ERIC EJ1116789: Investigating the Effectiveness of Group Work in Mathematics

2016·2 MB·English

by  ERIC

education
sciences
Article
Investigating the Effectiveness of Group Work
in Mathematics
AnastasiaSofroniou*andKonstantinosPoutos
SchoolofComputingandEngineering,UniversityofWestLondon,St.Mary’sRoad,LondonW55RF,UK;
[email protected]
* Correspondence:[email protected];Tel.:[phone]
AcademicEditor:EilaJeronen
Received:23June2016;Accepted:12August2016;Published:1September2016
Abstract: Group work permits students to develop a range of critical thinking, analytical and
communication skills; effective team work; appreciation and respect for other views, techniques
andproblem-solvingmethods,allofwhichpromoteactivelearningandenhancestudentlearning.
This paper presents an evaluation of employing the didactic and pedagogical customs of group
workinmathematicswiththeaimofimprovingstudentperformanceaswellasexploringstudents’
perceptionsofworkingingroups. Theevaluationofgroupworkwascarriedoutduringtutorial
timewithfirstyearcivilengineeringstudentsundertakingamathematicsmoduleintheirsecond
semester. Theaimwastoinvestigatewhethergroupworklearningcanhelpstudentsgainadeeper
understandingofthemodulecontent,developimprovedcriticalandanalyticalthinkingskillsand
seeifthismethodofpedagogycanproducehigherperformancelevels. Thegroupworksessions
wereconductedoverfourweekswhilststudyingthetopicofintegration. Evaluationsurveyswere
collected at the end of the intervention along with an investigation into the examination results
from the end of semester examinations. In order to derive plausible and reasonable conclusions,
theseexaminationresultswerecomparedwithananalogouscohortoffirstyearmathematicsstudents,
alsostudyingintegrationintheirengineering-baseddegree. Theinvestigationintotheeffectiveness
ofgroupworkshowedinterestingandencouragingpositiveoutcomes,supportedbyacombination
ofqualitativeandquantitativeanalysis.
Keywords: groupwork;enhancingmathematicallearning;collaborativeandcooperativelearning
1. Introduction
Thispaperevaluatestheeffectivenessofimplementinggroupworkinmathematics,intermsof
studentperformanceandstudents’perceptionsofthisdidacticformoflearningduringtutorialsessions.
Mathematicseducatorsarealwaysstrivingtoimprovelearnerperformanceandachievementsinthe
fieldofmathematics. Theissuesoflearningproblemsinmathematicsandthelackofmetacognitive
awarenessofmathematicalthinkingandproblem-solvingskills[1]stillseemtopersist,anddespite
differencesamongsteducatorsonaneffectivelearningmethodology,itcanbesuggestedthatthere
is at least a concurrence with respect to the reduced level of accomplishment amongst learners in
mathematics[2].
In the mid-1980s there was a reform movement in mathematics education as a reaction to
dissatisfaction with conventional teaching approaches [3]. Specific reports recommending the
restructuringofmathematicaldelivery[4]markedtheneedformodificationsinteachingmethodology.
TheNationalCouncilofTeachersofMathematics[5]endorsestheuseofincreasinglyintensiveand
effectiveinstructionalinterventionsforstudentslearningmathematics,suggestingthatthesecanbe
usedduringtutorialsessionsaswell. Employingmultiplemodelsandwaysofstructuringtopicscan
presentrichadaptionsofmathematicscontenttoeffectivelysupportstudent’sneeds[5]. Educators
Educ.Sci.2016,6,30;doi:10.3390/educsci6030030 www.mdpi.com/journal/education
Educ.Sci.2016,6,30 2of15
must therefore be encouraged to present active learning activities so that students can construct
knowledge,andonewaytoaccomplishthisistofamiliarisestudentswithgroupwork[4,6].
The current delivery of lectures often finds university students learning mathematics through
conservativebehaviouristicmethods[1],leavingthemtobepassiveanddependentontheirlecturers[7].
Modern,enhancedtaughtmathematicsfocusesonaconstructivistapproach,askingstudentstoface
newchallengeswithpriorknowledgeandtoabsorbandadoptnewinformation,thusallowingthem
toformtheirownsignificantinterpretationandmeaningfulunderstandingofthetaughtmaterial[8].
Withoutdenyingtheimportanceoftraditionalmathematicallecturing,andacknowledgingthat,in
acompetitiveacademicenvironment,studentsaremoreoftenrewardedforindividualeffort,thisstudy
aimstoreinforceandaddtothecurrentresearchliteratureongroupwork,thoughwithaparticular
emphasisonthefieldofmathematicsatahighereducationallevel. Thiswouldallowonce-skeptical
educators who have perceived group work as ineffective and problematic in this subject area to
recogniseandappreciatethevalueandbenefitsofalsoassigninggroupworktotheirstudents[9].
Moreexplicitly,theresearchquestionposedisthefollowing:cangroupworkbeconsideredaneffective
methodoflearningforthesubjectofmathematics,andcanitenhancethestudentlearningexperienceat
ahighereducationallevel? Thisstudyinvestigatestheeffectivenessofgroupworkinuniversity-level
mathematics,ahigher-levelapplicationperhapsslightlylackinginresearchoutput,byexaminingany
improvedstudentperformanceuponadoptionofgroupworkinteractionaswellasexaminingstudent
perceptionsofworkingingroups. Inaddition,thestudyconsiderswhethergroupworklearningcan
deepenstudentunderstandingofthemodulecontentandaidthemindevelopinghighercriticaland
thinkingskills.
This paper begins with a brief literature review documenting the adoption of group work in
education,particularlythoserelatingdirectlytomathematics. Collaborativeandcooperativegroup
work are highlighted, including a description of the main shortcomings and benefits experienced
by the practitioner. The paper continues with the methodology used to carry out the evaluation
oftheeffectivenessofgroupworkinmathematicsduringtutorialsessions. Thefindingsfromthe
investigation are then discussed and analysed using both qualitative and quantitative techniques.
Finally,someconcludingremarksandpossiblefutureassessmentsarepresented.
2. LiteratureReview
Groupworkiscenteredupontheconstructivismmodeloflearning[10–13]. Accordingtothe
report from the National Council of Teachers of Mathematics [4,5], it is said that group work in
mathematical education plays an essential role in students’ question acquisition and in criticising
constructively[14],allleadingtoproductiveandbeneficialoutcomesinstudentlearning.
The number of research studies carried out over recent years has increased noticeably in the
field of mathematics at the primary and secondary school levels [15]. Substantial research within
themathematicseducationsectorindicatesthatemployingsmallgroupsforvariousactivitiesand
exercisesdoesleadtoconstructiveandbeneficialoutcomesforstudentlearning.
FromareviewbyWebb[16,17]concerningstudiesinvestigatingpeerinteractionandachievement
in small scale groups, various compatible outcomes were achieved. Conveying a clarification or
simplification of an idea, solution or method to another group member was positively related to
achievement, whereas experiencing non-responsive feedback from a group member, specifically
no feedback or feedback that was irrelevant to what one has said or done, was characterised by
anegativerelationtoachievement[16,17]. Webb’sreviewalsointerestinglyrevealedthatgroupwork
was most useful when students were taught how to work in groups and how to present, provide
andacceptassistance. Thisreceivedaidwasmostfruitfulandfunctionalwhenitwasintheform
ofdetailedexplanationsandthenappliedbythestudenttotheexistingtaskortoadifferenttask.
Slavin’sresearchshowedpositiveeffectsfromgroupworkoncross-ethnicrelationsandenhancing
studentachievement[18]. Yackel,CobbandWoodfoundthatsmall-scalegroupworkproblem-solving
followedbywholeclassdialoguegeneratedmanylearningopportunitiesthatdonotusuallyoccurin
Educ.Sci.2016,6,30 3of15
aconservativetutorialorclass,comprisingopportunitiesforcollaborativediscussionandresolutionof
contrastingviewpoints[19].
Over the past years, many studies have been conducted in order to investigate how effective
competitive, individualistic, and cooperative group work methodologies are in endorsing and
encouraging productivity and achievement [20,21]. Acknowledging these studies and using
meta-analysis to study achievement in cooperative learning, the results showed that the average
studentlearningthroughcooperativeapproachesperformedatabouttwo-thirdsastandarddeviation
above the average student learning within a competitive (an effect size of 0.67) or individualistic
(effectsizeequalto0.64)structuredlesson[22],promptinghigherachievementlevelswhenconsidering
cooperativegroupworklearningcomparedtocompetitiveorindividualisticlearningstrategies.
Groupworkplaysafundamentalrolebothincooperativeandincollaborativelearningmethods,
andhasattractedsignificantresearchinterest[21–29]. Studiesdemonstratethatthesepedagogical
customs of group work do produce higher achievement and more positive relationships amongst
students,comparedtocompetitiveorindividualisticexperiences.
Researchsuggeststhatcollaborativelearninghasquicklyturnedintoastrongpromoterofgroup
workineducationalinstitutionsatalllevels[24]. Incollaborativelearning,participantsbrainstorm,
share information and work, tackle the same problem together continuously within their groups
andlearnfromeachothersotheircombinedcollaborativeachievementsurpassesthesimplesumof
individualcontributions[29]. AsDamonandPhelpsclearlystate,thisisstructurallydifferentfrom
cooperativelearning,whichreferstodiscretepracticesandconceptssuchasspecificroleassignments
inagroupandgoalrelatedliabilityofbothmembersandthegroup,sothateachstudentisresponsible
fortheentireconcludingresult[23]. Curtisdiscussesthatcooperativelearningmostlydealswithtasks
thataredivisibleintomoreorlessindependentsubtasks,wherecooperatingpartiesworkinparallel
toprocessindividualsubtasksinanautonomous,independentway[28]asopposedtocollaborative
learningwhereasharedsolutiontoaproblemisbuiltsimultaneously,collectivelyandinliaisonwith
allmembersofthegroup.
Group collaboration can take a variety of forms and has been investigated in a broad range
of contexts, including classroom-based learning [30], computer-based learning [31], web-based and
e-learning[32].Whatthesecollaborations,however,haveincommonisthattwoormorelearnersinteract
inasynchronousformtonegotiatesharedmeaningandjointlyandcontinuouslysolveproblems[26].
Sincelearningmathematicscanoftenbeviewedasalonely,individualisticorcompetitivematter,
withstudentsdevelopingmathematicalanxietyoravoidance,collaborativeandcooperativelearning
throughgroupworkcanaddresstheseproblemsandenhancestudents’progressandachievements[33].
Groupworkinteractionhelpsallmemberslearnconceptsandproblemsolvingstrategies,improve
self-confidenceandovercomethefearofmistakes[6,14,34]. Mathematicsdoesofferopportunities
forcreativethinking,exploringopenendedquestions,andposingintriguingproblems,andgroup
workcanhelptofacethesetrialsanddifficulttasksthatarewellbeyondthecapacitiesofindividual
work at that developmental phase. Group work can also be a convenient and helpful tool to help
developasupportiveattitudetowardslearning. InastudybyBernero,thestudentswhostruggled
withmathematicscontinuedtostressandstrainaboutitandbecamediscouragedwithindividual
work,butimprovedbothacademicallyandsociallywhenitcametogroupwork,duetoanincreasein
self-assurance[34].
Groupwork,however,canalsosometimesleadtounsuccessfuloperation,mainlyduetoalack
of understanding of the important elements that arbitrate its effectiveness. Group efforts can be
unproductiveinmanyaspects. Forinstance,lesscapablemembersofthegroupcansometimesleave
it to others to accomplish and conclude the group’s exercises [35], whereas more capable student
membersmightputinlessefforttoavoiddoingallthework[35]. Theamountoftimespentexplaining
conceptscanbepositivelycorrelatedwiththeamountoftimelearning,somorecapablemembers
mightlearnagreatdealbyprovidingdetailedexplanationsofthetaughtmaterialtolessablestudents
strugglingtocomprehendasacaptiveaudience[35].
Educ.Sci.2016,6,30 4of15
The educator plays a vital role in the effective running of group work. During group work,
the educator should act ‘both as an academic expert and as a classroom manager’ [20], be able to
specify the academic objectives and aims of the lesson, make instructional decisions, and explain
the task clearly defining the assignment goals [25]. There are different grading models available
forassessinggroupwork. Someassesstheendproductonly, whileothersassessboththeprocess
andthefinaloutcome. Thegradingcanbeconductedentirelybytheeducatorsorbythestudents
usingaformofpeerassessment. Thebenefitsofpeerassessmentforstudentlearninghavebeenwell
documented[36,37]. Anotheroptionisfortheeducatortoawardanoverallmarkfortheendproduct
whereeachindividualgroupmemberhasascaledgradeaccordingtotheirlevelofcontributionas
determinedbytheirpeersorlecturer,ensuringthatallgradingmustalignwiththelearningoutcomes
forthemodule[38].
3. Methodology
ThisinvestigationwascarriedoutduringtutorialtimetofirstyearCivilEngineeringstudents,
undertakingaMathematicsmoduleintheirsecondsemester.Thegroupworksessionswereconducted
overfourweekstothewholeclass,whilststudyingthespecifictopicofIntegration. Theremaining
tutorialsessionsofthesecondsemesterinvolvedpracticalexercisesintheoutstandingchaptersof
thesyllabus,withstudentsattemptingtheseinanindividualisticmanner. Previousexperiencehas
led to the opinion that students find Integration the most challenging and difficult to understand
topicwithinthewholesyllabus. Asaresult,selectingthischapterseemedtobesuitableinorderto
demonstratethepotentialeffectivenessofgroupworkinenhancingthestudentslearningexperience.
Thetutorialsessionshadasteadyattendanceof23students,ofwhich4werefemale. Noneofthe
studentssurveyedhadbeeninagroupworkenvironmentinMathematicsbefore,buthavehadthis
formoflearningexperienceintheirothermodules.Allthestudentswhoattendedagreedtoparticipate
inthisresearch.
3.1. GroupWorkSetup
Group work was conducted whilst studying the Integration chapter, over four weeks during
onehourtutorialsessionswhichrantwiceperweek,andthefollowingmaterialrelatingtoIntegration
wascovered:
• Week1: IntegrationbySubstitution;
• Week2: IntegrationbyParts;
• Week3: IntegrationusingPartialFractiondecomposition;
• Week4: ApplicationsofIntegrationintheCivilEngineeringfield.
Forthisinvestigation,theeducatorprovidedavitalroleintheeffectiverunningofgroupwork
in mathematics. The lecturer was able to specify the academic objectives and aims of the session,
make instructional decisions (such as size group, how long groups should stay together, student
assignmentroles)andclarifythetaskclearlydefiningtheassignmentgoals.
Studentswerepairedupingroups,makingsurethateachgroupconsistedofamixtureofcalibers
ofstudents,inotherwords,weakerandstrongerstudentswerearrangedtoworktogether,butnever
agroupconsistingsolelyofweakstudents. Theproblemsthatthestudentshadtotackleintheirgroup
workwerebasedonthetheorytaughtinlecture,andwereeitherprovidedbythelecturerorsetbythe
actualgroupmembers.Thelatterwasamorecomplexchallengeforthestudents,astheyhadtothink
andproduce,withintheirgroups,suitableandworkableproblemsthatwerethengiventootherfellow
groupsforthemtotackle.Thegroupworkinteractionwasattimescollaborativebutalsocooperativein
nature,withstudentstacklingandworkingtogetheronthesameproblemoronspecificroleassignments.
Forinstance,studentswereaskedintheirrespectivegroupstoconsideracurveoftheirchoice,
whichhadtoconsistofaproductoffunctions,beabletoplotitonaCartesianplaneeithermanually
oremployinggraphicalsoftwaretools,andthen,byapplyingtheintegrationtechniqueslearntduring
Educ.Sci.2016,6,30 5of15
thelectures,theremainingtaskwastodeterminetheareaoftheregionboundedbythecurveand
theaxisorbythecurveandstraightlinesoftheirchoice. Inthisproblem,eachgroupmemberwas
assignedaroletofulfill,workingcooperatively,butsimultaneouslyeachstudentwasresponsiblefor
theconcludingsolution.
Duringtheintervention,theroleofeachgroupmemberwasobservedbythelecturer,makingsure
thattherewassufficientcollaborationandcooperationandthateachstudentcontributedequallytothe
finaloutcome. Theeducatorprovidedguidanceandsupportduringgroupworkactivities,observed
thegroupinteractionandstudentengagement,gavehintsorclarifications,providedencouragement,
drewmembersintothediscussion,behavedinafriendlyandconstructivemanner,managedtobalance
toomuchortoolittleassistanceandintervenedwhennecessaryinafacilitativewayinordertoenable
successfulcompletionofthetaskbythegroup.
Uponcompletionoftheproblems,theresultswerehandedbacktotheteamwhichhadposedthe
taskinitially,orsimplytoanotherfellowgroup,inordertomarkandprovideappropriatefeedbackto
theirpeers. Inthisway,notonlywerestudentsdeepeningtheirunderstandingofthetheorywiththe
helpoftheirclassmates,buttheywerealsolearningtocommunicate,todeliberate,toassessandto
improvetheirmistakesaccordingly.
In order to investigate the effectiveness of group work in mathematics, a more detailed and
substantialquantitativeapproachwasemployedusingtwosetsoflevel4classes,whereallstudents
hadengineering-basedbackgrounds. Forclarificationpurposes,thecohortwhichwasengagedin
group work shall be referred to as the Experimental class and the other class which had no group
work involvement during the semester shall be considered as the Control class. To benefit from
accurate and feasible conclusions on the effectiveness of group work, an indirect approach was
accomplishedbycomparingthesetwoclasses. Morespecifically,intheExperimentalclass,onlythe
teachingandlearningonIntegrationwasdeliveredintheformofgroupworkduringtutorialtime,
whereastheremainingsyllabuswascoveredundernormallearningarrangements. Thecontrolclass,
whichconsistedof16students,hadtheirteachingandlearningexperiencedeliveredundernormal
traditionalarrangementsthroughoutthewholesemester.
3.2. DataCollection
Aquestionnaire(seeAppendixA)wasadministeredontheexperienceofgroupworkduring
thesessions,aswellasaninvestigationintotheexamresultsfromtheendofsemesterexaminations.
Studentswereinvitedtoparticipateinthestudy,whichwasvoluntaryduetoethicalconsiderations
andinvolvedcompletionofquestionnaires,observationsofcollaborativeactivitywithhandwritten
observationsmadebytheeducator.ThesurveywasadministeredonlytotheExperimentalclass,withall
23studentscompletingthequestionnaires. Somequestionsrequiredopinionatedhandwrittenreplies
andtherestoftheresponsesweresoughton3-pointLikertscalesrangingfrom“Disagree”to“Agree”.
Attheendofthesemester,withtheaidoftheoutputsofthefinalexams,theperformanceofthe
studentsintheIntegrationquestionswascomparedwiththeanalogousperformanceofthestudents
intherestoftheassessedquestions(Integrationvs. Restofexaminablequestions). Thisdifferencein
performancebetweenthequestionsintheExperimentalclasswasadditionallylaterthencompared
withthecorrespondingdifferenceinperformanceofthestudentsintheControlClass.
TheIntegrationquestionswithintheendofyearexaminationsforeachcohort,theExperimental
and the Control Class, had a different percentage weighting, specifically 60% of the exam from
the Experimental Class had Integration questions assigned to it, whereas the examination for the
Control Class had 50% of Integration examinable material. When regarding the performance of
studentsinIntegrationquestionscomparedtotheirperformanceoftherestoftheassessedquestions,
thisweightingwastakenintoconsideration. Thus,notonlywasthestudent’sperformanceonthe
integrationtopicassessedrelativetotherestofthesyllabusfortheclasswithgroupworklearning,
butalsoacomparisonwasmadewiththeanalogousperformanceofstudentsnotexperiencinggroup
work from another cohort, the control class. Hence, any difference in the level of difficulty of the
Educ.Sci.2016,6,30 6of15
Integrationquestionswithrespecttotherestofthequestionsintheexamandanydissimilaritiesin
theaEcdaucd. Secmi. 2i0c1c6,a 6p, 3a0b ilitiesandstrengthsofthestudentsofthetwocohortsweretakenintoac6c oof u15n tin
theanalysis.
the academic capabilities and strengths of the students of the two cohorts were taken into account in
In this context the authors employed, as a tool to measure the effectiveness of group work,
the analysis.
the ratio of student performance on integration questions relative to their performance in the
In this context the authors employed, as a tool to measure the effectiveness of group work, the
remainingquestions,andfromhereonafterthisratioshallbeconsideredastheperformanceratio.
ratio of student performance on integration questions relative to their performance in the remaining
Thisperformanceratioshallbeusedasanindicatortoevaluatetheeffectivenessofgroupworking.
questions, and from here on after this ratio shall be considered as the performance ratio. This
Theauthorssuggestthatthisratiobecalculatedbyexaminingthequotientofstudent’sperformance
performance ratio shall be used as an indicator to evaluate the effectiveness of group working. The
inindividualintegrationquestionsovertheremainingexamquestionsrespectively.
authors suggest that this ratio be calculated by examining the quotient of student’s performance in
individual integration questions over the remaining exam questions respectively.
Total%marks from Integrationquestions
Performanceratio =
Performanceratio= TotalT%otmala%rksmfarrokms tfhroemReIsnttoegfrtahteioqnueqsutieosntsioinnstheexam
Total %marks fromthe Restof thequestionsintheexam
Forexample,intheExperimentalClass,arandomlyselectedstudentmanagedtoaccumulate
44outofthe60marksthatrelatetotheIntegrationtopic,henceapproximately73.3%((44/60)×100)
For example, in the Experimental Class, a randomly selected student managed to accumulate 44
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indimcaatorkr,s tfhroemp ethrfeo rremsta onfc teher aqtuioesftoiorntsh iins sthpee ceixfiacms. tAupdpelnytinwga tshe1 .s8u3g(g7e3s.t3e%d /p4er0f%or)m. ance indicator, the
pIetrmfourmstabnecen roatteido ffoorr tehlius csipdeactiifoicn sptuudrepnots wesatsh 1a.8t3a (p7e3r.3fo%r/m40a%n)c.e ratiovaluegreaterthan1.0indicates
that a stuItd menutstp ebref onromteedd fbore tetelurciindatthioeni nptuergproasteios nthsaetc tai opnerofofrtmheanecxea mraticoo mvapluaer egdretaotetrh ethraens t1o.0f the
indicates that a student performed better in the integration section of the exam compared to the rest
questionsintheexampaper,duetothevalueofthenumeratoroftheperformanceratioquotientbeing
of the questions in the exam paper, due to the value of the numerator of the performance ratio
greaterthanthedenominatorvalue.
quotient being greater than the denominator value.
4. ResultsandDiscussion
4. Results and Discussion
4.1. QualitativeAnalysis: DiscussionoftheFindingsfromtheQuestionnaireSurvey
4.1. Qualitative Analysis: Discussion of the Findings from the Questionnaire Survey
TheevaluationsurveyfilledinbyallstudentsoftheExperimentalclassisthemainsourceof
The evaluation survey filled in by all students of the Experimental class is the main source of
feedback examined as the qualitative analysis section of this project. The results of the first three
feedback examined as the qualitative analysis section of this project. The results of the first three
questionsofthesurvey,whichrequiredindividualcommentsofopinion,havebeensummarisedand
questions of the survey, which required individual comments of opinion, have been summarised and
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Figure 1. Student responses to Q1–3 of the Questionnaire (see Appendix A).
Figure1.StudentresponsestoQ1–3oftheQuestionnaire(seeAppendixA).
Educ.Sci.2016,6,30 7of15
Educ. Sci. 2016, 6, 30 7 of 15
From these responses, it is deduced that in general students perceive mathematics as a difficult,
Fromtheseresponses,itisdeducedthatingeneralstudentsperceivemathematicsasadifficult,
challenging and yet rewarding subject, with all students agreeing that their group work experience
challengingandyetrewardingsubject,withallstudentsagreeingthattheirgroupworkexperience
in this hard module has been helpful and enjoyable. More detailed individual comments are that
in this hard module has been helpful and enjoyable. More detailed individual comments are that
group work was found to be constructive, deepening the student’s understanding of Integration. The
group work was found to be constructive, deepening the student’s understanding of Integration.
majority of the participants believe that working in groups positively affected the way they learn
Themajorityoftheparticipantsbelievethatworkingingroupspositivelyaffectedthewaytheylearn
mathematics and allowed them to develop their critical thinking and analytical skills.
mathematicsandallowedthemtodeveloptheircriticalthinkingandanalyticalskills. Acknowledging
Acknowledging that group work allows for collaboration between classmates, it strengthened their
thatgroupworkallowsforcollaborationbetweenclassmates,itstrengthenedtheirconfidenceinthe
confidence in the subject, and it served as another learning approach to reinforce their mathematical
subject,anditservedasanotherlearningapproachtoreinforcetheirmathematicalknowledge.
knowledge.
Aspartoftheopinionedresponses,acoupleofstudentsdidmentionafewpossibleforeseeable
As part of the opinioned responses, a couple of students did mention a few possible foreseeable
drawbacks of working in groups, namely that it can slow down the lesson and that this form of
drawbacks of working in groups, namely that it can slow down the lesson and that this form of
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ofeQffueecstitvioenne4ssin oft hQeuqeusteisotnio 4n inna tihree. questionnaire.
An unexpected outcome of this specific question is that only a few students (4 out of the 23
An unexpected outcome of this specific question is that only a few students (4 out of the
students) consider teaching mathematics to be more effective when it uses technology. In this era,
23students)considerteachingmathematicstobemoreeffectivewhenitusestechnology.Inthisera,
with the current advancements in technology, it can only be assumed that students would perhaps
withthecurrentadvancementsintechnology,itcanonlybeassumedthatstudentswouldperhapsexpect
expect or demand the teaching delivery to be more updated and in compliance with the changing
ordemandtheteachingdeliverytobemoreupdatedandincompliancewiththechangingtechnological
technological improvements. However, based upon these responses, it seems that students do not
improvements.However,basedupontheseresponses,itseemsthatstudentsdonotconsideritnecessary
consider it necessary for mathematics to conform to a more technological method of delivering
formathematicstoconformtoamoretechnologicalmethodofdeliveringeffectiveteaching.
effective teaching.
Educ.Sci.2016,6,30 8of15
Educ. Sci. 2016, 6, 30 8 of 15
FFigiguurree 33 ddeeppiiccttss uussiinngg aa bbaar rchcahratr, ta,na nanaanlyasliyss oisf tohfet LhiekeLritk secratles cdaaletad oaft taheo fqtuheestqiounensatiioren. nTahiree .
Tshigensiifgincaifinct acnotnccolunscilounssi ohnesreh aerree tahraett thhaet mthaejomriatyjo orift ystuofdsetnutds eangtrseea gthreaet tthheayt tlheaerynl efraormn fwroomrkwinogr aksi nag
agsraougpro, ubepl,iebveel itehvaet tghraotupgr wouoprkw iso ar kgoisoda igdoeoad, eindjeoay,eedn tjaokyiendg tpaakritn ign pgarortupin wgororku panwd othrkinakn tdhatth ainllk
thgarotuapll mgreomupbemrse wmebreer sgiwveenre agni veeqnuaaln oepqpuoarltuonpiptyo rttou cnoitnytrtiobuctoen ttori bthuet efitnoatl hoeufitcnoamleo uotfc othme egorofuthpe
garoctuivpitayc.t ivity.

Figure 3. Bar chart showing the number of students responding to the Likert scale questions in
Figure 3. Bar chart showing the number of students responding to the Likert scale questions in
the questionnaire.
thequestionnaire.
Most students also seem to be indifferent to the issue that group work allows some students to
Most students also seem to be indifferent to the issue that group work allows some students
be free riders, or that they learn more by being in a group as opposed to working individually.
to be free riders, or that they learn more by being in a group as opposed to working individually.
Additionally, taking into account the educators’ views of group work for this intervention, it can be
Additionally,takingintoaccounttheeducators’viewsofgroupworkforthisintervention,itcanbe
assumed that group work becomes useful for social reasons as well as the positive effects on learning
amssautmheemdathtiacts.g Irto wuapsw noortekdb tehcaotm leeasrnuisnegfu wlfitohrinso gcriaolurpesa shoenlpseads two eimllpasrotvhee sptousditeinvtes’e affteticttusdoen tolewaranrdinsg
mmaaththeemmaatitcicss. Iatnwda sanllootwededt htahtel esatrrnuignggliwngit hsitnudgeronutsp stoh eglpete dovtoeri mthperiorv eansxtuiedteyn tasb’oauttti ttuhdee stouwbjeacrdt. s
mMatohreemovaetric, sthainsd waallyo wofe ldeathrneinstgr usgegemlinegd sttou dbeen mtsotroe gfeutno avnedr tehnejioryaanbxliee tfyora bleoaurntethrse asussbijsetcint.gM thoermeo vtoe r,
thleisarwn atyhroofulgeahr dniisncgussesieomne idnsttoeabde omf omreemfuonriasnadtioenn jdouyaribnlge fmoratlheaermnaetriscsa slessisstoinngs. themtolearnthrough
discussioninsteadofmemorisationduringmathematicslessons.
4.2. Quantitative Analysis: Findings from the Data Retrieved from the End-of-Year Examinations
4.2. QuantitativeAnalysis: FindingsfromtheDataRetrievedfromtheEnd-of-YearExaminations
The end-of-year mathematics examination results for the respective semesters were retrieved
and Tohuetpenudts- owf-eyreea rgmatahtehreemd aitnic soredxearm tion aetxiotrnapreoslualttes ifnotretrheestrinesgp eacntdiv evasleumaebslete rcsonwceluresiroentrsi efvoerd thanisd
oruetspeuartschw setruedgya. tThoe rdeedteirnmoirndee wrthoetehxetrr agprooluapte winotrekr ewstaisn egffaencdtivvea liun atbhlee lceoanrncilnugsi oofn msfaotrhtehmisatriecsse, athrceh
stmuadiyn. oTbojedcteivteer mofi nthee winhveetshteigragtiroonu, pit wwoarsk nwecaessseafrfye cttoiv bee ianbtlhe etol eparrondinugceo afnm eamthpeirmicaatli cinsd, itchaetomr atoin
oabijde citni vtheios fatnhaelyisnivs.e Estxiagmatiinoinn,gi tewacahs sntuedceesnsta’sr ypetorfobremaabnlecet oraptiroo d(ruecfeera tno seemctpioirnic 3a.l2 itnod rieccaatlol rhtoowa itdhiisn
thraistiaon walayss iisn.dEivxaidmuianlilny gcaelaccuhlastteudd)e innt ’bsoptehr ftohrem Eaxnpceerirmateiont(arle faenrdt othsee cCtioonntr3o.2l tcolarsesceasl,l thhoew fotlhloiswriantgio
waavserinagdeiv piderufaolrlmyacanlcceu rlaattieods) winerbeo dthertihveedE,x appeprirmoxeinmtaalteadn dtot htherCeeo dnetrcoimlcalla spsleasc,etsh: e followingaverage
performanceratioswerederived,approximatedtothreedecimalplaces:
Average Performance Ratio for the Experimental Class (with group work) = 1.807
AveragePerformanceRatiofortheExperimentalClass(withgroupwork) = 1.807
Average Performance Ratio for the Control Class (no group work) = 0.863
Educ.Sci.2016,6,30 9of15
Educ. Sci. 2016, 6, 30 9 of 15
These average performance ratios show that students working in groups performed better in the
AveragePerformanceRatiofortheControlClass(nogroupwork) = 0.863
integration-related questions compared to the class which did not have any group work
arrTanhgeesemeanvtesr. aTghee pdeartfao arnmaalynscies irnadtiicoastessh tohwat twhhaetns tsutuddeennttss wwoorrkkeindg ini ngrgoruopusp tshepire rpfeorrfmoremdanbceett er
(1.807−0.863)
initnh tehein itnetgergartaitoionn-r reelalatteedd qquueessttiioonnss icmopmropvaerde dbyto artohuencdl a1s0s9%w h(ich did not hav×e1a0n0y=g1r0o9u.p4%w)o rk
arrangements. Thedataanalysisindicatesthatwhenstudentsworked0in.8g6r3oupstheirperformancein
thecoinmtepgarraetdio tno trhelea pteedrfqorumesatniocne soifm thper ostvueddenbtys athroaut natdte1n0d9e%d (a( 1n.8o0r7m−a0.l8 6c3la)s×s e1n0v0ir=on1m09e.n4t%. )comparedto
0.863
theperFfoigrmuraen 4c ebeolfowth eillsutustdraetnetss tthhea pteartftoernmdeadncae nraotrimo oafl cthlaes sstuendvenirtosn tmhaetn att.tended the experimental
class (blue) against this of the students that attended the control class (red). The ratios present the
Figure4belowillustratestheperformanceratioofthestudentsthatattendedtheexperimental
individual students’ performances and are displayed in increasing performance value. It must be
class(blue)againstthisofthestudentsthatattendedthecontrolclass(red). Theratiospresentthe
noted that as the cohort numbers of these classes were different, specifically 23 students for the
individualstudents’performancesandaredisplayedinincreasingperformancevalue.Itmustbenoted
experimental class and 16 for the control class, the upper and lower end values of the performance
thatasthecohortnumbersoftheseclassesweredifferent,specifically23studentsfortheexperimental
ratios have been truncated in order to provide a more realizable, feasible and longitudinal
classand16forthecontrolclass,theupperandlowerendvaluesoftheperformanceratioshavebeen
comparison.
truncatedinordertoprovideamorerealizable,feasibleandlongitudinalcomparison.
Performance Ratio: IntegrationVs Rest of the examquestions
2.5
2.0
o
Rati1.5
e
c
n
a
m
r
o1.0
f
r
e
P
Experimental Class Performance Ratio
Integration Vs Rest of Questions
0.5
Control Class Performance Ratio Integration Vs
Rest of Questions
0.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Students

FigFuigruer4e. 4E. xEpxepreirmimenentatlala annddC Coonnttrrooll ccllaassss ppeerrffoorrmmaannccee rraattiiooss oof fInIntetgegrartaitoino nquqeusetisotinosn csocmopmapreadre tdo tthoet he
resrteostf othf teheex eaxmaminianbalbeleq uquesetsitoionnssa aggaaininsstt tthhee rreessppeeccttiivvee nnuummbbeerr ooff ssttuuddeenntst.s .
The analysis of these results indicate that, throughout the spectrum, the performance ratio
Theanalysisoftheseresultsindicatethat,throughoutthespectrum,theperformanceratiovalues
values of students learning integration in the experimental class were always higher than those of the
ofstudentslearningintegrationintheexperimentalclasswerealwayshigherthanthoseofthestudents
students of the control class, as can be seen by the blue line always having an upward trend above
ofthecontrolclass,ascanbeseenbythebluelinealwayshavinganupwardtrendabovetheredline.
the red line. Hence, this figure clearly portrays and supports the benefits of group work on the topic
Heonfc ien,tethgirsatfiiognu.r e clearlyportraysandsupportsthebenefitsofgroupworkonthetopicofintegration.
Figure5belowpresentsthepercentageofstudentsthatperformedbetterintheIntegrationtopic
Figure 5 below presents the percentage of students that performed better in the Integration topic
comcopmapraerdedto tot hthee rreesstt ooff ththee quqeusetsiotinosn isn tinhet ehxeamex faomr efaocrh eclaacshs. cRleacsasl.l tRheact aal pletrhfaotrmaapnecref orartmioa gnrceeatrear tio
grethaatenr 1t.h0 ainnd1i.c0atiensd ai cbaettetsera pbeerftotermr panercfeo irnm thane cinetiengrtahteioinn steegctriaotnio onf tsheec teixoanmo. fTthhee reexsuamlts. sThohwe rtehsaut lts
showwhetnh asttuwdhenetns swtuodrkeendt sinw gorrokuepds i4n7.g8r%o uopf sth4e7 .c8l%asso afcthhieevcelads sbeatctehri emvaerdkbs eintt eInrtmegarraktisoinn (I1n1t eogurt aotfi on
(11thoeu 2t3o pfethrfeor2m3apnecref orarmtioasn wceerrea tgiroesawtere rtheagnr ethaete vratlhuaen 1)t hwehvilasltu oen1ly) 3w7h.5i%ls toof nthlye s3t7u.5d%entosf ptherefosrtmudeedn ts
pebrfeotrtemr eidn binettetegrraitnioinn tweghreanti ownowrkhinegn iwn onrokrimngali nclnaossr mararlacnlgaesmsaernrtasn (g6e omuet notfs t(h6eo 1u6t sotfutdheen1ts6).s tTuhdeesne ts).
Thpeesrecpenertacgenest aaglseos hailgsohlhigighht tlihgeh etftfhiceieenfcfiyc ioefn gcryouopf gwroourkp iwn toerakchinintge amchatihnegmmaatitchse. m atics.
Educ. Sci. 2016, 6, 30 10 of 15
EdEudc.uSc.c Si.c2i.0 21061,66, ,63, 030 10 1o0f 1o5f 15

Figure5. PercentageofstudentsperformingbetterinIntegrationquestionsvs. therestoftheexam
FFiigguurree 55.. PPeerrcceennttaaggee ooff ssttuuddeennttss ppeerrffoorrmmiinngg bbeetttteerr iinn IInntteeggrraatitoionn q quueesstitoionns sv vs.s .t hthe er ersets to fo ft hteh ee xeaxmam
questionsforboththeExperimentalandControlclass.
qquueessttiioonnss ffoorr bbootthh tthhee EExxppeerriimmeennttaall aanndd CCoonnttrrooll ccllaassss. .
Figure6presentstheaverageresultachievedbystudentsinintegrationquestionswithrespect
FFiigguurree 66 pprreesseennttss tthhee aavveerraaggee rreessuulltt aacchhiieevveedd bbyy ssttuuddeennttss i nin i ninteteggraratitoionn q quuesetsitoionns sw witiht hr ersepsepcetc t
tottoot h ttehhede didfififefffreeerrneentntrt arrnaanngggeeeo oofffo oovvveeerarraallllllp ppeeerrrffofoorrrmmmaaannnccceee iiinnn ttthhheee eeexxxaaammm.. . SSStttuuudddeeennntsttss w wweeererree c cclulluustssettreeerrdeed di niin np pepreefrroffroomrrmmanaacnnecc ee
cacctaaettgeegogoroirreiiesesso ovovevererr2 2020%0%%i niinntetteerrrvvvaaalsllss... SSStttuuudddeeennntttsss wwweeerrreee aaarrrrrraaannngggeeeddd iininn ttthhheeessseee c ccaaatettegeggooorirreiiese ssi niin no orodrrdedree rtr otto oa saasssessseesss sgs rggorruoopuu pp
wwowrookrrkek f eeffefffceetccitvtiievvneenenseesssssf o ffororrt htthheeed ddifiifffeffeererreennnttta aacccaaadddeeemmmiicicc s ssttrtrreeennngggtththh l leleevvveeelllsss oo offf tt hthheee s ssttutuudddeeennnttsts.s ..

FiFgiugruere6 .6T. Thheea vaveeraraggeer reessuulltt ((%%)) aacchhiieevveedd bbyy ssttuuddeennttss iinn iinntteeggrraatitoionn qquuesetsitoinosn swwithit hrersepsepcet ctto ttohteh e
Figure 6. The average result (%) achieved by students in integration questions with respect to the
didffieffreernetnrta rnagnegeo foof voverearlalllp peerfroforrmmaanncceei inn tthhee eexxaamm ffoorr bbootthh tthhee EExxppeerriimmeenntatal laanndd CCoonntrtorol cllcalsass.s .
different range of overall performance in the exam for both the Experimental and Control class.
The results illustrate the beneficial effect of group work for almost all student categories. For
TThheer reessuultltss iilllluussttrraattee tthhee bbeenneefificciaial lefeffefcetc tofo gfrgoruopu wpowrko rfkor faolrmaolsmt oasllt satulldsetnutd ceantetgcoartieegs.o Frioers .
example, students achieving a final result between 60% and 80% in their exam presented an average
Foexraemxapmlep, lset,usdtuednetsn atschaciehvieinvgin ag fainfianl arlerseuslut lbtebtewtweeene n606%0% anadn d808%0% inin ththeieri reexxaamm ppreresseenntetedd aann aavveerraaggee
mark of 70.2% in the integration section when working in groups. In the Control class this percentage
mmarakrko fof7 07.02.2%%i nint htheei ninteteggrraatitoionns seeccttiioonnw whheenn wwoorrkkiinngg iinn ggrroouuppss.. IInn tthhee CCoonnttrrooll ccllaassss tthhiiss ppeerrcceennttaaggee
corresponded to 64%. This trend was similar throughout the performance categories and emphasises
cocrorrersepspononddededt oto6 644%%..T Thhisist trreennddw waass ssiimmiillaarr tthhrroouugghhoouutt tthhee ppeerrffoorrmmaannccee ccaatteeggoorriieess aanndd eemmpphhaassiisseess
the effectiveness of group work in mathematics for this study.
thtehee feffefcetcitvivenenesessso offg grorouuppw woorkrki ninm maaththeemmaatticicssf foorrt thhiiss ssttuuddyy..