
ACT:FormerlyknownasAmerican College Testing.Anationalstandardizedassessmentusedincollegeadmissions,developedasacompetitorfortheSATandsometimestakeninplaceoforalongwithit .Pronouncedasinitialsandidentifiedonlybythem .
Advanced Placement (AP):Capitalizewhenspelledout;proprietarynameofaninternation-allyrecognizedprogram .CapitalizenamesofspecificAdvancedPlacementcourses:Advanced Placement Calculus; AP Calculus; AP Calculus exam. SimilartreatmentforInternationalBaccalaureate(IB) .
assessment:Morecommonlyusedthanevaluation todenoteameasurementofstudents’learning .Assessmentsareofdifferenttypes,includingformative assessment, summative assessment,anddiagnostic interview .
benchmark (n .andv .); benchmarked (adj .)
childcare (n .anda .)
children with challenges:Allchildrenfacechallenges .Donotuseasadescriptionofchil-drenwhostruggletolearnmathematics;usestudents with special needs orstudents with disabilities .
Common Core State Standards (CCSS); Common Core Standards; Common Core State
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Standards for Mathematics (CCSSM):K–12standardsforcollegeandcareerreadiness,releasedin2010bythestate-ledCommonCoreStateStandardsInitiative,spearheadedbytheNationalGovernorsAssociationCenterforBestPracticesandtheCouncilofChiefStateSchoolOfficers .DevelopedtobringcoherencetocurriculaacrosstheUnitedStatesintheteachingofmathematics(CCSSM)andEnglishlanguagearts .
Useromantypeinregulartextwhenspecifyingthestandardsthemselves,intotalorinpart,ratherthanthepublication,butitalicizeinallcitations,toindicatethepublication .ThefullbibliographicalcitationforCCSSandCCSSMfollows:
NationalGovernorsAssociationCenterforBestPractices(NGACenter)andCouncilofChiefStateSchoolOfficers(CCSSO) .2010 .Common Core State Standards for Mathematics. Washington,DC:NGACenterandCCSSO .http://www .corestandards .org .
CCSSMincludesStandardsforMathematicalPracticeandStandardsforMathematicalContent,whichaddresscoremathematicsprocessesandcontent,respectively .CCSSM’sStandardsforMathematicalPractice(referredtoas“SMP1,”etc .)arecloselyrelatedtoNCTM’sProcessStandards(Principles and Standards for School Mathematics)andReasoningHabits(Focus in High School Mathematics: Reasoning and Sense Making) .
ShowthenamesofthesetwoclassesofstandardswithinCCSSMwithinitialcaps .
coursework
critical thinking; critical thinking skills:Nohyphen;donotsubstitutesynonymsforcritical,whichhasparticularmeaninginthisphrase .
curriculum(sing .); curricula(pl .;notcurriculums); curricular (adj .)
data:Alwaysplural .Ifasingularnounisdesirable,useinformation.
data-driven(adj .)
decision maker (n .); decision-making(n .andadj .)Butpolicymaker;policymaking(n .andadj .)
differentiated instruction:Specific,individualizedinstruction .
elementary school(n .andadj .):Nohypheninanyposition .Today,elementary school usuallydesignateskindergarten–grade5;previously,itcommonlymeanteducationthroughgrade6 .Sometimestheadjectivephraseelementary school isclearerincontextthanthesinglewordelementary .Forexample,thephrase“elementaryschoollearning” denotesaspecificlevelofeducationinaneutralway,whereas“elementarylearning”maybeinterpretedasabasiclevelofachievement,possiblyinadisparagingorderogatorysense.
English as a foreign language (EFL)
English as a second language (ESL)
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English for speakers of other languages (ESOL)
English language learner (ELL); English language learners (ELLs); English learners (ELs)
faculty:Collectivenoun;treatassingular;sameforstaff
field test(n .); field-tested (adj .); field-test (v .)
formative assessment:Openinanyposition .
general education:Useinsteadofregular educationindifferentiatingfromspecial education.
gifted; gifted and talented:Useonlyasadjectives(gifted students;gifted and talented edu-cation);nohyphensingifted and talented.Donotuseasnouns (the gifted; education for the gifted and talented). Giftedandtalentededucation issometimesreferredtobytheinitialismGATEorasGT education .Seealsolearningdisabledgiftedandtalented(LDGT)students .
grade; grade level(n .); grade-level (adj .):Theschoolgradesareconventionallythenumberedlevels1–12;kindergarten(K)andprekindergarten(PK)arenot,strictlyspeaking,grades.Use“PK–12”ratherthanthephrase“gradesPK–12.” Todenoteaparticulargradelevel,useacardinalnumberaftergrade (e .g .,grade2)oranordinalnumber(spelledout)before grade(e .g .,secondgrade) .Useahyphenbetweenanordinalnumberandgrade inanadjectivalphrase(e .g .,second-gradestudents),butgrade followedbyacardinalnumbershouldbeopeninsuchaphrase(e .g .,grade2students) .NoteNouns before NumeralsinAppendixB .
hands-off; hands-on(adj .)
high-needs (adj.):Astudentorstudentswithspecialneeds:high-needsstudent;high-needsstudents .
high school:Grades9–12 .Alsocalledsecondary school. Nothyphenatedinanyposition .
incentivize:Jargon;donotuse .Substitute“provideanincentivefor .”
individualized education program; individualized education plan (IEP)
in-service(adj .); preservice (adj .): Preservice andin-service bothappearinWebster’s,thefirstclosedup,andthesecondwithahyphen .Thus,theadjectivesthatwecustomarilyusetodesignate,respectively,thosewhoarepreparingtoentertheteachingprofessionandteacherswhosecareersareunderwayarenotparallelinform .
International Baccalaureate (IB) program: See Advanced Placement.
Iowa Tests of Basic Skills (ITBS)
IRE:Commonquestioningpattern:ateacherinitiatesaquestion,astudentresponds,andtheteacherevaluatesthestudent’sresponseaseitherrightorwrong .
kindergarten (K): See grade.
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KWL:Athree-partinstructionalframeworkforhelpingstudentsconsider(1)whattheyknow,(2)whattheywant toknow(orlearn),and(3)whattheyhavelearned .
learning:Singular;notlearnings .
learning disabled gifted and talented (LDGT) students:Usenointernalpunctuation .Alsoknownastwice exceptional children.
limited English proficiency(n .); limited-English-proficient (adj .)
login(n .); log in (v .):Uselogintoinsteadofloginto .
logon(n .); log on (v .): Uselog ontoinsteadoflog onto .
middle school; middle-grades(adj .):Usuallydesignatesgrades6–8;sometimesreferstogrades5–8 .
Multi-Tiered System of Support (MTSS)
multiple choice(n .); multiple-choice (adj .)
multiple intelligences(n .); multiple-intelligences (adj .)
National Assessment of Educational Progress (NAEP)
National Board certification (n .); National Board–certified (adj .,withendash); National Board Certified Teacher (NBCT); National Board Certified Teachers (NBCTs)
NCATE standards; National Council of Accreditation for Teacher Education (NCATE) standards
on task, off task(adv .oradj .notfollowedbyanoun); on-task, off-task (adj .precedinganoun):“Heremainedontask .”“Heroff-taskdiscussionwasdistracting .”
paper-and-pencil test; paper-and-pencil activity(Orthereverse:pencil-and-papertest;pencil-and-paperactivity .)
policymaker (n .); policymaking(n .andadj .)
prekindergarten (PK):UsetheshortenedformPKnotpre-K .
preservice: See in-service.
pretest; posttest (n .andadj .)
primary grades; lower grades:Generally,Kindergarten–Grade2 .Nothyphenatedinanyposition .Primary grades ismorecommonthanlower grades.
problem-based learning (PBL)
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problem solver; problem solving (n .); problem-solving (adj .)
professional learning community (PLC)
pull-out program
QR code:Abbreviationfor“quickresponsecode .”Amatrixbarcodethatisreadablebyasmartphoneandgivesaccesstoinformationontheweb .
read aloud (n .)
real world (n .); real-world (adj .)
Response to Intervention (RTI)
results-based
risk taking (n .); risk taker (n .); risk-taking (adj .)
SAT; SAT Reasoning Test (SAT I); SAT Subject Tests (SAT II):Originally,thetestdevisedbytheCollegeBoardandreferredtoastheSAT Reasoning Test (orSAT I)wascalledtheScholastic Aptitude Test (orlater,the Scholastic Assessment Test) .TheSAT Subject Tests(alsoknownasSAT II)wereformerlyknownastheScholastic Achievement Tests. TheCollegeBoardwebsitedoesnotcurrentlyattachwordstotheinitialsSAT.
SATs; SAT scores
scaffold(n .,v .): Hasaparticularmeaningineducationandiswidelyused;however,providingabriefdescriptioncanbehelpfulinsomecontexts .To scaffold learningistoerectastructurethatallowsstudentstoadvancewithmaximumindependencefromthelevelthattheyhavemasteredtothenextlevelthattheyarecapableofattaining .
school-age children:Notschool-agedchildren .
scope and sequence (n .); scope-and-sequence (adj .)
seatwork
secondary school:Generally,grades9–12 .Nothyphenatedinanyposition .Seehighschool .
sense making (n .); sense-making (adj .):NCTMstylediffersfromthatofMerriam-Webster .
socioeconomic status (SES):TheabbreviationSESisoftenmodifiedbytheadjectivelow(e .g .,lowSESstudents)inreportsexaminingdisparitiesinachievementamongstudentsgroupedbydemographic,ethnographical,cultural,oreconomiccharacteristics .Insomecon-texts,themeaningofSEScanbeassumedtobecleartotheaudience,butinmostcontexts,thetermshouldbespelledoutonthefirstappearance .
special education (See general education .)
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special needs (n .); special-needs (adj .)
standardized test; standardized testing
Standards of Learning (SOLs)
STEM; STEM education:Acronymforscience, technology, engineering, and mathematics education. Insomecontexts,themeaningofSTEMcanbeassumedtobecleartotheaudience,butinmostcontexts,thetermshouldbespelledoutonthefirstappearance .
student teacher:Nothyphenatedinanyposition .
students with disabilities; students with special needs
subject area(n .); subject-area (adj .):Lowercaseschoolsubjectsunlesstheyarepropernouns(e .g .,geometry,history,English),butcapitalizethenamesofparticularcourses .
subject matter (n .); subject-matter (adj .)
teachable moment:Quotationmarksareunnecessary .
teacher leader:Ateacherleaderhasprofessionalresponsibilitythatexceedsthatofaclass-roomteacher,contributinghisorhertimeandtalentstotheeducationalcommunityortospecialinterestgroupsinthatcommunity .Donothyphenateinanyposition .
Third International Mathematics and Science Study (TIMSS)
turnaround school:Federaldesignationforalow-performingschoolthathasmadedramaticimprovement .
twice exceptional children:Donothyphenate .(Seelearning disabled gifted and talented students .)
upper elementary grades; upper grades: Generally,grades3–5 .
worksheet: Activity sheet ispreferable .
MathematicsEducation
AAA:Similaritytheoremfortriangles,sometimeswrittenas“angle-angle-angle .”Lettersareroman .
AAS; ASA; SAS; SSA; SSS:Congruencetheoremsfortriangles,sometimeswrittenas“angle-angle-side”;“angle-side-angle”;“side-angle-side”;“side-side-angle”;and“side-side-side,”respectively .Lettersareroman .
box-and-whisker plot
Cartesian; Cartesian plane; Cartesian grid
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“chunking” numbers
data set
distributive property of multiplication over addition; distributive property:Givewholenamethefirsttime .Allpropertiesofnumbersandoperationsarelowercase .
double count
equals sign:Useinsteadofequal sign. Thisequals that .
fundamental theorem of arithmetic; law of large numbers; etc.:Lowercaselaws,theorems,andthelike,accordingtoChicagostyle(seeChicago 8 .147) .
greatest common factor (GCF):TheinitialsGCFarecustomarilyroman .
least common denominator (LCD):TheinitialsLCDarecustomarilyroman .
least squares line of best fit; least squares line of fit; least squares regression line:SomeNCTMpublicationshavehyphenated“leastsquares”;leavingthephraseopenismoreconventional .
line A; segment AB; point P; angle ABC; etc.:Ingeneral,italicizedlettersusedforlines,seg-ments,angles,andsoon,appeareitherafteraworddescriptor,suchaslineorangle, asabove,orinassociationwithasymbol(e .g .,AB, ∠ABC ) .Usingbothwordsandsymbolsisredundant .
line of best fit
mathematical discourse community (MDC)
mathematize (v .)
mental math
N, n. Instatistics,capitalN referstopopulationsize,andlowercasenreferstosamplesize .
ordered pair:Showinparentheses,withacommafollowedbyaspace:(x,y),(4,52)
part-whole relationship
Pascal’s triangle; Pythagorean theorem:Capitalizeonlythepropernames,whichoftenappearinpossessiveoradjectivalforms .
place value (n .); place-value (adj .)
relatively prime numbers
regression equation
scatterplot
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skip-count (v .); skip counting (n .)
stem-and-leaf plot
story problem:Usedmorefrequentlytodaythanword problem.
x- and y-values; x- and y-axis
xy-plane
zeros. Useinsteadofzeroes.
MaterialsintheMathematicsClassroom
base-ten blocks
blackline; blackline master
counters
connecting cubes
Cuisenaire® Rods
dot paper
five-frame
flip chart
geoblocks
geoboard
geodot paper
The Geometer’s Sketchpad; GSP onsecondreference
GPS. Global positioning system;noneedtospelloutinmostcontexts .
grid paper. Useinsteadofgraph paper.
hundred chart; hundred board
isometric dot paper; isodot paper
math manipulative; manipulative aid
Mira. Asmallplasticproductthatcreatesareflectionofafigure .
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number cube
pan balance. Orjustbalance.
pattern blocks
place-value blocks
random number generator
semilog graph paper
ten-frame
TI-84:Identifycalculatorsbythemakerandmodelnumber .TI iswidelyknowntostandforTexas Instruments andmaybeusedwiththemodelnumber .
Guidelines for Style and UsageAbbreviations
Restricttheuseofmostabbreviationstoparentheses,tables,orotherlocationswherespaceisatapremium .
US:Showwithoutperiods,anduseasanadjective .USisalsoallowedasanoun,butonlyifthemeaningisclearfromcontext .
Academic degrees:Showabbreviationswithoutperiods,asabove .Ingeneral,NCTMdoesnotincludedegreeswithauthors’ormembers’names .
BachelorofArts(BA);bachelor’sdegree;bachelor’s
MasterofArts(MA);master’sdegree;master’s(master’sthesis)
DoctorofPhilosophy(PhD);doctorate;doctoraldegree(PhDdissertation;doctoraldissertation;doctoralthesis)
DoctorofEducation(EdD)
Acronyms and other abbreviations formed from initials (initialisms):Showinparenthe-sesafterthefirstappearanceofafullyspelled-outname—forexample,“NationalCouncilofTeachersofMathematics(NCTM) .”Iftheabbreviatedformisnotusedsubsequentlyintext,introducingitisunnecessary,anditshouldusuallybeomitted .Notethatthe doesnotordi-narilyprecedeacronymsorinitialismsandthattheseshortformsarecustomarilytreatedassingular,evenifthefullnamesareplural .
State abbreviations:Usetwo-letterpostalabbreviationsovertraditionalabbreviationswhenstatenamesareusedinreferencelists,tables,etc .Spelloutstatenameswhentheystandaloneinrunningtext:“NCTMheadquartersarelocatedinVirginia .”
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Spelloutstatenameswhenusedwiththenameofacity(exceptforDC):“NCTMheadquartersarelocatedinReston,Virginia .”
Summing Upandnewsreleasesusethetraditionalabbreviationsforparentheticalreferences—forexample,“HarryReid(D-Nev .) .”
Units of measure:Metricabbreviationsappearwithoutperiods(e .g .,cm,mg,dL;abbrevi-ateliterasLinsteadofl forreadability) .Metricabbreviationsfortimedifferfromcustomary(English)abbreviationsforthesameunits(e .g .,svs .sec .) .Abbreviationsofcustomaryunitstakeperiods(e .g .,ft .,yd .) .
Retaintheperiodsinallexpressionsusingcustomaryabbreviations—forexample,“2ft .+3ft .”;“ft ./sec .”
Unitsofmeasurearespelledoutinrunningtext .
Types of files:Intextreferringtoafiletype,useallcaps(e .g .,PDF,JPEG,TIFF) .
Saint; St.:Intext,capitalizeandspelloutSaint inthenamesofsaints .However,followcustom-arypracticeorknownpreferencesinthenamesofpeople,places,organizations,orpublica-tions(e .g .,St .Louis,Missouri;St .Mary’sCollegeofMaryland) .Ifyouareunabletodeterminecommonpracticeorpersonalpreference,spelloutSaintinthename .(SeeChicago10 .20and10 .30) .
Eras:UseBCE(before the Common Era)andCE (of the Common Era)insteadofBCandAD,respectively .BothBCEandCEshouldappearwithoutperiodsandfollowtheyear(e .g .,513CE) .
ActiveVoice
Sentenceswithverbsintheactivevoicearegenerallystrongerandmoredirectthansentenceswithverbsinthepassivevoice .Inactiveconstructions,thesubjectoftheverbisthedoerratherthanthereceiver oftheactionoftheverb,asinpassiveconstructions .
Passive voice: LarrywastaggedoutbyMaryafterhewaswavedhomebyJeanne .
Active voice: MarytaggedLarryoutafterJeannewavedhimhome .
Recastsentencesandclausesthatappearinthepassivevoiceasconstructionsintheactivevoicewhendoingsoispossibleandeffective .Trytominimizetheuseofpassiveconstructions .
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CampusesofUniversities
Todeterminehowtorepresentthenamesofcollegesanduniversities,checktheirwebsites .Clickingon“About”onthehomepageisoftenausefulwaytofindanofficialname .TheAssociationofAmericanCollegesandUniversitiesmaintainsanextensivelistofmemberinsti-tutionsofhighereducation .Thelisthaslinkstoeachmember’swebsiteandcanbebookmarkedforquickreference:http://www .aacu .org/membership/list .cfm .Someinstitutionsuseacommatosetoffaplacename(e .g .,CaliforniaStateUniversity,Northridge) .Ifsuchanameappearsinthemiddleofaclause,asecondcommashouldfollowtheplacename .Otherinstitutionsuseadashtosetoffaplacename;useanendashinthesecases(e .g .,UniversityofWisconsin–Madison)withnopunctuationaftertheplacename(seeChicago6 .46and6 .81) .Someuniver-sitiesretain“at”intheirnames,suchastheUniversityofTexasatAustin .DonotusethewordThe,withacapitalT,asthefirstwordinthenameofauniversityorcollegeunlesstheinstitu-tion’swebsiteclearlyindicatesthatThe ispartoftheofficialname .(PennStateisanexampleofonesuchuniversity—thewebsitegives“ThePennsylvaniaStateUniversity”astheofficialname .TheOhioStateUniversity(OSU)isanother;notethatitdiffersfromUniversityofOhio .)
Capitalization
Entities within NCTM:SeeNCTM-SpecificTermsforwordsthatarecapitalizedwhentheyrefertoNCTMentities(e .g .,Council,Board,Affiliate, Standard).
Names of committees:Useinitialcaps,butlowercasethewordcommitteewhenitisusedalonetorefertothecommittee(seeNCTM-SpecificTerms) .
Example: WewillmeetwiththeRegionalServicesCommitteetomorrow .Membersofthecommitteewillfurnishthenamesofvolunteers .
Titles of persons:Capitalizewhentheyprecedethename;lowercasewhentheycomeafterthename(seeNCTM-SpecificTerms) .
Example: NCTMPresidentJaneTaylorwillspeakonfractals .JamesPrime,NCTMpresident-elect,willpresideatthemeeting .
Titles of works:Alwayscapitalizethefirstandlastwords;capitalizeallotherwordsexcepta, an, the,prepositions,andcoordinateconjunctions .
School subjects and courses:Lowercasegeneralsubjects(e .g .,algebra,geometry,trigo-nometry),exceptforpropernouns(e .g .,Euclideangeometry,Americanhistory,French) .Treatfirst-yearalgebraandsecond-yearalgebra(oftencalledalgebra 1 andalgebra 2,respectively)asgenericsubjectsandusearabicnumeralstodesignatetheyear .Capitalizecoursenamesthatidentifyaspecialtopicforstudy(e .g .,Problem-SolvingStrategiesinGeometry) .CapitalizeAdvanced Placement(AP)andInternational Baccalaureate (IB)andthenamesofspecificAPandIBcourses(e .g .,APCalculusAB) .
OK:Usethetwo-letterformwithnoperiodsinsteadofokay .
Laws, theorems, principles, and the like:Capitalizeonlyassociatedpropernames(e .g .,Moore’slaw,Avogadro’stheorem,lawofcosines).
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The initial letter in a quotation:Itispermissibletochangeaninitialletterinthefirstwordinquotedmaterialtoacapitalorlowercaselettertoconformtothesurroundingtext .Ifaquo-tationthatisonlypartofasentenceintheoriginalformsacompletesentenceasquoted,aninitiallowercaselettermaybechangedtoacapitalwherethestructureofthetextsuggestsit .(SeeChicago 13 .13 .)
Seasons:Lowercaseinordinaryuseinrunningtext;uppercaseinreferencecitations .
State:Capitalizestate whenitappearsaspartofapropernoun:NewYorkState .
Contractions
Withtheexceptionoflet’s,NCTMpublicationsalmostalwaysspelloutpronounsaswellasformsofto beratherthanusingcontractionssuchashe’s,we’re,you’re .However,theseandothercontractionsareacceptableandconventionalinmarketingandwebcopy,instancesofdialogue,andincopyforSumming Up.
Dates
Usetheconventionalmonth,day,yearstyle(September3,2019)ratherthananinvertedstyle(3September2019) .
Writeoutthemonthinsteadofusinganumber:October11,not10/11or10-11 .
Useacardinalnumberratherthananordinalnumberinadate:May15,notMay15th .
Donotuseacommabetweenmonthandyearinadategiveninmonth-yearform(September2019),butuseacommaaftertheyearinadategiveninmonth-day-yearformifthedateappearsinrunningtext:“OnSeptember3,2019,Mariaannouncedherdecision .”
EllipsisPoints
Usethreedotstoindicateanomissionwithinaquotation .Athree-dotellipsismayindicateanomissionwithinasentenceoralongerpassage .Whenthelastpartofasentenceisomittedinaquotationthatcontinuesbeyondthatsentence,usefourdotstoindicatetheendofthesentenceandtheomission .Thefirstwordofthesentencefollowingthefourdotsmaybecapitalizedeventhoughitisnotthefirstwordofthesentenceintheoriginal .Donotmarkanomissionatthebeginningortheendofaquotationwithanellipsis .Athree-dotellipsismayalsobeusedtoindicatefalteringspeechorspeechthattrailsoff .
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HyphensandRelatedMatters
Compoundwordsthatarenothyphenatedcannotbehyphenated(e .g .,audiotapesandvideotapes;notaudio-andvideotapes) .
CLOSED-UP WORDS
blackline
childcare (n .)
classwork
copyeditor (n .)
coursework
eBook, eChapter (forNCTMproductlines)
fundraising (n .)
guideline
login(n .)
nonprofit
ongoing
online
prealgebra, precalculus
schoolchildren
schoolteacher
schoolwork
socioeconomic
timeline
timetable
toolbox
voicemail
website
HYPHENATED WORDS
box-and-whisker plot
CD-ROM
e-commerce, e-reader
e-Standards
fourth-grade (adj .): fourth-gradestudents
health-care (adj .): health-carereform
middle-grades (adj .): middle-gradesstudents—butmiddle school students (nohyphen)
off-site (adj .;adv .): off-sitetraining;daycareoff-site
on-site (adj .;adv .): on-siteregistration;printedon-site
second-year (adj .): second-yearalgebra
self-aware (similarly,self-conscious,self-assessment)
skip-count (v .); skip counting(n .)(open)
ten-frame (similarly,ten-bar,hundred-square,etc .)
toll-free call (butcall toll free)
two-year-old (n .;adj .)
warm-up(n .;adj .)
Adjectivesmodifiedbywell, lesser,etc .arehyphenatedbeforethenoun(e .g .,awell-educatedpublic)andopenafteranoun(e .g .,thepublicwaswelleducated) .
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OPEN PHRASES
African American student:(ingeneral,donothyphenatedescriptionsofpeople)
algebraic thinking activities
blackline master
cooperative learning groups
count on(v .):“Tosolvetheproblem,wecountonfromseven .”
cross multiplication
decision maker
early childhood education
fourth grade, fourth graders(n .)
game board
group work
health care (n .)
hundred board, hundred chart
log in (v .)
mathematics education community
mathematics teaching force
Native American student
peer assessment
professional development program
reform mathematics movement
road map (n .)
skip counting (n .);skip-count(v .)(closed)
special education class
staff development seminar
teacher education programs
tool kit:NCTMproductsarereferredtoastoolkits
warm up (v .)
whole number system
Lists*(APA style differs from Chicago style; see APA pp. 63–65.)
Allentriesinlistsshouldbeparallelinform .Thisrulealsoappliestosecond-andthird-ordersubheadsinbooksandarticles,sincethesesubheadsrepresentlistsinoutlineform .Listscanbeverticalorhorizontal,dependingonlength,complexity,anddesiredvisualimpact .
HORIZONTAL, RUN-IN LISTS
Short,relativelysimplelistscanbe“runin”horizontallywithregulartext .Introduceeachitembyanarabicnumeraloralowercaseitalicletterenclosedinparenthesesifdoingsoincreasesclarity .
Example: Thethreeideasthatthestudentsneededtounderstandwere(1)thatanisoscelestrianglehastwoequalsides,(2)thatatrianglethathastwoequalsidesalsohastwoequalangles,and(3)thatifanisoscelestriangleisarighttriangle,theneachofthetwoequalanglesmeasures45degrees .
VERTICAL LISTS
Longerlistsareoftenmoreeffectiveinverticalarrangements .Useabullet,anumber(followedbyaperiod),oraletter(lowercaseitalic,enclosedinparentheses)tointroduceentriesinverticallists .Verticallistsareoftwotypes,dependingontheirsyntacticalrelationshiptothesentencethatintroducesthem:
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A vertical list following a colon:Averticallistfollowsacolononlyifthesentencethatintro-ducesitformsacompletethought(isanindependentclause,withasubjectandaverb) .Suchalisthasthefollowingcharacteristics:
• Thefirstletterofeachitemiscapitalized .
• Nopunctuationappearsattheendofanyitem,includingthelast,unlesstheitemisacom-pletesentence,whichtakesaperiod .
A vertical list following an em dash:Averticallistfollowsanemdashifitsitemsaresyntac-ticallynecessarytocompletethesentencethatintroducesit .Insuchalist—
• thefirstletterofanitemislowercase;
• asemicolonappearsattheendofeachitemexceptthelast,whichhasaperiod;and
• theinclusionofandispermissiblebeforethelastentry,afterthesemicolonattheendofthenext-to-lastitem .
Whenalistfollowsanemdash,thesyntaxofthesentencethatincludesthelistfrequentlycallsforand beforethelastitem.
Anylist,whetherverticalorrunin,mustenumeratetheitemsifthetextthatprecedesitspecifiesthenumberofitems .However,anylistmaybeenumeratedforclarity,evenifthetextthatprecedesitdoesnotspecifythenumberofitems .
MathematicsandSymbols
Ifitisnecessarytobreakanequationattheendofalineinrunningtext,makethebreakafteranoperationsignorrelationsymbol(×,=,>,<,etc .) .
Ifitisnecessarytobreakanequationthatisdisplayed(setofffromtheregulartext),makethebreakbeforeanoperationsignorarelationsymbol .
Byconvention,nopunctuationfollowsadisplayedequationthatisprecededbyacolon .Insuchacase,thesentencethatintroducestheequationformsacompletethought(itisanindepen-dentclause,withasubjectandaverb) .Bycontrast,whenadisplayedequationissyntacticallypartofthesentencethatintroducesit,itisfollowedbyanypunctuation(e .g .,comma,period)thatthesyntaxrequires .
Ingeneral,spelloutpercentafteranumeralintext .Thesymbol%canbeusedsomecontexts:inparentheses,inproblemspresentedtostudents,andintabularandotherclose-setmatter .Itcanalsobeusedinsteadofthewordpercent inmath-intensivematerialwherethesymbolismoreconventionalthantheword .
Byconvention,theshortenedformsofmetricunitsareregardedassymbols,notabbrevia-tions,andthusdonottakeperiods(e .g .,cm,k,g,L) .Retaintheperiodsinoperations(e .g .,2ft .+3ft .=6ft .) .
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Themeasureofanangle—say, ∠ABC—isrepresentedsymbolicallyasm∠ABC,withanitalicm.
DonotuseaGreekdelta(Δ)tostandforatriangle .Ifatrianglesymbolisnotavailable,write“triangleABC” insteadof“ABC .”
Numbers
Spelloutnumbersfromonethroughnine,andusenumeralstorepresentnumbers10andhigher .This is a departure from Chicago and from previous NCTM style.
Spelloutnumbersatthebeginningofasentence .
Example: Forty-fivestateshaveadoptedtheCommonCoreStateStandards .
Rewritewhenspellingoutanumberthatrequiresalongphraseorresultsinasentencethattreatsnumbersindifferentways,makingcomparisonschallenging:
Example: Twohundredfifty-sixstudentsgraduatedwithhonors,with137planningtogotocollege .
Possible Of256studentsgraduatingwithhonors,137studentswereplanningto
revision: gotocollege .
Spelloutroundnumbersorapproximations .
Example: AboutthirtythousandstudentsparticipatedintheWorld’sLargestMathEventlastyear .
Usenumeralswhenfocusingdirectlyonnumbers,operations,ornumericalresults .
Withinaparagraphandthroughoutaproblem,numericalformsshouldbeconsistentunlesstheauthorconsciouslywishestovarytheusage .
Inactivitysheetsforstudents,usenumerals .
Numeralsshouldalwaysbeusedwithametricsymbol(e .g .,2cm,10dL) .
Numeralsshouldalwaysbeusedbeforethewordpercentorapercentsymbol(e .g .,37percent,37%) .
Beconsistentinexpressingrangesofnumbers:Use,forexample,“from1956to1967,”not“from1956–67 .”
Inabbreviationsofordinalnumerals(1st,2nd,3rd,4th,5th,etc .)usefull-sizecharactersintheendings-th, -nd, andsoon .DonotallowWordto“autocorrect”thesecharacterstosmallsuperscriptedforms .Observethispracticeofusingfull-sizecharacterswithexpressionssuchas“nth”and“zeroth .”
TitleI;Chapter1 .Usearomannumeralandanarabicnumeral,respectively,forthesegovern-mentprograms .Capitalizethenounbeforethenumeralintheseandothersuchdesignations
24
ofpartsoflegislation .(Thisisanexceptiontothegeneralruleaboutlowercasenounsbeforenumerals .)
Spelloutthepluralformofanumberinanexpressionsuchas“countbyones,”butuseanumeralinanexpressionsuchas“multiplyby5 .”
Indesignationsofplacevalue,spelloutones, tens, hundreds, andsooninsuchphrasesas“onesdigits”and“tensplace,”usingthepluralwithnopossessive .
• Inexpositorytext,usebase-ten numeration system, or base-ten system, butincopythatfocusesonnumbers,usenumeralsinphrasessuchas“base2”and“modulo7 .”
• In a departure from previous NCTM style,innumberswithfourdigits(andmore),sepa-rategroupsofthreedigitsintheconventionalwaybyusingcommas(e .g .,4,567) .Yearsortemperaturesareexceptionstothisrule .
• Displayedfractionscanusecustomaryspacing .
Parallelism
Partsofasentencethatareparallelinmeaningshouldbeparallelinstructure .Examplesofthisprincipleoccurofteninseriesorinlists .
Incorrect: DoyousuggestthatIactnowortowaituntiltomorrow?
Correct: DoyousuggestthatIactnoworwaituntiltomorrow?
Incorrect: Hunting,fishing,andtotellajokewellwerehisgreatestpleasures .
Correct: Hunting,fishing,andtellingajokewellwerehisgreatestpleasures .
Incorrect: Thisplanisquick,easy,effective,andmakesgoodsense .
Correct: Thisplanisquick,easy,andeffectiveandmakesgoodsense .
Incorrect: Sheisnotonlyintelligentbutsheisalsopretty .
Correct: Sheisnotonlyintelligentbutalsopretty .
Parentheses
Useparenthesestosetofftextthathasnonecessaryconnectiontotherestofthesentenceordiscussioninwhichitappears .
Useparenthesestosetofflettersornumbersthatidentifyitemsinaseriesinasentence—forexample,“Thestudyidentified(a)thecauses,(b)themanifestations,and(c)theconsequencesofthestudents’confusion .”Donotitalicizeanyofthelisteditemsintheseries .
Useparenthesestogroupmathematicalexpressions .
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Possessives
Avoidusinganapostrophewiththenameofanorganizationorprogramconsistingofmorethanoneword .
Incorrect: TheNationalCouncilofTeachersofMathematics’sgoalwassimple .
Incorrect: EducatorsrecognizeRacetotheTop’simportanceinUSeducationpolicy .
Recastsuchsentences:
Example: EducatorsrecognizetheimportanceofRacetotheTopinUSeducationpolicy .
Usinganapostrophewiththeacronymofanorganizationorprogramisacceptableifthefullnamehasbeenintroducedpreviouslyinthetext .
Example: NCTM’sgoalwassimple .
Possessivesareformedbyadding’stoasingularnameorword .Pluralsaddjusttheapostro-phe .(Examples:Charles’smanuscript;thegirls’toys)
students’ work; student work:Workby studentsmaybeidentifiedaseitherstudent work orstudents’ work, dependingonwhichissmootherandclearerincontext. Workfor students(pre-paredforandassignedtostudents)isstudent work.
PunctuationandGrammar
Usethattointroducearestrictiveclause;usewhichtointroduceanonrestrictiveclause .Arestrictiveclauseprovidesinformationthatisessential;anonrestrictiveclauseprovidesextrainformation .Acommaalwaysprecedeswhich inanonrestrictiveclausebutneverprecedesthat inarestrictiveclause.
Nonrestrictive: Myfavoritetree,whichIoftenclimbedwhenIwasyoung,istheredoakinourbackyard .(Clause gives extra information about the favorite tree.)
Restrictive: ThetreethatIclimbedmostoftenisthesugarmapleinourbackyard .(Clausegivesinformationthatisessentialforidentifyingthetreeinquestion .)
Usetheserial,orOxford,comma—acommabeforetheconjunctioninaseries .
Useacommabeforeacoordinatingconjunctionthatjoinstwoindependentclausesinacom-poundsentenceunlesstheclausesareveryshortandcloselyconnected .
Examples: ArneDuncandiscussedhisdepartment’sprioritiesforeducation,andhisdeputyfocusedontheadministration’sRacetotheTopprogram .
MaryranandJackskipped .
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Thisguidelinealsoappliestocompoundsentenceswithimperativeverbs .
Examples: DiscusstheCouncil’splansforprofessionaldevelopment,andbesuretofocusontheupcomingsummerinstitutes .
Runfortenstepsandskipforfive .
Donotuseacommabeforeaconjunctioninaclausewithasimplesubjectandacompoundverb .
Incorrect: SecretaryofEducationArneDuncandiscussedhisdepartment’spriorities,andfocusedontheObamaadministration’sRacetotheTopprogram .
Inmostcases,donotuseacommabeforeaninternaladverbialclausethatprecedesaclauseonwhichitdepends .Anexamplecansimplifywhatotherwiseseemstobeacomplicatedguideline(notethatnocommacomesbeforeif below):
Example: Smithporedoverthedocuments,andifJoneshadnotintervened,hewouldundoubtedlyhavediscoveredtheforgery .
Donotusethepronountheirtorefertoasingularantecedent .Beespeciallycarefulinthecaseofantecedentslikeaudience,group, company, andothersingularnounsthatrepresentcollections.
Incorrect: Thegrouppresentedtheirsolutiontotheproblem .
Correct: Thegroupmemberspresentedtheirsolutiontotheproblem .
Or: Thegrouppresenteditssolutiontotheproblem .
Just as … soisacorrelativeconjunction(likenot only … but also) .Bothpartsoftheconjunc-tionmustbeused .
Theadverbonlyshouldbeplacedsothatitclearlymodifieswhatitisintendedtomodify .
Incorrect: Fundingonlyplaysarolewhentheprojectiswellfunded .
Correct: Fundingplaysaroleonlywhentheprojectiswellfunded .
Asplitinfinitiveispermissible .
QuotationMarks
Usequotationmarkstosetoffthetitlesofexhibits;thethemesofmeetings,institutes,andconferences;andthetitlesoftheunitsormodulesinacurriculum .
Usequotationmarkstosetoffthetitlesofjournalarticles,chapters,individualpoems,andthelike .
Usequotationmarkstosetoffcoinedwords(suchas“guizzinta”forgoes into)orwordsusedinunconventionalways(seeneologisminMerriam-Webster) .
27
Foracoinedphraseorforanunusualuseofanadjectivalphrase,useeitherhyphensorquota-tionmarksbutnotboth(e .g .,“richgetricher”patternorrich-get-richerpattern) .
Usesinglequotesinsideofdoublequotestosetoffquotedtextwithinalongerquotation .
ReferencesandCitations
NCTMfollowsthestylesetoutin“DocumentationII:Author-DateReferences”(CMS,chapter15) .
• NCTMstyledepartsfromChicagostyleintheuseofp., whichChicagostyleomits. Inauthor-datecitationsfordirectquotationsorcloseparaphrasesofscholarlywork,usep.beforeapagenumber .
Example: (Lopez1958,p .234)
SexismandRacism
NCTMmaterialshouldreflectanappropriatemixofgenders,races,andculturesinphotographs,names,andcontent .TheAPAmanualoffersanexcellentdiscussionofreducingbiasinlanguage .Asthisdiscussionstresses,itisimportanttobesensitivetolabels,oftenputtingthepersonfirst(e .g .,learnerwithdisabilities)andneverequatingthepersonwiththecondition(e .g .,theLDs) .Avoidhyphensinmodifiersofmorethanonewordforracialandethnicgroups(e .g .,AsianAmericanstudents)togiveequalimportancetoalldescriptors .Capitalizealldescriptorsofrace(seealsoWord Usage) .
Inmattersrelatedtogender,problemswithpronounagreementcanoftenberesolvedbychangingthereferenttoapluralorbyrecastingthesentence .Otherwise,usehisand her,her and his,or—whentheyapplytodifferentreferents—hisandheralternately .Neverusetheyortheirtorefertoasingularreferent .
Example: Onestudentgaveheranswer,andaclassmateofferedhisalternativesolution .
Correct but
awkward: Eachstudenthadhisorherownpencils .
Better: Allstudentshadtheirownpencils .
Never: Eachstudenthadtheirownpencils .
Usegender ratherthansex:gender issues,gender differences,gender studies .Gender referstoroleandiscultural;sexreferstobiology .
Useheorshe,orsheorhe,not(s)he .
SoftwarePrograms
Showthe™symbolorthe®symbolafterthefirstmentionofsoftwarethatis,respectively,aregisteredtrademarkoranunregisteredtrademark .SeeAppendixCfornamesandappropriatesymbols .
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Subject-VerbAgreement
Thephrasemore than oneissingular .
Example: Morethanonesourcehasbeencited .
Thetitleofabookalwaystakesasingularverb .
Example: Principles and Standards for School Mathematicsissuesacallforallstudentstoengageinmorechallengingmathematics .
Theworddataisplural .
Example: Thedatashowanincreaseinproductivity .
Thewordmathematics issingular .
Example: Themathematicsofthissituationismorecomplexthanonemightthink .
SubstitutesforOverusedWordsandPhrases
case: situation,example,instance
critical; crucial: necessary,indispensable,unavoidable,fundamental,vital,cardinal,essential,basic,inherent,intrinsic,urgent,pressing,severe,serious
given: because,since,asaresultof,dependingon
inform:indicate,guide,affect,modify,adjust,influence(decisionsaboutorthedevelopmentof),impingeon,benefit,inspire,animate,enlighten,serveasabasisfor,shape,takeintoaccount,direct;informed by:permeatedby,basedon,characterizedby,reliedon,usedele-mentsof .
key:important,essential,fundamental,vital,primary,pivotal,strong,notable
lens, insuchphrasesasuse as a lens; take as a lens: bringintofocus,provideausefulvan-tagepoint,giveaframeofreference,offera newperspective;sharpenthefocuson
motivate: inspire,stimulate,generate,introduce,provoke,produce,prompt,influence,induce,suggest,enhance,assist,encourage
provide: furnish,supply,produce,offer,yield,present,propose,suggest,submit,afford,give,reveal,demonstrate,support,create,maintain,facilitate,serveas,promote,foster,pose,outfit,forge,formulate,examine,guarantee,actas,lend,allow,generate,set,establish,compose,develop
springboard, insuchphrasesasact as a springboard: introduce,provideanentrypoint,serveasabridge,lead(into)
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TablesandFigures
Mathematics Teacher: Learning & Teaching PK–12 (MTLT)andNCTMbooksfollowtheguidelinesoutlinedbelow:
• Inafigurecaption,abbreviate,useaninitialcap,boldface,anditalicsforthewordfigure:Fig. 8.1 .
• Useaperiodafterafigurecaptiononlywhenitisacompletesentence .
• Forafigurereferenceinthetext(includingwithinparentheses),usebodytext(nobold,nocaps,noitalics)andspelloutfigure.
Treatastablesonlythoseelementsthatreallyaretabularmatter .Otherelementsconsistingoftextshouldbetreatedasfigures .
TelephoneNumbers
NCTMshowstheareacodesoftelephonenumbersinparentheses:(202)365-0226;(1-800)977-8000 .Extensionsfollowthenumberasshown:(703)620-9840,ext .2278 .
Titlesofgames
tic-tac-toe:Thistraditionalgamehasmanynamevariants .NCTMprefersthisform .
Awidelyknownandlong-establishedgamethatisnottrademarkedislowercase .
Example: Thefamilyplayedrummyduringthestorm .
Atrademarkedgamehasaninitialuppercaseletter .Showthesymbol®orthesymbol™aftersuchagame .
Example: ThefamilyplayedMonopoly®duringthestorm .
Showamade-upgame,ofteninventedbyateacher,inquotationmarkswithinitialcaps .
Example: Tohelpherstudentsunderstandplacevalue,Ms .Wilsondevisedacountinggamethatshecalled“HensandChickens .”
Titlesofproblems
Lowercasethetitlesofwell-knownproblems(treatinthesamewayaslawsandtheorems) .
Example: Hewasintriguedbythefour-colorproblem .
Useinitialcapsforthetitleofaparticularproblemthatisstatedanddiscussedatlengthintext .Lowercasethewordproblemwhenitfollowsthetitleinrunningtext .
Examples: StudentsstudiedtheRoadAheadproblemtocalculatedistances .
ThestudentsenjoyedsolvingDecimalDilemma .
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Titlesofworks
Useheadline-stylecapsandsetinquotationmarksthetitlesoffolktales,fables,etc .
Themes(e .g .,ofconferences)andtitlesofsections(heads)inachapter,ofworkshops,andofmeetingsessionsarecapitalizedandshowninquotationmarks .
Thetitlesofprojectsarecapitalizedandsetinromantype,withnoquotationmarks(forinstance,ConnectedMathematicsProject,TeamLearninginSchoolsproject) .(Notethatproject issometimespartofthetitleandcapitalizedandsometimesisnotpartofthetitleandlowercased .)
Thetitlesofregulardepartmentsinamagazineorjournalhaveheadline-stylecapitalizationbutnoquotationmarks(Chicago,8 .177,14 .190,and14 .195) .
Example: ProblemstoPonderisadepartmentinthenewMTLT journal .
WordUsageandTerminology
above:Alternativesincludeprevious,preceding,andearlier .
Incorrect: Theaboveexampleinvolvesaquadraticequation .
Correct: Theexampleaboveinvolvesaquadraticequation .
afterward; backward; toward:Notafterwards,backwards,towards
affect; effect:Affect andeffect arebothverbs,andbotharealsonouns .However,affectusu-allyfunctionsasaverb,meaningto influence or have an impact on—andismuchmorelikelythaneffect tobethecorrectverbtochoose .
Example: Workingingroupscanaffectstudents’regardfortheirclassmates .
Bycontrast,effect usuallyfunctionsasanoun,meaningresult—andismuchmorelikelythanaffect tobethecorrectnountochoose .
Example: Researchhasexaminedtheeffectsofgroupworkintheclassroom .
Asanoun,affect appearsprimarilyinthecontextofpsychology,whereitindicatesemotionorarangeofemotionsthatsomeoneexpresses(e .g .,aflataffect,abluntedaffect) .Asaverb,effect appearsratherinfrequentlyandmeansto bring about (e .g .,toeffectachange) .
all- (combining form): all-around,all-out,all-clear,all-time
all of:Deleteof ifpossible .Use,forexample,“allthestudents”inplaceof“allofthestudents .”
alternate; alternative:Theverbalternateindicatesthattwothingsoccurinturn,firstoneandthentheother .Similarly,thenounalternate usuallyindicatestheotheroneoftwopossibilities .Alternativeoftensimplyindicatesanotherchoice—oneoftwoor morepossibilities—andisoftenthebetterwordtouse .
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altogether; all together:Altogethermeansentirely,wholly,orintotal .
Example: Showingtwobeansinherlefthandandanothertwoinherright,thekindergartnerannouncedthatshehadfourbeansaltogether .
All together indicatesacollectingorgatheringofasetofpeopleorthingsinoneplaceatonetime .
Example: Whenthestudentswerealltogether,theteacherledthemoutofthemuseumandontothebus .
and/or:Avoidand/or;useoneortheother .(Asimpleorisinclusive—thatis,itmeans“oneortheother,orboth .”Thus,orusuallycoverstheoptionsthatwritersintendtopresentbyusingand/or .)
as:Donotuse as tomeansince orbecause.
author:Donotuseauthorasaverb;substitutewrite .
based on; on the basis of:Usebased on phrasesadjectivally .Thetwosentencesbelowincludenouns(book andreport,respectively)modifiedbyparticipialphrasesbeginningwithbased on:
Correct: Ialwaysenjoyabookbasedonactualexperience .
Correct: Basedonincompleteresultsandfaultymethods,teamA’sreportwasworthless .
Donotusebasedonphrasesadverbially .Inthefollowingtwosentences,basedonisusedincorrectlybecauseitpointstotheactionoftheverbsdecidedandchanged,respectively:
Incorrect: Basedonwhatthestudentssaid,theteacherdecidedthatthetestwasunfair .
Incorrect: ThedriversuddenlychangeddirectionbasedoninformationfromherGPS .
Substitutingtheadverbialphraseon the basis of forbased on canrepairtheproblemintheseandmanysimilarsentences:
Correct: Onthebasisofwhatthestudentssaid,theteacherdecided thatthetestwasunfair .
Correct: ThedriversuddenlychangeddirectiononthebasisofinformationfromherGPS .
between; among:Usebetweenwhentwopeople,things,orideasareinquestion .Useamongincasesofmorethantwo .Betweencanalsobeusedwithmultipleobjectsconsideredastwogroups .
Example: Therelationshipbetweenthex-valueandthey-valuewasunclear .
Example: Therelationshipamongtheareasofthethreetriangleswasoneofsimilarity .
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Example: Theresearchexaminedtherelationshipbetweentheninthgraders’scoresandthetenthgraders’scores .
Black; White; Latinx; Native American:Capitalizealldescriptorsofrace .
board:Thewordboardcanbeappliedtoachalkboardawhiteboard,or,dependingonthecir-cumstances,evenaSMARTBoard .
case: Case issometimesusedformallyforalegalormedicalsituationoramathematicalcase:“case1,”“case2 .”However,itcanalsobeusedinlessformalcontexts,inphraseslike“insuchacase”or“inthiscase .”Althoughitshouldnotbeoverused,case canbeausefulsubstituteforexample, instance, situation incontextswherethesewordsareoverused .
compared to; compared with:Usecompared towhenlookingspecificallyforsimilarities .Usecomparedwithwhenlookingforbothlikenessesanddifferences .
Examples: Patrickcomparedtheearthtoanorange .Ms .DaviscomparedJenny’ssolutionwithMichael’s .
comprise, compose:Thewholecomprisestheparts;thepartscompose thewhole .Thepassiveconstructionis comprised ofisincorrect;substituteconsists of,is composed of, is made up of, oris constituted by .
couple of:Includeof beforeanoun(forexample,a couple of students;nota couple students).
due to:Usedue to onlyasanadjective,notasanadverb:
Incorrect: Hewontheraceduetohisamazingsurgeinthelastlap .
Correct: Hersuccesswasduetoherhardworkandgoodrelationswithothers .
Possiblerepairsfortheincorrectadverbialuseofduetointhefirstsentenceincludethefollowing:
Change to
adjectival
“due to”: Hiswinintheracewasduetohisamazingsurgeinthelastlap .
Replace
“due to”with
“because of”: Hewontheracebecauseofhisamazingsurgeinthelastlap .
each other; one another:Useeach otherwhentwopeople,things,orideasareinvolved;useone anotherwhenmorethantwoareinvolved .
Each other: PabloandTanyatalkedtoeachotherabouttheirsolutions .
One another: Thestudentsintheclasslookedatoneanotherwhentheteacherwrotethewronganswerontheboard .
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elementary; secondary:Considerthecontexttodecidewhetherschool shouldbeinsertedaftertheseadjectives .Forexample,woulditbebettertosay“elementaryschoolteachers”and“secondaryschoolteachers”thantosaysimply“elementaryteachers”and“secondaryteach-ers”? Sometimesaddingoromittingschool makesasignificantdifference;consider“elemen-tarymathematics” versus“elementaryschoolmathematics.” However,inothercontexts,themeaningisclearwithoutschool,andthelongerphraseisunnecessary .
enough; sufficient:Afteradjectivesofsufficiency,useaninfinitive,notasubordinateclause .
Incorrect: Providestudentswithenoughknowledgethattheycansolveproblems .
Correct: Providestudentswithenoughknowledgeto enable them to[orfor them to]solveproblems .
etc.; i.e.; e.g.:Theabbreviationsetc., i.e., and e.g.arepermissibleonlyinparentheses .Intext,changei.e. tothat is, changee.g. tofor example, andchangeetc.toand so on,orand so forth,orand the like. Reservetheabbreviationse.g. and i.e. forformalscholarlyorresearch-orientedcontexts,givingpreferenceelsewheretotheEnglishequivalents .
first, second, third…:Theseordinalsarecorrecttouseinenumeratingpointsintext;itisincorrecttousefirstly,secondly, thirdly. . . .
grade levels:Usegrades beforearangeofgradelevels:
Incorrect: 9–12teachers
Correct: Teachersofgrades9–12
Strictlyspeaking,prekindergartenandkindergartenarenotgrades .Theschoolgrades arethenumberedlevels1–12 .Shortenkindergarten toKandprekindergarten asPK .
Incorrect: Teachersofgradespre-K–2
Correct: TeachersofPK–grade2
hopefully; thankfully:Avoidusinghopefullyandthankfully colloquially,assentenceopenersthatservetomodifythesentencesinageneralwayratherthantomodifytheverbsinaclearandspecificway .
Incorrect: Hopefully,wewillhaveenoughmoneytogetbyuntilpayday .
Incorrect: Thankfully,theriverstoppedrisingbeforeitreachedourdoor .
Insuchsituations,forhopefullysubstituteIhope,wehope,itishoped;forthankfullysubstitutefortunately,wearethankful,wearegrateful .
Correct: Wehopethatwewillhaveenoughmoneytogetbyuntilpayday .7
Correct: Wearethankfulthattheriverstoppedrisingbeforeitreachedourdoor .
34
Usinghopefully andthankfullyispermissibletomodifytheverbinaspecificandmeaningfulway:
Correct: Withhisdiplomainhand,hesteppedhopefullyintothefuture .
Correct: Whenthefloodwatersreceded,westumbledthankfullytowardourhouse .
if; whether: Useifinconditionalstatements .
Example: Wewillgoiftheweatherholds .
Usewhetherinstatementsthatincludeindirectquestionstowhichtheanswerisyesorno .
Example: Hewonderedwhethertheanswerwas2 .
Itisusuallyunnecessarytofollowwhetherbythephraseor not .
impact: Avoidusingimpactasaverb .Substituteaffectorinfluence .
index: Usethepluralindiceswhenindexreferstoanindicator .Usethepluralindexeswhenindexreferstoalistattheendofabook .Seealsovertex .
inform: Alongwith“togiveinformationto,”oneofthelong-standingmeaningsofinformis“togiveformorcharacterto”or“betheformativeprincipleof .”Aparticularvisionofmath-ematicseducationcan,forexample,informamathematicscurriculum .Thisusageshouldnotbeconsiderededucationjargonordiscountedoutofhand .Nevertheless,insomecases,analternativesuchasshape,guide,orinfluence,maycommunicatethemeaningtoreadersmoreclearlythaninform .
in order to:Usetoorso that .
in-service:Thehyphenatedformisanadjectiveandmustmodifyanoun(e .g .,in-serviceprogram,in-serviceactivity,in-serviceteacher);thecounterpartpreserviceisclosedup,nothyphenated .
in terms of:Minimizetheuseofthisphrase,reservingitprimarilyformathematicalcon-texts(e .g .,“Expressxintermsofy”) .Useaboutoranotheraptwordorphraseinmostothersituations .
key:Keycanmeanleading,prominent,oressential;itdoesn’thavetorefertosomethingthatmetaphoricallyopensorunlocks .
less; fewer:Useless withmassamounts(e .g .,lesssugar,lessoil,lessoxygen);usefewer withcountablethings(e .g .,fewerchildren,fewerpurchases,fewermiles) .However,less issometimesappropriateinphrasesinvolvingcountableobjectsthatareassociatedwithmassamounts,suchastime,money,anddistance—forexample,“withlessthantendaysremainingbeforetheelection,”“withlessthantendollarsinhispocket,”“heneededtotravellessthantenmiles .”
35
likely:Useasanadjectivetoindicatethataneventisprobable. Donotuseadverbially,asasynonymforprobably.
Incorrect: Shewilllikelywintheall-schoolmathematicscompetition .
Correct: Sheislikelytowintheall-schoolmathematicscompetition .
man-made:Usemanufactured.
math:Inmanyformalcontexts,spellout: mathematicsor mathematical. However,NCTMjournalsusemath, asdoSumming Up andNCTMmarketingmaterials .Math appearsinsuchphrasesasmath lab,math anxiety,andmental math .”
may; might:May suggestswhatispossibleorlikely; might suggestswhatishypotheticaloruncertain .
more important:Usemore important,notmore importantly,tointroduceamoreimportantpoint .
motivate:Motivate means“giveamotiveto”or“stimulateaninterestinoranenthusiasmfor .”Thus,itispossibletomotivateanimatebeings,butitdoesnotmakesensetosuggestthatsomethingthatisinanimatecanbemotivated .Sometimesauthorsassertthataparticularidea“motivatesthecurriculum,”or“motivatesthelesson .”NCTMregardsthisuseofmotivateasnonstandard .Oftenachangefrommotivate todrive ormove forwardissufficient .
on-site; off-site:Webster’snowhyphenatesthesephrasesasadverbsaswellasadjectives .
Adverbial use: Thebookswereprintedon-site .
Adjectival use: Thecompanyhadscheduledoff-sitetraining .
on the other hand; Use only when completing a pair with on the one hand.
over:Usemore thaninplaceofoverwhenreferringtonumberorquantity(e .g .,morethantwoweeks,morethan750) .
percent; percentage:Percentmeans“per,oroutof,onehundred .”Strictlyspeaking,percent isnotanounbutalwaysfollowsanumberinaphrase(e .g .,17percent)indicatinghowmanyoutofonehundred .Thephrasegivesthepercentage,andpercentage isthenounform .
Example: Inthestudy,17percentofthesubjectsdevelopedhighbloodpressure .Thispercentagewashigherthanexpected .
Incopythatisheavilystatistical,andtosavespace,itissometimespreferabletousethepercentsymbol% .
36
rather than; instead of:Rather than takestheinfinitive;instead of takesthegerund .(Notethattointheinfinitiveiscustomarilysuppressedinconstructionswithrather.)
Examples: Ratherthantakeachanceontheweather,wepurchasedindoorticketsfortheWolfTrapconcert .
Insteadoftakingachanceontheweather,wepurchasedindoorticketsfortheWolfTrapconcert .
reference: Avoidusingreference asaverb .Inasentencesuchas,“HereferencedSmithandStein’sresearch,”substitutecitedorreferred toforreferenced.
scaffold (n., v.):Scaffold hascometohaveaparticularmeaningineducation .To scaffold learningistoerectastructurethatallowsstudentstoadvancewithmaximumindependencefromthelevelthattheyhavemasteredtothenextlevelthattheyarecapableofattaining .
sense making (n.); sense-making (adj.):NCTMusessense making tomeanthe process of making sense of. Webster’sgivestheclosedformsensemaking asanadjectivemeaningsen-sible, reasonable, practicable, asin“a sensemakingproposal .”NCTM’suseofsense making shadesoffinadifferentdirection .A“sense-makingactivity”isnotasensibleorpracticableactivitybutonethatengagesstudentsactivelyintheprocessofmaking sense ofmathematics .HyphenatingadjectivalinstancescommunicatesNCTM’sparticularmeaningmoreclearlythantheone-wordadjective .
since:Toavoidambiguityofthissort,followtheconventionofusingsince onlyinatemporalsenseatthebeginningofasentence:
Example: Since1989,NCTMhasreleasedanumberofdocumentsoutliningtheCouncil’sStandards .
Changeacausalsinceatthebeginningofasentencetobecause:
Example: Since Becausehehadtheflu,hestayedhome .
text; textbook:Usetext whenreferringtothemainbodyofaprintedwork .Usetextbookwhenreferringtoabookusedinthestudyofasubject .
There is; There are; It is:Ifpossible,recastsentencestoomitpassiveopeners .
Example: Therearenowforty-fivestatesthathaveadoptedtheCommonCoreStateStandards .
Simple revision: Forty-fivestateshavenowadoptedtheCommonCoreStateStandards .
toward; towards:Usetoward,nottowards .
upon; on:Ingeneral,useon,forbrevity,simplicity,anddirectness .However,upon ispermis-sibleintheformula“onceuponatime”andtomean“ontheoccasionof”insuchphrasesas“UponhisarrivalinEngland .”
37
utilize:Donotuseutilize,whichsoundspretentious .Substituteuseoranotheraptword .Synonymsforutilizeincludeapply,employ,operate,drawon,makeuseof;relatedwordsincludehandle,manipulate,wield,work .
various vs. variety of: Eitherisgrammaticallycorrect .Avariety ofismoreeffectivethanvarious toindicatearepresentativesample;variousoftenmeansjustdifferentorofanindefi-nitenumber .Insomecircumstances,itmaybepreferabletosubstituteseveralordifferentforvarious.
via:Useonlyinageographicalsense,toindicatearouteoftravelbetweentwopointsinspace .Donotuseinthemoregeneralsenseofby means of.
Incorrect: Wecommunicatedviae-mail .
Correct: WetraveledtoSaintPaulviaChicago .
vertices:Usevertices asthepluralofvertex .Likewise,useindices asthepluralofindex, butonlywhenusingindex tomeanindicator. Inthecontextofbooks,useindexes asthepluralofindexandappendixes asthepluralofappendix.
while:Usewhileonlytoshowthattheactionintwoclausesissimultaneous .Otherwise,usealthough orwhereas.
38
Appendix A: Style for ReferencesBook Shute,William,WilliamShirk,andGeorgePorter .1957 .Solid Geometry.
NewYork:AmericanBook .
Electronic Book Shaughnessy,J .Michael,BethChance,andHenryKranendonk .2009 .Focus in High School Mathematics: Reasoning and Sense Making in Statistics and Probability. Reston,VA:NationalCouncilofTeachersofMathematics .PDFe-book .
For a downloaded e-book, indicate format as the last part of the cita-tion. For a book consulted online, indicate the URL or the DOI as the last part of the citation. For a freely available electronic edition of an older work, include the URL as the last element.
NCTM Yearbook NationalCouncilofTeachersofMathematics(NCTM) .1989 .New Directions for Elementary School Mathematics,1989YearbookoftheNationalCouncilofTeachersofMathematics,editedbyPaulR .Trafton .Reston,VA:NCTM .
Article in a Book Oakes,Jeannie .1995 .“OpportunitytoLearn:CanStandards-BasedReformBeEquity-BasedReform?”InSeventy-Five Years of Progress: Prospects for School Mathematics,editedbyIrisM .Carl,pp .78–98 .Reston,VA:NationalCouncilofTeachersofMathematics .
Article in an NCTM Yearbook
Usiskin,Zalman .1986 .“ReasonsforEstimating .”InEstimation and Mental Computation,1986YearbookoftheNationalCouncilofTeachersofMathematics(NCTM),editedbyHaroldL .Schoen,pp .1–15 .Reston,VA:NCTM .
Article in a Book in a Series
Good,ThomasL .,andBruceJ .Biddle .1988 .“ResearchandtheImprovementofMathematicsInstruction:TheNeedforObservationalResources .”InEffective Mathematics Teaching,editedbyDouglasA .GrouwsandThomasJ .Cooney,pp .114–42,vol .1,ResearchAgendaforMathematicsEducation .Reston,VA:NationalCouncilofTeachersofMathematics .
39
PhD Dissertation Akdag,FusunSemiha .1985 .“TheEffectsofComputerProgrammingonYoungChildren’sLearning .”PhDdiss .,TheOhioStateUniversity .
McGalliard,WilliamA .1982 .“SelectedFactorsintheConceptualSystemsofGeometryTeachers .”Doctoraldiss .,UniversityofGeorgia .Dissertation Abstracts International44(1983):1364A .
Paper Presented at a Conference
Lehrer,Richard,andPaulSmith .April1986 .“LogoLearning:IsMoreBetter?”PaperPresentedattheAnnualMeetingoftheAmericanEducationalResearchAssociation,SanFrancisco .
Article in a Journal
Craine,Timothy,andRhetaRubenstein .1993 .“AQuadrilateralHierarchytoFacilitateLearninginGeometry .”Mathematics Teacher86(January):30–36 .
ORMathematics Teacher86(1):30–36 .(SeeCMS15 .47)
ORMathematics Teacher86,no .1(January):30–36 .
Electronic Journal Article
Battista,MichaelT .2002 .“BuildingProperlyStructuredMentalModelsforReasoningaboutVolume .”ON-Math: Online Journal of School Mathematics 1(Winter) .http://my .nctm .org/eresources/journal_home .asp?journal_id=6 .
Newspaper Article
Citationsofnewspaperandmagazinearticlesareusuallysufficientwithinthetext .SeeCMS14 .19815 .49 .Ifabibliographicorreferencelistentryisneeded,itwouldappearasfollows:
Braun,R .J .1993 .“SchoolsThatFlunk .”Star-LedgerSpecialReportseries .Newark (N.J.) Star-Ledger,October24–31,1993 .
Tyler,Marshall .1985 .“200thBirthday .”Los Angeles Times .March15, 1985,sec .1A,p .3 .
Letter Pope,Alexander .1956 .LettertoWilliamFortescue,September23,1725 .InThe Correspondence of Alexander Pope,editedbyE .G .Sherburne,vol .2,pp .323 .Oxford:ClarendonPress .
Personal Communication
Referencestopersonalcommunication(telephoneconversations,e-mailmessages,andthelike)areusuallygivenparentheticallyinthetextinsteadofappearinginareferencelist .
(DeborahGlass,April10,2009,pers .comm .) .
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Appendix B: Chicago Style vs. APA Style at a GlanceNounsbeforeNumerals
Chicagostylelowercasescommonnounsbeforenumerals(e .g .,figure1,grade4,day3,andsoforth) .
APAstylecapsnounsbeforenumeralsinanumberedseries(e .g .,Figure1,Grade4,Day3,etc .) .
PrepositionsinTitles
Chicagostylelowercasesprepositions,regardlessoflength,withrareexceptionsforprepositionsthatreceiveemphasisinatitle,suchasthroughinA River Runs Through It.
APAstylecapsallwordsoffourormoreletters .
TablesandFigures
JRMEandMTEfollowAPAstylewheneditingtablesandfigures:
• Allfiguresandtablesmustbementionedinthetext .Capitalizetheword,andspellitout .
• InAPA style,thecaptionforatableisinitialcappedroman*andinitialcappeditalic**withnoendingpunctuation:
Example: *Table3**Percentage of Teachers With Qualification and Experience Characteristics by Attribute Mastery
• InAPAstyle,thecaptionforafigureisinitialcappeditalic*andsentencecaseroman**withendingpunctuationregardlessofwhetherthesentenceiscomplete:
Example: *Figure 11. **Proportionofmasterybyattribute .
Author-DateStyleforCitingScholarlyWork
Authorswhoseworkiscitedintextareusuallynamedinparentheses,alongwiththedateoftheirwork .Whenauthorsarenameddirectlyinthetext,usuallyasthesubjectofasentenceintextthatdiscussestheirwork,Chicagostylenamesuptothreeauthorsinauthor-datecitationsandtreatsworkbymorethanthreeauthorsinadifferentmanner .Bycontrast,APAstylenamesuptofiveauthorsinauthor-datecitationsintextandtreatsworkbymorethanfiveauthorsinadifferentmanner .Notethedifferenceincommauseandtheampersand .Inaparentheticalauthor-datecitation,Chicagostyledoesnotuseacommatoseparatetheauthors’namesfromtheyearandspellsoutand .APAstyleusesacommatoseparatetheauthors’namesfromtheyearandusesanampersandbeforethelastname .APAstyleuseset al.inthemaintextaswellasinparentheticalcitations .
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CHICAGO
Up to three authors:
Parenthetically:
(Brown,Smith,andJones2004)
In text:
Brown,Smith,andJones(2004)
More than three authors:
Parenthetically:
(Brownetal .2004)
In text:
Brownandcolleagues(2004)
APA
Up to five authors:
Parenthetically:
(Brown,Smith,Jones,Pike,&Johnson,2004)
In text:
Brown,Smith,Jones,Pike,andJohnson(2004)
More than five authors:
Parenthetically:
(Brownetal .,2004)
In text:
Brownetal .(2004)
BibliographicalCitations
ThefollowingexamplesillustrateessentialdifferencesbetweenChicagoandAPAreferencestyles .
CHICAGO
Journal articleBishop,JoyceW .,AlbertD .Otto,andCheryl
A .Lubinski .2001 .“PromotingAlgebraicReasoningUsingStudents’Thinking .”Mathematics Teaching in the Middle School 6,no .9(May):508–14 .
BookStein,MaryKay,MargaretS .Smith,Marjorie
A .Henningsen,andEdwardA .Smith .2000 .Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development. NY:TeachersCollegePress .
Chapter in a bookBlanton,MariaL .,andJamesJ .Kaput .2004 .
“InstructionalContextsThatSupportStudents’TransitionfromArithmetictoAlgebraicReasoning:ElementsofTasksandCulture .”InEveryday Matters in Science and Mathematics: Studies of Complex Classroom Events, editedbyRicardoNemirovsky,AnnS .Rosebery,JesseSolomon,andBethWarren,pp .211–34 .Mahwah,NJ:LawrenceErlbaumAssociates .
APA
Journal articleBishop,J .W .,Otto,A .D .,&Lubinski,C .A .
(2001) .Promotingalgebraicreasoningusingstudents’thinking .Mathematics Teaching in the Middle School,6,508–514 .
BookStein,M .K .,Smith,M .S .,Henningsen,M .,
&Smith,E .A .(2000) .Implementing standards-based mathematics instruction: Acasebook for professional development. NewYork,NY:TeachersCollegePress .
Chapter in a bookBlanton,M .L .,&Kaput,J .J .(2004) .
Instructionalcontextsthatsupportstudents’transitionfromarithmetictoalgebraicreasoning:Elementsoftasksandculture .InR .Nemirovsky,A .S .Rosebery,J .Solomon,&B .Warren(Eds .),Everyday matters in science and mathematics: Studies of complex classroom events,pp .211–234 .Mahwah,NJ:Erlbaum .
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Appendix C: Trademarked ProductsRS1/Departments/Journals/RegisteredTrademarks/RegisteredTrademarks .xls
AlgebraTiles™
Apple®
BlackBerry®
BlackboardCollaborate™
BlackboardConnect™
BlackboardInc .
BlackboardLearn™
BlackboardMobile™
BlackboardTransact™
CabriGeometry™
CalculationNation®
CD
CD-ROM
ConnectingCuisenaire®Rods
Cuisenaire®Rods
Dell™
Digi-Block
DynamicGeometry®
e-reader
Excel®
FathomDynamicData™Software
GeoGebra
Geometer’sSketchpad®
GoogleEarth™
GoogleMaps™
GoogleReader™
IBM®SPSS®Statistics
Intel®
iPad®
iPod®
iPhone®
InternetExplorer®
iTunes®
JMP®software
Kaleidomania!™
Sketchup™
LabPro®
LegoDUPLO®
LEGO®
LoggerPro®
M&M’s®
Mac®
MagneticAlgebraTiles™
MagneticCuisenaire®Rods
MapleNet™
MaplePrimes™
MapleSim™
Maple™
Mathematica®
MATLAB®
MicrosoftOffice
MINITAB®
Minitab®StatisticalSoftware
multifixcubes
NikeSwoosh®
OneNote®
Polyspace®
Popsicle®
Post-it®
PowerPoint®
Safari®
ScientificCalc-U-Vue®
Senteo™
Simulink®
SMARTBoard™
smartphone
smarttech™
SMART™
SnowLeopard®
TabletPC
TexasInstruments™
TheGeometer’sSketchpad®
TI-84Plus™
TI-Navigator™
TI-nspire™
TI-SmartView™
Unifix®cubes
WeighToo®LearnAlgebraBalance
Whiteboard
Winplot
YouTube™
