CalculusCourses’AssessmentData

MattiPaunaUniversityofHelsinki

DepartmentofMathematicsandStatistics

2001:HelsinkiLearningSystem

CalculusCourses’AssessmentData

• Onlinecourses• Curriculumdevelopment• Assessmentanddata

SingleVariable Calculus 2004

Modules

CourseNavigator

OnlineCalculus

Eachmodulecontains

• YouTubevideos• Readingmaterials• Quizzes(Automatic

assessment)• Workshops(Peer

assessment)• Discussionforum,calendar,gradebook,

etc.

LearningPaths

Theoryandworkedoutexamplesexplainedin

YouTubevideos- Viewablealsowithmobiledevices

Course Design

Supports individual study paths

OnlineCalculusCourses

• SingleVariableCalculus2004• CalculusI&II• AdvancedCalculus2013(Realanalysis)Completenesspropertyofrealnumberswithℇ - 𝛿proofmethod• OptiontotakeUHundergraduateCalculuscurriculumcompletelyonlineandinEnglish2014

OnlineCourse

Content Credits TraditionalCourse

Content Credits

Calculus I Limits,Differentiation,Antiderivatives,RiemannSums

8 Limits Completeness,Supremum,TheoryofLimits

5

Calculus II AdvancedIntegration,ImproperIntegrals,ConvergenceofSeries,TaylorSeries

8 Differentiation Continuity,Bolzano’sTheorem,Differentiation

5

AdvancedCalculus

Completeness,Continuity,Bolzano-WeirstrassTheorem

6 Integration RiemannSums,Antiderivatives,ImproperIntegrals

5

Series ConvergenceofSeries,TaylorSeries

5

Total ECTCcredits

22 20

HomeworkandAssessment

• Diagnostic,Formative,andSummative• AutomaticwithimmediatefeedbackimplementedwithSTACK,WEPSalsosupportsWeBWorK

• Peertopeer

MathematicalCompetencies(Pointon &Sangwin 2003,Rämö,Oinonen,Wikberg 2015)

1.Factualrecall2.Carryoutaroutinecalculationoralgorithm3.Classifysomemathematicalobject4.Interpretsituationoranswer5.Proof,show,justify(generalargument)6.Extendaconcept7.Constructexample/instance8.Criticizeafallacy9.Informationtransfer

STACKassistswiththe

correctinputofformulas

Automatic&ImmediateFeedback

• SystemssuchasSTACKandWeBWorK takestudent’sanswerasamathematicalobject• Evaluatewhethertheanswersatisfiesthemathematicalpropertiesrequired• Givefeedbackalsoaboutcommonmisconceptions• Assessmentisobjective:Thesamecriteriaareconsistentlyappliedtoallanswers

PeerFeedbackWorkshopmoduleinMoodle:

1. Studentsaregivenhomeworkproblemsaskingacompleteandclearpresentationofasolution.

2. Afterthesubmissiondeadline,anexamplesolutionisprovided3. Accordingtothemodelsolutionandassessmentinstructions,

studentsgradeandgiveconstructivefeedbacktootherstudentseventoyourself

Pedagogicalgoals:• Studentsstudyexampleandotherstudens’solutions• Learningfromotherwaystosolve,commonmistakesandprovidecorrectivefeedback• Createsinteractionbetweenstudentsinanonlinecourse• ScalabletoMOOCs

StudentFeedbackonPeerReview

AssessmentData

• Eachactionislogged:Clickstreamdataaboutbehaviorinanonlinecourse• Attempts,answers,scoresinquizzes• Workshopsubmissions,grades&feedbackgivenandreceived• Questionnairesaboutlearningstyles,self-efficacy,motivation

QuizLogData

AchievementandhomeworkUHCalculusCoursessince2012

390registeredstudents110took1st exam82eithertookbothexamsorpassedthecoursewithgrade1

Conclusions

• E-AssessmentisbecomingmorepopularinFinland• Digitalizingteachingnotinthecoreoftheinstitutionorbecauseoflackofresources• Imaginativewaystoassesshighercompetenciesautomatically• Moredatabecomingavailable(Spring2016:statisticscourses900cases)