Motivation and Ability as Factors in Mathematics Experience and Achievement
Author(s): Ulrich Schiefele and Mihaly Csikszentmihalyi
Source: Journal for Research in Mathematics Education, Vol. 26, No. 2 (Mar., 1995), pp. 163181
Published by: National Council of Teachers of Mathematics
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Journalfor Researchin MathematicsEducation
1995, Vol. 26, No. 2, 163-181
MOTIVATIONAND ABILITYAS FACTORSIN
MATHEMATICSEXPERIENCEAND
ACHIEVEMENT
ULRICHSCHIEFELE,Universityof the Bundeswehr,Munich
MIHALY CSIKSZENTMIHALYI,The Universityof Chicago
This studyexaminedrelationshipsamonginterest,achievementmotivation,mathematicalability, the qualityof experiencewhen doingmathematics,andmathematicsachievement.One hundredeightfreshmenandsophomores(41 males,67 females)completedinterestratings,an achievementmotivationquestionnaire,andthe PreliminaryScholasticAptitudeTest. These assessments
were followed by 1 week of experiencesampling.Mathematicsgradeswere availablefrom the
year before the study started,from the same year, and from the following 3 years. In addition,
a measureof the students'course level in mathematicswas included.The results showed that
quality of experience when doing mathematicswas mainly related to interest. Grades and
course level were most stronglypredictedby level of ability. Interestwas found to contribute
significantlyto the predictionof gradesfor the secondyear andto the predictionof courselevel.
Qualityof experiencewas significantlycorrelatedwith gradesbut not course level.
In light of the prominentrole of mathematicsamong subjectmattersin school
thatmucheducationalandpsychologicalresearch
(e.g.,Jones,1988),it is notsurprising
has been devotedto the identificationof factorsthatenhancethe learningandteaching of mathematics (e.g., Grouws, 1992). Extensive research (see reviews by
Reynolds & Walberg, 1991; Steinkamp& Maehr, 1983) has led to the identification of threemajorgroupsof factorsinfluencingachievementin mathematics,as
well as in other subjects:studentcharacteristics(e.g., use of learningstrategies),
home environment(e.g., occupationof parents),and school context (e.g., quality
of instruction).The majorityof studiesconfirmthatcognitivestudentcharacteristics
explaina largepartof the observedvariancein achievement.Motivationalandemotional factors, such as attitude, anxiety, interest, or task motivation (McLeod,
1990), were often foundto be less important(Aiken, 1970, 1976;Schneider& B6s,
1985; Steinkamp& Maehr, 1983; Willson, 1983).
Although the modest impact of motivation and emotion on mathematics
achievement seems well supported,it would not be justifiable to neglect affective variables (McLeod, 1990; McLeod & Adams, 1989). Thereareseveralreasons for giving thesevariablesa crucialrole in explainingdifferencesin mathematics
achievement.The firstreasonhas to do with the magnitudeof explainedvariance.
Although cognitive predictorswere usually found to explain large amounts of
This researchwas supportedby a grantfrom the SpencerFoundationto the second author.
The opinions expressed are our own and do not reflect the positions or policies of the
SpencerFoundation.The writingof this articlewas madepossible in partby a grantfrom the
Deutsche Forschungsgemeinschaftto the first author. We thank Kevin Rathunde, Sam
Whalen, and MariaWong for theirhelp in analyzingthe data.
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164
MathematicsExperienceand Achievement
variance (up to 50%) in achievement,detailedanalyses showed thatthe variance
explainedby cognitive factorsis reducedto 25%when motivationalvariablesare
held constantby statisticalmeans (Schneider& BOs,1985). Second, the impactof
affective variables is often underestimatedbecause they tend to have indirect
ratherthan direct effects on achievement (Meece, Wigfield, & Eccles, 1990;
Reynolds & Walberg,1991; Schneider& Bbis,1985). For example,Reynolds and
Walberg(1991) found thatmotivationinfluencedscience achievementonly indirectlythroughamountof out-of-schoolreadingandengagementin schoolwork.Third,
a numberof findings suggest thatproblemsolving, creativity,and deep comprehension of learningmaterialrequirehigh levels of positive emotions andintrinsic
motivation(Csikszentmihalyi,1988b;McLeod, 1990; McLeod & Adams, 1989;
Schiefele, 1992). Fourth, there is evidence for a decreasing trend in average
mathematicsperformance(especially on tasks thatrequirea deep understanding
of mathematics), accompanied by a significant decline of students' interest in
mathematics during the course of high school (e.g., Jones, 1988; Reynolds &
Walberg, 1992). Many recommendationsto overcome the deficit in mathematics
achievementstressthe importanceof institutingchangesto facilitatestudents'interest (see Jones, 1988, p. 329). This implies a need for investigating more intenprocesses.
sively the emotionalandmotivationaldynamicsof achievement-related
These considerationshave importantimplicationsfor research.First,cognitive
predictors,such as mathematicalability, should be complementedby motivationalpredictorsin orderto reacha more completeunderstandingof mathematics
achievement.In doing so, differentmotivationalconcepts shouldbe comparedto
identifythose most conduciveto the learningof mathematics.Second, the quality
of affectiveexperiencewhilebeingengagedin learningmathematicsshouldbe investigatedas an outcomemeasurein its own right.As mentionedabove,positive feelto students'creativity,
capacity,anddeepcomprehension.
problem-solving
ingscontribute
Furthermore,the qualityof experienceduringlearningis a crucialfactorfor future
motivation to learn (Csikszentmihalyi & Nakamura, 1989; Csikszentmihalyi,
Rathunde,& Whalen, 1993; Matsumoto& Sanders,1988).
The presentstudy was concernedwith both the issues outlinedabove. In addition to mathematicalability,two differentmotivationalvariableswere includedas
predictorsin the presentstudy:interestin mathematicsand achievementmotivation. Both variablesare consideredimportantfactorsin explainingdifferencesin
schoolachievement
(e.g.,Aiken,1970,1976;Eccles,1983;Schiefele,Krapp,& Winteler,
motivational
a subject-matter-specific
factor,whereasachieve1992).Interestrepresents
ment motivationcan be regardedas a more generalmotivationalorientationthat
capturesa student'smotivationto performwell withoutspecifyinga particularsubject area(e.g., Brophy, 1983). We speakof interestwhen a studentattributeshigh
value to a particularsubjectarea(Schiefele, 1991).
Althoughpriorstudieshave investigatedrelationsbetween cognitive andmotivationalpredictorsandaffective outcomemeasures,such as self-esteem, satisfaction,attitude,anxiety,andotherspecificemotions(e.g., Matsumoto& Sanders,1988;
Meece et al., 1990;Reynolds& Walberg,1992;Ryan,Connell,& Deci, 1985),there
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Ulrich Schiefele and Mihaly Csikszentmihalyi
165
is a neglectof indicatorsthatmeasuresubjectiveexperiencesof studentsbeingengaged
in mathematicsin naturalsettings. In the presentstudy, the qualityof experience
in mathematics
classeswasassessedduring1 weekby meansof theExperience
Sampling
Method (describedlater).
Quality of experience is a multidimensionalconstruct that consists of emotional,motivational,andcognitiveaspectsof experience(Csikszentmihalyi,1988a).
The core dimensionsof this constructincludeaffect (happy,cheerful,etc.), potency
(alert, active, etc.), cognitive efficiency (concentration,self-consciousness,etc.),
andintrinsicmotivation(wishto do the activity,involvement,etc.) (Csikszentmihalyi
& Larson,1987).Dependingon thedomainunderstudy(e.g.,sports,leisure,or school),
additional dimensions addressing unique aspects of experience not shared by
other domains may be assessed (e.g., the experience of risk when climbing a
mountain).Because qualityof experienceis regardedhere as an outcomemeasure
in its own right, we examinedwhetherqualityof experiencein mathematicsclass
is relatedto interest,achievementmotivation,andmathematicalability.In addition,
the relationbetween qualityof experienceand achievementwas explored.
The empiricalevidence came from a large-scalelongitudinalstudyconductedat
the Universityof Chicago(Csikszentmihalyiet al., 1993). The studywas begunin
1985 andwas designedto tracethe developmentof talentedstudentsover a period
of 4 years.A wide arrayof measuringinstruments,includingpersonalitytests,questionnaires,interviews,andexperiencesampling,were applied.Forpurposesof the
presentstudy only a partof the originalmeasureswas analyzed.
The issues we have discussedso far lead to the following researchquestionsthat
are addressedin this article:(a) Is qualityof experiencewhen doing mathematics
more dependenton abilityor motivationalcharacteristics?(b) Are subject-matterspecificmeasuresof motivationmorepredictiveof experienceandachievementthan
generalmeasuresof motivation?(c) Do motivationalcharacteristicsandqualityof
experiencewhendoingmathematics
predictachievementin mathematics
independently
of ability?
On the basis of theoreticalconsiderationsand empiricalevidence, the following
hypotheseswere derived:(a) Ability is a betterpredictorof the qualityof experience in mathematicsclass andachievementthaneitherinterestor achievementmotiwithpriorresearch(e.g.,Meeceet al., 1990;Reynolds& Walberg,
vation.In accordance
we
assumed
that
1992),
ability factors are the most powerfulpredictorsof affective experienceand cognitive performancein achievementsettings. (b) Interestis
a better predictorof quality of experience and achievement than achievement
motivation.This hypothesisis basedon the assumptionthatsubject-matter-specific
variables are more predictive of affective and cognitive outcomes than more
globalvariables(e.g., Gottfried,1985).(c) Bothinterestandachievementmotivation
predict quality of experience and achievement independently of ability. Prior
researchhas shown thatmotivationalvariablescan predictemotionalandachievementoutcomesindependentlyof abilityfactors(e.g., Meece et al., 1990;Schneider
& BOs, 1985).
The presentstudywas not designed explicitly to investigategenderdifferences.
However,becausepriorresearch(e.g.,Hyde,Fennema,& Lamon,1990;Hyde,Fennema,
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MathematicsExperienceand Achievement
166
Ryan, Frost, & Hopp, 1990; Jones, 1988) has repeatedlyfound significantdifferences betweenboys andgirlswithrespectto mathematicalability,achievement,and
motivation,analyses of genderdifferenceswere included.
METHOD
Overview
The following section providesinformationon the presentsample,independent
anddependentmeasures,the procedure,and specific featuresof the dataanalyses.
Independentvariableswere interestin mathematics,achievementmotivation,and
mathematicalability.Dependentvariableswerequalityof experiencein mathematics
class (components:potency,affect,concentration,intrinsicmotivation,self-esteem,
importance,perceivedskill) andmathematicsachievement(grades,courselevel).
Sample
The sampleconsistedof 108 freshmenand sophomoresfrom two Chicago suburbanhigh schools.The majorityof participants
camefromwhitemiddle-classfamilies. About38%of the samplewas male (n = 41; 17 freshmen,24 sophomores)and
62% was female (n = 67; 24 freshmen,43 sophomores).All studentswere nominatedby teachersas beingtalentedin one or moreof five subjectmatters:mathematics,
science,music, art,and athletics.Seventy-onepercentof the sample was selected
as talentedin one areaonly, whereas29%had multipletalents.Altogether,37 students(34%)werenominatedin mathematics,30 (28%)in science,43 (40%)in music,
14 (13%) in art, and 31 (29%) in athletics.In mathematics,12 boys and 25 girls
were nominated.
The sample of the present study is a subgroupof a largernumberof students
(n = 228) who completed the experience sampling procedurein different classrooms. The presentsample is made up only of those studentswho providedmeasures for all of the following variables:experiencein mathematicsclass, interest
in mathematics,achievementmotivation,mathematicalability, and mathematics
grades(at least for one of the includedfive school years).
IndependentMeasures
Interestin Mathematics
As partof a largerquestionnaireon backgroundvariables(e.g., life-events), the
studentswere askedto indicate,using five-pointratingscales, the extent to which
mathematicsis their favorite subject area ("Mathematicsis my favorite subject:
not at all, a little, somewhat, very, extremely").These ratingswere used as indicatorsof interestin mathematics.In a priorstudy (Schiefele & Csikszentmihalyi,
1994) it was shown thatthis measureof interestcorrelatespositively with intrinsic learninggoals and negativelywith extrinsiclearninggoals, suggestingthatthis
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Ulrich Schiefele and Mihaly Csikszentmihalyi
167
single-itemmeasureof interestis valid. In addition,interestwas foundto be uncorrelated with gradepoint average (GPA), achievementmotivation,and scholastic
aptitude(PSAT).
AchievementMotivation
Different definitions of achievement motivation as an individual difference
variablehavebeenputforwardin thepast(cf. Heckhausen,1991;McClelland,1987).
Most of these definitionsdefine achievementmotivationas a preferencefor high
standardsof performanceor as the willingnessto workhardandpersistentlyto reach
these standards.Two subscalesfromthePersonalityResearchForm(PRF,Jackson,
were used to generatea measure
1984), namely "Achievement"and "Endurance,"
of achievementmotivationbecausethey capturevery well the meaningof priordefinitions.The Achievementsubscalemeasuresthe preferencefor high standardsof
performanceand the willingness to invest intensive effort in one's work. The
Endurancesubscaletaps the level of persistencea personshows when workingon
a task.Both scales have provedto be reliableandvalid predictorsof academicsuccess (e.g., Clarke, 1973; Harper,1975; Jackson, 1984).
Individualvalues of achievementmotivationwere computedby averagingthe
Achievement and Endurancesubscales (each contains 16 items). The decision to
combine the subscales into a single indicator of achievement motivation was
based on theirhigh intercorrelation(r = .74, p < .01; see also Jackson, 1984) and
the fact thatpriorfactoranalyses have shown thatthey have high loadings on the
samefactor(Jackson,1984).Forthe combinedachievementmotivationscale a coefficient alphaof .84 was obtained.
MathematicalAbility
Mathematicalability was measuredby means of the mathematicssubtestof the
PreliminaryScholastic AptitudeTest (PSAT). The PSAT is a widely appliedtest
of scholasticaptitudeespecially designedfor high school sophomoresandjuniors.
It is composedof two parts:mathematics
(PSAT-M)andverbal(PSAT-V).ThePSATM requires examinees to apply basic mathematicalreasoning skills. Specific
knowledge of mathematicalsubjectmatterpast elementaryalgebraand geometry
is notnecessary(Becker,1990).ThePSATis a reliablepredictorof academicachievement. In the presentstudy a correlationof .53 (p < .01) between PSAT and GPA
was obtained.Most of the studentstook the PSAT duringtheir sophomoreyear.
Althoughit seems legitimateto use PSAT-Mscoresas indicatorsof ability,a certain extent of overlap(thatcannotbe attributedto abilityfactors)between PSATM andmeasuresof achievementis to be expected.Separatingabilityand achievement is difficult in a domainwhere people have received formaltraining(Carroll
& Horn, 1981).
DependentMeasures
Qualityof Experience
This section is divided into three parts: (a) description of the Experience
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168
MathematicsExperienceand Achievement
SamplingMethodas used in the presentstudy,(b) selectionof relevantdimensions
of the qualityof experience,and (c) informationon the reliabilityof the experience
samplingmeasures.
Experience Sampling Method. Quality of experience was assessed with the
& Larson,1987).TheESM
ExperienceSamplingMethod(ESM)(Csikszentmihalyi
allows the repeatedmeasurementof everydayactivities,thoughts,andexperience
in the naturalenvironment.It consists of providing respondentswith an electronicpageranda blockof self-report
formswithopen-endedandscaleditems.Usually,
respondentswearthe pagerfor a week andarepagedabout55 timesatrandomintervals from 7 a.m. until 10 p.m. Wheneverthe respondentis signaled,he or she fills
out a page of the booklet,indicatingactivity,location,andcompanionship,as well
as describingthe qualityof the experienceat the time on a varietyof dimensions.
Detailedinformationon the validityof theESM is summarizedby Csikszentmihalyi
andLarson(1987). Forexample,priorstudieshave shownthatESM reportsof psychologicalstatescovaryin expectedways with physiologicalmeasuresandthatthe
ESM differentiatesbetween groupsexpected to be different(e.g., patientor nonpatientgroups).
In the presentstudy, studentscarriedelectronicpagersfor 1 week (7 days) and
answeredquestionson the ExperienceSamplingForm(ESF) wheneverthey were
signaled. Seven to nine signals per day were received by every student.The ESF
in the presentversionconsists of seven open-endedquestionsand29 items (a copy
of theESFusedherecanbe foundin Csikszentmihalyi
& Larson,1987).Open-ended
questions(e.g., "Whatwere you thinkingabout?")were not analyzedin the present
study. The items were eitherwrittenin a seven-pointsemanticdifferentialformat
(13 items) or in a ten-pointunipolarformat(16 items). They measurea few basic
dimensionsof experienceas well as a numberof single aspects of experience.
Studentswhose protocolscontainedfewer than15 ESFs for the whole week were
not included.This was truefor 20 out of 228 students.Only those formscompleted
within30 minutesafterthesignalwereaccepted.Generally,70%of theESFswerefilled
out immediatelyafterthe signaland88%werecompletedwithin5 minutesof thesigTheaveragereportedlatencybetween
nal.Lessthan1%of allESFshadto be discarded.
receivingthe beepersignalandbeginningto fill out the ESF was 2.5 minutes.
For the whole week duringwhich the ESM was conducted,the averagenumber
of completedESFs per studentwas 35.64 (SD = 10.06, range:15-63).' Duringregular class time (includingmathematics),an averageof 11.26 (SD = 4.79, range:
3-29) completedESFs was obtained.In mathematicsclass, a total of 231 signals
were available,with an averageof 2.14 signalsper student(SD = 1.14, range:1-5).
The signals obtainedin mathematicsclass formthe databasis of the presentstudy.
'Thisvalue is considerablylowerthanthe numberof signalsreceivedby each student(about55). This
is due to the fact that thereare many situationsin which filling out an ESF is very hardfor objective
or subjectivereasons. These situationsinclude, for example, driving a car, writingan exam, or being
involved in an interestingdiscussion with a close friend.
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Ulrich Schiefele and Mihaly Csikszentmihalyi
169
Dimensions of experience. For purposes of the present study, we analyzed
only those items or dimensionsthatcapturedrelevantaspectsof the qualityof experience in learning situations. As a consequence, we decided not to consider
items measuring,for example, social aspects of experience(e.g., lonely-sociable,
cooperative-competitive)or physical aspects(e.g., feelings of pain or discomfort).
In accordance with prior studies (see Csikszentmihaly & Larson, 1987;
et al., 1993),thefollowingdimen& LeFevre,1989;Csikszentmihaly
Csikszentmihaly
sions were included: potency, affect, concentration,intrinsic motivation, selfesteem, importance, and perceived skill. The correspondence between these
dimensions and individualitems is based on priorstudies that used factor analyses to classify the variousESF ratingscales (see Csikszentmihaly& Larson,1987).
As can be seen in Table 1, some dimensionsare measuredby single items, others
by two or more items. Zero-ordercorrelationsrevealedthatitems were highly correlatedwithindimensions(withrs rangingfrom.50 to .83, mediancorrelation= .62).
Relationsbetweendimensionsprovedto be less strong(with rs rangingfrom .06
to .55, mediancorrelation= .28). For those dimensionsmeasuredby two or more
items, mean values were computedfor each student.
In contrastto prioranalyses,no scalefor"cognitiveefficiency"was includedbecause
"Wasit hardto conthe correspondingitems ("Howwell were you concentrating?"
not
correlated.
were
centrate?"clear-confused)
Instead,we decided
significantly
This
of
concentration.
item seemed to
item
for
amount
include
the
to
asking
only
be most appropriateto capturethe meaningof cognitive efficiency.
Table 1
Classificationof ExperienceSamplingVariables
Items
Dimensions of Experience
Describe your mood as you were beeped:activePotency
passive, strong-weak,alert-drowsy,excited-bored
Describe your mood as you were beeped:happy-sad,
Affect
cheerful-irritable
How well were you concentrating?
Concentration
Do you wish you had been doing somethingelse?
IntrinsicMotivation
Were you living up to your own expectations?Were
Self-Esteem
you satisfied with how you were doing? Were you
succeeding at what you were doing?
How importantwas this activity in relationto your
Importance
overall goals? Was this activity importantto you?
How were your skills in the activity?
Skill
Note. Bipolaritems were ratedon 7-point semanticdifferentialscales. Unipolaritems were ratedon
10-pointscales.
Reliabilityof experiencesamplingmeasures.To estimatethereliabilityof theESM,
Csikszentmihalyiand Larson(1987) comparedthe means of various dimensions
of experienceobtainedin the first half of the week with those obtainedin the second half. They foundonly small andnonsignificantdifferencesbetweenmeanvalcorrelationsbetweenmeansin the firstandthe secondhalf of the
ues. Furthermore,
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MathematicsExperienceand Achievement
170
week were all significant.The mediancorrelationcoefficient rangedfrom .60 for
adolescentsto .74 for adults.Even over a 2-year periodthe stabilityof responses
rangedfrom r = .45 to r = .75.
Because of the relativelysmallnumberof "beeps"on which individualscoresof
subjectiveexperiencewere based in the presentstudy,it seemed necessaryto provide evidence for the reliabilityof these scores. Since the majorityof subjects(n =
71) providedtwo or more ESFs, it was possible to comparevalues takenat different times of the week. Forthose studentswho filled out exactly two ESFs, the values obtainedat Time 1 were comparedwith thoseobtainedat Time 2. Forthose students who had availablethreeor moreESFs, composite scores were calculatedto
arriveat two differentmeasuresfor each dimensionof experience.For example,
in the case of studentswith five ESFs, the values of the first and second ESF and
the values of the third,fourth,andfifth ESF were aggregated.The resultingmeans
were comparedto one another.
First of all, the reliabilityanalysis revealedno significant(p < .10) differences
betweenmeansat Time 1 andTime 2 for any ESM variables.Second, correlations
between ratingsat Time 1 andTime 2 were all significantand rangedfrom .44 to
.64, with a mean correlationof .52. The size of the mean correlationis almost as
high as thatreportedby CsikszentmihalyiandLarson(1987) for adolescents(.60).
MathematicsAchievement
Semestergradeswere used as an indicatorof mathematicsachievement.Grades
were available for the school years 1984/85, 1985/86, 1986/87, 1987/88, and
1988/89. However, not all studentsprovidedgradesfor all 5 years. This is partly
due to the fact thatthe sampleconsisted of studentsfrom two differentgradelevels andthatmathematicscoursesin highergradesarenot compulsory.The sample
sizes were: 1984/85:n = 67; 1985/86:n = 108; 1986/87:n = 106; 1987/88:n = 90;
and 1988/89: n = 35.
It is importantto note thatfor 1985/86 we includedonly gradesfrom the second
semester.Because interestratingstook place duringthe first and second semester
of the academicyear 1985/86, it is only for gradesfrom the second semesterthat
we areableto claima predictiverelationbetweeninterestandachievement.Forabout
half of the subjects(n = 50) interestwas measuredduringthe first semesterandfor
the remainingsubjects(n = 58) duringthe second semester.
An importantfeatureof the presentstudy is its use of course level as a measure
of performance
(cf. Eccles, 1983;Maple& Stage,1991;Meeceet al., 1990).To determine individualcourselevels, the highestlevel of coursestakenby the end of high
school was assessed for each student.Therewas a wide arrayof differentcourse
levels. In 1987/88,for example,studentstook coursesthatrangedfromplanegeometry to AdvancedPlacementcalculus. On the basis of carefulcontentanalyses of
the schools' mathematicscurriculaa rankorderof the final mathematicscourses
takenby the studentswas derived.Rankvaluesrangedfrom 1 to 17 (see Appendix).
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Ulrich Schiefele and Mihaly Csikszentmihalyi
171
Procedure
Each studentwas scheduled to meet with a memberof the researchstaff three
to four times in an office at the school. During the first meeting, the use of the
pager and items in the ESF were explained. In addition, the achievement motivation test was administeredalong with a questionnaireincludingthe interestrating described above.
The ESFs wereboundin smallpads(5.5 in. x 8.5 in.), eachconsistingof 15 forms.
One week afterthe firstmeeting,the pagingprocedurestarted.The firstday of paging was alwaysa weekday.Thereweresevento ninerandomsignalsperday,between
7 a.m. and 10 p.m. on SundaythroughThursday,9 a.m. and 12 p.m. on Fridayand
Saturday.On weekdaystwice as many signals were sent before 3 p.m., in orderto
get a morerepresentativesampleof the classes the studentstook. Immediatelyafter
every signal the studentshad to fill out one ESF.
After completingthe ESFs for 1 week, the studentsreturnedfor a second meeting. Duringthis meetingthey were debriefedandaskedto describetheirexperience
duringthe week andthe problemsthey had with the pager.The ESM datawere collected over a nine-monthperiod (October,1985 to June, 1986).
Data Analysis
All analyses were carriedout at the subjectlevel (i.e., using the individualstudentas the unitof analysis).Therefore,aggregatedscoresfor all ESF variableswere
computedfor each student.As a consequence,it seemedunnecessaryto use z-scores
as is usuallyrecommendedfor beep-levelanalyses(Larson& Delespaul,1990).Data
correlationcoefficients
were analyzedmainlyby meansof Pearsonproduct-moment
andmultipleregressionanalyses.Pearsonproduct-momentcorrelationswere used
to demonstrate
the strengthof the associationbetweenpredictorsandcriteria.Multiple
regressionanalysesservedto assess the uniquecontributionof each predictorto the
predictionof dependentvariables.
Because of the largenumberof significancetests conducted,a proceduredevelopedby Holm(1979) was appliedto controlforTypeI errorrate.Accordingto Holm,
in orderto generateadjustedlevels of alpha,p values shouldbe rankedaccording
to their size. Then the smallestp is tested againstalphasof .05/k or .01/k (k being
the totalnumberof testsof significance),the secondsmallestpis comparedto alphas
of .05/(k-1) or .01/(k-1), and so on. As soon as a particularp value does not reach
the adjustedlevel of significance,the procedureis aborted.Holm's methodis less
conservativethanthe sometimes appliedBonferroniinequality(Klauer,1990).
In the presentstudy, a total of 13 multipleregressionanalyses were conducted.
Fromthese 13 analyses,we obtained11 significantmultiplecorrelationcoefficients
(afterapplyingHolm's procedureto adjustalpha).In these cases, significancetests
of individualpredictorswere performed.These resultedin a total of 38 individual
tests of zero-ordercorrelationsand correspondingpartialregressioncoefficients.
Therefore,in applyingHolm's procedure,the smallestp value was tested against
alphasof .05/38 and .01/38, the second smallestp value againstalphasof .05/37
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172
MathematicsExperienceand Achievement
and .01/37, and so on. It shouldbe noted thatthe total numberof individualtests
does not include analysesthatwere performedonly for descriptiveor exploratory
reasons(e.g., intercorrelationsamongpredictorvariables).However,the adjusted
levels of significance resulting from Holm's procedurewere applied to these
analyses as well.
RESULTS
Inthissection,we firstreportdescriptivestatisticsforthekey variablesof the study.
Next,thepowerof interest,achievementmotivation,ability,andgenderto predictquality of experienceis analyzed.Finally,the samepredictors,as well as qualityof experience,arethentestedfor theircontributionsto predictgradepointsandcourselevel.
DescriptiveStatistics
Table2 reportsdescriptivestatisticsfor all variablesinvolvedin the presentstudy.
The averagePSAT-V and PSAT-M scores of the presentsamplewere well above
the 70th percentilefor college-boundjuniors. In accordancewith this result,relatively high meanvaluesfor GPA andmathematicsgradeswere obtained.The mean
score for achievementmotivationis almostexactly equivalentwith a standardized
scoreof 50, indicatingthatthepresentsamplewas notdifferentfromtheunderlying
population.No significantdifferencesbetween females and males were found.
Table 2
DescriptiveStatisticsfor all Variables
Variable
PSAT-Verbal
PSAT-Math
GPAa
AchievementMotivation
Interestin Mathematics
Qualityof Experience
Potency
Affect
Concentration
Motivation
Self-Esteem
Importance
Skill
MathematicsGradesa
1984/85
1985/86
1986/87
1987/88
1988/89
CourseLevel
Note. n = 108.
"0= failure,4 = gradeA.
Range
20-80
20-80
0-4
0-16
1-5
M
48.21
53.53
3.15
10.13
2.57
SD
9.99
11.46
.69
3.16
1.36
1-7
1-7
1-10
1-10
1-10
1-10
1-10
4.29
4.46
6.19
3.41
6.50
6.34
6.68
.97
1.10
2.03
2.46
1.87
2.20
2.06
0-4
0-4
0-4
0-4
0-4
1-17
2.99
2.94
2.95
2.82
2.96
10.70
.89
.83
.94
.95
.77
3.73
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Ulrich Schiefele and Mihaly Csikszentmihalyi
173
Studentstalentedin mathematicshad significantlyhighervaluesfor mathematics
ability,bettergradesforthe first4 years,anda highercourselevel thanthosetalented
in otherareas(see Table3). The two groupswere not differentwith respectto interest, achievementmotivation,verbalability,andqualityof experience.
Table 3
SignificantDifferencesbetweenStudentsTalentedin Mathematicsand StudentsTalentedin
OtherAreasa
TalentArea
Variable
n
37
Mathematics
M
SD
8.16
59.89
n
71
PSAT-Math
Math Grades
46
21
3.74
.38
1984/85
71
.60
37
3.42
1985/86
.71
71
37
3.43
1986/87
.71
55
35
3.26
1987/88
71
37
13.41
CourseLevel
2.39
"aDifferences
between means were significantatp < .001 (t-test, two-tailed).
Other
M
50.21
SD
11.58
2.65
2.85
2.70
2.55
9.30
.85
.87
.95
.98
3.53
Positive but nonsignificantintercorrelationsamonginterest,achievementmotivation, and mathematical ability were obtained. Specifically, the correlation
between ability and interestwas .19, between ability and achievementmotivation
.25, andbetweeninterestandachievementmotivation.07. Fromthesizeof theobtained
correlationsone can concludethatthe variouspredictorsactuallytapdifferentunderlying factors.The low correlationsobtainedbetween indicatorsof motivationand
ability are in line with priorresearchfindings (Steinkamp& Maehr, 1983).
Predictingthe Qualityof Experience
In orderto evaluatethe relationshipsbetween interest,achievementmotivation,
ability, gender, and the quality of experience in class, we performedmultiple
regressionanalyses (see Table4). Predictorswere enteredsimultaneouslyinto the
regressionequation.Interactionaltermswere not included.2
The resultsclearlyindicatethatinterestwas the strongestpredictorof qualityof
experiencein mathematicsclass. Specifically,interestshowed significantrelations
to potency,intrinsicmotivation,self-esteem,importance,andtheperceptionof skill.
Surprisingly,level of mathematicalabilitywas not relatedto experienceat all, not
even to the perceptionof skill. Although achievementmotivationexhibitedpositive relationsto all dimensionsof experience,none became significant.3
2Exploratoryanalyses did not reveal significanttwo-way interactioneffects.
3Furtheranalyses showed that the strengthof relationsbetween the predictorsand quality of experience were nearly the same for those students who had just one beep and those who had two and
more beeps.
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174
MathematicsExperienceand Achievement
AdditionalregressionanalysesrevealedthatreplacingPSAT-Mscoresby grades
for 1985/86 (both semesters) did not affect the relations between interest and
qualityof experience.4Thus, it can be concludedthatthe interest-experiencerelation was independentof the students'levels of ability and achievement.
Table 4
Regressionof Experienceon Interest,AchievementMotivation,Ability,and Gender
AchMot
Genderb
Experiencein Class
Ability
Weights"a Interest
r
.18
-.07
-.03
.33***
Potency
B
.37***
.22
-.19
.07
r
Affect
.21
-.02
-.01
.19
B
.21
-.11
.23
.07
r
Concentration
.06
.18
-.08
.11
B
.11
-.14
.23
.15
r
Motivation
.39***
.26*
.24
-.33***
B
.31**
.18
.10
-.21
r
Self-Esteem
.37***
.12
.04
-.11
B
.37***
.10
-.06
-.02
r
.25
.21
.06
.11
Importance
B
.29*
.23
-.02
.21
r
Skill
.32***
.15
.16
-.14
B
.29*
.10
.07
-.04
Note. n = 108.
*p < .10, **p < .05, ***p < .01 (adjustedsignificancelevels).
= zero-ordercorrelation,B = standardizedregressioncoefficient.
"ar
bMalewas coded as 1 and female as 2.
R
.42***
.30
.28
.51***
.38**
.38**
.35**
PredictingGrades
In the first part of the following section, we consider interest, achievement
motivation, ability, and gender as predictors of grade points in mathematics.
Second, we analyze the relationbetween qualityof experienceand achievement.
Interest,AchievementMotivation,Ability,and Genderas Predictorsof Grades
The strengthof relationsbetween the predictorsand gradesfrom three successive school years (1985/86, 1986/87, 1987/88) were tested by means of multiple
regressionanalyses(see Table5). As mentioned,1985/86gradesincludedonly grades
fromthe second semesterin orderto reducethe probabilityof achievementeffects
on interest. 1988/89 gradeswere not includedbecause only 48 studentsprovided
gradesfor thatschool year.
In accordancewith expectations,abilitywas the best predictorof grades.Interest
provedto be a moderateand significantpredictorof 1985/86 grades.
41985/86 gradeswere not significantlycorrelatedwith any dimensionof experience.
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Ulrich Schiefele and Mihaly Csikszentmihalyi
175
The causalrelationshipbetween interestand achievementcannotbe determined
with the presentdata.However,the availableevidence suggests thatinterestis not
simply an outcome of successful performance.The correlationbetween 1984/85
gradesandinterestmeasuredduringthe firstsemesterof the year 1985/86 was positive butnot significant(r = .24, n = 45)5. This resultsuggeststhatpast achievement
is not a strongpredictorof subsequentinterest.
Table 5
Regression of Achievementand CourseLevel on Interest,AchievementMotivation,Ability,
and Gender
Interest
AchMot
Weightsa
Ability
Grades
r
1985/86
.32**
.23
.56**
B
.27**
.16
.48**
(n = 108)
r
1986/87
.23
.63**
.15
B
.10
.01
.58**
(n = 106)
r
1987/88
.16
.09
.44**
B
.15
-.02
.49**
(n = 90)
r
Courselevel
.72**
.34**
.28*
B
.23*
.11
.66**
(n = 108)
Note. *p < .05, **p < .01 (adjustedsignificance levels).
ar = zero-ordercorrelation,B = standardizedregressioncoefficient.
bMalewas coded as 1 and female as 2.
Genderb
.04
.21
-.15
-.03
.08
.18
-.08
.11
R
.64**
.64**
.50**
.76**
Qualityof Experienceas a Predictorof Grades
For purposes of the present analysis all dimensions of experience were combined into a single composite score. A composite score was used here in orderto
reducethe overallnumberof statisticaltests.This scorewas computedin two steps:
(a) Individual values for all dimensions of experience (potency, affect, etc.)
were z-standardized;(b) z-standardizedvalues were then summedfor every student. The resultingcomposite value indicatesthe overall qualityof experience in
mathematicsclass. Becausewe used individualdimensionsof experienceas "items"
of a more general scale, it seemed appropriateto determinethe reliabilityof this
general scale. A reliability coefficient (alpha) of .72 was obtained.
A correlationalanalysisrevealeda positiveand significantrelationbetweenquality of experience(compositescore)and 1985/86grades(r = .29,p < .05). Wheneach
dimensionof experiencewas looked at individually,correlationsrangingfrom .02
(concentration)to .26 (perceivedskill) were found (all nonsignificant).
In orderto examine whetherthe correlationbetween qualityof experience and
gradeswas independentfrom otherpredictors,a regressionmodel was tested that
5As was notedbefore, gradesfrom the school year 1984/85 were availableonly from those students
(n = 67) who were in 10thgradewhen the studystarted.Outof this group,45 studentscompletedinterest ratingsduringthe first semesterof the subsequentyear.
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176
MathematicsExperienceand Achievement
includedqualityof experience,ability,achievementmotivation,andgenderas predictors. Interest was not included in the regression equation to avoid multicollinearity(interestandqualityof experiencewere substantiallycorrelated,r = .45,
p < .01). The resultsof the regressionanalysis showed thatqualityof experience
failed to contributesignificantlyand independentlyof otherpredictorsto the prediction of achievement(f3= .24, ns).
PredictingCourseLevel
Interest,AchievementMotivation,Ability,and Gender
as Predictorsof CourseLevel
A regressionanalysisincludinginterest,achievementmotivation,ability,andgender as predictorswas performed.In accordancewith expectations,the results(see
Table5) confirmedthatabilitywas the strongestpredictorof courselevel. In addition, interest,but not achievementmotivation,contributedsignificantlyand independentlyof ability to the predictionof course level.
Qualityof Experienceas a Predictorof CourseLevel
A correlationalanalysis revealed that quality of experience was not significantly related to course level. The correlationbetween the composite measure
of experience and the level of courses amountedto .17 (ns). Also, no significant
correlations between individual dimensions of experience and course level
were obtained.
DISCUSSION
The resultsof the presentstudy suggest thatqualityof experienceand achievement in mathematics depend on different factors. Quality of experience in
mathematicsclass was mainly relatedto interestin mathematicsand, to a lesser
extent, to achievementmotivation.Inconsistentwith our hypothesis, ability was
not at all correlatedwith experience. Even feelings of self-esteem, concentration, or skill seemed to be unaffected by ability.
Achievement, however, was most strongly related to level of mathematical
ability. Interest could also account for a significant, though small, portion of
achievementvariance.Thiswas,however,only trueforgradesfromthe secondsemesterof 1985/86.The size of the correlationobtainedbetweeninterestandgrades(.32)
is in accordancewith resultsof a recentlyconductedmeta-analysison the relation
betweenmeasuresof subjectmatterinterestandachievement(Schiefeleet al., 1992),
where an averagecorrelationcoefficient of .31 was found.
In ourview, qualityof experiencein class is an outcomevariablein its own right.
Even if researchdoes not revealsignificantrelationsbetweenqualityof experience
andacademicperformance,positive affect shouldbe amongthose criteriaused for
evaluating instructional techniques and variables of the school environment.
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Ulrich Schiefele and Mihaly Csikszentmihalyi
177
However,given the empiricallyconfirmedimpactof intrinsicmotivationon meaningfulor conceptuallearning(e.g., Ryanet al., 1985), it is likely thataffectivestates
arecrucialfor achieving success in school. By definition,intrinsicmotivationis a
form of motivationthatis directedat activitiesthatareinherentlyenjoyable,interesting, or challenging(Csikszentmihalyi& Nakamura,1989;Deci & Ryan, 1985).
Therefore,it seems reasonableto assumethatintrinsicmotivationcan only be maintainedas long as learningactivitiesleadto a certainlevel of positiveemotionalexperience. Indeed, the presentresults show thatinterest(which can be regardedas a
proximalantecedentof intrinsicmotivation;see Schiefele, 1991) and experience
are significantlyrelated.In contrast,abilitywas not at all predictiveof experience.
This is an importantfindingbecause it underlinesthe independentand significant
role affective variablespossibly play for learningmathematicsin school.
Thepositiverelationbetweeninterestandachievementis corroborated
by theanalysis of courselevel. Ourresultssuggestthatinterestin mathematics,measuredat the
beginning of high school, is a significantand independentpredictorof how far a
studenthas progressedby the end of school. Althoughinterestwas not able to predict grades(which may be seen as quantitativeindicatorsof mathematicalknowledge or skills) acquired in a particularcourse in subsequent years (1986/87,
1987/88;see Table5), it contributedsignificantlyandindependentlyof mathematical
abilityto the predictionof the qualitativelevel of mathematicalproficiencystudents
attemptedto master.Similarresultswere reportedby Maple and Stage (1991) and
Meece and her colleagues (1990), who used causal modeling techniques.Maple
and Stage found thatattitudetowardmathematicssignificantlyinfluencedchoice
of mathematicsmajorbut not grades.Meece andher colleagues obtainedfor task
value (a measuresimilarto interest)a strongereffect on course enrollmentintentions than grades.
In addition,the results of our study supportthe hypothesisthat subject-matterspecificmotivationalmeasuresaremorepredictiveof experience-andachievementrelatedvariablespertainingto a particularsubjectareathan generalmotivational
orientations.Specifically,interestin mathematics,butnot achievementmotivation,
provedto be a significantpredictorof experiencein class, grades,andcourselevel.
Theseresultspointto the needto investigatemorethoroughlythe content-specificity
characteristics
of motivational
(e.g.,Gottfried,1985)andtheirrelationto generalmotives
of behavior.
Ourfindings are in line with the assertionthat interestand achievementmutually influenceone another.On the one hand,a positive,thoughnonsignificant,correlation(.24) was foundbetweenlevel of achievementin 1984/85 and interestthat
was measuredduringthe followingschoolyear(1985/86).On the otherhand,a positive andsignificantcorrelation(.32)emergedbetweeninterestandgradesfromthe second semester of 1985/86. Recently, a number of studies and reviews have
addressedthe problemof causal relationsbetween affect and achievement (e.g.,
Reynolds& Walberg,1991; Steinkamp& Maehr,1983; Willson, 1983). Although
thereis some disagreementaboutwhich variablepossesses moreweight,the majority of authorsconclude that affect and achievement influence one another.In a
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178
MathematicsExperienceand Achievement
meta-analysisof relevantresearch,Willson (1983) foundthatthe relationbetween
affect and scienceachievementchangeswith age or gradelevel. Duringearlystages
of schooling, affect is determinedby achievement, whereas later achievement
becomes more and more dependenton affect. A similar result was obtainedby
Helmke (1990) with respect to the relationof self-concept of ability to achievement in mathematics.On the basis of these studies,one would expect thatfor 9thor 10th-gradestudentsinterestis a betterpredictorof achievementthanachievement is of interest. It is precisely this result that we have obtained in our study.
However, despite the evidence emerging from different sources, one should
bearin mindthattherealnatureof theinterest-achievement
relationhasto be explored
by causal analyses of longitudinaldata.
SUGGESTIONSFOR FUTURERESEARCH
A numberof suggestionsfor futureresearchensue fromthe presentstudy.First,
the interestmeasureused in the study(as well as in otherstudies,e.g., Feather,1988)
was basedon a single item.Althoughwe haveprovidedsome evidencefor its validity, it seems desirablefor futurestudies to include a more differentiatedand reliable measurethattriesto capturea student'sinterestin a certainsubjectareamore
directly (Schiefele, 1991). Second, since grades are problematicindicators of
achievement(especially with respectto theirreliability),a replicationof the present resultsis recommendedby using carefullyconstructedtests of mathematical
knowledge. Third, generalizationof the present results is limited because the
sampleused in our studywas composedof high-abilitystudents.Therefore,a replication of the presentstudy is warrantedwith a samplethat is more representative
of the averagestudent.Fourth,we were not able to disentanglethe causalrelations
betweeninterestandachievement.Accordingto suggestionsby Helmke(1990), an
adequate causal analysis would require conducting a longitudinal study that
includesat least threewaves. Fifth,Meece andher colleagues (1990) have shown
that ability perceptionshave a strongimpacton value perceptions(such as interest). Therefore,futureresearchshouldincludenot only test-basedindicatorsof ability, but also measuresof perceived competenceor ability. Sixth, a furtherimportanttask for futurestudies would be the explorationof variablesthatmediatethe
Forinstance,as researchby Pintrich
positiverelationbetweeninterestandachievement.
andDe Groot(1990) suggests,use of learningstrategiesplays a crucialrole in mediatingthe effect of motivationalvariableson grades.Seventh,the applicationof the
ESM couldbe improvedin two ways. First,theESM shouldbe used duringa longer
periodof timethanin the presentstudy.Second,the ESM shouldnot only be applied
to in-school but also to out-of-school learningsituations.Thus, a more complete
pictureof the qualityof experienceduringlearningmathematicswould emerge.
Weiss (1990) recentlyfoundthatmathematicsteachersof all gradesmost heavily
emphasizeas instructionalobjectives"tohave studentslearnmathematicalfactsand
principlesandto havethemdevelopa systematicapproachto problemsolving"(Weiss,
1990, p. 151). However,havingthe studentsbecome interestedin mathematicsand
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Ulrich Schiefele and Mihaly Csikszentmihalyi
179
in dailylife wereamong
havingthembecomeawareof theimportanceof mathematics
the least emphasized objectives of senior high school teachers. The most preferredinstructionalactivitiesof seniorhigh school teachersarelecture,discussion,
and seatwork assigned from the textbook. The least preferredactivities are use
of hands-onor manipulativematerial,use of computers,workingin small groups,
and completingsupplementalworksheets.These facts confirmthatthe usual way
of teaching mathematicsin high school is not apt to increase students'interestin
the subject.Thepresentstudysuggeststhatincreasingstudents'interestin mathematics
mayresultin higherqualityof experiencewhile doingmathematicsandin higherlevels of achievementandknowledge.Therefore,educatorsshouldbe encouragedto
focus more stronglyon facilitatinginterest.As pointedout by Weiss (1990), this
cannot be accomplished by increasingthe teachers' qualification as mathematicians; rather,the teachers' "inappropriatevision of the mission of mathematics
educationseems to be a much more serious andpervasiveproblem"(p. 154). If a
higherlevel of interestis desired,then instructionshouldinvolve more active and
student-centered
activities,suchas mathematicslaboratoryactivitiesor mathematics
projects.In addition,learningaboutthe applicationof mathematicsconceptsin the
real world could facilitateincreasedinterestin the subject(see also Meece et al.,
1990, p. 69), which in turn should lead to higher levels of involvement and
achievementin mathematics.
REFERENCES
Aiken, L. R. (1970). Nonintellectivevariablesandmathematicsachievement:Directionsfor research.
Journal of School Psychology, 8, 28-36.
Aiken, L. R. (1976). Updateon attitudesand otheraffective variablesin learningmathematics.Review
of EducationalResearch,46, 293-311.
Becker,B. J. (1990). Itemcharacteristicsandgenderdifferenceson the SAT-M for mathematicallyable
youths.AmericanEducationalResearchJournal, 27, 65-87.
Brophy,J. (1983). Conceptualizingstudentmotivation.EducationalPsychologist, 18, 200-215.
Carroll,J. B., & Horn,J. L. (1981). On the scientificbasis of abilitytesting.AmericanPsychologist,36,
1012-1020.
Clarke,D. E. (1973).Measuresof achievementandaffiliationmotivation.Reviewof EducationalResearch,
43, 41-51.
Csikszentmihalyi,M. (1988a). The flow experienceand its significancefor humanpsychology. In M.
Csikszentmihalyi& I. S. Csikszentmihalyi(Eds.),Optimalexperience(pp. 15-35). Cambridge,MA:
CambridgeUniversityPress.
Csikszentmihalyi,M. (1988b). Motivationand creativity:Towardsa synthesisof structuraland energistic approachesto cognition. New Ideas in Psychology, 6, 159-176.
Csikszentmihalyi,M., & Larson,R. (1987). Validityandreliabilityof the experience-samplingmethod.
TheJournal of Nervous and MentalDisease, 175, 526-536.
Csikszentmihalyi,M., & LeFevre, J. (1989). Optimal experience in work and leisure. Journal of
Personality and Social Psychology, 56, 815-822.
Csikszentmihalyi,M., & Nakamura,J. (1989). The dynamicsof intrinsicmotivation:A study of adolescents.In C. Ames & R. Ames (Eds.),Researchon motivationin education.Vol.3: Goals and cognitions (pp. 45-71). New York:Academic Press.
Csikszentmihalyi,M., Rathunde,K., & Whalen,S. (1993). Talentedteenagers.Therootsof success and
failure. Cambridge,MA: CambridgeUniversityPress.
Deci, E. L., & Ryan,R. M. (1985). Intrinsicmotivationand self-determinationin humanbehavior.New
York:PlenumPress.
This content downloaded from 128.192.114.19 on Wed, 18 Sep 2013 13:01:20 PM
All use subject to JSTOR Terms and Conditions
180
MathematicsExperienceand Achievement
Eccles,J. (Parsons).(1983).Expectancies,
values,andacademicbehaviors.InJ. T. Spence(Ed.),Achievement
and achievementmotives (pp. 75-146). San Francisco:Freeman.
Feather,N. T. (1988). Values,valences,andcourseenrollment:Testingthe roleof personalvalueswithin
an expectancy-valenceframework.Journalof EducationalPsychology, 80, 381-391.
Gottfried,A. E. (1985). Academic intrinsicmotivationin elementaryandjuniorhigh school students.
Journal of EducationalPsychology, 77, 631-645.
Grouws,D. (Ed.). (1992). Handbookof researchon mathematicsteaching and learning.New York:
Macmillan.
Harper,F. B. W. (1975). The validity of some alternativemeasurementsof achievementmotivation.
Educationaland Psychological Measurement,35, 905-909.
Heckhausen,H. (1991). Motivationand action. Berlin:Springer.
Helmke, A. (1990). Mediatingprocesses between children'sself-conceptof ability and mathematical
achievement:A longitudinalstudy. In H. Mandl,E. de Corte,N. Bennett& H. F. Friedrich(Eds.),
Learningand instruction(Vol. 2.1, pp. 537-549). Oxford:PergamonPress.
Journalof Statistics,
Holm,S. (1979).A simplesequentiallyrejectivemultipletestprocedure.Scandinavian
6, 65-70.
Hyde, J. S., Fennema,E., & Lamon,S. J. (1990). Genderdifferencesin mathematicsperformance:A
meta-analysis.Psychological Bulletin, 107, 139-155.
Hyde,J. S., Fennema,E., Ryan,M., Frost,L. A., & Hopp,C. (1990).Gendercomparisonsof mathematics
attitudesand affect. Psychology of WomenQuarterly,14, 299-324.
Jackson,D. N. (1984). Personalityresearchform manual.PortHuron,MI:ResearchPsychologistsPress.
Jones, L. V. (1988). School achievementtrendsin mathematicsand science, and what can be done to
improvethem. In E. Z. Rothkopf(Ed.), Review of Research in Education(Vol. 15, pp. 307-341).
Washington,DC: AmericanEducationalResearchAssociation.
Klauer,K. J. (1990). Uber SignifikanztestsoderWenigerist manchmalmehr [On significancetests, or
Sometimesless is more]. Psychologie in Erziehungund Unterricht,37, 131-136.
Larson, R., & Delespaul, P. (1990). Analyzing experience sampling data:A guidebook for the perplexed. In M. de Vries (Ed.), The experience of psychopathology. Cambridge,MA: Cambridge
University Press.
Maple,S. A., & Stage,F. K. (1991). Influenceson the choice of math/sciencemajorby genderandethnicity. AmericanEducationalResearchJournal,28, 37-60.
Matsumoto,D. & Sanders,M. (1988). Emotionalexperiencesduringengagementin intrinsicallyand
extrinsicallymotivatedtasks.Motivationand Emotion,12, 353-369.
McClelland,D. C. (1987). Humanmotivation.Cambridge,MA: CambridgeUniversityPress.
McLeod, D. B. (1990). Information-processingtheoriesandmathematicslearning:The role of affect.
InternationalJournalof EducationalResearch, 14, 13-29.
McLeod, D. B., & Adams, V. M. (Eds.). (1989). Affect and mathematicalproblem solving. New
York:Springer.
Meece, J. L., Wigfield,A., & Eccles, J. S. (1990). Predictorsof mathanxietyandits influenceon young
adolescents'courseenrollmentintentionsandperformancein mathematics.Journalof Educational
Psychology, 82, 60-70.
Pintrich,P. R., & De Groot,E. V. (1990). Motivationalandself-regulatedlearningcomponentsof classroom academicperformance.Journal of EducationalPsychology, 82, 33-40.
modelof scienceachievement.Journalof Educational
Reynolds,A. J.,& Walberg,H. J. (1991).A structural
Psychology, 83, 97-107.
modelof highschoolmathematicsoutcomes.Journal
Reynolds,A. J. & Walberg,H. J. (1992).A structural
of EducationalResearch,85, 150-158.
andselfRyan,R. M., Connell,J. P., & Deci, E. L. (1985). A motivationalanalysisof self-determination
regulationin education.In C. Ames & R. Ames (Eds.), Research on motivationin education. Vol.
2: Theclassroom milieu (pp. 13-51). London:AcademicPress.
Schiefele, U. (1991). Interest,learning,and motivation.EducationalPsychologist, 26, 299-323.
Schiefele, U. (1992). Topic interest and levels of text comprehension.In K. A. Renninger,S. Hidi,
& A. Krapp(Eds.), The role of interestin learning and development(pp. 151-182). Hillsdale, NJ:
LawrenceErlbaum.
This content downloaded from 128.192.114.19 on Wed, 18 Sep 2013 13:01:20 PM
All use subject to JSTOR Terms and Conditions
Ulrich Schiefele and Mihaly Csikszentmihalyi
181
M. (1994).Interestandthe qualityof experiencein classrooms.European
Schiefele,U., & Csikszentmihalyi,
Journal of Psychology of Education,9, 251-269.
Schiefele,U., Krapp,A., & Winteler,A. (1992). Interestas a predictorof academicachievement:A metaanalysis of research.In K. A. Renninger,S. Hidi, & A. Krapp(Eds.), The role of interestin learning and development(pp. 183-212). Hillsdale, NJ: LawrenceErlbaum.
Schneider, W., & Bis, K. (1985). ExploratorischeAnalysen zu Komponenten des Schulerfolgs
[Exploratoryanalysesof componentsof school achievement].ZeitschriftffirEntwicklungspsychologie
und Piidagogische Psychologie, 17, 325-340.
Steinkamp,M. W., & Maehr,M. L. (1983). Affect, ability,and scienceachievement:A quantitativesynthesis of correlationalresearch.Reviewof EducationalResearch, 53, 369-396.
Weiss, I. R. (1990). Mathematicsteachersin the United States. InternationalJournal of Educational
Research, 14, 139-155.
Willson, V. L. (1983). A meta-analysisof the relationshipbetween science achievementand science
attitude:Kindergartenthroughcollege. Journalof Research in Science Teaching,20, 839-850.
APPENDIX
Rankingof CourseLevels
Foundationsof Algebra4 .....................................
Plane Geometry 1 ..................
..........
...............2.....
Plane Geometry2 ...........................................
IntermediateAlgebra 1 .......................................
IntermediateAlgebra2 .......................................
IntermediateAlgebra 3 .......................................
IntermediateAlgebra4 .......................................
AdvancedAlgebra2 ...................
......................
1
3
4
5
6
7
7
8
8
9
10
10
Trigonometry.............................................
AdvancedAlgebra/Trigonometry1 ................
................
AdvancedAlgebra/Trigonometry2 ..............................
........................
College Algebra...................
College Algebra/Trigonometry2 ...................................
Analytic Geometry ..........................................
11
......................
ProbabilityStatistics ..................
11
AdvancedPlacementCalculusAB 1 ...............................
12
AdvancedPlacementCalculusAB 2 .............................
13
AdvancedPlacementCalculusBC 1 .................................
14
AdvancedPlacementCalculusBC 2 .............................
. 15
Advanced MathematicsTopics 1................
16
................
AdvancedMathematicsTopics 2 .............................
.......17
AUTHORS
ULRICH SCHIEFELE, Assistant Professor, FakultditfuirSozialwissenschaften, Universitditder
BundeswehrMiinchen,Werner-Heisenberg-Weg39, D-85577 Neubiberg,Germany
MIHALY CSIKSZENTMIHALYI, Professor of Psychology and of Education, Department of
Psychology, The Universityof Chicago, 5848 South UniversityAvenue, Chicago, IL 60637
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