Chapter4
The Effects of Interest and Utility Value on
Mathematics Engagement and Achievement
SUNG-IL KIM, YI JIANG,
and JUYEON
SONG
It is known that the relationship between achievement and either interest or utility value is mediated by engagement. Although utility values are positively related to interest, they are often in
conflict with each other, and their relative predictive power on engagement and achievement
among adolescents is not known. Therefore, we aimed to investigate the predictive power of students ’ interest and perceived utility value in mathematics on both classroom engagement and
academic achievement. We ψrther examined how predictive power changed across di￦rent
grade levels (i.e., 6th grade in elementary school, 9th grade in middle school, and 10th grade in
high school) and tested the moderating 〈야ct of perceived competence in predicting the relationships of both interest and utiliη value with engagement and achievement. The final sample
included 7,702 sixth graders, 5,809 ninth graders, and 5,396 tenth graders in Korea from the
National Assessment of Educational Achievement database. We conducted structural equation
modeling (SEM) to test the hypothesized relationships among interest, utility value, engagement,
and academic achievement in mathematics. We also carried out multψle-sample SEM between
students with high and low peπeived competence within each grade level. ηie results indicated
that for classroom engagement aηd achievement across all three grades, interest is a stronger
predictor than utility value. Moreoveη the d ‘ fji rence in predictive power between interest and
utility value became more pronounced as students moved to higher grades. In particulaη the
predictive power of interest on classroom engagement and achievement increased as the grade
level rose, whereas the predictive power of utility value decreased. Multiple-group comparison
ψrther revealed that the predictive power of utility value decreased only among those who had
low perceived compet,감ice but remained significant for those who had high perceived compeκnce.
Taken together, these results suggest that for middle and high school students who lack mathematics competence, it is more help_ψl for educators to facilitate students’ interest toward mathematics, rather than emphasizing its utility value, if they hope to enhance their students'
classroom engagement and achievement.
Introduction
Mathematics is a core subject for all students from elementary to high school, yet mathematics
is commonly perceived as a difficult and demanding subject (Eccles, Adler, & Meece, 1984;
Stod이sky, Salk, & Glaessner, 1991). As such, it is imperative for educators to find methods
of helping students develop positive attitudes toward mathematics. Previous research has
63
64
I The Effects ofInterest and Utility 얘Jue on Mathematics fa뺑!gement and Achievement
shown that intrinsic motivation, task value, and positive attitudes toward mathematics
predict subsequent mathematics performance and mathematics courses taken (Gottfried,
1990; Ma, 1997; Meece, Wigfield, & Eccles, 1990; Wigfield & Eccles, 200이.
Academic motivation is the force that drives students to engage in academic activities,
and it can be either intrinsic or extrinsic (Ryan & Deci, 2000). These two ηpes of motivation
differ in terms of the underlying reasons behind student behavior. Ryan and Deci (2000)
argued that intrinsic motivation is driven by interest in or enjoyment of an activity in itself,
whereas extrinsic motivation is driven by the utility or instrumental value that can be
attained from the activity.
Interest refers to a psychological state that contains both positive affect and heightened
cognitive engagement emerging from an interaction with a particular task or topic (Hidi &
Harackiewicz, 2000; Krapp, 2002). By contrast, utility value refers to the perceived usefulness
or instrument하ity, the extent to which a particular task is perceived as relevant and useful
for present or future go떠s (Vansteenkiste et al., 2004; Wigfield & Eccles, 2000). Some researchers have argued that utility value can be either intrinsic or extrinsic depending on
whether the value is important to the person (Malka & Covington, 2005; Simons,
Vansteenkiste, Lens, & Lacante, 2004). However, if a person engages in an activity to obtain a
given outcome, the utility value of the activity should be viewed as extrinsic rather than intrinsic because the external outcome is separable from the activiη itself. As such, goal attainment drives a person’s engagement in instrumental actψity. For example, if students have
high utility value on mathematics in order to be admitted to university, they are extrinsically
motivated to study mathematics.
Developmental Trends in Interest and Utility Value
Although a large body of research suggests that motivation plays a critical role in students’
school engagement and achievement, many studies have also pointed out that students'
achievement motivation tends to decrease as they move into higher grade levels (Eccles et
al., 1984). This trend exists for many key motivational constructs, including interest in
learning (Epstein & McPartland, 1976), perceived value of various subjects (Eccles et al.,
1989; Wigfield, Eccles, Mac Iver, Reuman, & Midgley, 1991), perceived competence (Marsh,
1989), and self-esteem (Simmons, Blyth, Van Cleave, & Bush, 1979). It has been established
that the largest decrease in students' achievement motivation occurs during the transition
period from elementary school to middle school. Specifically, students appear to more
strongly dislike the subject of mathematics as they grow older. For instance, in a longitudinal
study, Wigfield et al. (1997) investigated the changes in elementary students’ interest and
perceived task utility in various subjects. The results showed that elementary students'
interest and belief in the usefulness and importance of mathematics decreased across the
three years of the study. Similarly, Eccles et al. (1989) and Wigfield et al. (1991) found that
students' interest in and value for mathematics decreased when they entered middle school.
Furthermore, students' perceived importance of mathematics decreased continuously from
eighth grade onward (Jacobs, Lanza, Osgood, Eccles, & Wigfield, 2002).
Sung-ii Kim, Yi Jiang, a뼈 fuyeon Song
I 65
Although students’ interest in and utility value for mathematics tend to decline as their
grade levels rise, the roles of these factors in facilitating class engagement and academic
achievement may remain the same. However, the predictive power of interest and utility
value on engagement and achievement across grades has rarely been studied. According to
Wigfield (1994), students are able to distinguish between interest and utility value from
fifth grade onward and can differentiate better as they age (Wigfield et al., 1997). However,
in previous research, interest and utility value have generally been considered as components
of task v외ue rather than as independent constructs (Wigfield & Eccles, 2000). A caveat of
this approach is that there is scant research on systematic comparisons of the different
roles of interest and utility value in predicting students' engagement and academic achievement across different school grades. Given these lacunae, the aims of the present study
were to investigate and clarify the relative predictive power of interest and utility value in
contributing to students' mathematics engagement and achievement and to further examine
whether there exist age-related differences and moderating effects of perceived competence
in these relationships.
The Role of Interest and U디lity Value in Mathematics Achievement
It is known that both interest and utility value predict achievement-related behaviors such
as deep engagement, effort reg비ation, and academic achievement (e.g., Brophy, 1999;
Schiefele, 1996; Simons, Dewitte, & Lens, 2004). Previous studies have indicated that students'
interest is associated with in-depth learning (Renninger, Ewen, & Lasher, 2002), persistence
(Ainley, Hidi, & Berndorff, 2002), and academic performance (Schiefele, Krapp, & Winteler,
1992). However, two longitudinal studies revealed contradictory findings with respect to
the prediction of early mathematics interest on later mathematics achievement. Koller,
Baumert, and Schnabel (2001) showed that mathematics interest in 7th grade did not
predict achievement in 10th grade, although mathematics interest in 10th grade predicted
achievement in 12th grade. In contrast, Simpkins, Davis-Kean, and Eccles (2006) found
that mathematics interest in 6th grade predicted mathematics grades in 10th grade.
Ryan and Deci (2000) suggested that when individuals are not interested in a particular
task, a high perceived utility value may motivate them to engage in the task. Simons,
Vansteenkiste, et al. (2004) argued that utility value is an important motivational factor
that can promote performance in educational settings. A number of studies have demonstrated that utility value predicts a variety of motivational outcomes, such as performance
(Bong, 2001; Durik, Vida, & Eccles, 2006; Simons, Dewitte, et al., 2004), effort (Cole, Bergin,
& Whittaker, 2008), and course enrollment intentions (Meece et al., 1990). Research on
perceived instrument떠ity has also shown that perceived relevance and usefulness predict
motivation and performance (Husman & Lens, 1999; Malka & Covin양on, 2005). Focusing
on mathematics learning, previous studies have revealed that the degree to which students
have utility value in mathematics positively relates to their mathematics achievement and
their use of self-regulation strategies, cognitive and metacognitive strategies, and effort in
mathematics class (Chouinard, Karsenti, & Roy, 2007; Greene, DeBacker, Ravindran, &
66
I The E￦cts of Interest and Utility Value on Mathemati다 Engagement and A대ievement
Krows, 1999; Pokay & Blumenfeld, 1990). In a longitudinal study, however, Simpkins et al.
(2006) found that beliefs about mathematics importance in 6th grade did not predict mathem atics grades in 10th grade.
Given the inconsistent findings on 버e effect of interest and utility value on important
educational outcomes, it is neζessary to explore the interactive relationship among interest,
utility value, engagement, and achievement. Although utility values are positively related to
interest (Hulleman, Durik, Schweigert, & Harackiewicz, 2008; Hulleman & Harackiewicz,
2009), they are often in conflict with each other. For instance, although students may not
enjoy an activity, they may have high utility value for an outcome it produces (Wigfield,
1994). The activity must be instrumental to their pursuit of goals. Or students may feel interest in a specific task that is low in utility v려ue. If there is a conflict between interest and
utility values, which one would be the relatively more influential variable in determining
the choice of an action?
Cole et al. (2008) investigated the relative contributions of importance, usefulness, and
interest to task-specific effort and performance on a standardized test. They found that
usefulness significantly predicted effort and performance, whereas interest did not. However,
one should be cautious in generalizing their findings, because their participants were college
students and they administered a low-stakes test. Thus, we aimed to investigate the relative
predictive power of adolescents’ interest in and utility value for mathematics on classroom
engagement as well as academic achievement. We further examined how these predictive
patterns would change across different grade levels.
The Moderating Role of Perceived Competence
According to Hidi and Renninger’s (2006) Four-Phase Model of Interest Development,
utility value can promote interest. However, the effect of utility value on interest can be
moderated by initial level of interest or level of competence. Recent experimental studies
have found that individual and cultural differences in initial interest moderate the effectiveness of utility value interventions. Durik and Harackiewicz {2007) conducted an experiment that provided the utility value information about a new mathematics technique for
American college students and measured their motivation (i.e., interest, involvement, and
competence) in the technique. They found that utility value promoted motivation only for
participants with high individual interest in mathematics. However, Shechter, Durik,
Miyamoto, and Harackiewicz {2011) compared cultural differences in responses to utility
value and found that utility value intervention enhanced the motivation (task interest and
effort) only for East Asian college students with low initial interest in mathematics. Although
they concluded that East Asians with low interest would be more sensitive to utility value
than those with high interest, the same pattern was found among American high school
students in a field experiment (Hulleman & Harackiewicz, 2009). Hulleman and Harackiewicz
(2009) found that a utility value intervention promoted interest in science and course
grades only for students with low success expectations.
Besides the relationship between utilityv혀ue and interest, it is likely that perceived competence
acts as a moderator of the relationship between utility value and engagement and achievement.
Sung-ii Ki;η퍼 Jiang,‘ and f uyeon Song
I 67
According to White’s (1959) notion of effectance motivation, to feel competent is an innate
desire of human beings, and people engage in activities to experience competence. Also,
perceived competence determines individuals' percep디ons of control of achievement in an academic task (Bandura, 1997; Skinner, Wellborn, & Connell, 1990). Ry;따l and Deci (2000) 값맹ed
that perceived competence is the prerequisite for extrinsic instrumental-triggered engagement.
In other words, utility value may not be sufficient to make students engage in academic tasks
unless they have high perceived competence. For example, low-competence students may not
engage in a task even though they are aware of its usefulness, because they do not believe that
their engagement would lead to a desired outcome. Although it is an interesting question
whether utility value would differently predict engagement and achievement depending on the
level of perceived competence, little empirical evidence directly supports the potential moderating
role of perceived competence. In addition, it also remains unclear whether the relationship between interest and engagement is moderated by perceived competence.
Empirical Study
Sample and Data Sources
We used the National Assessment of Educational Achievement (NAEA) database, provided
by the Korea Institute for Curriculum and Evaluation (KICE). In the Korean school system,
a typical academic year runs from March to December, with the first semester continuing
from March to mid-July and the second semester running from August to December. NAEA
data were collected during the middle of the second semester in October 2003. Sixth-grade
(elementary school), 9th-grade (middle school), and 10th-grade (high school) students
were sampled. The sample size represented 1% of the total number of students in each
grade for the whole country. The sample selection was based on the stratified two-stage
cluster sampling method, in which school was the sampling unit at the first stage and class
was the sampling unit at the second stage (Korea Ministry of Education, Science and Technology, Korea Institute for Curriculum and Evaluation, 2006). After excluding participants
whose responses were incomplete or otherwise inadequate or who did not have NAEA
achievement scores, the final sample sizes for elementary, middle, and high school students
were, respectively, 7,702 (4,033 male and 3,669 female students), 5,809 (3,168 male students,
2,639 female students, and 2 students of unreported gender), and 5,396 (2,440 male students,
2,951 female students, and S students of unreported gender).
Measures and Data Analysis
Interest, utility value, classroom engagement, and perceived competence were assessed with
regard to mathematics on 4-point, Likert-마pe scales ( 1 = strongly disagree, 4 = strongly
agree). All scales were developed by the KICE. Table 1 displays items and reliabilities for
each scale for the elementary, middle, and high school samples. The ratio of the variance of
achievement scale to the variance of other scales was greater than 10, and this scale was
therefore ill scaled. Because an ill-scaled covariance matrix can cause problems in structural
equation modeling (SEM) analysis, the achievement score was rescaled by multiplying by
1/100, as suggested by Kline (2005).
68
I The E￦cts ofInterest and Utility Value on Mathematics En요맹ement and Achievement
Table 1. Items and Reliabilities of Scales
Variable
Interest
Item
1. I prefer math problems that cannot be easily solved.
2. I 피<e dealing with numbers.
3. Math is an interesting subject.
4. I hate studying math [reversed].
Utility
value
1. Learning math is useful for logical thinking.
2. Math is useful for studying other subjects such as science.
3. Learning math is useful r diverse careers in the future.
Classroom
engagement
1. I listen veη carefully during math class.
2. I answer the teacher’s questions during math class.
3. I prepare for math class.
“
4. After math class, I review what I have learned.
Perceived
competence
1. I can explain a mathematical formula to friends.
2. I can solve more difficult math problems.
3. Math is difficult no ma야er how hard I try [reversed].
4. I think math is more difficult for me than for other people [reversed].
Reliability
6th grade
a=.81
9th grade
a=.84
10th grade
a= ‘ 85
6th grade
a=.69
9th grade
a.= .72
10th grade
a.= .74
6th grade
a.= .74
9th grade
a.= .79
10th grade
Cl.= .80
6th grade
a= .74
9th grade
a.= .77
10th grade
a.= .78
Across three grades, the missing rate per item ranged from 0.0% to 0.4%, and missing
rates for achievement scores ranged from 0.1 % to 3.0%. An expectation-maximization algorithm was used to replace missing values for analysis of variance (AN OVA) using SPSS,
and the full-information maximum likelihood method was used for SEM analysis using
AMOS (Gr하iam, 2009). In SEM, items were used as observed indicators for each corresponding latent factor. To evaluate the goodness of fit of the models, we applied several
goodness-of-fit indices and the x2 statistics including the Tucker-Lewis index (TLI), comparative fit index (CFI), and root mean square error of appro잉mation (RMSEA). For the
CFI and TLI, coefficients above .90 imply acceptable fit (Hu & Bentler, 1999); and for the
RMSEA, values under .OS indicate close appro씨mate fit and values between .OS and .08
suggest reasonable fit (Browne & Cudeck, 1993).
Results and Discussion
Mean Level Differences Among Grades
The means of various motivational constructs toward mathematics, including interest,
utility value, and perceived competence, decreased with higher grade levels. Multivariate
ANOVA revealed significant univariate main effects of grade level for interest, F(2, 18,894)
Sung-ii Kim, Yi Jiang, and Juyeon Song
I 69
Table 2. Descriptive Statistics of Observed Variables
6th Grade
9th Grade
(n = 7,702)
(n = 5,809)
Variable
M
SD
Interest
Utility value
Perceived competence
Classroom engagement
2.58
3.03
2.73
2.56
0.71
0.59
0.61
0.62
10th Grade
(n = 5,396)
M
SD
M
SD
2.41
2.88
2.46
2.39
0.76
0.65
0.67
0.67
2.33
2.79
2.31
2.32
0.76
0.67
0.65
0.68
=192.16,p < .001; utility value, F(2, 18,894) =248.28,p < .001; perceived competence, F(2,
18,894) =721.30,p < .001; and classroom engagement, F(2, 18,894) =251.50,p < .001. Post
hoc tests further indicated that all four motivation variables decreased significantly across
each grade level.
As Table 2 shows, the largest decreases occurred between sixth and ninth grade. This
result is consistent with those of previous studies that have reported decreases in students'
mathematics motivation as they move through the grades (Gottfried, Marcoulides, Gottfried, & Oliver, 2009; Wigfield & Eccles, 2000). There are several possible interpretations
for this developmental decline in motivation. It has been well established that the transition
from elementary to middle school is coupled with decreases in students' intrinsic motivation,
interest, evaluation of importance, and perceived competence (Eccles et al., 1993; Wigfield
et al., 1991). The changes in the learning environment from elementary to middle school,
including severe competition, frequent social comparison, and impersonalization, may
also affect perceived competence and interest (Eccles et al., 1993). In addition, decontextualization of mathematics learning and formal classroom instruction may contribute to
the decline of utility value and engagement. In Korea, parents and teachers start to εmphasize
academic achievement and put pressure on students when they enter middle school. These
environmental changes during adolescence may undermine academic motivation (Fredricks
& Eccles, 2002).
Relative Predictive Power of Interest and Utility Value on
Classroom Engagement and Achievement
Although mean levels of interest and utility value tend to decline in more advanced grades,
their roles in predicting classroom engagement and achievement may remain the same. To
test the relative predictive power of interest and utility value on students' classroom engagement and achievement, we first tested the measurement models using the maximumlikelihood method with AMOS 7.0. We covaried the errors of classroom engagement (Items
3 and 4) because of the similarity of the item content and high item correlations across all
grade levels. The results revealed that the measurement models were adequate for all three
grade levels (see Table 3).All factor loadings were significant at p < .001 in the three models.
Table 4 presents the correlation coefficients among the latent variables.
Multiple-group analyses based on grade level were then conducted to test the different
predictive power of interest and utility value on classroom engagement and achievement,
70
I The Effects ofInteri잉t and Utility Value on Mathematics Enga양ment and Achievement
Table 3. Goodness-of-Fit Indices of Measurement Models
xi
Model
df
TLI
CFI
RMS EA
6th-grade measurement model 1,039.860
48
.945
.966
.052
.057
957.595
.946
.967
9th-grade measurement model
48
10th-grade measurement model
855.389
48
.952
.970
.056
Note.CFI =c。mparative fit index; RMSEA =root mean square error of approximation; TLI =Tucker-Lewis index.
as well as the different predictive patterns among the three grade levels. To generate the
fin외 model, we first tested the measurement model with equality-constrained factor loaφngs
for the purpose of examining whether indicators measured the same constructs in different
samples. The fit of the measurement model was not worse than that of the unconstrained
models. Therefore, we were able to assume that the indicators measure the factors in comparable ways (Kline, 2005). Following this, we examined the structure model with equality
constraints on all structural paths to test structural path invariance. Next, we examined the
paths, which were rejected in the hypothesis testing about the assumption of equal structural
path coefficients, and varied them on the basis of results of the cumulative multivariate statistics from the structure model. If the model retained comparable goodness-of-fit indices
compared with the structure model, we treated it as a final model (see Table 5).
As depicted in Figure 1, interest strongly predicted classroom engagement and achievement
across the three grade levels, whereas utility value consistently demonstrated relatively low
predictive power compared with interest. Moreover, as grade level rose, the predictive power
of interest on classroom engagement and achievement increased, while the predictive power
Table 4. Zero-Order Correlation Coefficients Among Latent Variables
.65*
.75*
.40*
-찌
꺼n
써
Variable
6th grade
!. Interest
2. U비ity value
3. Classroom engagement
4. Aιhievement
9th grade
1. Interest
2. Ut피tyvalue
3. Classroom en행gement
4. Achieγ·ement
10th grade
1. Interest
2. U비ity value
3. Classroom engagement
4. Achievement
•p < .001.
2
3
.62*
.37*
.53*
.58*
.36*
.54*
.56*
.37*
.53*
---
.68*
.74*
.50*
Sung-ii Kim, Yi Jiang, and fuyeon Song
I 71
Table 5. Goodness-of-Fit Indices for Grade-Level Multiple Group Analysis
x2
df
TLI
CFI
RMSEA
Model
Grade-level multiple comparison
.032
2,852.850
.948
.968
Unconstrained model
144
3,044.515
160
.950
.966
.031
Measurement model
3,146.092
.965
.D30
170
.951
Structure model
2,852.850
144
.948
.968
.032
Final model
Note.CF!= c。mparative fit index; RMSEA = r。ot mean square err。r of appr。ximation; TU= Tucker-Lewis index‘
of utility value on classroom engagement and achievement decreased. Of particular note was
that utility value failed to directly predict achievement for middle and high school students.
These results indicate that interest turned out to be a stronger predictor of classroom engagement and achievement across 따l three grades than ut피ty value and that this trend was
more pronounced in higher grades. Although students’ mathematics interest decreased as
they moved up the grade levels, the predicative power of interest on classroom engagement
and achievement did not decrease but, rather, increased from elementary to middle school
years. This suggests that the role of interest in classroom engagement and achievement
becomes more prominent with age because students' interests develop to deeper levels as
they get older. This explanation par와leis the development of interest described in Hidi and
Renninger’s (2006) Four-Phase Model of Interest Development. Although they described
the development of individual interest as beginning with the triggering of a situational
interest and possibly growing into a well-developed interest, we suggest that a similar developmental pattern is reflected in the interests of younger compared with older students. We
suggest that young children’s interests are more likely to be situational interests, whereas relatively older students are positioned to develop emerging individual interests. Our finding
indicates that (situational) interests for elementary students did not predict achievement directly, whereas (individual) interests for middle and high school students directly predicted
achievement.
Figure 1. Standardized path coefficients from grade-level multiple group analysis (6버 grade/9th grade/10th
grade). Disturbance terms are omitted for clarity. Coefficients in boldface represent significant difference
among grades at p < .OS.
72
J
The Effects of Interest and Utility Value on Mathematics Engagement and Achievement
Table 6. Independent-Samples tTests on Mean Values of Variables
Between Competence Groups
High Competence
Variable
6th grade
Interest
Utility value
Classroom engagement
Achievement
9th grade
Interest
Utility value
Classr。om engagement
Achievement
10th grade
Interest
U버ityvalue
Classroom engagement
Achievement
Low Competence
M
SD
M
SD
2.89
3.18
2.80
163.71
0.64
0.55
0.58
7.65
2.17
2.83
2.25
156.24
0.58
0.59
0.52
7.30
50.95*
27.31 *
43.64*
43.55*
2.95
3.ll
2.76
264.91
0.59
0.57
0.59
8.25
2.02
2.72
2.12
256.39
0.62
0.65
0.60
6.59
57.88*
23.97*
40.45*
41.88*
2.80
2.96
2.62
363.78
0.60
0.63
0.63
9.12
1.89
2.63
2.04
357.24
0.61
0.66
0.60
7.13
55.42*
18.98*
34.59*
28.84*
‘ p < .001.
In contrast, we found that in 9th and 10th grades, ut피ty value failed to predict achievement.
This finding is not consistent with previous research, which has shown that students' perceptions of value are positively related to adaptive academic behaviors and outcomes such as
effort (Cole et al., 2008) and performance (Hulleman & Harackiewicz, 2009; Simons, Dewitte,
et al., 2004). Thus, we tried to test whether utility value’s predictive power on classroom engagement and achievement would depend on students' competence levels.
The Moderating Effect of Perceived Competence
Multigroup analyses between students with high and low perceived competence within
each grade level were conducted to test how perceived competence would moderate the relationships among the variables in the model. Groups with high and low perceived competence were created by median split. Independent-samples t tests revealed significant differences between competence groups for the mean values of the motivation variables and
achievement (see Table 6). We followed the same procedure as we used in the grade-level
multiple-group comparison. Table 7 reveals that all model comparisons among three grades
resulted in good fit indices.
Interest predicted classroom engagement regar버ess of grade level and competence group.
In particular, the predicative power of interest on classroom engagement was higher for lowcompetence students than for high-competence students. Similarly, classroom engagement
demonstrated higher predictive power on achievement for low-competence students than for
high-competence students across all three grade levels. On the contrary, for both 9th- and
10th-grade students, utility value predicted classroom engagement and achievement only for
high-competence students. Figure 2 shows significant paths for the three grade levels.
Sung-il Kim, Yi Jiang, and fuyeon Song
I 73
Table 7. Goodness-of-Fit Indices for Competence-Level Multiple Group Analysis
Model
6th grade
Unconstrained model
Measurement model
Structure model
Final model
9th grade
Unconstrained m。del
Measurement model
Structure model
Fin혀 model
x2
df
TLI
CFI
RMSEA
1,177.659
1,211.910
1,240.948
1,214.634
96
104
109
105
.916
.921
.923
.921
.948
.947
.946
.947
.038
.037
.037
.037
1,008.290
1,075.301
l,123.699
1,076.140
96
104
109
105
.921
.922
.922
.923
.951
.948
.946
.948
.040
.040
.040
.040
10th grade
Unconstrained model
Measurement model
Structure model
847.800
96
.939
.962
1,085.139
.926
.951
104
1,178.545
109
.923
.946
.962
Fin허 model
847.800
96
.939
Note. CF! = comparative fit index; RMSEA = root mean square error of approximation; TL! = Tucker-Lewis index.
.038
.042
.043
.038
Interestingly, we witnessed that utility value failed to predict classroom engagement and
achievement for middle and high school students with low perceived competence, whereas
utility value consistently emerged as a positive predictor of classroom engagement and
achievement for students with high perceived competence. We assume that this result might
be explained by the fact that students with low perceived competence may also feel that
they lack control of their mathematics ability. This perception may in turn prevent them
from engaging in classes, leading to a vicious cycle resulting in poor performance. We
imagine that this trend could occur regardless of whether students perceive mathematics as
a useful subject, because their feelings about lack of control may lead them to view their situations as impossible to overcome. On the other hand, although interest failed to predict
achievement directly for low-competence students in middle and high school, it did significantly predict classroom engagement, which is moderately linked to achievement.
Conclusions, Implications, and Future Work
Using a large national cross-sectional data set of 6th, 9th, and 10th graders in Korea, we
were able to compare the relative predictive power of interest and utility value on classroom
engagement and achievement in mathematics. We also examined whether the predictive
power of interest and utility would change across grade levels and whether the predictive
patterns would differ depending on students' perceived competence.
We confirmed that interest turned out to be a stronger predictor of classroom engagement
and achievement than utility value. Moreover, the predictive power of interest on engagement
and achievement increased as grade level rose. The predictive power of interest increased
most from elementary school to middle school, although students' interest decreased the
74
I The E￦cts of Inκrest and Utiliη Value on Mathematiα Engagement and A찌1α·ement
9th Grade
Figure 2. Standardized path coefficients from competence-level multiple group analysis. Coefficients to the
left of the slash are for the high-competence group; coefficients to the right of the slash are for the low-competence group. Disturbance terms are omitted for clarity. Coefficients in boldface represent significant duference between the groups with high and low perceived competence at p < .05.
most during the same period. Interest, as an intrinsic motivation, has been linked to adaptive
school functioning and academic performance (e.g., Renninger et al., 2002; Schiefele et al.,
1992). Because the transition period from elementary to middle school appears to be a
critical period for interest development, it is imperative to design learning environments to
promote interest in middle school. For example, it would be beneficial to develop interests
of middle school students by providing learning materials that they find relevant and restricting normative evaluation.
Contrary to our expectations, the predictive power of utility value decreased as grade
level rose. However, we further found that this result should be interpreted together with
students' competence levels. In particular, the decreased predictive power of utility was
observed only among students with low competence. In other words, utility value could
lead students to engage in their classes or to improve achievement only when their perceived
competence is high. Thus, it may not be effective for students with low competence to provide utility value interventions or to emphasize the high utility value of mathematics.
These findings shed light on how we can help students with different perceptions of
their own competence improve their mathematics achievement. For students who have low
Sung-ii Kim, Yi Jiang, and Juyeon Song
I 75
mathematics competence, it is more helpful for educators to facilitate students' interest in
mathematics than to emphasize its utility value, if the goal is to enhance students' classroom
engagement and achievement. By contrast, for students who have high mathematics competence, emphasizing the utility value of mathematics appears to be as important as eliciting
interest to facilitate their classroom engagement and achievement.
There are several empirical findings pointing to the effectiveness of a simple form of
utility value intervention such as providing utility information for a topic or asking students
to generate relevant uses of a topic (Durik & Harackiewicz, 2007; Hulleman & Harackiewicz,
2009). However, findings on the interactive nature of utility value intervention and perceived
competence are mixed. Whereas previous research has pointed out that students with low
interest or low competence would be more sensitive to utility value (Hulleman & Barackiewicz, 2009; Shechter et al., 2011 ), the present study showed that utility value was more related to engagement and achievement for students with high competence. Clarification is
needed to show whether these inconsistent findings might be due to differential cultural
context, age, or academic domain. Further research is required to identify developmental,
cultural, and methodological differences and to resolve contradictory findings. In addition,
longitudinal studies are needed to further understand developmental trends in the relative
predictive power of interest and utility value on achievement within individuals. In particular,
it may also be important to investigate situational and individual interest as distinct phases
to explain when and how situational interest develops into individual interest.
Acknowledgments
This research was supported by a grant from the College of Education of Korea University
awarded in 2012.
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