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Intrinsic motivation and achievement in mathematics in elementary school: A longitudinal investigation of their association


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This study examined the associations between intrinsic motivation and achievement in mathematics in a sample of 1478 Canadian school-age children followed from grades 1 to 4 (age 7-10). Children self-reported their intrinsic motivation toward mathematics, whereas achievement was measured through direct assessment of mathematics abilities. Cross-lagged models showed that achievement predicted intrinsic motivation from grades 1 to 2, and from grades 2 to 4. However, intrinsic motivation did not predict achievement at any time. This developmental pattern of association was gender invariant. Contrary to the hypothesis that motivation and achievement are reciprocally associated over time, our results point to a directional association from prior achievement to subsequent intrinsic motivation. Results are discussed in light of their theoretical and practical implications.
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Intrinsic Motivation and Achievement in Mathematics in Elementary School:
A Longitudinal Investigation of Their Association
Gabrielle Garon-Carrier
School of Psychology, Universit
e Laval
Michel Boivin
School of Psychology, Universit
e Laval and Institute of
Genetic, Neurobiological, and Social Foundations of Child
Development, Tomsk State University
eric Guay
Department of Basic and Applied Education,
e Laval
Yulia Kovas
School of Psychology, Goldsmiths, University of London and
Laboratory for Cognitive Investigations and Behavioural
Genetics, Tomsk State University
Ginette Dionne
School of Psychology, Universit
e Laval
Jean-Pascal Lemelin
Department of Psychoeducation, Universit
e de Sherbrooke
Jean R. S
Department of Psychiatry, Universit
e de Montr
eal and
CHU Ste-Justine Research Center, Universit
e de Montr
Frank Vitaro
Department of Psychoeducation, Universit
e de Montr
Richard E. Tremblay
Institute of Genetic, Neurobiological, and Social Foundations of Child Development, Tomsk State University and
Department of Pediatrics and Psychology, Universit
e de Montr
eal and University College Dublin
This study examined the associations between intrinsic motivation and achievement in mathematics in a sample of
1,478 Canadian school-age children followed from Grades 1 to 4 (ages 710). Children self-reported their intrinsic
motivation toward mathematics, whereas achievement was measured through direct assessment of mathematics
abilities. Cross-lagged models showed that achievement predicted intrinsic motivation from Grades 1 to 2, and
from Grades 2 to 4. However, intrinsic motivation did not predict achievement at any time. This developmental
pattern of association was gender invariant. Contrary to the hypothesis that motivation and achievement are recip-
rocally associated over time, our results point to a directional association from prior achievement to subsequent
intrinsic motivation. Results are discussed in light of their theoretical and practical implications.
The question as to whether intrinsic motivation pre-
dicts academic achievement has attracted much
attention among education researchers and school
professionals (Reeve, 2002). Under self-determina-
tion theory (SDT), intrinsic motivation refers to
being engaged in an activity because of ones inher-
ent interest and pleasure for this activity rather than
due to external contingencies (Ryan & Deci, 2000).
It is conceptualized as a natural catalyst for learn-
ing and achievement (Gottfried, 1985, 1990; Ryan &
Deci, 2009).
This research was supported by grants from the Qu
ebec Min-
istry of Health, the Fonds Qu
ecois de la Recherche sur la
e et la Culture (FQRSC), the Social Science and Humanities
Research Council (SSHRC), the Canadian Institutes for Health
Research (CIHR), and Grant 11.G34.31.003 from the Russian Fed-
eration. Michel Boivin is supported by the Canada Research
Chair Program. We are grateful to the parents of the children
participants to the Qu
ebec Longitudinal Study of Child Develop-
ment (QLSCD). We thank the Qu
ebec Institute of Statistics, Mir-
eille Jett
e, and the GRIP staff members for data collection and
management, and Bei Feng and H
ene Paradis for assistance
with statistical analyses.
Correspondence concerning this article should be addressed to
Michel Boivin, CRC in Child Development,
Ecole de psychologie,
e Laval, Qu
ebec, Canada G1K 7P4. Electronic mail may
be sent to
[Correction added after online publication on November 9,
2015: an authors name was corrected from Jean S
Jean R. S
©2015 The Authors
Child Development ©2015 Society for Research in Child Development, Inc.
All rights reserved. 0009-3920/2016/8701-0014
DOI: 10.1111/cdev.12458
Child Development, January/February 2016, Volume 87, Number 1, Pages 165175
Intrinsic motivation and academic achievement
are seen as developmentally interlocked; intrinsic
motivation lies at the core of self-determined activity
(Ryan & Deci, 2000) and is expected to be recipro-
cally associated with achievement. According to
SDT, intrinsic motivation is driven by two cognitive
processes: (a) the degree to which individuals per-
ceive that their action fullls their need for autonomy
and (b) the degree to which they feel effective in an
activity. When the psychological needs of autonomy
and competence are satised, intrinsic motivation
and achievement are mutually reinforced; intrinsi-
cally motivated individuals will persist at the task,
and thus will be more likely to achieve. Concur-
rently, higher achievement in a given activity (i.e.,
good marks in a school subjects) promotes perceived
competence, which subsequently leads to greater
intrinsic motivation in this activity.
In this study, we focus on intrinsic motivation
for mathematics. Mathematics skills are clearly
important for overall academic and professional
achievement (Duncan et al., 2007; Organisation for
Economic and Co-operation and Development,
2010; Reyna & Brainerd, 2007). Previous research
suggests a positive association between intrinsic
motivation (sometimes indexed as math interest)
and achievement in mathematics across childhood
and adolescence (Aunola, Leskinen, & Nurmi, 2006;
Denissen, Zarrett, & Eccles, 2007; Lepper, Hender-
long Corpus, & Iyengar, 2005; Viljaranta, Lerkka-
nen, Poikkeus, Aunola, & Nurmi, 2009; Wilkins &
Ma, 2003). However, the direction of this develop-
mental association remains unclear. Consistent with
SDT, some studies have shown that intrinsic moti-
vation predicts achievement and learning behaviors
in mathematics (Areepattamannil, Freeman, & Klin-
ger, 2011; Gottfried, 1985; Murayama, Pekrun,
Lichtenfeld, & vom Hofe, 2013; Spinath, Spinath,
Harlaar, & Plomin, 2006), but others did not (Bouf-
fard, Marcoux, Vezeau, & Bordeleau, 2003; Marsh,
Trautwein, L
udtke, Koller, & Baumert, 2005). A few
other studies found that intrinsic motivation and
achievement in mathematics are reciprocally related
over time (Aunola et al., 2006; Henderlong Corpus,
McClintic-Gilbert, & Hayenga, 2009; Koller, Bau-
mert, & Schnabel, 2001; Luo, Kovas, Haworth, &
Plomin, 2011; Viljaranta et al., 2009).
In addition to appearing inconsistent, previous
ndings were also tainted by features limiting their
interpretation. First, intrinsic motivation has been
measured in various ways in past studies; while
some studies used a task-value scale in mathematics
(Aunola et al., 2006; Viljaranta et al., 2009), others
used a multidimensional scale measuring challenge-
seeking, independent mastery, and curiosity-driven
engagement (Henderlong Corpus et al., 2009; Lepper
et al., 2005). Second, most studies did not specically
test for bidirectional associations, with only a few
studies taking advantage of a longitudinal cross-
lagged design to more clearly document the direc-
tion of the association between intrinsic motivation
and achievement (Luo et al., 2011; Marsh et al., 2005;
Viljaranta et al., 2009). Specically, Marsh et al.
(2005) found evidence for bidirectional associations
between self-concept (or self-perceived ability) and
achievement in mathematics, but not for intrinsic
motivation and achievement. Bidirectional associa-
tions were found in Luo et al. (2011), but using a
combined score of intrinsic motivation and academic
self-concept items. Intrinsic motivation and academic
self-concept are clearly related (Guay et al., 2010),
but they should not be confounded as they imply
self-agency versus self-description, respectively. As
there is substantial evidence for bidirectional associa-
tions between academic self-concept and achieve-
ment (Guay, Marsh, & Boivin, 2003; Marsh et al.,
2005), the composite score may have blurred the pat-
tern of associations. Finally, Viljaranta et al. (2009)
clearly showed a bidirectional association between
intrinsic motivation and achievement, but their
study only used two data points to cover a short
developmental period within the 1st year in school.
While this period may set the stage for later intrinsic
motivation and achievement, it is also important to
document the nature of these associations in the fol-
lowing years of school. There is indeed a docu-
mented decline in intrinsic motivation for
mathematics with age (Gottfried, Fleming, & Got-
tfried, 2001; Gottfried, Marcoulides, Gottfried, Oli-
ver, & Guerin, 2007; Wigeld, Eccles, Schiefele,
Roeser, & Davis-Kean, 2006). This decline in motiva-
tion could be due to the growing challenges of math-
ematics compared to other school subjects (Smith,
2004; Stodolsky, Salk, & Glaessner, 1991). This
increased pressure to perform in mathematics, com-
bined with an improved capacity to self-evaluate
their competence with age (Boivin, Vitaro, & Gag-
non, 1992) could increase the likelihood of reciprocal
associations between intrinsic motivation and
achievement in mathematics over time.
In the present study, we followed a representative
sample of children from Grades 1 to 4 (ages 710) to
examine possible transactional associations between
intrinsic motivation and achievement in mathemat-
ics. This study aimed to overcome limitations of pre-
vious studies. First, it focused on a precise denition
of intrinsic motivation grounded in SDT theory.
Accordingly, intrinsic motivation toward mathemat-
166 Garon-Carrier et al.
ics was dened as enjoyment and interest in that
topic (Guay et al., 2010; Ryan & Deci, 2000). Second,
it used a longitudinal follow-up to conduct cross-
lagged analyses on intrinsic motivation and achieve-
ment in mathematics from school entry to Grade 4.
Third, achievement in mathematics was operational-
ized through age-
appropriate direct assessments of knowledge and
abilities, rather than by indirect measures such as
teacher assessments. Fourth, children were also
assessed on their nonverbal cognitive abilities to pre-
cisely capture, through statistical control of uid cog-
nitive skills, the association between achievement
and intrinsic motivation (Kytt
a & Lehto, 2008). On
the basis of SDT and previous research, we predicted
that intrinsic motivation and achievement toward
mathematics would be reciprocally related over time.
The study also provided a unique opportunity to
test for possible sex differences in intrinsic motiva-
tion and achievement in mathematics (Cleary &
Chen, 2009; Jacobs, Lanza, Osgood, Eccles, & Wig-
eld, 2002). Previous studies found boys to be more
intrinsically motivated toward mathematics than
girls (Guay et al., 2010). One study showed sex dif-
ferences favoring males in mathematics in the
beginning of junior high school, but no such differ-
ence in the early grades of elementary school
(Leahey & Guo, 2001). To date, few longitudinal
studies tested for the possible sex difference in both
achievement and intrinsic motivation, and in their
pattern of associations.
The Qu
ebec Longitudinal Study of Child Devel-
opment is a representative birth cohort of 2,223
children born between October 1997 and July 1998
to mothers residing in the province of Quebec,
Canada, with the exception of those born at less
than 24 weeks, at more than 42 weeks of gestation,
or living in the Far North Quebec region. Of 2,940
families initially recruited, 2,223 families partici-
pated in the study when they were 5 months old,
and 2,120 families agreed to be evaluated almost
yearly (Jett
e & Des Groseillers, 2000). Participants
were longitudinally assessed from 5 months to
15 years on various child and family characteristics.
In the province of Quebec, school attendance is
mandatory for all children up to age 16. Schooling
starts with 7 years of elementary school (generally in
the same school), that is, kindergarten (ages 56) and
Grades 16 (ages 712), and follows with 5 years of
secondary school (ages 1317), then leading to col-
lege and university. This article describes ndings
from the elementary school follow-up that took place
in Grade 1 (N=1,528; age: M=85.82 months,
SD =3.06), Grade 2 (N=1,451; age: M=8.10 years,
SD =0.26), and Grade 4 (N=1,334; age:
M=10.14 years, SD =0.26). Participating children
started school the same year. The average attrition
rate from ages 7 to 10 was 4.37% per year, although
it varied slightly across measures and analyses (be-
tween 1,323 and 1,478; see Table 1).
Achievement measures in mathematics were
individually administrated at school, or at home by
a trained research assistant. Motivation was
assessed through a questionnaire lled out by chil-
dren during a face-to-face interview.
Motivation in Mathematics
Children self-reported their intrinsic motivation
in mathematics with three items from the Elemen-
tary School Motivation Scale (Guay et al., 2010), I
like mathematics;Mathematics interest me a lot;
Table 1
Descriptive Statistics of Intrinsic Motivation and Achievement in
Mathematics by Sex
nMSDMin. Max. Mode
Intrinsic motivation in mathematics
Grade 1
Boys 702 3.22 .75 1 4 4
Girls 776 3.07 .80 1 4 4
Grade 2
Boys 698 3.14 .83 1 4 3.67
Girls 769 2.91 .89 1 4 3
Grade 4
Boys 625 3.14 .75 1 4 3.67
Girls 698 2.82 .88 1 4 3.67
Achievement in mathematics
Grade 1
Boys 697 19.88 4.03 1 27 22
Girls 764 19.56 3.82 8 27 21
Grade 2
Boys 699 13.39 4.70 0 21 17
Girls 767 12.89 4.70 1 21 18
Grade 4
Boys 630 14.76 3.66 0 20 16
Girls 698 14.82 3.18 0 20 16
Number Knowledge Test.
Canadian Achievement Test.
Motivation and Achievement in Mathematics 167
I do mathematics even when I am not obliged to
do so.Six independent experts had reviewed the
items and approved the content and response for-
mat; a conrmatory factor analysis also revealed an
adequate factor structure (Guay et al., 2010). Chil-
dren answered each item using a 4-point Likert
scale ranging from 1 (never enjoying)to4(always
enjoying) mathematics. The internal consistency of
the scale ranged from 0.75 to 0.81, from Grades 1 to
3 (Guay et al., 2010).
Achievement in Mathematics
Achievement in mathematics was measured
through a series of age-appropriate assessments in
Grades 1, 2, and 4. Two standardized instruments
were used: the Number Knowledge Test (NKT; Oka-
moto & Case, 1996) in Grade 1 and the Canadian
Achievement Test (CAT; Canadian Test Center,
1992) in Grades 2 and 4. The NKT is a reliable 27-
item test of basic arithmetic skills, such as magnitude
comparisons and counting abilities (Gersten, Clarke,
& Jordan, 2007; Gersten, Jordan, & Flojo, 2005). Its
internal consistency was a=.79. The NKT was also
signicantly associated with the CAT in Grades 2
(r=.53) and 4 (r=.47), thus supporting its validity.
The CAT measures childrens capacity to perform
arithmetic operations. Addition, subtraction, and
multiplication were assessed in Grades 2 and 4. Divi-
sion operations were only assessed in Grade 4. Chil-
dren had to choose the right answer of the four
choices within a limited time. Internal consistencies
of the CAT were a=.76 and a=.81 in Grades 2 and
4, respectively, and CAT scores were fairly stable
(r=.50) between Grades 2 and 4 (see Table 2).
General Cognitive Abilities
Nonverbal cognitive abilities were assessed dur-
ing a laboratory visit when the participants were
6 years old using the Block Design subtest of the
Wechsler Preschool and Primary Scale of Intelli-
genceRevised (WPPSIR; Wechsler, 1989). The
Block Design is highly correlated with the full
WPPSIR scale (r=.62). The scores were adjusted
for age as instructed in the test manual. As in pre-
vious research (Kuncel, Hezlett, & Ones, 2004;
Spinath et al., 2006), nonverbal cognitive abilities
were positively associated with achievement in
mathematics (r=.35 in Grade 1, r=.36 in Grade 2,
and r=.27 in Grade 4).
Missing data were examined with the MVA
module in SPSS 20.0 for Windows (SPSS, 2011).
According to Littles missing completely at ran-
dom (MCAR) test, participating children in Grade
1 did not differ from those lost due to attrition
with regard to motivation, but slightly differed on
the level of achievement in mathematics
=84.30, df =38, p=.00). A series of ttests
showed that children whose achievement scores
were missing tended to have lower mathematics
achievement and were from lower socioeconomic
background at all ages. Missing data were treated
through full information maximum likelihood
(FIML). FIML treats missing data by tting the
model to all nonmissing data for each observation.
It yields the least biased and most reliable esti-
mates (Graham, Olchowski, & Gilreath, 2007;
Peugh & Enders, 2004). All statistics reported in
this article were estimated using FIML.
We used cross-lagged structural equation mod-
eling to examine the direction of the predictive
associations between intrinsic motivation and
achievement in mathematics across Grades 1, 2,
and 4 (see Figure 1). This model assessed the sta-
bility of motivation and achievement in mathemat-
ics, as well as changes in these constructs over
time. It also controls for initial levels of motivation
and achievement in the associations. Four longitu-
dinal stability paths were estimated: two paths
linking mathematics achievement across time
(paths aand b) and two paths linking intrinsic
motivation in mathematics across time (paths c
and d). Four cross-lagged paths predicting change
over time were also estimated: two paths cap-
turing the prediction from achievement to later
intrinsic motivation (paths a1 and b1) and two
paths reecting the prediction from intrinsic moti-
vation to later achievement (paths a2 and b2).
To test our hypothesis, the cross-lagged paths
were constrained to equality (a1 =a2 and b1 =b2).
Table 2
Sample Correlation Matrix of Intrinsic Motivation (IM) and Achieve-
ment in Mathematics (AM)
1. IM Grade 1
2. IM Grade 2 .30
3. IM Grade 4 .18 .39
4. AM Grade 1 .13 .11 .15
5. AM Grade 2 .08 .11 .15 .53
6. AM Grade 4 .11 .10 .22 .47 .50
Note. All coefcients are signicant at p<.01. Concurrent corre-
lations between measures are indicated in boldface.
168 Garon-Carrier et al.
A nondeterioration of the model t would suggest
equal reciprocal associations between intrinsic
motivation and achievement in mathematics,
whereas a deterioration of the model t would
suggest that one direction is more predictive than
the other.
We also tested the sex invariance in the associa-
tions between achievement and intrinsic motivation,
as well as the measurement invariance of intrinsic
motivation across time. The models were tested
with Mplus 7.11 (Muth
en & Muth
en, 19982012). In
all models, we controlled for nonverbal cognitive
abilities in time-specic scores of achievement in
mathematics, and included the correlated unique-
ness estimates specic to matching items of intrinsic
motivation in Grades 1, 2, and 4 (Marsh et al.,
Descriptive statistics are presented in Table 1. The
mean statistic of the intrinsic motivation scores sug-
gests an overall decrease in the level of intrinsic
motivation in mathematics for both boys and girls.
Trends in Motivation
To test whether intrinsic motivation signicantly
decreased across age and sex, a 3 (time) 92 (sex)
repeated measures analysis of variance (ANOVA)
was performed. The Sex 9Time interaction was sta-
tistically signicant, F(1.98, 2,385.46) =5.66, p<.01,
=.005. Boys showed a signicantly higher level of
intrinsic motivation than girls at all ages (ps<.01).
Girlsmotivation signicantly decreased from
Grades 1 to 2, but not from Grades 2 to 4 (p>.05). A
3 (time) 92 (sex) repeated measures ANOVA also
tested for sex difference in mathematics achievement.
The Sex 9Time interaction was statistically signi-
cant, F(1.97, 2,329.13) =4.23, p<.05, g
=.004. Boys
performed signicantly better than girls in Grades 1
and 2 (ps<.05), but not in Grade 4 (p>.05). How-
ever, for both intrinsic motivation and achievement,
the effect sizes indicate that these sex differences
account for a small percentage of the variance.
Grade 2
Grade 4
Grade 1
Grade 2
Grade 4
Grade 1
Q1 Q2 Q3 Q1 Q2 Q3 Q1 Q2 Q3
L2 + − ×
L1 + − × ÷
Figure 1. Cross-lagged model of achievement and intrinsic motivation in mathematics. Achievement in mathematics was measured by
the Number Knowledge Test in Grade 1 and the Canadian Achievement Test for mathematics in Grades 2 and 4. The cross-lagged
paths were constrained to equality (a1 =a2 and b1 =b2).
Motivation and Achievement in Mathematics 169
Associations Between Motivation and Achievement in
The correlation matrix is presented in Table 2.
Cross-sectional correlations indicated that intrinsic
motivation for mathematics was increasingly posi-
tively correlated to achievement in mathematics
(r=.13 in Grade 1 to r=.22 in Grade 4).
Testing the Direction of the Associations
The t statistics of the cross-lagged models are
presented in Table 3. The chi-square goodness-of-t
statistics showed signicant deterioration of the t
when the cross-lagged paths were equated,
(2) =10.17, p=.00, suggesting that the associa-
tions between achievement and intrinsic motivation
in mathematics were not reciprocal. Accordingly,
the nonconstrained model was retained as the best
tting and nal model. This nal standardized
model is presented in Figure 2.
The nonconstrained model showed small, but
signicant cross-lagged paths connecting prior
achievement to subsequent intrinsic motivation. The
cross-lagged paths from motivation to achievement
were not statistically signicant. The stability paths
for achievement were 0.76 from Grades 1 to 2 and
0.74 from Grades 2 to 4. The stability paths for
intrinsic motivation in mathematics were somewhat
lower, but slightly increased over time from 0.31 to
0.42, although the increase did not reach signi-
cance when the longitudinal stability paths were
constrained to equality (c=d; see Figure 1), as
shown by a nonsignicant deterioration of the t,
(1) =0.55, p=.46 (results available from the
The measure of intrinsic motivation was invari-
ant over time, with nonsignicant difference in the
model t when factor loadings for matching items
of intrinsic motivation were constrained to equality,
(4) =3.92, p=.42 (results available from the
Sex Differences
To test for possible sex differences in these pat-
terns of longitudinal associations, we conducted a
sex-invariant model. The factor loadings, the stabil-
ity links, the cross-links, and the covariance were
constrained to equality across sex. Compared to the
nonconstrained model, the t of the sex-invariant
model was not deteriorated, Δv
(26) =36.26,
p=.08, comparative t index =0.97, TuckerLewis
index =0.96, root mean square error of approxima-
tion =0.034 [0.030, 0.038]. Thus, the associations
between intrinsic motivation and mathematics
achievement did not vary across sex.
The present study examined the developmental
association between intrinsic motivation and
achievement in mathematics during elementary
school. Specically, a longitudinal cross-lagged
design with three data points extending from
Grades 1 to 4 was used to disentangle, and speci-
cally test for the directions of these associations.
Controlling for early nonverbal cognitive abilities,
achievement in mathematics was found to system-
atically predict later intrinsic motivation in mathe-
matics over time. However, there was no evidence
for the reverse; intrinsic motivation for mathematics
did not predict later (or changes in) achievement in
mathematics. This pattern was similar for both
sexes, despite small mean sex differences. On aver-
age, boys performed better in mathematics in the
early grades, and were more motivated than girls,
whereas girlsintrinsic motivation signicantly
declined over time.
The nding of such a systematic directional pre-
diction from achievement to intrinsic motivation
runs in contrast to studies that found a reverse
(Areepattamannil et al., 2011; Gottfried, 1985; Mur-
ayama et al., 2013; Spinath et al., 2006) or a recipro-
Table 3
Summary of Fit Statistics for Achievement in Mathematics and Intrinsic Motivation in Mathematics Cross-Lagged Models
Models v
371.76 133 0.00 0.97 0.96 0.033 [0.029, 0.037] ––
381.93 135 0.00 0.97 0.96 0.033 [0.029, 0.037] 10.17 0.00
Note. Represents the change in Δv
and degrees of freedom for a particular model against the nonconstrained model, in which it is
nested. CFI =comparative t index; TLI =TuckerLewis index, RMSEA =root mean square error of approximation.
170 Garon-Carrier et al.
cal (Aunola et al., 2006; Henderlong Corpus et al.,
2009; Luo et al., 2011; Viljaranta et al., 2009) pat-
tern. As argued previously, a prominent explana-
tion for this discrepancy is that most previous
studies did not use a cross-lagged design and thus,
did not specically test for reciprocal associations.
Of those that did, one failed to nd a specic asso-
ciation for intrinsic motivation (Marsh et al., 2005),
and another found a bidirectional association, but
for a score combining intrinsic motivation and aca-
demic self-concept in mathematics (Luo et al.,
2011). Only in Viljaranta et al. (2009) was a clear
bidirectional association revealed, but only over a
short period in the 1st school year. It is thus possi-
ble that an early bidirectional association exists, but
only over a short period of time.
The present results challenge the view that
intrinsic motivation naturally leads to higher
achievement in mathematics, and thus raise ques-
tions regarding the theoretical assumptions under-
lying this predictive association. Contrary to SDT
tenets, intrinsic motivation did not translate into
higher achievement in mathematics. According to
SDT, this directed link is expected when the needs
for autonomy and competence are fullled. It may
be that the typical learning process in mathematics
in the early years of school is mostly driven by
school contingencies, such as mandatory schedule,
homework, and learning exercises; these conditions
may create an unfavorable context for self-deter-
mined activity and thus for intrinsic motivation to
bring about consequent learning behavior in mathe-
matics. The possible interplay of these contextual
factors should be investigated further in future
The nding that higher achievement in mathe-
matics led to higher intrinsic motivation in mathe-
matics, while consistent with SDT, may be
interpreted in various ways. The simplest explana-
tion for this predictive association is that achieve-
ment in mathematics is self-reinforcing and thus
brings about an increase in intrinsic motivation. A
more stringent test of SDT would involve testing
the mediating role of self-concept in mathematics in
this predictive association. Indeed, SDT posits that
academic self-concept develops with integrated
Grade 1
Grade 2
Grade 4
Grade 1
Q1 Q2 Q3 Q1 Q2 Q3 Q1 Q2 Q3
L2 + − ×
L1 + − × ÷
.31 .42
.76 .74
.60 .78 .76 .76 .55 .64 .67 .65 .60
.90 .87 .38 .89 .91 .46 .89 .94 .50
Grade 2
Grade 4
.20 .08 .18
Figure 2. Final cross-lagged model of achievement in mathematics and intrinsic motivation in mathematics. Standardized solution of
the nonconstrained model; all signicant paths unless indicated otherwise (ns =nonsignicant). Not shown are the correlated unique-
ness. Achievement in mathematics was controlled for general cognitive abilities. L1 and L2 =Level 1 and Level 2 in the Number
Knowledge Test. The symbols (+,,9,) indicate the mathematics dimensions of the achievement measure.
Motivation and Achievement in Mathematics 171
feedback from past and actual school evaluations.
Accordingly, it has been associated with achieve-
ment and engagement in activities, as well as with
intrinsic motivation in mathematics (Marsh et al.,
However that may be, to put these ndings in
perspective, one has to consider the differential sta-
bility observed for intrinsic motivation versus
achievement in mathematics over the primary
school years. Indeed, an enduring feature of the
present results is that individual differences in
mathematics achievement were highly stable
despite variation in the measures. In contrast, indi-
vidual differences in intrinsic motivation toward
mathematics were initially moderate, but became
increasingly stable during elementary school.
Clearly, intrinsic motivation in mathematics
behaved as a developmental construct; it was more
likely to change at school entry, but became pro-
gressively more crystallized later in children devel-
opment, partly due to previous achievement in
Implication for Educational Practices
Interventions in education try to increase intrin-
sic motivation, and hopefully achievement, through
promoting students autonomy in instructional set-
ting (e.g., opportunity to select work partners and
assignment tasks; Koller et al., 2001). The present
ndings could mean that these practices may not
be the best approach in the early school years
(Cordova & Lepper, 1996; Wigeld & Wentzel,
2007). However, we should refrain from concluding
too hastily. The present study shows that intrinsic
motivation does not lead to higher achievement in
mathematics, but does not speak specically to the
impact of intervention on intrinsic motivation and
achievement. It may still be possible to improve
intrinsic motivation through intervention, but at the
population level, intrinsic motivation does not nat-
urallyincrease achievement in mathematics. It
could also be that within the population, the rela-
tion between intrinsic motivation and performance
in mathematics differs as a function of ability level
(Cleary & Chen, 2009; J~
ogi, Kikas, Lerkkanen, &
agi, 2015) or the nature of the mathematics skills
(Cerasoli, Nicklin, & Ford, 2014). For instance,
intrinsic motivation more likely predicts the quality
(i.e., complex task that seeks more skills and com-
mands personal investment) than the quantity (i.e.,
task with less personal cognitive investment) of
achievement (Cerasoli et al., 2014). Further research
is needed to verify whether this pattern can be
reproduced using different samples, different mea-
sures of intrinsic motivation and achievement, and
different types of motivation (see Ryan & Deci,
2009). Future research should also examine whether
the actual results may be generalized to other
school subjects, as well as to other school period
(Green, Martin, & Marsh, 2007; Marsh et al., 2005).
Most importantly, future research should conduct
experiments, ideally randomized controlled trials,
to test if intrinsic motivation can be fostered in
young children, and if so, to what extent and how
it leads to increased achievement.
Finally, an important feature of the present
results is that achievement level in mathematics
was fairly well established early in primary school,
and subsequently predicts intrinsic motivation
toward mathematics. This stability of achievement
and the ensuing consistent motivational trend in
mathematics underscore the need to document the
early school years as a crucial period for the assess-
ment and fostering of early numeracy.
Several limitations should, however, be acknowl-
edged. First, measures of achievement in mathemat-
ics differed over time. However, the high stability
of achievement in mathematics across ages suggests
that these measures tap into a similar ability con-
struct. Second, the present ndings were specicto
mathematics and may only apply to mathematics
(Green et al., 2007; Guay et al., 2010; Marsh et al.,
2005). The same could be said about the age range;
the ndings covered the early years of primary
school and may only be relevant to that school per-
iod. Third, the present study dened intrinsic moti-
vation as a combination of interest and enjoyment.
However, enjoyment may also be seen as part of
academic interest (Krapp, Schiefele, & Winteler,
1992). It would have been relevant to distinguish
academic interest from intrinsic motivation. Unfor-
tunately, the focused nature of the motivation scale
did not allow this distinction. Finally, the statistical
t comparison between the nonconstrained and the
constrained cross-lagged models was based on the
chi-square goodness of t. This statistical index is
sensitive to sample sizes (see Bentler & Bonett,
1980), so that the t deterioration of the constrained
model, in comparison to the nonconstrained model,
could partly be a consequence of the sample size.
These limitations notwithstanding, this study
convincingly showed that contrary to the hypothe-
sis that intrinsic motivation drives achievement or
that motivation and achievement entertain recipro-
cal inuences over time, it is rather achievement
that predicts later intrinsic motivation in mathemat-
ics during the primary school years. The results also
172 Garon-Carrier et al.
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Motivation and Achievement in Mathematics 175
... Motivation does not precede learning -rather successful learning precedes motivation. In fact, a longitudinal study ranging across elementary grades in a mathematics setting found that intrinsic motivation, at no time predicted student achievement but rather that prior achievement predicted subsequent intrinsic motivation (Garon-Carrier et. al., 2016). When learners get a taste of success, even in small bites, it builds up internal motivation to continue on. An effective educator, then, will build in opportunities to ensure small successes for your learner and leverage those for a lifetime of motivated learning rather than trying to get them motivated first. Success leads to motivati ...
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... Intrinsic motivation and academic achievement are seen as developmentally interconnected; intrinsic motivation lies at the core of self-determined activity (Ryan and Deci 2000) and is expected to be reciprocally associated with achievement. However, the relationship between intrinsic motivation and mathematics achievement is not clear: some studies have found that intrinsic motivation is positively correlated with achievement (e.g., Walker et al. 2006;Ayub 2010;Garon-Carrier et al. 2016), while other studies have found a moderate or no relationship (Bouffard et al. 2003;Marsh et al. 2005;Spinath et al. 2006). ...
In this chapter, we argue for a conceptualisation of thinking, doing and feeling as inseparable. We argue that affect is not a property of an individual, but rather a distributed and relational flow among participants and objects. We also draw on the notion of ritualisation, within the teaching and learning of mathematics, as pointing towards activity which may be mute but is far from unthinking. Using empirical data from a series of one-to-one teaching sessions, we propose that it is possible to analyse affective flows, for example, in affective aligning, or misaligning. We have tentative evidence that ritualisation activity supports affective aligning and hence has a potentially powerful role to play in learning mathematics.
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The correlation between motivational beliefs and foreign language learning has been widely explored. However, there has been little investigation of this link among learners with different foreign language levels. Based on expectancy-value theory (EVT), this research examined the association between motivational beliefs and English achievement of 11,854 Chinese secondary students. Data were collected using students’ self-reported English self-efficacy, intrinsic value, utility value, and English achievement test. The results of ANOVA showed that self-efficacy, intrinsic value, and utility value of high-achieving English learners were significantly higher than that of medium-achieving ones, followed by low-achieving ones. Multiple regression analysis demonstrated that after controlling for socioeconomic status and gender, intrinsic value was most correlated with high- and medium-achieving learners’ English achievement, followed by self-efficacy, while utility value was not significantly associated with English achievement of the two groups. In addition, utility value was most strongly related with low-achieving learners’ English achievement, followed by intrinsic value, but self-efficacy was not positively linked with their English achievement. These findings not only extend EVT and validate the situative perspective of motivation research, but also have practical implications for foreign language education.
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Based on stereotype threat and stereotype lift theory, this study explores implicit stereotype threat effects of gender stereotypes on the performance of primary school children in mathematics. Moreover, effects of implicit gender stereotypical cues (gender-specific task material) on motivational aspects were explored, which have revealed mixed results in stereotype threat research in the past. N = 151 German primary school children (47.7% female; mean age: M = 9.81, SD = 0.60) calculated either stereotypical or neutral mathematical text problems before motivational aspects were assessed. Contradicting our expectations, results neither revealed a stereotype threat effect on girls’ performance nor a lift effect on the boys. Instead, girls calculating stereotypical tasks outperformed girls in the control group, whereas boys’ performance did not significantly differ compared to the control group. Regarding motivational aspects, only traditional gender differences emerged as girls reported significantly more pressure and tension calculating the mathematical tasks. The discussion focuses on the way in which stereotypes can affect children’s cognitive performance and in turn, their mathematical performance.
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This study examines the extent to which self-determination theory (SDT) explains the academic achievement and mental well-being of students at a women’s university in Japan. According to SDT, if students meet their basic psychological needs (autonomy, competence, and relatedness), they will have more internalized motivation, which in turn will lead them to perform better. However, this study does not find that SDT fully applies to its respondents, who are all college students at a women’s university. Students who obtain autonomy support from their parents meet their basic psychological needs and feel that they are competent, which is in line with the theory. In contrast to the theory, however, high perceived competence does not bring more internalized motivation to the students in this study. Students with high perceived competence levels tend to act out of a sense of obligation (external motivation) or to please others (introjected motivation) rather than based on their values (identified motivation) or interests (intrinsic motivation). Moreover, as opposed to SDT, the level of internalized motivation, measured by the relative autonomy index (RAI), has no statistically significant impact on either the academic achievement or the happiness of the students in this study. Instead of self-motivation (which is a late-stage variable in SDT), this study finds that autonomy support from parents and the basic psychological need satisfaction (BPNS) of students (which are early-stage variables in SDT) have a statistically significant impact on both the grades and the happiness of students.
The present chapter provides a step‐by‐step tutorial on using SPSS Custom Dialogs to perform Direction Dependence Analysis (DDA). We present a Graphic User Interface (GUI) that translates inputs into DDA macro commands which makes DDA accessible via the regular SPSS dropdown menu. To illustrate the application of DDA in SPSS, we use data from the High School Longitudinal Study 2009 (Ingels et al., 14.25) and evaluate the causal direction of association between intrinsic motivation and mathematics achievement in 9th grade Asian students (n = 674). DDA results indicate that a model of the form achievement → motivation finds more empirical support than the causally reversed model motivation → achievement.
The present study aims to identify personal and contextual factors predicting the mathematics achievement of Italian students in the fourth and eighth grades who participated in TIMSS (Trends in International Mathematics and Science Study). Structural equation modeling was used to assess the effects of socioeconomic and cultural background and students’ self-concept and attitudes towards mathematics on achievement utilizing Mplus. The results showed that all measures were significantly associated with mathematics achievement test scores. Additionally, self-concept was the strongest factor associated with mathematics achievement, and the relationship between these two variables was more relevant in lower secondary school. Possible implications for the Italian school system are discussed.
Cognitive ability and educational success predict positive outcomes across the lifespan, from higher earnings to better health and longevity. The shared positive outcomes associated with cognitive ability and education are emblematic of the strong interconnections between them. Part of the observed associations between cognitive ability and education, as well as their links with wealth, morbidity and mortality, are rooted in genetic variation. The current review evaluates the contribution of decades of behavioural genetic research to our knowledge and understanding of the biological and environmental basis of the association between cognitive ability and education. The evidence reviewed points to a strong genetic basis in their association, observed from middle childhood to old age, which is amplified by environmental experiences. In addition, the strong stability and heritability of educational success are not driven entirely by cognitive ability. This highlights the contribution of other educationally relevant noncognitive characteristics. Considering both cognitive and noncognitive skills as well as their biological and environmental underpinnings will be fundamental in moving towards a comprehensive, evidence-based model of education.
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The aim of the article is an analysis of personality, regulatory and motivational predictors of academic success specificity at different stages of education. The first part of the article considers features of the relationship between the Big Five personality traits and academic achievement at different stages of education. The second part analyzes regulatory predictors of academic success, especially conscious self-regulation. The third part of the article focuses on the contribution of motivational constructs based on self-concept and self-efficacy, and internal and external motivation to academic achievement. The article concludes with a statement on the need for a comprehensive study of individually-typological features of the relationship between the regulatory, motivational and personality predictors of academic achievement in students of different ages.
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Missing data analyses have received considerable recent attention in the methodological literature, and two “modern” methods, multiple imputation and maximum likelihood estimation, are recommended. The goals of this article are to (a) provide an overview of missing-data theory, maximum likelihood estimation, and multiple imputation; (b) conduct a methodological review of missing-data reporting practices in 23 applied research journals; and (c) provide a demonstration of multiple imputation and maximum likelihood estimation using the Longitudinal Study of American Youth data. The results indicated that explicit discussions of missing data increased substantially between 1999 and 2003, but the use of maximum likelihood estimation or multiple imputation was rare; the studies relied almost exclusively on listwise and pairwise deletion.
More than 4 decades of research and 9 meta-analyses have focused on the undermining effect: namely, the debate over whether the provision of extrinsic incentives erodes intrinsic motivation. This review and meta-analysis builds on such previous reviews by focusing on the interrelationship among intrinsic motivation, extrinsic incentives, and performance, with reference to 2 moderators: performance type (quality vs. quantity) and incentive contingency (directly performance-salient vs. indirectly performance-salient), which have not been systematically reviewed to date. Based on random-effects meta-analytic methods, findings from school, work, and physical domains (k = 183, N = 212,468) indicate that intrinsic motivation is a medium to strong predictor of performance (ρ = .21-45). The importance of intrinsic motivation to performance remained in place whether incentives were presented. In addition, incentive salience influenced the predictive validity of intrinsic motivation for performance: In a "crowding out" fashion, intrinsic motivation was less important to performance when incentives were directly tied to performance and was more important when incentives were indirectly tied to performance. Considered simultaneously through meta-analytic regression, intrinsic motivation predicted more unique variance in quality of performance, whereas incentives were a better predictor of quantity of performance. With respect to performance, incentives and intrinsic motivation are not necessarily antagonistic and are best considered simultaneously. Future research should consider using nonperformance criteria (e.g., well-being, job satisfaction) as well as applying the percent-of-maximum-possible (POMP) method in meta-analyses. (PsycINFO Database Record (c) 2014 APA, all rights reserved).
The purpose of the present study was to evaluate the factor structure, reliability, and convergent validity of a French version of the Self-Perception Profile for Children among primary schoolchildren. The study was conducted during the spring term and entailed group administration of a French version of Harter's Self-Perception Profile for Children to 466 second grade, 350 third grade, 274 fourth grade children, and 247 sixth grade children. Teacher evaluations, individual sociometric interviews, and collective administration of a peer assessment measure were also collected but for second, third, and fourth grade samples only. The factor structure was evaluated by means of the confirmatory factor analytic procedure. The convergent validity of each subscale was tested by correlating self-assessment scores with teachers' and peers' assessments on similar dimensions for each age group. The results generally supported the five factor solution for all age groups (similar to the English version) although the magnitudes of the phi estimates indicated a substantial lack of self-concept differentiation among second and third grade children. The internal consistency values also indicated that each dimension could be reliably measured at each age level. Significant convergent validity was evidenced for all dimensions with the exception of physical appearance.
This article provides an introduction and overview to this special issue of Educational Psychologist, titled Promoting Motivation at School: Interventions That Work. This issue is devoted to the topic of interventions that emphasize different aspects of motivation for enhancing students' academic and social outcomes in school. The interventions range from programs focused on individual students to large-scale school reform. The programs described in this issue emphasize both students' academic motivation and their social motivation and focus on a variety of important achievement outcomes. Authors also discuss the effectiveness of various interventions for ethnic minority children. The importance of attending to social aspects of motivation in these kinds of interventions is a major theme of this special issue. Brief overviews of each article are provided.
The authors used data from the Longitudinal Study of American Youth to investigate variables related to change in students' attitude toward and beliefs about mathematics in middle school and high school. Using hierarchical linear modeling techniques, the authors modeled variation in students' rate of change with variables associated with student characteristics, instructional experiences, and environment. They also identified variables that differentially affect change at different levels of secondary school (i.e., middle school vs. high school) and for different affective dimensions (i.e., attitude toward mathematics, beliefs about the social importance of mathematics, and beliefs about the nature of mathematics). Results showed a substantial negative change in students' attitudes toward and beliefs about the social importance of mathematics throughout secondary school. However, students' notions of the nature of mathematics did not change throughout secondary school. The authors identified variables related to change and found that they differed according to the level of secondary school and affective dimensions.
Math and social studies differ in the usual instructional pattern found in elementary classrooms, in the goals sought, and of course in the actual content. Based on documented differences in the two fields, we expected pupils to hold different ideas about how to learn each subject and to express different reasons for positive and negative experiences in each subject. Sixty fifth grade pupils from 11 classrooms were interviewed to explore their attitudes and conceptions about learning math and social studies. The interviews included pupils' definitions of each school subject, descriptions of typical classroom activities, probes regarding how each subject was actually learned, and descriptions of times liked and disliked in each subject. Students' conceptions and attitudes regarding math and social studies were different. Consistent with expectations, pupils characterized positive and negative experiences in math in regard to their success or ability to do the work while social studies experiences were evaluated more in terms of whether they were interesting or boring. Among other differences, more students thought they could learn social studies on their own than math.
Research has established that academic intrinsic motivation, enjoyment of school learning without receipt of external rewards, significantly declines across childhood through adolescence. Math intrinsic motivation evidences the most severe decline compared with other subject areas. This study addresses this developmental decline in math intrinsic motivation, and also serves as a resource for applied researchers by providing exemplary illustrations of approaches to longitudinal modeling. Using a multivariate latent change model, the longitudinal relationship between academic intrinsic math motivation and math achievement among participants (n = 114) aged 9—17 years was examined to explain this motivational decline. On average, both math motivation and achievement decreased over time. This study reveals that math achievement is a significant contributor to the developmental decline in intrinsic math motivation from childhood through adolescence. In addition, academic intrinsic math motivation was found to be related to initial and later levels of mathematics achievement. These findings enhance understanding of developmental processes whereby early motivation and achievement are related to subsequent declines in mathematics.