The Effects of Interest and Utility Value on ...

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 further examined how predictive power changed across different grade levels (i.e., 6th grade in elementary school, 9th grade in middle school, and 10th grade in high school) and tested the moderating effect of perceived competence in predicting the relationships of both interest and utility 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 multiple-sample SEM between students with high and low perceived competence within each grade level. The results indicated that for classroom engagement and achievement across all three grades, interest is a stronger predictor than utility value. Moreover, the difference in predictive power between interest and utility value became more pronounced as students moved to higher grades. In particular, 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 further revealed that the predictive power of utility value decreased only among those who had low perceived competence but remained significant for those who had high perceived competence. Taken together, these results suggest that for middle and high school students who lack mathematics competence, it is more helpful 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; Stodolsky, 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 | The Effects of Interest and Utility on Mathematics Engagement 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, 2000). 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 types 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 instrumentality, the extent to which a particular task is perceived as relevant and useful for present or future goals (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 activity itself. As such, goal attainment drives a person’s engagement in instrumental activity. 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-il Kim, Yi Jiang, and Juyeon Song | 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 value 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 Utility Value in Mathematics Achievement It is known that both interest and utility value predict achievement-related behaviors such as deep engagement, effort regulation, 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. Köller, 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 instrumentality has also shown that perceived relevance and usefulness predict motivation and performance (Husman & Lens, 1999; Malka & Covington, 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, &


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 mathematics grades in 10th grade. Given the inconsistent findings on the effect of interest and utility value on important educational outcomes, it is necessary 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 value. 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 utility value and interest, it is likely that perceived competence acts as a moderator of the relationship between utility value and engagement and achievement.


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’ perceptions of control of achievement in an academic task (Bandura, 1997; Skinner, Wellborn, & Connell, 1990). Ryan and Deci (2000) argued 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 5 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-type 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).


Table 1. Items and Reliabilities of Scales Variable

Item

Reliability

Interest

1. I prefer math problems that cannot be easily solved. 2. I like 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 for diverse careers in the future.

Classroom engagement

1. I listen very 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 matter how hard I try [reversed]. 4. I think math is more difficult for me than for other people [reversed].

6th grade α = .81 9th grade α = .84 10th grade α = .85 6th grade α = .69 9th grade α = .72 10th grade α = .74 6th grade α = .74 9th grade α = .79 10th grade α = .80 6th grade α = .74 9th grade α = .77 10th grade α = .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 (ANOVA) using SPSS, and the full-information maximum likelihood method was used for SEM analysis using AMOS (Graham, 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 χ2 statistics including the Tucker-Lewis index (TLI), comparative fit index (CFI), and root mean square error of approximation (RMSEA). For the CFI and TLI, coefficients above .90 imply acceptable fit (Hu & Bentler, 1999); and for the RMSEA, values under .05 indicate close approximate fit and values between .05 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)


Table 2. Descriptive Statistics of Observed Variables 6th Grade (n = 7,702)

9th Grade (n = 5,809)

10th Grade (n = 5,396)

Variable

M

SD

M

SD

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

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 emphasize 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,


Table 3. Goodness-of-Fit Indices of Measurement Models Model 6th-grade measurement model 9th-grade measurement model 10th-grade measurement model

χ2

df

TLI

CFI

RMSEA

1,039.860 957.595 855.389

48 48 48

.945 .946 .952

.966 .967 .970

.052 .057 .056

Note. CFI = comparative 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 final model, we first tested the measurement model with equality-constrained factor loadings 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 Variable 6th grade 1. Interest 2. Utility value 3. Classroom engagement 4. Achievement 9th grade 1. Interest 2. Utility value 3. Classroom engagement 4. Achievement 10th grade 1. Interest 2. Utility value 3. Classroom engagement 4. Achievement *p < .001.

1

2

3

— .65* .75* .40*

— .62* .37*

— .53*

— .68* .77* .51*

— .58* .36*

— .54*

— .68* .74* .50*

— .56* .37*

— .53*


Table 5. Goodness-of-Fit Indices for Grade-Level Multiple Group Analysis Model Grade-level multiple comparison Unconstrained model Measurement model Structure model Final model

χ2

df

TLI

CFI

RMSEA

2,852.850 3,044.515 3,146.092 2,852.850

144 160 170 144

.948 .950 .951 .948

.968 .966 .965 .968

.032 .031 .030 .032


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 all three grades than utility 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 parallels 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.

Interest

ns/.24/.25 .61/.69/.68

.65/67/.68

Utility Value

Classroom Engagement .22/.12/.09

.48/.36/.32 Achievement

.08/ns/ns

Figure 1. Standardized path coefficients from grade-level multiple group analysis (6th grade/9th grade/10th grade). Disturbance terms are omitted for clarity. Coefficients in boldface represent significant difference among grades at p < .05.


Table 6. Independent-Samples t Tests on Mean Values of Variables Between Competence Groups High Competence Variable 6th grade Interest Utility value Classroom engagement Achievement 9th grade Interest Utility value Classroom engagement Achievement 10th grade Interest Utility value Classroom engagement Achievement

Low Competence

M

SD

M

SD

t

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 3.11 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, utility 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 regardless 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.


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 model Measurement model Structure model Final model 10th grade Unconstrained model Measurement model Structure model Final model

χ2

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 1,123.699 1,076.140

96 104 109 105

.921 .922 .922 .923

.951 .948 .946 .948

.040 .040 .040 .040

847.800 1,085.139 1,178.545 847.800

96 104 109 96

.939 .926 .923 .939

.962 .951 .946 .962

.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 | The Effects of Interest and Utility on Mathematics Engagement and Achievement Interest

ns/–.18 .47/.54

6th Grade

.66/.46 .28/.22 Utility Value

Classroom Engagement

ns/ns .41/.61

.68/.58 .29/.10 Utility Value

.46/.57 .74/.61 .26/ns Utility Value

Classroom Engagement

.14/.42

Achievement

.15/ns

Interest

10th Grade

Achievement

.13/.07

Interest 9th Grade

.29/.47

.23/ns Classroom Engagement

.21/.41

Achievement

.10/ns

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 difference 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


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 & Harackiewicz, 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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