Doing the Scholarship of Teaching and Learning in Mathematics

227 Pages·2014·2.14 MB·English

by  Jacqueline M. Dewar

Doing the Scholarship of Teaching and
Learning in Mathematics
Cover Art: The source text for the wordle (www.wordle.net) consisted of Chapter 20
Synthesis of the Value and Benefits of SoTL Experienced by the Contributors with the
namesofindividualsandtheword“chapter”removed.
(cid:2)c 2015by
TheMathematicalAssociationofAmerica(Incorporated)
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PrintISBN978-0-88385-193-7
ElectronicISBN978-1-61444-318-6
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Doing the Scholarship of Teaching and
Learning in Mathematics
Edited by
Jacqueline M. Dewar
and
Curtis D. Bennett
Loyola Marymount University
PublishedandDistributedby
TheMathematicalAssociationofAmerica
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19. VisualizationinTeachingandLearningMathematics,CommitteeonComputersinMathematicsEducation,SteveCunningham
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25. TheConceptofFunction:AspectsofEpistemologyandPedagogy,GuershonHarelandEdDubinsky,Editors.
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31. ResourcesforCalculusCollection,Volume5:ReadingsforCalculus,UnderwoodDudley,Editor.
32. EssaysinHumanisticMathematics,AlvinWhite,Editor.
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35. You’re the Professor, What Next? Ideas and Resources for Preparing College Teachers, The Committee on Preparation for
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36. PreparingforaNewCalculus:ConferenceProceedings,AnitaE.Solow,Editor.
37. APracticalGuidetoCooperativeLearninginCollegiateMathematics,NancyL.Hagelgans,BarbaraE.Reynolds,SDS,Keith
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38. ModelsThatWork:CaseStudiesinEffectiveUndergraduateMathematicsPrograms,AlanC.Tucker,Editor.
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42. ResourcesforTeachingLinearAlgebra,DavidCarlson,CharlesR.Johnson,DavidC.Lay,A.DuanePorter,AnnE.Watkins,
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51. UsingHistorytoTeachMathematics:AnInternationalPerspective,VictorJ.Katz,Editor.
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58. Fractals,Graphics,andMathematicsEducation,BenoitMandelbrotandMichaelFrame,Editors.
59. Linear Algebra Gems: Assets for Undergraduate Mathematics, David Carlson, Charles R. Johnson, David C. Lay, and A.
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60. InnovationsinTeachingAbstractAlgebra,AllenC.HibbardandEllenJ.Maycock,Editors.
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81. UndergraduateMathematicsfortheLifeSciences:Models,Processes,andDirections,GlennLedder,JennaP.Carpenter,and
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Contents
Foreword xiii
DavidM.Bressoud
Preface xv
JacquelineM.DewarandCurtisD.Bennett
PartI. GettingStartedinSoTLasaMathematician
1. UnderstandingSoTLandItsPotentialBenefits 3
JacquelineM.DewarandCurtisD.Bennett
(cid:2)
TheOriginsofSoTLinHigherEducation 3
(cid:2)
DistinguishingSoTLfrom“Good”and“Scholarly”Teaching 4
(cid:2)
ForgingDisciplinaryConnectionsforSoTL 4
(cid:2)
SoTL’sEmergenceinMathematics 5
(cid:2)
SoTLandRUME 6
(cid:2)
EvaluatingandValuingSoTL 8
(cid:2)
SpecialConsiderationsforJuniorFacultyMembers 8
(cid:2)
TheBenefitsofSoTL 9
2. InitiatingaSoTLInvestigation 13
JacquelineM.DewarandCurtisD.Bennett
(cid:2)
ATypicalStartingPoint 13
(cid:2)
ATaxonomyofSoTLQuestions 14
(cid:2)
UsingDisciplinaryKnowledgetoNarrowaQuestion 15
(cid:2)
UndertakingaLiteratureSearch 16
3. GatheringandAnalyzingEvidence 19
JacquelineM.Dewar
(cid:2)
TriangulatingData 19
(cid:2)
ChallengesthatEducationalResearchDesignPresentsforSoTL 19
◦
DealingwiththeLackofaControlGroup 20
◦
AligningtheAssessmentMeasurewithWhatIsBeingStudied 22
◦
ToSeekStatisticalSignificanceorNot? 22
◦
WhichMeasureofChange? 23
(cid:2)
QuantitativeversusQualitativeData 23
(cid:2)
DataSourcesFamiliartoMostMathematicians 24
◦
SurveyDesignConsiderations 25
(cid:2) (cid:2) EssentialStepsinDesigningaSurvey 25
DataSourcesLessFamiliartoMathematicians 27
◦
KnowledgeSurveys 27
◦
Think-Alouds 31
(cid:2) AdviceforConductingaThink-Aloud 32
vii
viii Contents
◦
FocusGroups 33
(cid:2) (cid:2) ModelforConductingaFocusGroup 34
AnalyzingQualitativeData 35
◦
Rubrics 36
(cid:2) HowtoCreateaRubric 36
◦
CodingData(ContentAnalysis) 39
(cid:2) ProcessforCodingData 40
(cid:2) AssessingtheQualityofContentAnalysis 41
4. ResourcesforPursuingSoTLandGoingPublic 45
JacquelineM.Dewar
(cid:2)
HumanSubjectsConsiderations 45
(cid:2)
FindingCollaboratorsandSupport 46
(cid:2)
GoingPublicwithResults 47
◦
Conferences 47
◦
Journals 47
PartII. IllustrationsofSoTLWorkinMathematics
Theme1:ExperimentswithApproachestoTeaching
5. AssessingtheEffectivenessofClassroomVisualCues 51
GretchenRimmaschandJimBrandt
Can instructor use of visual cues improve student performance in recognizing and correctly applying
proceduralrules?Specifically,dothecueshelpstudentstosimplifyexponentialexpressionsandcalculate
derivatives?
SoTL Process—Pilot study; Control group; IRB; Evidence: pre- and post-tests and surveys; use of a
rubric.
6. (Re)discoveringSoTLThroughaFundamentalChallenge:HelpingStudentsTransition
toCollegeCalculus 59
RannBar-On,JackBookman,BenjaminCooke,DonnaHall,andSarahSchott
Can algebra review and study group sessions improve student retention and performance in beginning
calculus?
SoTLProcess—Evolutionoftheinterventionandthestudy;Collaborationbetweenfacultymembersand
academicsupportstaff;IRB;Evidence:participationrates,coursegrades.
7. AQuantitativeandQualitativeComparisonofHomeworkStructuresinaMultivariable
CalculusClass 67
LynnGieger,JohnNardo,KarenSchmeichel,andLeahZinner
How does the use of online homework affect student attitudes, motivation, and performance? Will it
leadstudentstostudymorefrequently,bemoreengagedandresponsiblefortheirlearning,andleadto
improvedhomeworkgrades,testgrades,orcoursegrades?
SoTLProcess—Collaborationacrossmultipledisciplines;Evidence:pre-andpost-surveys,focusgroup,
homeworkgrades;Codingqualitativedata.
Contents ix
8. PlayingGamestoTeachMathematics 77
EdwinHerman
Doestheuseofgamesinclassforpracticeorreviewresultinbetterlearningorimprovestudentattitudes
andsatisfaction?
SoTLProcess—Evolutionoftheinterventionandthestudy;Quasi-controlgroupexperiment;Evidence:
studentevaluations,chapterexamgrades,finalexamgrades.
9. InvestigatingHowStudents’LinkingHistoricalEventstoDevelopmentsinMathematicsChanged
EngagementinaHistoryofMathematicsCourse 87
PamCrawford
Does the guided discovery teaching technique of having students investigate links between historical
events and developments in mathematics improve students’ engagement with historical material when
comparedwithmypreviousteachingmethods?
SoTLProcess—IRB,includingpreviouslycollecteddata;Evidence:pre-andpost-coursesurveys,exam
essayquestions;SoTLcomparedtoRUME.
Theme2:CraftingLearningExperiencesaroundReal-WorldDataorCivicEngagement
10 UsingSoTLtoAssesstheOutcomesofTeachingStatisticsThroughCivicEngagement 99
CindyKaus
Will incorporating civic engagement into a general education statistics course increase retention and
studentconfidenceintheirabilitytodoandcommunicatestatistics?
SoTL Process—Control groups and ethical concerns; Evidence: pre- and post-course surveys, student
evaluations,coursegrades;Surveyresponserates.
11.APedagogicalOdyssey 107
MichaelC.Burke
A vision of the possible: How would a mathematics course that used data-based integrative writing
assignmentsaffectstudents?
SoTL Process—Evolution of the intervention and the study; Evidence: systematic analysis of essays,
studentreflectivewriting,finalexams.
12.PresentingEvidencefortheFieldThatInventedtheRandomizedClinicalTrial 117
JohnHolcomb
Avisionofthepossible:Canteamwritingprojectsusingrealdataleadtoindividualacquisitionofdesired
dataanalysisskills?
SoTLProcess—Controlgroupsandethicalconcerns;IRB;Evidence:takehomedataanalysiscomponents
of midterm and final exams, surveys; Survey response rates; Survey design issues; Coding qualitative
data.