Chapter 4 Student Involvement: The Effect of Individual Learning Prerequisites in the
4.4 Results
Correlations and Descriptive Statistics
The primary goal of the current study was to examine the relationship between individual learning prerequisites and student involvement in mathematics learning and whether the tablet use moderated the relationship. Examining the intercorrelations between the study variables was the basis of the subsequent regression analyses. Table 4.1 presents a correlation matrix for the key constructs of the current study. It shows that the three constructs of the individual learning prerequisites were significantly correlated with students’ situational interest.
Each construct of the learning prerequisites also significantly and positively correlated with students’ cognitive engagement in mathematics classes. Furthermore, regarding the descriptive statistics of the key constructs, Table 4.2 presents the means, standard deviations, and ranges of each study variable for the tablet and non-tablet class conditions.
Table 4.1
Intercorrelations of Study Variables
Construct 1 2 3 4 5
1. Math prior knowledge —
2. Intrinsic motivation in math .33** —
3. Math self-concept .28** .75** —
4. Situational interest in math .17* .63** .49** —
5. Cognitive engagement in math .13* .48** .41** .63** —
Note. All the correlation coefficients are standardized.
*p < .05, 2-tailed. **p < .01, 2-tailed.
Table 4.2
Descriptive Statistics of Study Variables
Variable Non-tablet class Tablet class
M SD Min/Max M SD Min/Max
Learning prerequisites
Prior knowledge in matha 23.33 7.32 3/46 21.64 7.14 4/48 Intrinsic motivation 2.55 0.96 1/4 2.88 0.92 1/4 Math self-concept 2.64 0.68 1/4 2.89 0.73 1/4 Student involvement
Situational interest 2.39 0.98 1/4 2.89 0.90 1/4 Cognitive engagement 2.90 0.88 1/4 3.11 0.84 1/4
Note. Sample of non-tablet class condition n = 1,017; sample of tablet class condition n = 1,089. The study variables were measured using a 4-point Likert scale ranging from 1 (does not apply at all) to 4 (totally applies).
a Prior knowledge in math was assessed using a standardized test (i.e., the KRW), which contained 57 questions.
The total score ranged from 0 to 57.
RQ1: The Influences of Learning Prerequisites on Student Involvement
In the present study, since the student involvement consisted of two main constructs (situational interest and cognitive engagement), we conducted separate linear regression analyses. Both analyses involved multiple individual learning prerequisites as the predictor variables. In the first model, we regressed situational interest on three learning prerequisites (prior knowledge in math, intrinsic motivation in math, and math self-concept).
For the first regression model, the goodness of fit indices showed that the model with situational interest as the dependent variable had a good model fit: χ2 = 878.71, df = 60, p < .001;
SRMR = .05; RMSEA = .07, 95% CI [.07, .08]; and CFI = .95. Moreover, the results of the first regression model indicated that students’ prior mathematics knowledge was significantly predictive of higher situational interest in math classes: β = .21, SE = .10, 95% CI [.09, .23], p
= .02. From this standardized regression coefficient, we determined that adequate prior mathematics knowledge predicted a higher level of situational interest. Regarding the second learning prerequisite construct, the results pointed out that students’ intrinsic motivation in math significantly and positively predicted their situational interest: β = .53, SE = .03, 95% CI [.50, .63], p < .001. The significant standardized regression coefficient was consistent with our expectation that students’ intrinsic motivation positively predicts greater situational interest in
math classes. Furthermore, the results also indicated that the effect of students’ math self-concept on situational interest was statistically significant (β = .04, SE = .03, 95% CI [.03, .15], p < .01). This finding was consistent with the hypothesis that students’ academic self-concept in math was a positive predictor of their situational interest in mathematics classrooms.
In the second linear regression model, the dependent variable was the students’
cognitive engagement in mathematics classes. The goodness-of-fit indices showed a good model fit: χ2 = 982.80, df = 39, p < .001; SRMR = .06; RMSEA = .09, 95% CI [.09, .10]; and CFI = .90. Building on the adequate fitness, the results revealed that students’ prior mathematics knowledge positively predicted on cognitive engagement in mathematics classes:
β = .63, SE = .07, 95% CI [.49, .77], p < .001. The finding implied that higher prior mathematics knowledge predicted a greater level of cognitive engagement. For the second predictor variable, the results showed that students’ intrinsic motivation in mathematics significantly and positively predicted their cognitive engagement: β = .39, SE = .02, 95% CI [.31, .40], p < .001.
Based on the finding, we determined that students with higher intrinsic motivation seem to show greater cognitive engagement in mathematics classes. Furthermore, regarding the last individual learning prerequisite, the findings showed that students’ academic self-concept in math significantly impacted their cognitive engagement in mathematics: β = .09, SE = .03, 95%
CI [.04, .16], p < .001. In other words, students who had high math self-concept were more cognitively engaged in mathematics classes.
The above findings were consistent with our expectations regarding the effect of individual learning prerequisites. The results confirmed that the three individual learning prerequisites were positive predictors of students’ situational interest and cognitive engagement in mathematics learning.
RQ2: The Use of Tablet Computers as Moderator
In the current study, student involvement consisted of two constructs. To test whether the effect of individual learning prerequisites on student involvement depends on the use of tablet computers (RQ2), we conducted separate latent interaction analyses (i.e., multiple-group SEM). The first part of this research question investigated the moderation effect of using tablet computers on the effect of learning prerequisites on students’ situational interest.
First, the result indicated a good model fit of the simple linear regression models of the multiple-group SEM regarding intrinsic motivation and situational interest: χ2 = 10656.34, df
= 56, p < .001; SRMR = .02; RMSEA = .04, 95% CI [.03, .04]; and CFI = .99. Based on this
model, the results indicated that intrinsic motivation had a significant influence on situational interest in both the non-tablet group (βyx|0 = .65, SE = .02, 95% CI [.60, .70], p < .001) and tablet group condition (βyx|1 = .58, SE = .03, 95% CI [.52, .64], p < .001). Therefore, high intrinsic motivation for both groups of students was predictive of high situational interest in mathematics classes.
The regression lines of the two conditions were plotted in Figure 4.2. In the tablet group, the positive regression slop was slightly smaller than the slop in the non-tablet group. In other words, it is reasonable to interpret that under the tablet class condition (MT = 1), the change in situational interest associated with a 1-unit of intrinsic motivation is smaller than the ones in the non-tablet class condition (Mc = 0). Thus, the use of tablet computers significantly moderated the relationship between intrinsic motivation and situational interest in mathematics classes.
Figure 4.2
Interaction Effect of Using Tablets on the Relationship Between Intrinsic Motivation and Situational Interest
Note. This graph demonstrates two regression slopes, in which situational interest was regressed on intrinsic motivation. This graphical representation was based on the standardized scores in the regression equation. The dichotomous moderator is the use of tablet computers (0 = non-tablet group, 1 = tablet group).
Additionally, to compare the corresponding effects between the two groups, the overall variance in intrinsic motivation and situational interest was constrained across the two groups.
Based on the constrained model, the results indicated that the effect of intrinsic motivation and situational interest was significantly different between the tablet and non-tablet class conditions (β = -.09, SE = .04, 95% CI [-.17, .00], p = .05). The results of the constrained model found
-2 -1 0 1 2
-2 -1 0 1 2
Situational Interest in Math
Intrinsic Motivation in Math
Non-tablet group Tablet group
that the interaction effect explains a significant amount of the variance in students’ situational interest (βyx = -.09, SE = .04, 95% CI [-.17, .00], p = .05; across group R2 = .41, p < .001). In other words, for the tablet group, the impact of intrinsic motivation on situational interest was smaller than the non-tablet group; and statistically, the interaction effect accounted for 41% of the variation in situational interest. Therefore, the findings were consistent with our expectation that the use of tablet computers in mathematics classes significantly moderates the relationship between students’ intrinsic motivation and situational interest.
Moreover, the results of the second multiple-group SEM indicated that math self-concept significantly predicted situational interest in both the non-tablet group (βyx|0 = .44, SE
= .03, 95% CI [.37, .59], p < .001) and the tablet group (βyx|1 = .47, SE = .03, 95% CI [.39, .55], p < .001). Based on this finding, the regression lines of two groups were plotted in Figure 4.3.
The positive regression slope of the tablet group was slightly steeper than that of the non-tablet group. However, the results of the multiple-group SEM did not identify a significant difference between the two groups. Thus, the use of tablet computers did not significantly moderate the relationship between math self-concept and situational interest in mathematics classes.
Figure 4.3
Interaction Effect of Using Tablet on the Relationship Between Math Self-Concept and Situational Interest
Note. This graph demonstrates two regression slops, in which situational interest was regressed on math self-concept. This graphical representation was based on the standardized scores in the regression equation. The dichotomous moderator is the use of tablet computers (0 = non-tablet group, 1 = tablet group).
Nevertheless, regarding the third individual learning prerequisite, the results of the multiple-group SEM relating prior mathematics knowledge to situational interest did not show
-2 -1 0 1 2
-2 -1 0 1 2
Situational Interest in Math
Math Self-Concept
Non-tablet classes Tablet classes
a significant difference between the tablet and non-tablet class conditions. Therefore, the use of tablet computers in mathematics classes did not significantly moderate the relationship between students’ prior knowledge and situation interest in mathematics learning.
Since two constructs captured the student involvement in mathematics learning, the second part of RQ2 investigated the moderating effects of using tablet computers on the relationship between individual learning prerequisites and cognitive engagement in mathematics learning. Regarding the effect of intrinsic motivation on cognitive engagement, the results indicated a significant standardized regression in both the non-tablet group (βyx|0
= .48, SE = .03, 95% CI [.42, .54], p < .001) and the tablet group (βyx|1 = .47, SE = .03, 95% CI [.40, .53], p < .001). Nevertheless, after comparing the two regression coefficients, the results did not find a significant difference between the tablet and non-tablet groups (p = .96).
Therefore, the use of tablet computers did not significantly moderate the relationship between students’ intrinsic motivation and cognitive engagement in mathematics classes.
Furthermore, the results indicated that math self-concept significantly predicted the students’ cognitive engagement in both the non-tablet group (βyx|0 = .72, SE = .02, 95% CI [.58, .73], p < .001) and the tablet group (β yx|1 = .46, SE = .04, 95% CI [.39, .74], p < .001).
The regression lines of the two groups are depicted in Figure 4.4. The regression slope of the non-tablet group is steeper than that of the tablet group. Therefore, under the tablet class condition (MT = 1), the change in math self-concept associated with a 1-unit increase in cognitive engagement is smaller than under the non-tablet class condition (Mc = 0).
Figure 4.4
Interaction Effect of Using Tablet on the Relationship Between Math Self-Concept and Cognitive Engagement
Note. This graph demonstrates two regression lines, in which cognitive engagement was regressed on math
self-concept. This graphical representation was based on the standardized scores in the regression equation. The dichotomous moderator is the use of tablet computers (0 = non-tablet group, 1 = tablet group).
More importantly, the results revealed that the regression coefficients in relating math self-concept to situational interest were statistically different between the two groups (βyx = -.18, SE = .06, 95% CI [-.30, -.06], p = .05; ΔR2 = .61, p < .001). In other words, for those students in tablet group, the impact of their math self-concept on cognitive engagement was smaller than the non-tablet group. Thus, the use of tablet computers significantly moderated the relationship between math self-concept and cognitive engagement in mathematics classes.
Finally, when looking at the moderation effect between the prior mathematics knowledge and cognitive engagement in mathematic learning, the results did not show a significant interaction.