ArticlePDF Available

Developing Effective Mathematics Teaching: Assessing Content and Pedagogical Knowledge, Student-Centered Teaching, and Student Engagement

Authors:

Abstract and Figures

The Mathematics Teacher Transformation Institutes (MTTI) program attempts to develop math teacher leaders in part by providing content, inquiry and leadership courses aimed at making them more effective teachers. We assessed progress by observing teacher leaders' teaching practices, and encouraging them to introduce or extend studentcentered pedagogy in their classrooms. We found there was little relationship between our measures of mathematics content knowledge and student-centered pedagogy. But teachers who employed student-centered pedagogy tended to have more highly-engaged math students in their classrooms. © The Author(s) & Dept. of Mathematical Sciences-The University of Montana.
Content may be subject to copyright.
TME, vol10, no.3, p. 621
The Mathematics Enthusiast
, ISSN 1551-3440, Vol. 10, no.3, pp. 621-646
2013©The Author(s) & Dept. of Mathematical Sciences-The University of Montana
DevelopingEffectiveMathematicsTeaching:
AssessingContentandPedagogicalKnowledge,StudentCenteredTeaching,and
StudentEngagement
SerigneM.Gningue1,RogerPeach1,&BarbaraSchroder2
1LehmanCollege,CityUniversityofNewYork
2CenterforAdvancedStudyinEducation,GraduateCenter,CityUniversityofNewYork
Abstract:TheMathematicsTeacherTransformationInstitutes(MTTI)programattempts
todevelopmathteacherleadersinpartbyprovidingcontent,inquiryandleadership
coursesaimedatmakingthemmoreeffectiveteachers.Weassessedprogressbyobserving
teacherleaders’teachingpractices,andencouragingthemtointroduceorextendstudent‐
centeredpedagogyintheirclassrooms.Wefoundtherewaslittlerelationshipbetweenour
measuresofmathematicscontentknowledgeandstudent‐centeredpedagogy.But
teacherswhoemployedstudent‐centeredpedagogytendedtohavemorehighly‐engaged
mathstudentsintheirclassrooms.
Keywords:effectivemathematicsteaching;mathcontentknowledge;student‐centered
teaching;studentengagement.
Improvingstudentachievementinmathematicsandsciencehasbeenaconcernin
theUnitedStatesofAmericasincetheearly1980swheninternationaltestsbeganshowing
U.S.studentsfallingbehindmostdevelopedcountriesinmathematicsandscienceskills.
ManyU.S.studentsdonotobtaintheknowledgeandskills,particularlyinscience,
technology,engineering,andmathematics(STEM),whicharerequiredforsuccessinthe
globalmarketplaceofthe21stcentury(NationalAcademyofSciences,2006).

1Serigne.gningue@lehman.cuny.edu
Gningue, Peach & Schroder
Educators,educationalresearchers,andpolicymakershavenotalwaysagreed
aboutthereasonsforthefailureofU.S.studentstoperform.Somearguemany
mathematicsteachershaveinadequatemathematicalcontentknowledgethemselves,and
thusareunabletoteachtheirstudentstothehighestlevel(Ahuja,2006;Ginsburg,Cooke,
Leinwand,Noell&Pollock,2005).Others(Darling‐Hammond,2007;NationalCouncilof
SupervisorsofMathematics[NCSM],2008;NationalCouncilofTeachersofMathematics,
2000;OfficeofScienceandTechnologyPolicy,2006;U.S.DepartmentofEducation,2004;
NationalScienceBoard,2006),inpart,relatesuchaneducationalfailurenotonlytothe
lackofqualifiedteacherswithsolidcontentknowledgeinSTEM,butalsotoaprofoundlack
ofunderstandingofteachingandlearningingradesK‐12,whichmayleadtotheuseof
ineffectiveteachingpractices.ForBrownandBorko(1992),andBallandBass(2000),
understandingcontentknowledgeandmethodsofinquiryinmathematicsareatthecoreof
effectiveteachingandlearning.Theuseofinquiry‐basedapproachestoinstruction,in
whichstudentshaveopportunitiestoconstructtheirownunderstandingofbasicconcepts,
isthoughtbymanyeducationaltheoriststobemostappropriateindevelopingstudents’
understandingofmathematicsandscienceconcepts.Suchapproachescallforteachersto
beabletoengagestudentsincritical,in‐depth,higher‐orderthinkingthroughuseof
manipulatives,technology,cooperativelearningandotherpedagogicalapproachesthat
enablestudentstoconstructmathematicsconceptsontheirownthroughreasoning,
verifying,comparing,synthesizing,interpreting,investigatingorsolvingproblems,making
connections,communicatingideasandconstructingarguments(Grouws&Shultz,1996;
NationalCouncilofTeachersofMathematics[NCTM],2000).Theseapproachesare
characteristicofwhatisoftencalledstudent‐centeredteachingasopposedtotheso‐called
TME, vol10, no.3, p. 623
“traditional”approachesinwhichthepredominantviewisthatmathematicsteachingisa
show‐and‐tellaswellasasupervisionofdrillsandpractice(Davis,1988).Inthisview,itis
assumedthatlearningoccurspassivelywhenstudentsabsorbreceivedknowledgefroman
all‐knowingteacherorexpert.Thisapproachisoftenreferredtoas“teacher‐centered.”
TheMathematicsAssociationofAmerica(MAA,2008)arguesthatinordertoprepare
studentsfortheincreasinglycomplexmathematicsofthiscentury,astudent‐centered
approachtoteachingismoreappropriatethanthetraditionalteacher‐centeredapproach.
TheMAA(2008)assertstheneedtodeveloppedagogiesthatcouldbeusedeffectivelyto
facilitatestudents’mathematicalabilities.InessencetheMAA(2008)advocatesforan
increaseinstudent‐centeredteachingandlearningandadecreaseinteacher‐centered
pedagogy.Oneassumptionisthatanincreaseinstudent‐centeredteachingwillresultin
increasedstudentengagementinmathematicsand,byimplication,thisincreased
engagementwilllead,inturn,toincreasedstudentachievement.Forexample,various
researchersarguethatstudentsaremoreengagedandachievemorewhenteachersrelate
newlearningtopriorlearning,modelproblemsandprovidethemwithavarietyof
opportunitiestoapplyanduseknowledgeandskillsindifferentlearningsituations(Kemp
&Hall,1992;Rosenshine,2012;Taylor,Pearson,&Walpole,1999).
LogicModelandTheoryofActionfortheProject
OneoftheaimsoftheMathematicsTeacherTransformationInstitutes(MTTI)isto
encourageparticipantteacherstodevelopboththeirmathematicscontentknowledgeand
astudent‐centeredpedagogy,assumingthatthesedevelopmentswillleadtoincreased
studentengagementinmathematics.Thisresearchaimedtoseewhetherthegoalwas
met,andtheassumptionwasjustified.
Gningue, Peach & Schroder
MTTIisaNationalScienceFoundation(NSF)‐fundedprogramdesignedtosupport
thedevelopmentofteacherleaderstostrengthenmathematicsteachingandlearningin
NewYorkCity,especiallyinBronxmiddleandhighschools.MTTIdevelopedathree‐year
three‐dimensionalprogramthatfocusesondeepeningparticipatingteachers’content
knowledge,broadeningtheirpedagogicalrepertoirethroughtheprocessofinquiry,and
developingtheirleadershipcapacitiesacrossanumberofdomainswithinthecontextofa
professionalcommunity.Themodelengagesteachersinaprocessofinquirythatdoesnot
ceaseinaskingquestionsandunderstandingproblems,continuallyrevisitingcriticalissues
relativetoteachingandlearning,designingplanstoresolvetheissues,implementingthe
plans,andcollectingandanalyzingdatatoassesstheeffectivenessofthedesignedplans.As
teachersimprovetheirpedagogicalskills,theyincreasetheirabilitytoexplaintermsand
conceptstostudents,interpretstudents’statementsandsolutions,engagestudentsin
critical,in‐depth,higherorderthinking(Copeland,2003;Grouws&Shultz,1996;Hill,
Rowan,&Ball,2005;NationalCouncilofTeachersofMathematics[NCTM],2000).
Essentially,theaimistodevelopteachers’student‐centeredpedagogy.
MTTIisfundedtosupporttwocohortsof40teacherswithatleastfouryears
teachingexperienceoverfiveyears.Thefirstcohortcompletedtheprogramafterthree
yearsinJune2011.Thispaperreportsresultsfromthefirstcohort.Theresearch
componentofMTTIseekstobroadentheknowledgebaseonteachingandlearningin
mathematicsthroughnewunderstandingof:1)howthestudyofconceptually‐challenging
mathematics—particularlyinalgebraandgeometry—benefitsteachers;2)howclassroom‐
basedactionresearchcontributestocriticalandanalyticalunderstandingofthe
TME, vol10, no.3, p. 625
relationshipsbetweenteachingpracticesandstudentlearning;and3)howmulti‐levelsof
supportprepareteacherswithatleastfouryearsteachingexperienceforleadershiproles.
MTTI’stheoryofaction,depictedinFigure1,hypothesizesinessencethatteacher
backgroundandcharacteristics,schoolclimate(especiallyasrepresentedthroughteacher‐
teacherinteractions)andMTTIexperienceswillimpactparticipants’teacher‐leader
practices,oneofwhichiseffectiveteaching.ThethreemaincomponentsmakingupMTTI
experiencesaremathcontentcourses,inquiry‐basedactionresearchcourses(pedagogy),
andaleadershipcourse.
MTTIaimstosupplementmathteachers’contentknowledgeandhelpteachers
makeandsustainfundamentalshiftsinpractice.Ourhopeisthatsuchchangeswillresult
inmoreeffectiveteachingandteacherleadership.Inturn,wehopethateffectivemath
teachingwillleadtoincreasedstudentengagementinmath.
Students’
Outcomes
Teacher knowledge
Content/Pedagogy/
Leadership
Teacher-Leader
Practices:
Effective Teaching
Teacher
Background and
Characteristics
Teacher Self-
efficacy
Teacher-teacher
Interactions
MTTI
Experiences
School
Leadership/Climate
Gningue, Peach & Schroder
Figure1.MTTI’stheoryofaction.
MTTIProjectOutline
ImprovingTeachers’MathContentKnowledge 
 TwocoursesaimedatimprovingMTTIparticipants’mathcontentknowledgewere
runthroughoutthespringandfallsemestersof2009.Oneofthecourseswasinmath
fundamentalsandtheotheringeometry.Themathfundamentalscoursefocusedon
algebraandintegratedmathematics.Thegeometrycoursewasbasedaroundgeometric
proofs,andwasrelatedtotheNewYorkstatestandardsforgeometry.Participantsinthe
geometrycoursewererequiredtoundertakeprojectsrelatedtothetopicstaughtinthe
course.ThecoursesweretaughtbymembersoftheLehmanCollegemathematicsfaculty.
ActionResearchCourses
MTTIparticipantstookatwo‐partcourseseriesinclassroom‐basedinquiry
includingactionresearch.Thecourseseriesranforatotalof90classroomhours.Part1of
thisseriestookplaceduringspring2010,“ClassroomInquiryinMiddleandHighSchool
Mathematics.”Part2,“MathematicsInquiryApplications,”wasofferedduringfall2010.
ThesecoursesfocusedonhelpingMTTIteachersexaminetheeffectivenessoftheir
pedagogicalpracticesbyidentifyinganddescribingtheirstudents’errorsand
misconceptions,reviewingliteratureonresearchandtheoriesaboutmathematicsteaching
andlearning,andusingalternativeassessmentsandtechnology.DuringPart2,MTTI
teachersorteamsofteachersusedmixedmethodstodevelopandcompleteAction
ResearchProjects,toassesstheperformanceoftheirstudents.AsofMay2011,23MTTI
TME, vol10, no.3, p. 627
teachersdeveloped29ActionResearchprojects,involving1,017students:378from
middleschoolsand639fromhighschools.Thecourseserieswastaughtandcoordinated
byamemberoftheLehmanCollegesecondaryeducationdepartment.
StatisticsCourse
 Forsummer2010,allMTTIparticipantswereofferedachoiceofmathematics
courses,thelastmathematicscoursetheywouldbetakingaspartoftheprogram.They
couldchooseeitheraStatistics(andProbability)courseorasecondGeometrycourse.
VirtuallyallofthemchosetheStatisticscourseandweofferedtwosectionsofthecourseto
accommodatealltheparticipantswhowantedthecourse(anddidnotoffertheGeometry
course).TheMTTIparticipantswantedastatisticscourseforthreemainreasons:1)they
discoveredduringtheActionResearchcoursesthattheydidnotknowthestatistics
requiredtocompletetheirprojects;2)manyhadtheopportunitytobecomeinvolvedin
theirschool'sself‐evaluationandassessmentandfelttheyneededmorestatistical
knowledgetoanalyzetheoverwhelmingamountofdataavailabletotheminternally,and
theirprincipalswereeagerforthemtoserveontheseteams;and3)severalwerebeing
askedtoteachAdvancedPlacement(AP)Statisticsattheirhighschools.Itappearsthat
mostoftheteachers’preferredthestatisticscourseoverthesecondgeometrycoursefor
professionalreasonsotherthanadesiretoimprovetheirmathematicalknowledgefor
teachingstudents.
LeadershipSeminars1&2
TheLeadershipSeminar1beganinFebruary2011;LeadershipSeminar2beganin
May2011.TheDirectoroftheNewYorkCityMathematicsProject(NYCMP),andtheMTTI
Directorledtheseminars.InFall2010,theymetwiththeparticipantsthreetimesduring
Gningue, Peach & Schroder
theActionResearchcourse.Becauseitwasimportanttolaygroundworkforfurther
explorationoftheCommonCoreStateStandards(2010),thefirstmeetingfocusedonthe
Standards.Theothertwomeetingsfocusedonlevelsofcognitivedemandfor
mathematicaltasksaswellascasestudiesfromImplementingStandardsBased
MathematicsInstruction(Stein,Smith,Henningsen,&Silver,2009).
MTTITeacherConsultants
SixMTTIteacher‐consultantsvisitedparticipantsintheirschoolstoprovide
support.Theteacher‐consultantswereretiredmathematicsteacherswithmanyyears’
experience,andweredrawnfromtheteacher‐consultantswhoprovidedasimilarservice
fortheNYCMP.Theteacher‐consultantsvisitedparticipantstwicepermonthforonehalf‐
dayoneachvisit.Theysupportedparticipantsindealingwithpedagogicalandleadership
issues.
ResearchQuestions
TheMTTIprojectisextremelywide‐rangingandmadeupofseveralcomponents.
However,thispaperconcentratesonourattempttoanswerthefollowingthreeresearch
questions:
1. DidparticipatinginMTTIincreaseparticipants’mathematicaland
pedagogicalknowledge?
2. DidparticipatinginMTTIincreaseparticipants’useofstudent‐centered
pedagogyintheclassroom?
3. Didanyincreaseineithermathematicalcontentknowledgeorstudent‐
centeredpedagogyleadtoanincreaseinstudentengagementin
mathematics?
TME, vol10, no.3, p. 629
Method
MathContentKnowledge
Mathcontentknowledgewasmeasuredbytwosetsofpre‐posttestsdevelopedby
theUniversityofLouisville’sCenterforResearchinMathematicsandScienceTeacher
Education(Bush&Nussbaum,2004).OneofthetestswasforAlgebraandIdeas,andthe
otherwasinGeometryandMeasurement.Bothtestsweresetatthemiddleschoollevel.
ThetestswerepartoftheDiagnosticTeacherAssessmentinMathematicsandScience
(DTAMS)instrumentthatwasvalidatedusingasampleof1,600middle‐schoolteachers
(Saderholm,Ronau,Brown,&Collins,2010).Saderholmandhiscolleaguesdetermined
theequivalencyreliabilityofthepretestsandposttestsbycomputingthePearsonproduct
momentcorrelation.This,theyreport,wasgreaterthan.80.Inter‐scorerreliabilitywas
alsogreaterthan.80.ThetwoLouisvilletestswereadministeredbeforeandafterthe
relevantcontentcourseswerecompleted.
EachUniversityofLouisvilletestcontained20items.Thefirst10itemswere
multiple‐choiceitemsandacorrectanswerscored1point.Items11‐20wereopen‐ended
responseitemseachdividedintotwoparts.Acorrectansweronthefirstpartscored1
point.Amaximumof2pointswereavailableforanswerstothesecondpart,givinga
possiblescoreof40points.ThetestswereblindedandscoredattheUniversityof
LouisvilleCenterforResearchinMathematicsandScienceTeacherEducationbymembers
oftheresearchteamunderthesupervisionoftheCenter’sdirector.
Gningue, Peach & Schroder
ThetwoMTTIcourses,oneinmathfundamentalsandtheotheringeometry,took
placethroughoutthespringandfallsemestersof2009.Twopre‐posttestswereadministered
inassociationwiththesecourses.ThesetestsarereferredtoasMTTItests.TheMTTIAlgebra
andIdeastestdealtwith:patterns,functions,andrelationships;expressionsandformulas;
andequationsandinequalities.TheMTTIGeometryandMeasurementtestdealtwith:
two‐dimensionalgeometry;three‐dimensionalgeometry;transformationalgeometry;and
measurement.
ThesetwoMTTItestsweredesignedbyMTTImathfaculty.Thepossiblescoreonthe
MTTIfundamentalstestwas100,andthepossiblescoreontheMTTIgeometrytestwas90.The
sametestwasusedasboththepretestandtheposttestfortheMTTImathfundamentalsand
geometrytests.TheMTTItestswerescoredbyamemberoftheLehmanCollegemathfacultynot
associatedwiththetwoMTTIcourses,basedonrubricsdevelopedbythemathfacultymembers
whotaughtthecourses.
ThequestionsontheUniversityofLouisvilletestsassessedparticipants’general
contentknowledge.Incontrast,theMTTItestsweredirectlyrelatedtothecontenttaught
inthetwocourses.
MathPedagogicalKnowledge
Accordingtoourtheoryofaction,thesecondcomponentofamathteacher’s
capacityforteacherleadershipconcernstheirmasteryofpedagogicalpractices
appropriatebothfortheirstudentsandforthemathematicsconceptstheyteach.
InformationaboutthiscomponentcomesfromquestionsontheLouisvilleAlgebraand
IdeasandGeometryandMeasurementtests,classroomobservations,andteachers’workin
theclassroom‐basedinquirycourses.
TME, vol10, no.3, p. 631
Asmentionedabove,thesecondpartofitems16‐20ontheLouisvilletests
measuredpedagogicalcontentknowledgeandthemaximumpossiblescoreontheseitems
was10.Anexampleofaquestionmeasuringpedagogicalcontentknowledgeisasfollows:
Q.16Astudentclaimsthatallsquaresarecongruenttoeachotherbecausetheyallhave
fourcongruentsides.
a.Whyisthisclaimincorrect?
b.Explainhowyouwouldhelpthestudentunderstandtheerrorinhis
thinking.
Thepedagogicalcontentscoreswereanalyzedseparatelyfromthescoresontheother
questions.
ClassroomObservations
Threeretiredmatheducatorswhohadpreviousexperienceinobservingteachersin
theirclassroomsweretrainedtobeobserversfortheMTTIproject.Theyweretrainedto
useafive‐minutetime‐samplingsysteminwhichtheywereaskedtoobserveforfive
minuteblocksoftimeandnotewhetherornotanyoneormoreofthepedagogicand/or
managementbehaviors(examplesbelow)wasusedbytheteacher.Attheendoftraining,
inter‐raterreliabilitywas.71.
Beginninginthefall2009term,theobserversvisitedtheMTTIteachers’classrooms
atleastfourtimeseachterm.ThroughJanuaryof2011,265observationshadtakenplace.
Theclassroomobservationprotocol([COP],Lawrenz,Huffman,&Appledoorn,2000)
contains,amongotherthings,informationabouttypesofinstructionalactivities.Someof
theseactivitieswerejudgedaprioritobeindicationsofstudent‐centeredpedagogy,
includingsmallgroupdiscussions,classdiscussions,hands‐onactivities,cooperative
learning,studentpresentations,anduseofalearningcenterorstation.Somewere
Gningue, Peach & Schroder
consideredaprioritoindicateteacher‐centeredpedagogy,includinglecturing,lecturing
withlimitedclassdiscussion,modelingproblemsolving,anddemonstrationsbythe
teacher.Theexactnatureofsomeactivities(e.g.writingworkorreadingseatwork)could
notbedeterminedapriori.Inthesecases,theobserversusedtheirownjudgmentwhether
theactivitywasstudent‐centered,teacher‐centered,orindeterminate.
Onaverage,eachobservationlastedforabout50minutes,withmostobservations
beingfor45or50minutes.Anobservationwascappedat60minutes.Thevastmajorityof
observationsinhighschoolswereconductedinalgebra,integratedmath,orgeometry
classes.Afewobservationswereconductedinadvancedmathclasses,includingseven
observationsinpre‐calculusclassesandeightobservationsincalculusclasses.
StudentEngagement
Oneofthesectionsoftheobservationprotocolmentionedconcernedthelevelof
StudentEngagement(SE)ratedashigh,medium,orlow.Duringeachobservation,SEwas
ratedashighwhen80%ormoreofstudentswereengaged,aslowwhen80%ormoreof
studentswereoff‐task,andasmixedotherwise.Anengagedstudentwasseenasonewho,
duringthetimeoftheobservation,wasinvolvedinthelessoninmeaningfulways;thatis,
he/sheparticipatedinallclassroomactivities,collaboratedeffectivelywiththeteacherand
withotherstudents,andwasreflectiveabouthis/herlearning.
Thefindingsfromtheuseoftheinstrumentsoutlinedaboveforassessingmath
contentknowledge,pedagogicalknowledge,andstudent‐centeredpedagogywererelated
tothoseforstudentengagementoutlinedinthissectiontodetermineiftherewasany
relationshipamongthevariables.
Results
TME, vol10, no.3, p. 633
MathContentKnowledge
 Thirty‐twoparticipantstookboththepretestandposttestversionsofthetwoUniversityof
LouisvilletestsandtheMTTIfaculty‐designedtests.MeanscoresontheUniversityofLouisville
testofalgebraandideasincreasedsignificantlyfrom25.8atpretestto29.8atposttest.However,
meanscoresontheUniversityofLouisvilletestofgeometryandmeasurementdidnotdiffer
significantlyfrompretest(22.6)topost‐test(20.7)(Tables1&2).
ScoresontheMTTIfaculty‐designedfundamentalstestincreasedsignificantlyfrom
36.5atpretestto48.0atposttest.ScoresontheMTTIgeometrycoursecontenttestalso
increasedsignificantlyfrom26.6atpretestto36.0atposttest(Tables3&4).
Table1
Pre‐andposttestmeansfortheLouisvilleAlgebratest
 Mean Std.Deviation N
LouisvilleAlgebraPretestTotal/40 25.75 6.309 32
LouisvilleAlgebraPosttestTotal/40 29.81 5.544 32
Significant:t(30)=4.61,p<.001
Table2
Pre‐andposttestmeansfortheLouisvilleGeometrytest
 Mean Std.Deviation N
LouisvilleGeometryPretestTotal/40 22.56 7.211 32
LouisvilleGeometryPosttestTotal/40 20.72 6.371 32
Notsignificant:F(1,31)=3.45,p=.073
Table3
Pre‐andposttestmeansfortheMTTIFundamentalstest
 Mean Std.Deviation N
Gningue, Peach & Schroder
MTTIFundamentalsPretestTotal/100 36.47 6.567 32
MTTIFundamentalsPosttestTotal/100 48.00 5.639 32
Significant:t(29)=5.01,p<.001.
Table4
Pre‐andposttestmeansfortheMTTIGeometrytest
Mean Std.Deviation N
MTTIGeometryPretestTotal/90 26.58 6.421 32
MTTIGeometryPosttestTotal/90 36.03 5.894 32
Significant:t(30)=4.61,p<.001
PedagogicalContentKnowledge
TheaveragenumberofcorrectanswersforthefivequestionsoftheLouisville
AlgebraandIdeastestrelatingtopedagogicalcontentknowledgeincreasedsignificantly
from4.44to5.16acrosstestadministrations.ThissuggeststhatMTTIparticipants’
pedagogicalcontentknowledgeforalgebraandideasincreasedfollowingengagementwith
acourseinthefundamentalsofmathematics.Themeanpedagogicalcontentknowledge
scoresfortheLouisvilleGeometryandMeasurementtestdeclinedslightlyfrompretest
(3.90)toposttest(3.55)administrations,butthisdecreasewasnotsignificant(Tables5&
6).
Takentogethertheseresultsindicatethatingeneralparticipants’mathcontentand
pedagogicalcontentknowledgeincreasedfrombeginningtoendoftheMTTIcourse.
Table5
Pre‐andposttestmeansforthepedagogicalitemsontheLouisvilleAlgebratest
TME, vol10, no.3, p. 635
 Mean Std.Deviation N
LouisvilleAlgebraPretestTotal/10 4.44 1.722 32
LouisvilleAlgebraPosttestTotal/10 5.16 1.629 32
Significant:t(31)=2.49,p=.018.
Table6
Pre‐andposttestmeansforthepedagogicalitemsontheLouisvilleGeometrytest
 Mean Std.Deviation N
LouisvilleGeometryPretestTotal/10 3.90 2.146 32
LouisvilleGeometryPosttestTotal/10 3.55 2.602 32
Notsignificant:t(31)=.706,p=.486.

Asmentionedabove,fromtheclassroomobservationprotocols,instructional
activitieswerecodedasteacher‐centered,student‐centeredorindeterminate,at5‐minute
intervals.Forexample,lecturewasconsideredteacher‐centeredwhilecooperative
learningwasconsideredstudent‐centered.Howeverforsomeactivities(e.g.“writing”),
therewasinsufficientinformationontheobserver’sreporttodeterminethestudent‐
centerednessoftheactivity;theseweregivenacodingof“indeterminate.”Foreachlesson,
thepercentoftimespentineachofthesethreecategorieswasthencalculated.Acrossall
observationsandallteachersandallsemesters,therangeoftimespentwas:inteacher‐
centeredactivities,30.2%;instudent‐centeredactivities,30.4%;andinactivitiesthatcould
notbeclearlyclassifiedaseither,39.4%.Therewasnosignificantchangeacrossthe
semesterforthepercentoftimespentinteacher‐centeredvs.student‐centeredactivities
Gningue, Peach & Schroder
(χ2(10)=5.29,p=.87).Thus,itappearsthatstudent‐centeredpedagogydidnotincrease
overthetimespanoftheMTTIcourseforCohort1.
StudentEngagement
Inthefall2009,spring2010,andfall2010semesters,observersassessedthelevel
ofstudentengagementinmathclassatfive‐minuteintervals.Theyrecordedthreepossible
levelsofengagement:lowengagement(80%ormoreofstudentsoff‐task);medium
engagement(mixedengagement);andhighengagement(80%ormoreofstudents
engaged).Highengagementincreasedfromfall2009tospring2010.Inthespring
semester,highengagementhadincreasedsignificantlyfromabout40%ofobservationsto
63.5%ofobservations.Infall2010highengagementdecreasedto48%.However,across
thethreesemesterslowengagementdecreasedfromninepercentinfall2009tofour
percentinfall2010(Figure2).Thesefindingsprovidesomeevidenceforanincreasein
highstudentengagementoverthetime‐spanoftheMTTIproject,andcertainlyevidenceof
adecreaseinlowstudentengagement.
Figure2.Levelofstudentengagementbysemester.
Semester
Fall 2010Spring 2010Fall 2009
Percent
70
60
50
40
30
20
10
0
Low engagement
Mixed engagement
High engagement
TME, vol10, no.3, p. 637
StudentEngagement,MathContentandPedagogicalKnowledge,andStudentCentered
Teaching
Mathcontentknowledgeandpedagogicalcontentknowledgedidnotsignificantly
predictthepercentageclasstimefeaturingstudent‐centeredpedagogy(Tables7&8)or
percentageofhighstudentengagementinmathclass(Tables9&10).
Table7
MathcontentandpedagogicalcontentknowledgeasmeasuredbytheLouisvilletestsas
predictorsofstudentcenteredpedagogy.

Sumof
Squares
df
Mean
Square
F Sig.
Regression 205.206 4 51.302 .104 . 980
Residual 8390.215 17 493.542  
Total 8595.422 21   
a. Predictors:(Constant),GeometryContentKnowledgechange,GeometryPedagogical
KnowledgeChange,AlgebraContentKnowledgechange,AlgebraPedagogicalKnowledge
change
b. DependentVariable:PercentStudentCenteredPedagogy
Table8
MathcontentknowledgeasmeasuredbytheMTTItestsaspredictorsofstudentcentered
pedagogy.

Sumof
Squares
df
Mean
Square
F Sig.
Regression 619.584 2 309.792 .729 . 497
Residual 7228.263 17 425.192  
Total 7847.847 19   
a. Predictors:(Constant),MTTIGeometrychange,MTTIAlgebrachange
b. DependentVariable:PercentStudentCenteredPedagogy
Table9
MathcontentandpedagogicalcontentknowledgeasmeasuredbytheLouisvilletestsas
predictorsofhighstudentengagementinmathclass

Sumof
Squares
df
Mean
Square
F Sig.
Gningue, Peach & Schroder
Regression 5659.604 4 1414.901 .837 . 520
Residual 28728.310 17 1689.901  
Total 34387.915 21 
a. Predictors:(Constant),LouisvilleGeometryContentKnowledgechange,AlgebraContent
Knowledgechange,AlgebraPedagogicalKnowledgechange,GeometryPedagogicalKnowledge
change
b. DependentVariable:Percenthighengagement
Table10
MathcontentknowledgeasmeasuredbytheMTTItestsaspredictorsofhighstudent
engagementinmathclass.

Sumof
Squares
df
Mean
Square
F Sig.
Regression 5772.912 2 2886.456 1.973 . 170
Residual 24873.178 17 1463.128  
Total 30646.090 19 
a. Predictors:(Constant),MTTIGeometrychange,MTTIAlgebrachange
b. DependentVariable:Percenthighstudentengagement
Todetermineiftherewasarelationshipbetweenstudent‐centeredteaching(SCT)
andstudentengagement,wederivedtwogroupsofparticipants;GroupA(HighSCT)
consistedofthesixparticipantswhowereobservedtodisplaythemoststudent‐centered
teachingtechniquesasassessedbytheclassroomobserversacrossboththefall2009,
spring2010andfall2010semesters;andGroupB(LowStudentCentered)consistedofthe
sixMTTIparticipantswhoexhibitedtheleaststudent‐centeredteachingtechniques
assessedinthesamemanneracrossthesametimeperiod.ForGroupA,themean
percentageoftimespentinstudent‐centeredteachingactivitieswas48.7%(s.d.=9.0)
acrossallsemesters,whileforGroupB,itwasonly15.7%(s.d.=9.2).
Wethenexaminedtherelationshipbetweenstudentcenteredteachingandstudent
engagement.Wecalculatedthelevelsofstudentengagementforthetwogroups(highand
TME, vol10, no.3, p. 639
lowSCT)foreachsemesterandameanvalueacrosssemesters.Wefoundthatstudentsof
GroupA(highSCT)teachersweresignificantlymorelikelytobehighlyengagedintheir
mathclassesthanstudentsofGroupB(lowSCT)teachers:χ2(1)=5.81,p=.02(SeeTable
11).
Table11
LevelofstudentengagementfortheHighandLowSCTgroups
LevelofSCT HighEngagemen
t
MixedEngagemen
t
LowEngagemen
t
High 62.4% 33.4% 4.3%
Low 44.7% 48.7% 6.6%
Discussion
WefoundthatMTTIteachers’contentknowledgeinthefundamentalsof
mathematicsimprovedsignificantlyfollowingtheirparticipationintheprogram.However,
therewasnosignificantrelationshipbetweenteachers’increaseincontentknowledgeand
theiruseofstudent‐centeredteachingortheengagementleveloftheirstudentsinmath
class.Thismayhavebeenbecausethemeasuresweusedtoassesscontentknowledgedid
notadequatelytapintoparticipants’pedagogicalknowledge.Supportforthisviewcomes
fromadditionaldatafromtheobservations,whichshowthattheclassroomobservers
Gningue, Peach & Schroder
ratedteachers’masteryofmathconceptshighly.Theobserversalsoreportedthat
participantsmadeextremelyfewmathematicalerrorswhiletheywereteaching.
ItisalsoworthnotingthattheUniversityofLouisvilletestsweretestsofgeneral
mathematicsconceptsandpedagogy,whiletheMTTImathtestswererelatedtotheMTTI
mathcourses,butnotnecessarilytothespecificconceptsandpedagogythatMTTIteachers
wereusingintheirclassrooms.ThemathcontentoftheMTTIcourseswasdeterminedby
theLehmanCollegemathematicsfacultymemberteachingeachcourse.Ingeneral,the
contentofthemathcourseswasrelatedtotheNewYorkStatemathstandards,butitwas
notrelatedspecificallytothecontentthattheteacherswereteachingintheirclassroom.It
mightnotbesurprising,therefore,thattherewasnosignificantrelationshipbetweenMTTI
teachers’mathconceptknowledgeasmeasuredbytheLouisvilleandMTTItestsandtheir
classroompracticesasreportedbytheobservers.
WesuggestthatthediscrepancybetweentheUniversityofLouisvilleGeometryand
Measurementtestresults(lackofimprovement)andthoseoftheMTTIGeometrytest
results(significantimprovement)mayhavebeenduetothelackoffitbetweentheMTTI
geometrycourse,whichwasdesignedtocorrespondtoNewYorkState’ssecondary
geometrycurriculum,andtheitemsontheLouisvilleexam.
ThecontentoftheLouisvilletestshadbeenestablishedwithreferencetoteamsof
mathematicians,matheducators,andmathteacherswhoconductedliteraturereviewsfor
appropriatecontentasdefinedbynationalrecommendations(Saderholm,Ronau,Brown,&
Collins,2010).Thisresultedinteststhatcontainedcontentthatmathexpertsthoughtthat
mathteachersgenerallyoughttoknowandbeabletoteach,ratherthanitemsthat
TME, vol10, no.3, p. 641
assessedmasteryofspecificcoursecontentorwhatteachersneededtoknowtobeableto
teachparticularstudents.
Inaddition,fewerMTTIteachershadexperienceinorwerecurrentlyteaching
geometrycomparedtoalgebra.Thiswasinpartbecause,untilrelativelyrecently,most
emphasishadbeenplacedonalgebrabyNewYorkState’sBoardofRegents.Sinceteachers
werebeingaskedtofocusmoreonteachingalgebrathangeometry,thismightexplainwhy
theMTTIteachersgenerallyimprovedmoreontheAlgebraandFundamentalstestthanthe
Geometrytests.
Wediscoveredthatteacherswhoemployedahighlevelofstudent‐centered,
inquiry‐basedpedagogytendedtobemoreeffectiveasmathteachersthanthosewhoused
alowlevelofstudent‐centeredteaching,atleastifeffectivenessisassessedbytheextentto
whichtheirstudentswereengagedinthelesson.
Anecdotally,participantsreportedthatasaresultofparticipationintheclassroom‐
basedinquiry(actionresearch)courses,theychangedtheirownteachingpracticesand
sawimprovementsinmotivationtowardparticipatinginmathematicsonthepartoftheir
students.Thesefindingsarebasedonself‐report,andinthefuturewearegoingtoask
teacherstoformallyassesswhetherchangesinstudents’motivationtoengageactually
occur.
Forthisstudy,themainvariableusedforassessingtheeffectivenessofteachingis
levelofstudents’engagementinmathclass.Inpart,thiswasbecausewehaddifficultyin
gatheringpre‐andpost‐testdataforstate‐mandatedstudenttests.Tosomeextentthis
wasbecause,inordertoobtainethicalapprovalfromtheNewYorkCityDepartmentof
Educationforthestudy,wecouldnottrackindividualstudentsduringtheperiodofthe
Gningue, Peach & Schroder
research,norcouldMTTIteachersconductresearchactivitiesusingstudentsintheirown
classesasparticipants.
ForMTTICohort2,weareabletoaskMTTIteacherstocollectdatafromtheir
studentsaslongasthosestudents’identitiesarenotrevealed.Therefore,weareinthe
processofadministeringmathperformancetaskstothestudentsofMTTICohort2.These
performancetasksreflectthenewCommonCoreStateStandardsforMathematics(2010)
whicharebeingintroducedinNewYorkCityschoolsinthefall2012semester.Thisisin
anattempttoobtainstudentachievementdata.Wewillthenbeabletolookatthe
relationship,ifany,betweenstudent‐centeredpedagogy,studentengagement,andstudent
achievement.
TME, vol10, no.3, p. 643
References
Ahuja,O.P.(2006).World‐classhighqualitymathematicseducationforallK‐12American
students.TheMontanaMathematicsEnthusiast,3(2),223‐248.
Ball,D.L.&Bass,H.(2000).Interweavingcontentandpedagogyinteachingandlearning
toteach:Knowingandusingmathematics.InJoBoaler(Ed.),MultiplePerspectives
onTeachingandLearning(pp.83104).Westport,CT:AblexPublishing.
Brown,C.&Borko,H.(1992).Becomingamathematicsteacher.InD.GrouwsHandbookof
ResearchonMathematicsTeachingandLearning(pp.209–239).NewYork:
Macmillan.
Bush,B.&Nussbaum,S.(2004).InterpretingtheDTAMSmathscoringsummary.Centerfor
ResearchinMathematicsandScienceTeacherDevelopment:Universityof
Louisville.
CommonCoreStateStandardsInitiative.(2010).CommonCoreStateStandardsforMathematics.
Washington,DC:NationalGovernorsAssociationCenterforBestPracticesandtheCouncil
ofChiefStateSchoolOfficers.
CopelandM.A.(2003).Leadershipofinquiry:Buildingandsustainingcapacityforschool
improvement.EducationalEvaluationandPolicyAnalysis,25(4),375‐395.
Davis,R.B.(1988).Instructioninintroductoryalgebra.InP.J.Campbell&L.S.Grinstein,
(Eds.),MathematicsEducationinSecondarySchoolsandTwoYearColleges,a
Sourcebook(pp.97‐121).GarlandPublishing,Inc.:NewYork.
Ginsburg,A.,Cooke,G.,Leinwand,S.,Noell,J.&Pollock,E.(2005).ReassessingU.S.
internationalmathematicsperformance:Newfindingsfromthe2003TIMSSandPISA.
Washington,D.C.:AmericanInstitutesforResearch.
Gningue, Peach & Schroder
Grouws,D.A.,&Schultz,K.A.(1996).Mathematicsteachereducation.InJ.Sikula,T.J.
Buttery,&E.Guyton(Eds.),HandbookofResearchonTeacherEducation,2ndEd.(pp.
442‐458)NewYork:Simon&SchusterMacmillan.
Hill,H.C.,Rowan,B.&Ball,D.L.(2005).Effectsofteachers’mathematicalknowledgefor
teachingonstudentachievement.AmericanEducationalResearchJournal,42(2),
371‐406.
Kemp,L.,&Hall,A.H.(1992).Impactofeffectiveteachingresearchonstudentachievement
andteacherperformance:Equityandaccessimplicationsforqualityeducation.
Jackson,MS:JacksonStateUniversity.(ERICDocumentReproductionServiceNo.ED
348360)
Lawrenz,F.,Huffman,D.,&Appledoorn,K.(2002).Classroomobservationhandbook.CAREI,
CollegeofEducation&HumanDevelopment,UniversityofMinnesota:4.
MathematicalAssociationofAmerica.(2008).MAAreport:Algebragatewaytoa
technologicalfuture.Katz,V.J.(Ed.).MAA:UniversityoftheDistrictofColumbia.
NationalAcademyofSciences.(2006).Risingabovethegatheringstorm:Energizingand
employingAmericaforabrightereconomicfuture.CommitteeonProsperinginthe
GlobalEconomyofthe21stCentury,2006.
NationalCouncilofSupervisorsofMathematics[NCSM].2008.Theprimeleadership
framework:PrinciplesandindicatorsforMathematicsEducationLeaders.Indiana:
SolutionTree.
NationalCouncilofTeachersofMathematics.(2000).PrinciplesandStandardsforSchool
Mathematics.Reston,VA:NCTM.
TME, vol10, no.3, p. 645
Rosenshine,B.(2012).Principlesofinstruction:Research‐basedstrategiesthatallteachers
shouldknow.AmericanEducator,36(1),12‐39.
Saderholm,J.,Ronau,R.,Brown,E.T.,&Collins,G.(2010).ValidationoftheDiagnostic
AssessmentofMathematicsandScience(DTAMS)instrument.SchoolScienceand
Mathematics,110(4),180‐192.
Stein,M.K.,Smith,M.S.,Henningsen,M.A.&Silver,E.A.(2009).Implementingstandards
basedmathematicsinstruction:Acasebookforprofessionaldevelopment,2ndEd.New
York:TeachersCollegePress.
Gningue, Peach & Schroder
... The interest in providing mathematics teachers with effective teaching practices is necessary because it significantly impacts their students' mathematical achievement (Gningue et al., 2013). Students' poor performances on international tests and weak mathematics achievement are due to ineffective teaching practices. ...
... Ensuring mathematics teachers employ effective teaching practices is necessary due to the significant impact of these practices on students' mathematical achievements, as shown by many studies (e.g., Roberts, 2013;Serigne et al., 2013;Walkowiak et al., 2014). As indicated by Roberts (2013), teachers' practices play a considerable role in students' learning and achievements, and the teaching method strongly impacts students' understanding of what they learn. ...
Article
Full-text available
This study aimed to explore mathematics teachers’ awareness of the practices of effective teaching issued by the United States National Council of Teachers of Mathematics (NCTM, 2014a) in the Kingdom of Saudi Arabia and the Arab Republic of Egypt and to compare the results using the comparative descriptive method. The Saudi sample comprised 561 teachers and the Egyptian sample comprised 620 teachers. Data were collected through an awareness scale consisting of eight dimensions representing the practices of effective teaching. Among the study’s many findings, the most important was that there is a high level of awareness of effective teaching practices among teachers of mathematics in the Kingdom of Saudi Arabia and the Arab Republic of Egypt. In addition, no differences were found in the level of awareness among Saudi teachers based on any potentially differentiating variables (qualification, teaching experience, school stage). However, there were differences attributed to the gender variable, in favour of the female group. Among the Egyptian teachers, the results showed no statistically significant differences in level of awareness for gender and school stage, but there were those with higher qualifications (Master’s and doctorate degrees) presented significantly greater awareness, as did those with an average teaching experience of 5–9 years.
... As part of teaching presence, instructors are expected to synthesize and present information by referring to various sources and integrating them with their own knowledge and ideas as content experts (Garrison et al., 2000). While few studies directly explore the relationship between teachers' content knowledge and student engagement, Gningue et al. (2013) delved into the connection between instructors' content knowledge and their student-centered pedagogical practices in F2F learning settings aimed at enhancing student engagement. Their study findings indicated that the implementation of student-centered pedagogical practices by instructors had a greater impact on fostering engagement compared to variations in their content knowledge. ...
Article
Synchronous online courses (SOC), enabling real-time interaction, have become increasingly prevalent in higher education, particularly during emergency remote teaching (ERT). This surge in online education raised questions about how student engagement, a crucial factor for the quality of higher education practices, was achieved during ERT. To address these questions and offer insights into effective practices for fostering student engagement in SOC, this study explores the experiences of undergraduate students and instructors during ERT. While a substantial body of literature addresses student engagement, there is a gap in studies that comprehensively synthesize effective practices to engage undergraduate students in SOC across various departments. Therefore, the present study seeks to bridge this gap. Insights were gathered through semi-structured one-on-one interviews and a focus group with ten instructors and fifteen students across diverse departments and universities. The study findings unveil effective strategies and practices to promote student engagement in SOC. These strategies closely align with the elements of teaching, social, and cognitive presence within the Community of Inquiry (CoI) framework, emphasizing interaction-based pedagogical practices and the role of emotional communication in SOC. The study not only provides valuable strategies for enhancing student engagement during crises but also highlights their relevance in normal times.
... Other literature has explored preparation programs and the extent to which certain programmatic elements prompted shifts in MSs' beliefs, practices, and/or knowledge (Baker, 2022;Haver et al., 2017;Myers et al., 2020;Swars et al., 2018;Swars Auslander et al., 2024). Additionally, research has examined grant-funded PD opportunities for MSs (Campbell & Griffin, 2017;Ellington et al., 2017;Gningue et al., 2013;Jackson et al., 2015;Russell et al., 2020), which typically included coursework offerings to deepen MSs understanding of content, pedagogy, and leadership. Last, research has begun to explore how school districts provide ongoing PD to MSs (Jarry-Shore et al., 2023; Kane & Saclarides, 2022a, 2022bSaclarides & Kane, 2021). ...
... Furthermore, this research shows that such programs may offer more courses focused on building coaches' mathematics content knowledge, while offering less leadership courses that may focus on the interpersonal work of supporting teachers' learning (Goodman et al., 2017). Still other research has explored coaches' development as just one aspect of a large-scale research project (Campbell & Malkus, 2014;Gningue et al., 2013;Russell et al., 2020). ...
Article
Full-text available
Mathematics coaching is complex work, and coaches must be supported to become experts in mathematics, mathematics instruction, and mathematics coaching. Using video and interview data from 12 mathematics coaches and one district administrator in one public school district in the southeastern USA, this qualitative study explores how the performative aspect of one group of mathematics coaches’ doing the math routine opened up conversations about mathematics, mathematics instruction, and mathematics coaching. Findings indicate that as the coaches engaged in doing the math together, opportunities to discuss mathematics and mathematics instruction were opened up, while conversations about mathematics coaching rarely surfaced. In interviews, participants discussed the benefits and drawbacks of participating in doing the math. Implications for future research and practice are discussed.
... Programs that deal on subject matter instruction with teachers, having a narrow mathematical knowledge of the content has negative effects on pedagogical content knowledge and instructional quality and student progress which persist across their entire teaching careers [5]. The Mathematics Teacher Transformation Institute appraised usefulness of teaching by measuring student engagement in mathematics cited in [15] uncovered that teachers who employed a high level of learner-centered, inquiry-based pedagogy were more efficient algebra and geometry teachers than those who did not. Conversely, they also found out that there was no connection among the growth in content knowledge and a teacher's use of learner-centered imparting. ...
Article
Full-text available
A survey design was adopted in this study. Three senior high schools were randomly chosen for this study. Thirty (30) mathematics tutors and 100 learners were involved in the study. The Purpose of the study is to find out the factors that affect the actual teaching and learning of mathematics in senior high schools. To achieve this, three major questions were answered: (1) What quality teachers are teaching mathematics in our senior High schools? (2) What feelings do senior High School students display regarding the teaching and learning of mathematics? (3) What issues affect the efficient utilization of available instructional resources in the teaching of mathematics at the senior high schools? Questionnaire were used to collect data for the study. The results of the study showed that inadequate teaching and learning resources and quality tutors are some of the factors affecting the effective instruction and learning in mathematics the classroom at SHS level. From the results, the following were recommended; interactive methods of teaching mathematical concepts need to be used by mathematics teachers. In addition, stakeholders need to provide adequate teaching and learning resource to the various senior high schools.
Preprint
Full-text available
This research investigates the impact of innovative lesson starters on promoting active learning in school science education. We aimed to assess the effectiveness of these starters in enhancing student engagement, understanding, and critical thinking skills. By examining various active learning strategies, we analysed their potential to foster a deeper understanding of scientific concepts. We analysed the implementation of innovative lesson starters and measured their impact on student engagement and learning outcomes. Our findings indicate that these starters significantly influence student engagement and understanding. Comparative analysis revealed that problem-solving activities, discussions, and collaborative projects were the most effective lesson starters. Teacher feedback highlighted the importance of these strategies in facilitating active learning and the challenges faced in their implementation. Future research recommendations include exploring innovative lesson starters' long-term effects on student learning and engagement. In conclusion, our research provides practical insights, equipping educators with effective strategies to implement active learning in school science education. These findings offer valuable guidance for educators seeking to implement active learning strategies effectively in their classrooms.
Article
Mathematics coaches are often positioned as important mediators between district administrators and teachers regarding messages about ambitious and equitable instruction. Despite this, little research has sought to unpack the connection between what coaches learn at professional development and how they make their learning available to teachers. In this study, we partnered with one district administrator and four mathematics coaches and conducted 15 semi-structured interviews to better understand how these coaches made their professional learning available to teachers. Mathematics coaches emphasized using various structures and resources when making their professional learning available to teachers. Participants also highlighted challenges they encountered when striving to make their learning available. Implications for practice and research are discussed.
Article
Assessment is an issue that is central to the lives of educators and students alike. At all levels, from programmatic to course-specific, instructors strive to assess in a way that accurately measures achievement or progress relative to one’s goals. This paper reports on students’ experiences with alternative assessments in our undergraduate mathematics course for non-STEM (Science, Technology, Engineering and Mathematics) majors. The course, Creative Thinking in Mathematics, designed to fulfil the university’s general education requirement for mathematics, was recently revised and renamed to highlight the role of creativity in mathematics. In the course, students engage in mathematics using creative approaches and consider how these approaches connect to other disciplines, their career aspirations, and important mathematical discoveries throughout history. This shift in course emphasis necessitated revisions to assessments in ways that mirrored the course’s instructional approach. This article describes the alternative assessments, outlines the research study, and reports on the results relative to students’ experiences with these assessments, both prior to and during the course, highlighting a need for instructors to reconsider traditional assessments.
Thesis
Full-text available
Literatürde, öğrenci katılımının yükseköğretimdeki önemine vurgu yapan çok sayıda çalışma yer almaktadır. Bununla beraber, Covid-19 pandemi döneminde çevrim içi lisans derslerine yönelik öğrenci katılımı üzerine gerçekleştirilen sınırlı sayıda çalışmanın bulunduğu görülmektedir. Mevcut araştırmanın amacı, Covid-19 pandemi döneminde çevrim içi lisans derslerine yönelik öğrenci katılımının nasıl sağlandığının ortaya konulmasıdır. Araştırma deseni, nitel araştırma desenlerinden fenomenolojik desen olarak belirlenmiştir. Kartopu örnekleme yöntemi ile belirlenen çalışma grubu, Yükseköğretim Kuruluna bağlı vakıf ve devlet olmak üzere çeşitli üniversitelerde görev yapan 10 öğretim elamanı ile bu öğretim elemanlarının çevrim içi derslerini takip eden 15 lisans öğrencisinden oluşmaktadır. Araştırma verileri yarı yapılandırılmış görüşmeler ile odak grup görüşmesi aracılığıyla elde edilmiştir. Elde edilen veriler tümevarımsal tematik analiz yöntemiyle çözümlenmiştir. Analizler neticesinde ortaya çıkan kodlar ilişkili oldukları kategori ve temalar altında bir araya getirilmiştir. Araştırma bulguları, Covid-19 pandemi döneminde çevrim içi lisans derslerinde öğrenci katılımının sağlanmasının birçok faktöre bağlı olduğunu göstermektedir. Bu faktörler öğrenen/öğreten/öğrenme ortamı ile ilgili durumlar, ölçme ve değerlendirme ile ilgili durumlar, öğretim süreci ile ilgili durumlar ve teknik durumlar olmak üzere dört ana tema kapsamında detaylı olarak incelenmiştir. Araştırmadan elde edilen sonuçlar, çevrim içi lisans derslerine yönelik öğrenci katılımının önemini ortaya koymaktadır. Bu bağlamda, öğrenci katılımının sağlanmasında etkili durum ve stratejiler tartışılarak çevrim içi öğrenme/öğretim süreci ile ilişkili bazı tespit ve önerilerde bulunulmuştur.)
Article
Full-text available
In September 1989, the United States' Governors Conference in Charlottesville, Virginia set an ambitious goal by declaring that "By the year 2000, United States students will be first in the world in mathematics and science achievements". However, recent results of the 'Programme for International Student Achievement' and 'Trends in International Mathematics and Science Study' indicate that the United States students' achievements in mathematics are far below world class standards. This paper seeks to discuss issues in an international context related to the goal of creating world-class high quality mathematics education for all K-12 American students. In particular, the author also shares his reflections and depicts lessons from Singapore's success story in mathematics education.
Chapter
examines the process of becoming a mathematics teacher, focusing on the individual and on changes he or she undergoes in assuming the role of a professional teacher / review the research related to becoming a mathematics teacher / discuss implications of this research both for mathematics teacher education as well as for future research reflects the three research traditions within which most research on becoming a teacher has been conducted: learning to teach, socialization, and adult development / within the learning-to-teach perspective, we include research on teacher knowledge, beliefs, thinking and actions, with major emphasis on research conducted within the discipline of psychology and grounded in the assumptions of cognitive psychology (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Article
This article reports on findings from a longitudinal study of leadership in the context of a region-wide school renewal effort entitled the Bay Area School Reform Collaborative (BASRC). BASRC's theory of action is multifaceted, incorporating a focus on distributed leadership, continual inquiry into practice, and collective decision-making at the school. Analysis of qualitative and quantitative data sources suggests the use of an inquiry process is centrally important to building capacity for school improvement, and a vehicle for developing and distributing leadership. Within a sample of 16 schools where reform processes are most mature, the principal's role shifts to focus more narrowly on key personnel issues, framing questions and supporting inquiry processes. Findings provide evidence of the efficacy of policy strategies rooted in new understandings of school leadership.