Content uploaded by Gabrielle Garon-Carrier

Author content

All content in this area was uploaded by Gabrielle Garon-Carrier on Nov 30, 2020

Content may be subject to copyright.

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

Fr

ed

eric Guay

Department of Basic and Applied Education,

Universit

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

eguin

Department of Psychiatry, Universit

e de Montr

eal and

CHU Ste-Justine Research Center, Universit

e de Montr

eal

Frank Vitaro

Department of Psychoeducation, Universit

e de Montr

eal

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 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 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 one’s 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

eb

ecois de la Recherche sur la

Soci

et

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

el

ene Paradis for assistance

with statistical analyses.

Correspondence concerning this article should be addressed to

Michel Boivin, CRC in Child Development,

Ecole de psychologie,

Universit

e Laval, Qu

ebec, Canada G1K 7P4. Electronic mail may

be sent to michel.boivin@psy.ulaval.ca.

[Correction added after online publication on November 9,

2015: an author’s name was corrected from “Jean S

eguin”to

“Jean R. S

eguin.”]

©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 165–175

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 fulﬁlls 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 satisﬁed, 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

ﬁndings 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 speciﬁcally

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). Speciﬁcally, 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; Wigﬁeld, 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 7–10) 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 deﬁnition

of intrinsic motivation grounded in SDT theory.

Accordingly, intrinsic motivation toward mathemat-

166 Garon-Carrier et al.

ics was deﬁned 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 ﬂuid cog-

nitive skills, the association between achievement

and intrinsic motivation (Kytt€

al€

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-

ﬁeld, 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.

Method

Sample

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 5–6) and

Grades 1–6 (ages 7–12), and follows with 5 years of

secondary school (ages 13–17), then leading to col-

lege and university. This article describes ﬁndings

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).

Procedure

Achievement measures in mathematics were

individually administrated at school, or at home by

a trained research assistant. Motivation was

assessed through a questionnaire ﬁlled out by chil-

dren during a face-to-face interview.

Instruments

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

a

Boys 697 19.88 4.03 1 27 22

Girls 764 19.56 3.82 8 27 21

Grade 2

b

Boys 699 13.39 4.70 0 21 17

Girls 767 12.89 4.70 1 21 18

Grade 4

b

Boys 630 14.76 3.66 0 20 16

Girls 698 14.82 3.18 0 20 16

a

Number Knowledge Test.

b

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 conﬁrmatory 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

signiﬁcantly associated with the CAT in Grades 2

(r=.53) and 4 (r=.47), thus supporting its validity.

The CAT measures children’s 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-

gence–Revised (WPPSI–R; Wechsler, 1989). The

Block Design is highly correlated with the full

WPPSI–R 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).

Analyses

Missing data were examined with the MVA

module in SPSS 20.0 for Windows (SPSS, 2011).

According to Little’s 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

(v

2

=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 ﬁtting 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 reﬂecting 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)

123456

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 coefﬁcients are signiﬁcant at p<.01. Concurrent corre-

lations between measures are indicated in boldface.

168 Garon-Carrier et al.

A nondeterioration of the model ﬁt would suggest

equal reciprocal associations between intrinsic

motivation and achievement in mathematics,

whereas a deterioration of the model ﬁt 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, 1998–2012). In

all models, we controlled for nonverbal cognitive

abilities in time-speciﬁc scores of achievement in

mathematics, and included the correlated unique-

ness estimates speciﬁc to matching items of intrinsic

motivation in Grades 1, 2, and 4 (Marsh et al.,

2005).

Results

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 signiﬁcantly

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 signiﬁcant, F(1.98, 2,385.46) =5.66, p<.01,

g

2

=.005. Boys showed a signiﬁcantly higher level of

intrinsic motivation than girls at all ages (ps<.01).

Girls’motivation signiﬁcantly 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 signiﬁ-

cant, F(1.97, 2,329.13) =4.23, p<.05, g

2

=.004. Boys

performed signiﬁcantly 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.

Achievement

Mathematics

Grade 2

Achievement

Mathematics

Grade 4

Motivation

Mathematics

Grade 1

Motivation

Mathematics

Grade 2

Motivation

Mathematics

Grade 4

E

E

E

E

a

a1

a2

b1

b2

cd

b

Achievement

Mathematics

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

Mathematics

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 ﬁt statistics of the cross-lagged models are

presented in Table 3. The chi-square goodness-of-ﬁt

statistics showed signiﬁcant deterioration of the ﬁt

when the cross-lagged paths were equated,

Δv

2

(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

ﬁtting and ﬁnal model. This ﬁnal standardized

model is presented in Figure 2.

The nonconstrained model showed small, but

signiﬁcant cross-lagged paths connecting prior

achievement to subsequent intrinsic motivation. The

cross-lagged paths from motivation to achievement

were not statistically signiﬁcant. 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 signiﬁ-

cance when the longitudinal stability paths were

constrained to equality (c=d; see Figure 1), as

shown by a nonsigniﬁcant deterioration of the ﬁt,

Δv

2

(1) =0.55, p=.46 (results available from the

authors).

The measure of intrinsic motivation was invari-

ant over time, with nonsigniﬁcant difference in the

model ﬁt when factor loadings for matching items

of intrinsic motivation were constrained to equality,

Δv

2

(4) =3.92, p=.42 (results available from the

authors).

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 ﬁt of the sex-invariant

model was not deteriorated, Δv

2

(26) =36.26,

p=.08, comparative ﬁt index =0.97, Tucker–Lewis

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.

Discussion

The present study examined the developmental

association between intrinsic motivation and

achievement in mathematics during elementary

school. Speciﬁcally, a longitudinal cross-lagged

design with three data points extending from

Grades 1 to 4 was used to disentangle, and speciﬁ-

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 girls’intrinsic motivation signiﬁcantly

declined over time.

The ﬁnding 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

2

df p CFI TLI RMSEA Δv

2

p

Nonconstrained

model

371.76 133 0.00 0.97 0.96 0.033 [0.029, 0.037] ––

Constrained

model

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

2

and degrees of freedom for a particular model against the nonconstrained model, in which it is

nested. CFI =comparative ﬁt index; TLI =Tucker–Lewis 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 speciﬁcally test for reciprocal associations.

Of those that did, one failed to ﬁnd a speciﬁc 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 fulﬁlled. 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

research.

The ﬁnding 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

Motivation

Mathematics

Grade 1

Motivation

Mathematics

Grade 2

Motivation

Mathematics

Grade 4

E

E

E

E

Achievement

Mathematics

Grade 1

Q1 Q2 Q3 Q1 Q2 Q3 Q1 Q2 Q3

L2 + − ×

L1 + − × ÷

-.01ns

.09

.31 .42

.02ns

.14

.76 .74

.60 .78 .76 .76 .55 .64 .67 .65 .60

.90 .87 .38 .89 .91 .46 .89 .94 .50

Achievement

Mathematics

Grade 2

Achievement

Mathematics

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 signiﬁcant paths unless indicated otherwise (ns =nonsigniﬁcant). 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.,

2005).

However that may be, to put these ﬁndings 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

mathematics.

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

ﬁndings could mean that these practices may not

be the best approach in the early school years

(Cordova & Lepper, 1996; Wigﬁeld & 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 speciﬁcally 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-

urally”increase 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, &

M€

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 ﬁndings were speciﬁcto

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 ﬁndings covered the early years of primary

school and may only be relevant to that school per-

iod. Third, the present study deﬁned 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

ﬁt comparison between the nonconstrained and the

constrained cross-lagged models was based on the

chi-square goodness of ﬁt. This statistical index is

sensitive to sample sizes (see Bentler & Bonett,

1980), so that the ﬁt 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 inﬂuences 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.

provide a consistent pattern across gender and thus

warrant greater conﬁdence in their generalizability

and replicable nature for this time period.

References

Areepattamannil, S., Freeman, J. G., & Klinger, D. A.

(2011). Intrinsic motivation, extrinsic motivation, and

academic achievement among Indian adolescents in

Canada and India. Social Psychology of Education,14,

427–439. doi:10.1007/s11218-011-9155-1

Aunola, K., Leskinen, E., & Nurmi, J.-E. (2006). Develop-

mental dynamics between mathematical performance,

task motivation, and teachers’goals during the transi-

tion to primary school. British Journal of Educational Psy-

chology,76,21–40. doi:10.1348/000709905X51608

Bentler, P. M., & Bonett, D. G. (1980). Signiﬁcance tests

and goodness of ﬁt in the analysis of covariance struc-

tures. Psychological Bulletin,88, 588–606. doi:10.1037/

0033-2909.88.3.588

Boivin, M., Vitaro, F., & Gagnon, C. (1992). A reassess-

ment of the self-perception proﬁle for children: Factor

structure, reliability, and convergent validity of a

French version among second through sixth grade chil-

dren. International Journal of Behavioral Development,15,

275–290. doi:10.1177/016502549201500207

Bouffard, T., Marcoux, M.-F., Vezeau, C., & Bordeleau, L.

(2003). Changes in self-perceptions of competence and

intrinsic motivation among elementary school children.

British Journal of Educational Psychology,73, 171–186.

doi:10.1348/00070990360626921

Canadian Test Center. (1992). Canadian Achievement Test

(2nd ed). Retrieved from http://www.canadiantestcen-

tre.com/

Cerasoli, C. P., Nicklin, J. M., & Ford, M. T. (2014). Intrin-

sic motivation and extrinsic incentives jointly predict

performance: A 40-year meta-analysis. Psychological Bul-

letin,140, 980–1008. doi:10.1037/a0035661

Cleary, T., & Chen, P. (2009). Self-regulation, motivation,

and math achievement in middle school: Variations

across grade level and math context. Journal of School

Psychology,47, 291–314. doi:10.1016/j.jsp.2009.04.002

Cordova, D., & Lepper, M. R. (1996). Intrinsic motivation

and the process of learning: Beneﬁcial effects of contex-

tualization, personalization, and choice. Journal of Edu-

cational Psychology,88, 715–730. doi:10.1037/0022-

0663.88.4.715

Denissen, J. J. A., Zarrett, N. R., & Eccles, J. S. (2007). I

like to do it, I’m able, and I know I am: Longitudinal

couplings between domain-speciﬁc achievement, self-

concept, and interest. Child Development,78, 430–447.

doi:10.1111/j.1467-8624.2007.01007.x

Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson,

K., Huston, A. C., Klebanov, P., . . . Japel, C. (2007).

School readiness and later achievement. Developmental

Psychology,43, 1428–1446. doi:10.1037/0012-

1649.43.6.1428

Gersten, R., Clarke, B. S., & Jordan, N. C. (2007). Screen-

ing for mathematics difﬁculties in K-3 students. Research

Corporation, Center on Instruction. Retrieved from

http://www.centeroninstruction.org/ﬁles/COI%

20Math%20Screening1.pdf

Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early

Identiﬁcation and interventions for students with math-

ematics difﬁculties. Journal of Learning Disabilities,38,

293–304. doi:10.1177/00222194050380040301

Gottfried, A. E. (1985). Academic intrinsic motivation in

elementary and junior high school students. Journal of

Educational Psychology,77, 631–645. doi:10.1037/0022-

0663.77.6.631

Gottfried, A. E. (1990). Academic intrinsic motivation in

young elementary school children. Journal of Educa-

tional Psychology,82, 525–538. doi:10.1037/0022-

0663.82.3.525

Gottfried, A. E., Fleming, J. S., & Gottfried, A. W. (2001).

Continuity of academic intrinsic motivation from child-

hood through late adolescence: A longitudinal study.

Journal of Educational Psychology,93,3–13. doi:10.1037/

0022-0663.93.1.3

Gottfried, A. E., Marcoulides, G. A., Gottfried, A. W., Oli-

ver, P. H., & Guerin, D. W. (2007). Multivariate latent

change modeling of developmental decline in academic

intrinsic math motivation and achievement: Childhood

through adolescence. International Journal of Behavioral

Development,31, 317–327. doi:10.1177/0165025407077

752

Graham, J. W., Olchowski, A. E., & Gilreath, T. D. (2007).

How many imputations are really needed? Some prac-

tical clariﬁcations of multiple imputation theory.

Prevention Science,8, 206–213. doi:10.1007/s11121-007-

0070-9

Green, J., Martin, A. J., & Marsh, H. W. (2007). Motiva-

tion and engagement in English, mathematics and

science high school subjects: Towards an understanding

of multidimensional domain speciﬁcity. Learning and

Individual Differences,17, 269–279. doi:10.1016/j.lin-

dif.2006.12.003

Guay, F., Chanal, J., Ratelle, C. F., Marsh, H. W., Lar-

ose, S., & Boivin, M. (2010). Intrinsic, identiﬁed, and

controlled types of motivation for school subjects in

young elementary school children. British Journal of

Educational Psychology,80, 711–735. doi:10.1348/

000709910X499084

Guay, F., Marsh, H. W., & Boivin, M. (2003). Academic

self-concept and academic achievement: Developmental

perspectives on their causal ordering. Journal of Educa-

tional Psychology,95, 124–136. doi:10.1037/0022-

0663.95.1.124.

Henderlong Corpus, J., McClintic-Gilbert, M. S., &

Hayenga, A. O. (2009). Within-year changes in chil-

dren’s intrinsic and extrinsic motivational orientations:

Contextual predictors and academic outcomes. Contem-

porary Educational Psychology,34, 154–166. doi:10.1016/

j.cedpsych.2009.01.001

Jacobs, J. E., Lanza, S., Osgood, D. W., Eccles, J. S., &

Wigﬁeld, A. (2002). Changes in children’s self-

Motivation and Achievement in Mathematics 173

competence and values: Gender and domain differences

across grades one through twelve. Child Development,

73, 509–527. doi:10.1111/1467-8624.00421

Jett

e, M., & Des Groseillers, L. (2000). Survey description

and methodology. In la Direction Sant

eQu

ebec (Ed.),

Longitudinal Study of Child Development in Quebec

(ELDEQ 1998-2002) (Vol. 1, pp. 1–40). Quebec City,

Canada: Institut de la statistique du Qu

ebec.

J~

ogi, A.-L., Kikas, E., Lerkkanen, M.-K., & M€

agi, K.

(2015). Cross-lagged relations between math-related

interest, performance goals and skills in groups of

children with different general abilities. Learning and

Individual Differences,39, 105–113. doi:10.1016/j.lindif.

2015.03.018

Koller, O., Baumert, J., & Schnabel, K. (2001). Does

interest matter? The relationship between academic

interest and achievement in mathematics. Journal for

Research in Mathematics Education,32, 448–470.

doi:10.2307/749801

Krapp, A., Schiefele, U., & Winteler, A. (1992). Interest as

a predictor of academic achievement: A meta-analysis

of research. In K. A. Renninger, S. Hidi, & A. Krapp

(Eds.), The role of interest in learning and development (pp.

183–196). Hillsdale, NJ: Erlbaum.

Kuncel, N. R., Hezlett, S. A., & Ones, D. S. (2004). Aca-

demic performance, career potential, creativity, and job

performance: Can one construct predict them all? Jour-

nal of Personality and Social Psychology,86, 148–161.

doi:10.1037/0022-3514.86.1.148

Kytt€

al€

a, M., & Lehto, J. E. (2008). Some factors underlying

mathematical performance: The role of visuospatial

working memory and non-verbal intelligence. European

Journal of Psychology of Education,23,77–94.

doi:10.1007/BF03173141

Leahey, E., & Guo, G. (2001). Gender differences in math-

ematical trajectories. Social Forces,80, 713–732.

doi:10.1353/sof.2001.0102.

Lepper, M. R., Henderlong Corpus, J., & Iyengar, S. S.

(2005). Intrinsic and extrinsic motivational orientations

in the classroom: Age differences and academic corre-

lates. Journal of Educational Psychology,97, 184–196.

doi:10.1037/0022-0663.97.2.184

Luo, Y. L., Kovas, Y., Haworth, C., & Plomin, R. (2011).

The etiology of mathematical self-evaluation and math-

ematics achievement: Understanding the relationship

using a cross-lagged twin study from ages 9 to 12.

Learning and Individual Differences,21, 710–718.

doi:10.1016/j.lindif.2011.09.001

Marsh, H. W., Trautwein, U., L€

udtke, O., Koller, O., &

Baumert, J. (2005). Academic self-concept, interest,

grades, and standardized test scores: Reciprocal effects

models of causal ordering. Child Development,76, 397–

416. doi:10.1111/j.1467-8624.2005.00853.x

Murayama, K., Pekrun, R., Lichtenfeld, S., & vom Hofe,

R. (2013). Predicting long-term growth in students’

mathematics achievement: The unique contributions of

motivation and cognitive strategies. Child Development,

84, 1475–1490. doi:10.1111/cdev.12036

Muth

en, L. K., & Muth

en, B. O. (1998–2012). Mplus user’s

guide (7th ed.). Los Angeles, CA: Author.

Okamoto, Y., & Case, R. (1996). II. Exploring the

microstructure of children’s central conceptual struc-

tures in the domain of number. Monographs of the Soci-

ety for Research in Child Development,61(1–2), 27–58.

doi:10.1111/j.1540-5834.1996.tb00536.x

Organisation for Economic and Co-operation and Devel-

opment. (2010). PISA 2009 Results: What students know

and can do—Student performance in reading, mathematics

and science. (Vol. 1). Paris, France: Author. doi:10.1787/

9789264091450-en

Peugh, J. L., & Enders, C. K. (2004). Missing data in edu-

cational research: A review of reporting practices and

suggestions for improvement. Review of Educational

Research,74, 525–556. doi:10.3102/00346543074004525

Reeve, J. (2002). Self-determination theory applied to edu-

cational settings. In E. L. Deci & R. M. Ryan (Eds.),

Handbook of self-determination research (pp. 183–203).

New York, NY: University of Rochester Press.

Reyna, V. F., & Brainerd, C. J. (2007). The importance of

mathematics in health and human judgment: Numer-

acy, risk communication, and medical decision making.

Learning and Individual Differences,17, 147–159.

doi:10.1016/j.lindif.2007.03.010

Ryan, R. M., & Deci, E. L. (2000). Intrinsic and extrinsic

motivations: Classic deﬁnitions and new directions.

Contemporary Educational Psychology,25,54–67.

doi:10.1006/ceps.1999.1020

Ryan, R. M., & Deci, E. L. (2009). Promoting self-deter-

mined school engagement. In K. R. Wentzel & A.

Wigﬁeld (Eds.), Handbook of motivation at school (pp.

171–195). New York, NY: Routledge.

Smith, A. (2004). Making mathematics count: The report of

professor Adrian Smith’s inquiry into post-14 mathematics

education. Retrieved from http://www.mathsin-

quiry.org.uk/report/MathsInquiryFinalReport.pdf

Spinath, B., Spinath, F. M., Harlaar, N., & Plomin, R.

(2006). Predicting school achievement from general cog-

nitive ability, self-perceived ability, and intrinsic value.

Intelligence,4, 363–374. doi:10.1016/j.intell.2005.11.004

SPSS. (2011). SPSS Base 20.0 for Windows user’s guide. Chi-

cago, IL: Author.

Stodolsky, S., Salk, S., & Glaessner, B. (1991). Student

view about learning math and social studies. American

Educational Research Journal,28,89–116. doi:10.2307/

1162880

Viljaranta, J., Lerkkanen, M.-K., Poikkeus, A.-M., Aunola,

K., & Nurmi, J.-E. (2009). Cross-lagged relations

between task motivation and performance in arithmetic

and literacy in kindergarten. Learning and Instruction,

19, 335–344. doi:10.1016/j.learninstruc.2008.06.011

Wechsler, D. (1989). Manual for the Wechsler Preschool and

Primary Scale of Intelligence–Revised. San Antonio, TX:

Psychological Corporation.

Wigﬁeld, A., Eccles, J. S., Schiefele, U., Roeser, R. W., &

Davis-Kean, P. (2006). Development of achievement

motivation. In W. Eisenberg & R. M. Lerner (Eds.),

174 Garon-Carrier et al.

Handbook of child psychology: Social, emotional, and person-

ality development (pp. 933–1002). Hoboken, NJ: Wiley.

Wigﬁeld, A., & Wentzel, K. (2007). Introduction to moti-

vation at school: Interventions that work. Educational

Psychologist,42, 191–196. doi:10.1080/004615207016

21038

Wilkins, J. L. M., & Ma, X. (2003). Modeling change in

student attitude toward and beliefs about mathematics.

Journal of Educational Research,1,52–63. doi:10.1080/

00220670309596628

Motivation and Achievement in Mathematics 175