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SE 008 265
Curriculum Activities in Mathematics for Elementary
and Seconnary Schools.
National Science Foundation, Washington, D.C.
Apr 70
11p.
EDPS Price MP-$0.2 HC-$0.6s
*Annotated Bibliographies, *Curriculum Development,
*Flemcmtary School Mathematics, Mathematics
Pducation, *Seconrlary School Mathematics
National Science Foundation
This publication of the National Science Foundation
contains information about various programs related to the
'i evelopment of mathematics curriculum and materials; course materials
for elementary and secondary mathematics programs; and, materials for
both preservice and inservice teacher education in mathematics. (FL)
A
NATIONALSCIENCEFOUNDATION
CurriculumActivities
in
Mathematics
for
ElementaryandSecondarySchools
U.S.DEPARTMENTOFHEALTH, EDUCATION&WELFARE
OFFICEOfEDUCATION
THISDOCUMENTHASBEEN REPRODUCEDEXACTLYASRECEIVED FROMTHE
PERSONORORGANIZATIONORIGINATING IT. POINTSOfVIEWOROPINIONS
STATEDDONOTNECESSARILY
REPRESENTOFFICIALOFFICEOF EDUCATION
POSITIONORPOLICY,
April
CurriculumProjects
ElementaryandSecondarySchool
SchoolMathematicsStudyGroup(SMSG).E. G.Begle,10CedarHall,StanfordUniversity,
Stanford,Calif.
SMSGhaspreparedsampletextmaterialsforgrades1through12designedtoillustratethe
kindsofcurriculawhichtheStudyGroupfeelsaredemandedbytheincreaseduseofscience,
technology,andmathematicsinoursociety,andmaterialsdesignedtohelpteachersprepare
themselvestoteachsuchacurriculum.Extensiveclassroomtrialshavebeenconducted.A
secondmajoractivityoftheSMSGistheNationalLongitudinalStudyofMathematical
Abilitiesinwhichstudentsoriginallyingrades4,7,and10arebeingfollowedtodeterminethe
effectsofconventional,SMSG,andothernewcoursesequencesonperformanceinmathematics
andscienceinschoolandcollege.Thisstudyhasbeenextendedtothelowerprimarylevelin
ordertoprovideasoundbasisoffactualknowledgeforfurtherreforminmathematicsinthe
earlygrades.Specialtestsformeasuringmathematicsachievementhavebeendevelopedto
evaluatehighercognitiveskills.Thisstudyhasalsobeenconcernedwithsuchvariables as
socio-economicstatusandthetimingandplacementofexposuretomathematicalconcepts.
FurtherinformationandexperimentalmaterialsareavailablefromSMSG.
Publishedmaterials:
Textsandteachers'commentaries:
A.C.Vror-4,Inc.,367SouthPasadenaAve.,Pasadena,Calif.
NewMathematicalLibrary:
RandomHouse,Inc.,239GreatNeckRd.,GreatNeck,N.Y. 11021
TheL.W.SingerCompany,Inc.,501MadisonAve.,N.Y.
SchoolandLibraryServices,457MadisonAve.,N.Y.
Teachertrainingfilms:
ModernLearningAids,1212AvenueoftheAmericas,NewYork, N.Y.
PamentarySchool
ExperimentalTeachingofMathematicsintheElementarySchool. PatrickSuppes,Instituteof
MathematicalStudiesintheSocialSciences,Stanford,Calif.
Projecteffort is deviated tothedevelopmentofacomputer-basedlaboratoryforthe
experimentalteachingofelementary-schoolmathematics.Computerprogramshavebeen
developedfor acompletecurriculumforgrades 1 and2,asupplementarycoursein
mathematicallogicforupperelementaryschool,anddrillandpracticematerialssupplementing
arithmeticinstructionforgrades1through6.
Furtherinformationandprojectdocumentationareavailablefromtheprojectdirector.
Publishedmaterials:
AcademicPress,111FifthAve.,NewYork,N.Y.
MinnesotaSchoolMathematicsandScienceTeachingProject(MINNEMAST). JamesH.Werntz,
Jr.,MinnesotaSchoolMathematicsandScienceCenter,UniversityofMinnesota,Minneapolis,
Minn.
Themainpurposeoftheprojectwastoproduceacoordinatedmathematicsandscience
curriculumforlowerelementaryschool,withappropriateteacher-trainingmaterials.A
Cartesiancoordinatesystemandgraphicalalgorithmsfornumericaloperationsprovidedthe
mainfocusforthemathematicsmaterials.Thesciencematerialscenteredaboutoperationsa
scientistdoes(observing,describing,classifying,measuring,forminghypotheses,testing).Later
sciencematerialsincludethestudyofinvarianceandchangeunderdifferentphysical
transformationsinphysicalandbiologicalsystems.Thematerialsarepreparedforaverage
elementary-schoolchildrenwithsupplementaryenrichmentactivitiesforgiftedchildren,
MinnemastCenterquarterlyreportsareavailablefromtheprojectdirector.
Madison MathematicsProject. Syracuse University-Webster
College, RobertB.
Davis,
DepartmentofMathematics,SyracuseUniversity,Syracuse,N.Y.
Interventionatthelevelofactualschoolexperienceratherthanatthetextbook orcurriculum
levelistheMadisonProjectapproach.Presentemphasisisongrades1.9,andsubjectemphasisis
acombinationofarithmetic,axiomaticalgebra,coordinategeometry,rudimentarystudyof
functions,logic,limitofasequence,andsomephysics,Majorproductsincludefilmsand
writtenmaterialsforin-serviceeducationofteachers,andcurriculumunitsforchildren.
Newslettersandin-serviceseriesareavailablefromtheprojectdirector.
ImprovementProjectinMathematicsforSubculturalGroups.
E.GlenadineGibb,Science
EducationCenter,UniversityofTexas,Austin,Tex.
Thisprojectisanattempttoadapttolocalneeds,improvedmathematicscurriculadeveloped
onanationalbasis.Theprojecthopestodemonstratethat,throughlocaladaptationofexisting
curriculummaterials,desiredlevelsofmathematicalunderstandinganduseofmathematics can
beeffectivelydevelopedforallchildrenconsonantwiththeirabilitiesandneedsandwiththe
vitalaimsofamodernmathematicsprogram.
Furtherinformationandexperimentalmaterials areavailablefromtheprojectdirector.
SecondarySchool
UniversityofIllinoisCommittee onSchoolMathematics (UICSM).MaxBeberman,University
of!RindsCommitteeonSchoolMathematics, WestSpringfield,Urbana,Ill.61.
UICSMhasdevelopedtwotwo-yearsequences.Thefirstis apresentationofthearithmeticof
rationalnumbersandofintuitivemotiongeometryforunderachieving juniorhighschool
students;thesecond,avectorgeometry courseforseniorhighschool,
Publishedmaterials:
Juniorhighschoolsequence:
Harper&Row,49East33rdSt.,NewYork,N.Y.
Vectorgeometrycourse:
TheMacmillanCo,,60FifthAve., NowYork,N.Y.
Teachertrainingfilms:
Modern LearningAids, 1212AvenueoftheAmericas,NewYork,N.Y.
HighSchoolCourseinModernCoordinateGeometry.RobertA. Rosenbatio.,AcademicVice
President,WesleyanUniversity,Middletown,Conn.
Thedistinctivefeatureofthistenth-yeargeometry courseisthedevelopmentofaffine
geometrybeforeEucliden,usingcoordinatesattheoutset.
Publishedmaterials:
Textandteachers'commentary:
HoughtonMifflinCo.,2ParkSt.,Boston,Mass.
PreparationofMaterialsforPre-LimitCalculus.HaimReingold,Departmentof Mathematics,
IllinoisInstituteofTechnolcgy,Chicago,Ill.660)
Anewapproachforteachingcalculusinthelastyearofhighschoolincludes adevelopmentof
thetheoryofmaximaandminima,ofrateproblems,andofapplicationsofcalculus to
geometricquestions.Areaandvolumeproblemsaretreated asapplicationsofheintegral
calculus,
Furtherinformationisavailablefromtheprojectdirector.
AdvancedSecondarySchool
CommitteeontheUndergraduatePrograminMathematics(CUPM)
GeorgeB.Pedrick
(ExecutiveDirector),CommitteeontheUndergraduatePrograminMathematics,Box1024,
Berkeley,Calif.
TheCommitteeontheUndergraduatePrograminMathematicsisconcernedwiththesystem
consistingoftheundergraduatecurriculuminmathematics,thestudentsandtheirteachers,the
purposes ofthe program, its achievementsandshortcomings,and the facilities for
undergraduatemathematics.Theprincipalworkispartitionedintofourareas;(1)pre-service
trainingofelementaryandsecondaryschoolteachersandtheimprovedrecruitmentand
pre-service trainingofcollege mathematicsteachers; (2)mathematicsforstudentsof
engineeringandthephysicalsciences;(3)mathematicsforthebiological,management,and
socialsciences;and(4)pre-graduateeducationofpotentialresearchmathematicians,Detailed
curriculaandcoursesyllabihavebeendesignedforeachoftheaboveareas,
Furtherinformationandmaterialsareavailablefromtheexecutive(.14rec.,%.
PowerSeriesandtheElementaryFunctions.
HowardLevi,HerbertH.LehmanCollege
(CUNY),NewYork,N.Y.
Aone-semestercourseinelementaryfunctionsbasedonthesystematicuseofpowerserieswas
developed.Thecourseissuitableforcollegefreshmenandmayserveasaterminalcoursein
calculus.
Publishedmaterials:
Text:
D.VanNostrandCo.,Princeton,N.J.
GeometricandGraphicAidsforCollegeCalculus.GormanR.
Nelson,Departmentof
Mathematics,SchoolofEngineering,SouthDakotaStateUniversity,Brookings,S.D.
Sequencesofcolorslideshavebeendevelopedtosupplementconventionalchalkboardsketches
inconveyingthefundamentalconceptsincalculus.Audiotapesandwrittenmaterials were
producedtoincreasetheflexibilityandutilityoftheslidesequences.Thematerials canbeused
bythelecturerduringhispresentationandasreviewandself-teachingtoolsbystudents.
Furtherinformationisavailablefromtheprojectdirector.
ExperimentalUndergraduateInstructioninComputing.JohnG.Kemeny,Departmentof
Mathematics,andThomasE.Kurtz,ComputationCenter,DartmouthCollege,Hanover,N.H.
TheDartmouthComputationCenterwasdevelopedasaflexibleteachingdeviceforstudentsin
allfields.Studentselectingayearoffreshmanmathematicsarebeingtaughtthefundamentals
ofprogrammingin theBASIClanguageandtheuseofinput-outputstationstothe
Time-SharingSystem:-
Theprojecthasproducedseveralkindsofmaterials:(1)theuser'smanualfortheBASIC
langume;(2)adescriptionandblockdiagramoftheprincipalcomponentsoftheTime-Sharing
System,particularlytheBASICcompiler;(3)anumberofshortmonographscontaining
illustrativecomputerproblemstobeusedinconnectionwithavarietyofmathematics,physics,
andengineeringcourses.
Publishedmaterials:
Manualandsupplements:
DartmouthPublications,DartmouthCollege,Hanover,N.H.
Imolementation of Innovative MathematicsCourseWingan Auxiliary Undergraduate
Computing
Facility.JudahRosenblatt,DepartmentofMathematics,CaseWesternReserve
University,Cleveland,Ohio443Z
CaseWesternReserveUniversityhasmodifieditstwo-yearsequenceincalculussothatboth
freshmenandsophomoresareusingalargedigitalcomputerasatoolindevelopingtheir
comprehensionofmathematics.Thecomputerservesasanaidincomprehendingcertaintopics;
andstudentsenteringadvancedcoursesareequippedwithabasicunderstandingofcomputer
techniqueswhichmaybewiluableinsolvingproblemsthatarearegularpartofthecurriculum.
TheproceduresdevelopedatCasearebeingdocumentedandevaluated,andresultsofthework
willbepublished.
Furtherinformationisavailablefromtheprojectdirector.
DevelopmentofaComputer-RelatedCalculusSequence.
GuenterSchwarz,Director,Centerfor
ResearchinCollegeInstructionofScienceandMathematics,FloridaStateUniversity,
Tallahassee,Fla.
Theprojectdevelopedandistestingabasicundergraduatecalculussequenceinvolving
computer-relatedtopicsandmethods.Toincreasetheusefulnessofthecourseoncampuses
withwidelydivergentcomputingsystems,thematerialshavebeenpreparedsoastobeasnearly
machine.-independenraspossible.
Furtherinformationandsamplematerialsareavailablefromtheprojecttiirecttr.
IntroductoryCourseonProbabilityMatricesandCalculusforStudentsintheBiologicaland
SocialSciences.
G.BaleyPrice,DepartmentofMathematics,theUniversityofKansas,
Lawrence,Kans.
Materialssuitableforatwo-semestercourse probability,matrices,andcalculushavebeen
prepared.Onevolumecontainschaptersonsystemsoflinearequations,matricesandalgebraic
systems,elementarysettheory,countingproblems,andprobabilitywithapplicationsto
problemsinaccounting,business,economics,acceptancesampling,genetics,andsociology.The
secondvolumecontainsanelementarytreatmentofdifferentialandintegralcalculusina
settingofprobabilitytheoryandapplicationstothebiological,management,andsocial
sciences.Emphasisincalculuswillbeonconceptsandtheirapplicationsratherthanon
technique.
Publishedmaterials:
LinearEquationsandMatrices(Johnson,Price,&VanVleck)
Sets,Functions,andProbability(Johnston,Price,VanVleck)
AddisonWesleyPublishingCo.,Reading,Mass.
ExperimentalTeachingPrograminAlgebra.RobertJ.
Walker,DepartmentofMathematics,
CornellUniversity,Ithaca,N.Y.
Curriculaforthreeone-termcourseshavebeendeveloped;Basic
ConceptsofMathematics;
LinearAlgebra;andNumberTheory,Thecoursesare
designedprimarilyforfuturehighschool
teachers.Thegoalisfcrstudentstohaveathoroughgrasp
ofthefundamentalconceptsof
taodernabstracta!qebraandtheirelevancefor
otherfieldsofstudy.
Furtherinformationisavailablefromtheprojectdirector.
GeometryCourseforPrGspectiveHighSchoolMathematics
Teachers.SeymourSchuster,
MinnesotaSchoolofMathematicsandScienceCenter,
UniversityofMinnesota,Minneapolis,
Minn.
Materialsforacollegegeometrycourseforthetrainingof
prospectivehighschoolteachershave
beendevelopedwithemphasisonvisualmediaand
programmedinstruction.Tatecontent
includesmaterialrecommendedinCourseGuidesfortheTraining
ofTeachersofJuniorHigh
andHighSchoolMathematics,publishedbytheCommitteeon
theUndergraduateProgramin
MathematicsoftheMathematicalAssociationofAmerica.
Informationonfilmsandwrittenmaterialsisavailablefrom
theprojectdirector.
ProjectonLogicandProof.
MaxBeberman,UniversityofIllinois
CommitteeontheStudyof
Mathematics,UniversityofIllinois,Urbana,Ill,
Theneedsofprospectivesecondaryschoolteachersof
mathematicsandofadvanced
undergraduatesinmathematicslackingadequatetrainingin
theformulationofmathematical
proofsstimulatedthede.,,elopmentofthis
project.Paragraphproofsarethefocusofthecourse
developmenteffortandthetextualmaterialswillusea"guided
discovery"approach,
Furtherinformationisavailablefromtheproject
director.
FilmsandOtherTeachingMaterialsfor
CollegeMathematics.A.B. Wilcox,ExecutiveDirector,
MathematicalAssociationofAmerica,
ConnecticutAvenue,N.W.,Washington,D.C.
20036
This
)jectinvestigatedtheproduction,use,andevaluation
ofnewmedia--films,television,
progrianmedlearning,etc,-inmathematical
instructionatthecollegelevel.Filmsandwritten
materialsaresuitable:orpre-se,vicetrainingof
prospectivemathematicshighschoolteachers.
Publishedmaterials:
Texts:
W.A.Benjamin,Inc.,1ParkAvenue,
NewYork,N.Y.
Films:
ModernLearningAids,1212Avenueofthe
Americas,NewYork,N.Y.
In-service(Elementary)
UniversityofIllinoisArithmeticProject.DavidA.Page,EducationDevelopmentCenter,Inc.,
55ChapelSt,Newton,Mass.
Coursematerialsinmathematicsanditsteachingarebeingpreparedforelementaryschool
teachers.Mathematicaltopicsorschemeswhichofferinterrelatedproblemsthatchildrencan
do,whichcontainsignificantmathematicalideas,andwhichwillimprovecomputationalskills
areincorporatedin acourseforteachersdesignedforin-serviceuse.Materialsinclude
demonstrationfilms,extensiveproblemsequencesandwrittenhomeworkforteachers,andan
instructor'scorrectionanddiscussionguidecomprisingasemestercourseof30lessons.
Publishedmaterials:
Filmsandwrittenmaterials:
EducationDevelopmentCenter
Foundations s
MathematicsforElementarySchoolTeachers.E.GlenadineGibb,Science
EducationCenter,TheUniversityofTexas,Austin,Tex.
Twelve30-minutefilmsandaccompanyingtextprovideanintroductionandorientation
programforimprovingthemathematicstrainingofelementaryschoolteachers.
Publishedmaterials:
Films:
DirectorofFieldService,StateCollegeofIowa,CedarFalls,Iowa
TheMathematicsAidsProgram.AlvinN.Feldzamen,EncyclopediaBritanica,425N.Michigan
St.,Chicago,Ill.
Pilotprogramshavebeenproducedforanexperimentintelevisedin-serviceeducationin
mathematicsforelementaryschoolteachers.Theprograms,alsoaimedatageneralaudience,
takeupthepropertiesofthenumbersystemsofarithmeticandnewwaysofteaching
elementaryalgorithmsinalivelyandentertainingformat.
FurtherinformationisavailablefromChannel13,EducationBroadcastingCorporation,
304W.58thSt.,NewYork,N.Y.10019,orfromtheprojectdirector.
In-ServiceFilmsinMathematicsforElementaryTeachers.HarryD.Ruderman,Departmentof
Mathematics,HunterCollegeHighSchool,930LexingtonAve.,NewYork,N.Y.
Aseriesof10mathematicsfilms(16mm,color,30minuteseach)hasbeenproducedforusein
in-servicetrainingofelementaryteachers.Eachfilmisaccompaniedbytextmaterialsanda
teachersmanualforthewholeseries.Thecontentofthecourseisthedevelopmentofthe
wholenumbersystem,theoperationsinitandtheirproperties,ourcommondecimalsystemof
numeration,andtheusualalgorithms.
Publishedmaterials:
Films:
UniversalEducationandVisualArts,221ParkAve.South,NewYork,N.Y.
