Within-students variability in learning experiences, and teachers' perceptions of students' task-focus

We specified multilevel structural equation models (MSEM) in Mplus (Muthén & Muthén, 2012). At the within level we specified a latent state construct ξ_W1 using x₁ to x₃ as indicators (see Figure 2). At the between level, we specified a correspondence between level trait construct ξ_B1, equating factor loadings across the levels for metric invariance between the state and trait constructs (Morin, Marsh, Nagengast, & Scalas, 2014). We then specified a second between-level construct, which captures interindividual differences in intraindividual variability, ξ_B2 using k indicators.

Figure 2. MSEM of state- trait and variability constructs

Note: Indicators are raw data of time-points (t) nested in students (i). Circles above (at the between level, e.g., X1B) and below (at the within level e.g., X1W) the indicators depict latent constructs of decomposed between- and within-level indicators respectively. There is one within-level latent construct (ξW1) and two between-level constructs (ξB1 and ξB2), with factor loadings (λ, one-headed arrows) linking constructs to level-specific indicators. Variances of latent constructs are indicated in double headed arrows (ψ). Residuals of indicators are also depicted with double headed arrows (ε), at the within-level measurement error. The mean-structure (triangle with 1 inside) is estimated at the between-level (i.e., cluster-intercepts, τ).

In the dataset we created lagged variables (xkT+1) of each indicator (xkT) for each student. This gave 285 additional lines of data, one for each participant in our data-matrix, giving a total of nti = 3,718 lines of data (see Appendix 1). We then, in Mplus, defined intraindividual squared deviations (xkT+1 - xkT)2 which we used as indicators (see Appendix 2). The scalar of the MSSD equation, 1/(n-1), was not necessary to apply as there are n-1 number of successive differences for each participant. Calculating the average of the successive differences is to divide the sum of the squared successive differences by n-1. We specified MSEMs, presented in Figures 3-5, for each construct using one (difficulty), two (competence), and three indicators (intrinsic motivation) for each latent construct separately (Models 1-3). We then illustrated how to specify three multivariate models, presented in Figure 6 for investigating convergence between trait and variability constructs, and between variability and task-focus (Models 4-6). We inspected indices of convergence (association of higher magnitude where expected) and divergence (lack of association where expected; Campbell & Fiske, 1959).

Model fit was assessed by inspecting cut-offs for goodness of fit indices: ≤.06 for good model fit using the Root Mean Square Error of Approximation (RMSEA) and the Standardized Root Mean Square Residual for the within (SRMRW) and the between level (SRMRB), and ≥.90 for acceptable and ≥.95 for good model fit for the Comparative Fit Index (CFI; Browne & Cudeck, 1993). Assuming MAR we treated missing data (4.8% of the missing data-points, in the dataset with the non-lagged variables) using the default FIML algorithm in MPlus (Muthén & Muthén, 2012). We used the robust maximum likelihood estimator (MLR) which corrects standard errors for non-normality.

3. Results

In order to test structural validity of the state, trait, and variability-constructs of each learning experience, we present a univariate MSEM specified with one manifest indicator (task-difficulty), two indicators (competence evaluation), and three indicators (intrinsic motivation). To investigate the association between trait and variability-constructs we report on the correlation between these latent constructs.

3.1. Univariate models

As shown in Fig 3, we illustrate how to specify our proposed model using a single item indicator. To identify this model we fixed a number of parameters: all factor loadings (at 1), and residuals (at 0). The pooled within-level variance was ψ_W1= 0.88 and between ψ_B1 = 0.26, showing that 22.5% of the variance of task difficulty resided at the between level. We note that the variance of the variability construct, ψ_B2 = 2.05, was larger than the variance of the trait construct. The association between trait-task-difficulty and variability in task-difficulty was ρ = 0.46, that is the more difficult tasks appeared on average during the week, the more variability in task-difficulty (i.e., larger ups and downs in task difficulty during the week).

Figure 3. Multilevel structural equation model of latent state, trait and intraindividual variability of task difficulty.
Note: manifest indicators are diff = task-difficulty

As shown in Fig 4, we illustrate how to specify our proposed model using two indicators. The pooled within-level variance was ψ_W1 = 0.32 and between ψ_B1 = 0.13, showing that 29.5% of the variance of competence beliefs resided at the between level. We note that the variance of the variability construct, ψ_B2 = 0.66, was larger than the variance of the trait construct. The association between trait intrinsic motivation and variability in intrinsic motivation was ρ = -0.72, that is the more competent students thought they were on average during the week, the less variable they thought their competences were during the week (i.e., smaller ups and downs in competence belief during the week).

Figure 4. Multilevel structural equation model of latent state, trait and intraindividual variability of competence belief.
Note: manifest indicators are well = how well?, und = understanding

As shown in Fig 5, we illustrate how to specify our proposed model using three indicators. The pooled within-level variance was ψW1= 0.51 and between ψ_B1 = 0.32, showing that 38.7% of the variance of competence evaluation resided at the between level. We note that the variance of the variability construct, ψ_B2 = 1.26, was larger than the variance of the trait construct. The association between trait-task-difficulty and variability in task-difficulty was ρ = -0.35, that is the more intrinsically motivated students thought they were on average during the week, the less their motivation fluctuated during the week (i.e., smaller ups and downs in intrinsic motivation during the week).

Figure 5. Multilevel structural equation model of latent state, trait and intraindividual variability of intrinsic motivation.
Note: manifest indicators are enj = enjoyment, int = interest, and cho = choice.

3.2. Multivariate models

In models 4 to 6 we present three possible models for investigating convergent validity of the variability constructs (see Fig 6). In Model 4 we specified three state constructs at the within-level, with three corresponding trait constructs at the between-level, and three variability constructs. The structural parameters of interest are the associations between the trait-construct and variability-construct of task difficulty (ρ = 0.46), competence belief (ρ = -0.64) and intrinsic motivation (ρ = -0.35) respectively. These associations were similar to the ones found in the separate univariate models.

In Model 5 we specified associations between the three trait-constructs and teacher-reported student task-focus, and between variability constructs and task-focus. More task-focused students, on average during the week, found tasks easier (ρ = -0.19), felt more successful (ρ = 0.38), and were more intrinsically motivated (ρ = 0.25). More task-focused students found tasks of more equal difficulty (ρ = -0.26), fluctuated less in their competence beliefs (ρ = -0.35), but were not significantly less variable in their intrinsic motivation.

In Model 6 we specified a higher-order construct of variability. This means that the factor loadings of the higher-order construct explain the associations between the latent constructs. Students who were more variable overall (i.e., a higher value on the higher-order variability construct) found, on average during the week, task more difficult (ρ = 0.50), their competence lower (ρ = -0.62) and were less intrinsically motivated (ρ = -0.32).

Figure 6. Multivariate models of state, trait and variability constructs.
Note: Only structural parts of the models shown for clarity. Estimates (standardized correlations) are from Mplus 7.4 (Muthén & Muthén, 2012).

4. Discussion

In order to advance our understanding of students’ learning processes in real time, we investigated intraindividual variability in students’ learning experiences, and convergence between intraindividual variability and teacher-reported task-focus. Inclusion of such intraindividual variability construct(s) in process models of learning experiences would expand current modelling practices in the field. Up to now, models include: (1) decomposition of learning experiences into within (time-points) and between (students) components, (2) random (moderator) effects of perceptions of the context on learning experiences, and (3) fixed and moderation effects of personal characteristics on learning experiences. As the MSSD captures both magnitude and order of events (von Neumann et al., 1941; Jahng et al., 2008), we created a dataset with lagged variables and specified aggregated variables to use in MSEMs. We specified three latent constructs: a state-construct at the within-level, and a trait and an intraindividual variability construct at the between-level. In response to our first research question regarding the structural validity of state-trait and variability dimensions of learning experiences, we found support for the specificity of the intraindividual variability dimension. Importantly, this suggests that intraindividual variability in learning experiences such as motivation, adaptive behaviours, and competence evaluations capture an important dimension of students’ experiences of learning, in addition to variability of constructs in other fields of research, e.g., affect instability (Trull et al., 2008).

In response to our second research question, we confirmed the hypothesis that trait and variability dimensions of learning experiences converged with teacher-reported task focus. Importantly, teacher reports of higher task-focus were related to more adaptive learning experiences on average during the week (i.e., less difficulty, feeling more competent, experiencing higher intrinsic motivation), and to less variability in these same learning experiences (i.e., a smaller magnitude in momentary fluctuations from one learning episode to the next).

4.1. State, trait and individual differences in intraindividual variability

We found three sources of support for the distinction between state, trait and variability dimensions of the same construct. First, MSEM of each learning experience construct in turn (Models 1-3) suggested that state, trait and intraindividual variability are separable constructs. Importantly, this expands existing two-level models in which states and traits have been modeled at the within and between levels respectively (e.g., Roesch et al., 2010). Second, inspection of associations between trait and intraindividual variability constructs at the between level suggested convergence, that is traits and variability dimensions of each construct were moderately to strongly associated |ρ| = .35 to .64. Third, Model 6 suggested that intraindividual variability could be specified as a higher-order construct. Taken together, our MSEM using aggregates of MSSDs of each indicator was deemed successful for portraying the variability dimension. Going beyond previous studies (Malmberg et al., 2013; Schmitz & Skinner, 1993) which have shown that there is more variance within (i.e., intraindividual) than between students (i.e., interindividual difference), we suggest it is possible to retrieve systematic variance of intraindividual experiences by specifying intraindividual variability dimensions of constructs. Importantly, this demonstrates that there are systematic individual differences in how students vary within themselves. There are at least two research contexts in which it could be useful to implement the specification of such an intraindividual variability construct in its own right. First, it could be possible to design intervention studies with bursts of collections of intensive longitudinal data (Schmitz, 2015; Walls, Barta, Stawski, Collyer, & Hofer, 2011). If measures of intraindividual variability could be obtained at both pre- and post-tests, it would be possible to investigate treatment effects geared towards decreasing such intraindividual variability. Second, if reports of student-teacher interaction were possible to collect alongside collection of students’ self-reported learning experiences, it would be possible to specify models in which teacher sensitivity to disengagement or off-task behaviour might alleviate intraindividual variability.

With regard to questionnaire design, we suggest it could be possible to create at least two types of psychometric measures, for researchers who do not aspire to measure processes by collecting intensive longitudinal data. First, while previous self-report measures of emotional self-concept (i.e., emotional stability, meaning the perception of feeling calm, emotionally stable and worried; e.g., Marsh, 1989) and stability of self-esteem (Rosenberg, 1965), have indeed focused on intraindividual variability as a trait, the findings from our present study suggest that it could be possible to create a wider range of “variability-as-a-trait” constructs. Second, while present observation instruments of students’ engagement and task-focus are designed to capture trait aspects (Zhang et al., 2011), future instruments could focus on variability of such observations.

4.2. Intraindividual variability and teacher perceptions of task-focus

Task-focus, as a psychometric construct, is operationalized as a trait-level of students’ adaptive work habits in classrooms, the extent to which each individual student attempts difficult tasks, persists and stays focused on these (Nurmi, & Aunola, 1998; Aunola et al., 2000; Zhang et al., 2011). Model 5 showed that teacher-reported student task-focus was associated with less difficulty, stronger sense of competence and more intrinsic motivation, in line with Hypothesis 1. In a previous study, lower achievers were found to withdraw effort when confronted with a difficult task, while higher achievers exerted more effort (Malmberg, Walls, et al., 2013). Consistent with the idea that students who experience learning as inherently interesting, pay attention and focus on their task at hand in that learning situation (Nurmi et al., 2008), teacher rated task-focus was also related with higher levels of intrinsic motivation. This does not mean that teachers can "see" students' motivation as such (Lee & Reeve, 2012), but rather intrinsic motivation manifested as energized behaviour (Sheldon & Elliot, 1998). A higher level of task-focus was also related to students’ trait competence evaluation. Competence belief also varied from one learning situation to another. Future studies should investigate to what extent this is linked with experiences of particular school subjects or particular teachers. Taken together, the current and the previous study hint at the importance to further investigate stability and variability in the ways teachers support and place demands on students, that are optimal for students’ learning over time.

There were three important associations between task-focus and variability. A higher level of task-focus was related, first, to less variability in difficultly and competence beliefs, and, second, to a higher level of the higher-order variability-construct. Importantly, it appears that variability could be construed as a trait dimension in itself. The variability-construct might play an important role in models of self-regulation (Boekaerts & Corno, 2005), in which “top-down” self-regulation is typical of students who steer their learning processes by setting goals for enhancing their knowledge by sustaining motivation, rather than being obstructed by situational demands and setbacks typical of “bottom-up” self-regulation. An important future research task would be to investigate intraindividual variability in relation to self-set learning goals (or the lack of such goals).

There are two important implications of students’ variability in learning experiences for the different ways in which teachers can support different students. First, the variability in itself demonstrates that all students have ups and downs, less task-focused students more so than more task-focused students. It would be important for teachers to capture the “ups”, particularly of less task-focused students. Teachers want to capitalize on students’ “ups” as these would be teachable moments (Hamre & Pianta, 2005; Pianta & Hamre, 2009). Second, the variability in students’ learning experiences is inherently linked to experiences of the learning context. From the teachers’ point of view there lurks a danger in them classifying students as “engaged” or “disengaged” as all students have their ups and downs. This means that “engaged” students have their disengaged moments. These are moments when teachers can redirect students. It also means that “disengaged” students have their engaged moments. These moments are the ones to capitalize on for learning; the others for redirection. It would be important also for teacher educators to focus on the meaning of intraindividual variability, allowing prospective teachers to focus on changes in student behaviours and actions in real time.

In future studies, it would be important to combine studies of students’ intraindividual variability and measure of teacher support. Teachers in classrooms can promote students’ learning processes by supporting their autonomy (Reeve, Jang, Carrell, Jeon, & Barch, 2004), being involved with students and structuring the learning contents (Skinner & Belmont, 1993), providing task-contingent praise (Deci, Koestner, & Ryan, 1999), providing feedback directed at reducing discrepancies between current understanding and learning goals (Hattie & Timperley, 2007), and tailoring goals to individual learners (Hattie, Biggs, & Purdie, 1996; Butler & Winne, 1995; Pianta, Belsky, Vandergrift, Hours, & Morrison, 2008), in order to enhance motivation, effort, and selection of optimally difficult tasks.

4.3. Limitations

There were three limitations of the present study. First, the lagged variables we created spanned from 5 to 29 observations, which is shorter than the typical time-series model. However, for the purpose of calculating the MSSD the number of observations might be sufficient (Ebner-Priemer et al., 2009). Future studies of students’ learning processes should aim at collecting more repeated measures for the purpose of creating longer time-series. Such a demand needs to be carefully weighed against the risks of response fatigue of participants. Second, the model we applied assumes equivalent duration between each time-lag (e.g., Jahng et al., 2008). Thus our models do not account for unequal number of responses per day, unequal lags between each subsequent reports, and downtime when not at school. The current findings would need to be replicated with models more suitable for unequally spaced lagged data. Third, the empirical data stem from a particular age-group in a particular sociocultural context, England, so replications in other contexts and age-groups would be valuable to carry out.

4.4. Conclusions

Variability in intraindividual learning experiences captures the abruptness, frequency, order, and magnitude of students’ “ups and downs” in their engagement during a week at school. Teacher perceived student task-focus converged with both trait-levels and variability in task difficulty, competence beliefs and intrinsic motivation. Intraindividual variability formed a higher-order construct. Overall, our study provides support for intraindividual variability as a construct in its own right, which has the potential to provide novel insight into students’ learning processes.

Keypoints

• We investigated intraindividual variability of primary school students' experience of learning.
• We used the mean square successive differences (MSSD) as an index of magnitude of variability.
• We specified latent state, trait, and intraindividual variability constructs using multilevel structural equation models (MSEM).
• Higher teacher-reported-task-focus was related to less variability in learning experiences.
• Intraindividual variability is an important educational construct in its own right.

Acknowledgements

The Learning Every Lesson (LEL) study was funded by the John Fell Foundation, and carried out during the first author’s Research Councils UK (RCUK) fellowship 2007-12.

References

Aunola, K., Nurmi, J.-E., Parrila, R., & Onatsu-Arvilommi, T. (2000). Behavioral strategy relating scale II. Unpublished measurement instrument Jyväskylä: University of Jyväskylä, Finland.
Boekaerts, M., & Corno, L. (2005). Self-regulation in the classroom: A perspective on assessment and intervention. Applied Psychology: An International Review, 54, 199-231. doi: 10.1111/j.1464-0597.2005.00205.x
Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen, & J. S. Long (Eds.), Testing structural equation models (pp. 136-162). Beverly Hills, CA: Sage.
Butler, D. L., & Winne, P. H. (1995). Feedback and self-regulated learning: A theoretical synthesis. Review of Educational Research, 65, 245-281. doi:10.3102/00346543065003245
Campbell, D. T., & Fiske, D. W. (1959). Convergent and discriminant validation by the multitrait-multimethod matrix. Psychological bulletin, 56, 81-105. doi:10.1037/h0046016
Deci, E. L., Koestner, R., & Ryan, R. M. (1999). A meta-analytic review of experiments examining the effects of extrinsic rewards on intrinsic motivation. Psychological Bulletin, 125, 627–668. doi:10.1037/0033-2909.125.6.627
Ebner-Priemer, U. W., Eid, M., Kleindienst, N., Stabenow, S., & Trull, T. J. (2009). Analytic strategies for understanding affective (in)stability and other dynamic processes in psychopathology. Journal of Abnormal Psychology, 118, 195–202. doi:10.1037/a0014868
Eccles, J. S., Midgley, C., Wigfield, A., Buchanan, C. M., Reuman, D., Flanagan, C., & MacIver, D. (1993). Development during adolescence: The impact of stage-environment fit on young adolescents’ experiences in schools and in families. American Psychologist, 48, 90-101. doi:10.1037/0003-066X.48.2.90
Eccles, J. S., Wigfield, A., & Schiefele, U. (1998). Motivation to succeed. In W. Damon & N. Eisenberg, (Eds.), Handbook of child psychology, 5th ed.: Vol 3. Social, emotional, and personality development (pp. 1017-1095). Hoboken, NJ.: John Wiley & Sons.
Eid, M., & Diener, E. (1999). Intraindividual variability in affect: Reliability, validity, and personality correlates. Journal of Personality and Social Psychology, 76, 662-676. doi:10.1037/0022-3514.76.4.662
Eid, M., & Langeheine, R. (2003). Separating stable from variable individuals in longitudinal studies by mixture distribution models. Measurement: Interdisciplinary Research and Perspectives, 1, 179-206. doi:10.1207/S15366359MEA0103_01
Eizenman, D. R., Nesselroade, J. R., Featherman, D. L., & Rowe, J.W. (1997). Intraindividual variability in perceived control in an older sample: The MacArthur Successful Aging studies. Psychology and Aging, 12, 489-502. doi:10.1037/0882-7974.12.3.489
Georgiou, G., Manolitsis, G., Nurmi, J.-E., & Parrila, R. (2010). Does task-focused versus task-avoidance behavior matter for literacy development in an orthographically consistent language? Contemporary Educational Psychology, 35, 1−10. doi:10.1016/j.cedpsych.2009.07.001
Gill, P., & R. Remedios, R. (2013). How should researchers in education operationalise on-task behaviours? Cambridge Journal of Education, 43, 199-222. doi:10.1080/0305764X.2013.767878
Goetz, T., Frenzel, A. C., Stoeger, H., & Hall, N. C. (2010). Antecedents of everyday positive emotions: An experience sampling analysis. Motivation and Emotion, 34, 49-62. doi:10.1007/s11031-009-9152-2
Hamre, B. K., & Pianta, R. C. (2005). Can instructional and emotional support in the first-grade classroom make a difference for children at risk of school failure? Child Development, 76, 949-967. doi:10.1111/j.1467-8624.2005.00889.x
Hattie, J., Biggs, J., & Purdie, N. (1996). Effects of learning skills interventions on student learning: a meta-analysis. Review of Educational Research, 66, 99-136. doi:10.3102/00346543066002099
Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77, 81-112. doi:10.3102/003465430298487
Hirvonen, R., Tolvanen, A., Aunola, K., & Nurmi, J.-E. (2012). The developmental dynamics of task-avoidant behavior and math performance in kindergarten and elementary school. Learning and Individual Differences,22, 715-723. doi: 10.1016/j.lindif.2012.05.014
Hooker, K., Nesselroade, D. W., Nesselroade, J. R., & Lerner, R. M. (1987). The structure of intraindividual temperament in the context of mother-child dyads: P-technique factor analyses of short-term change. Developmental Psychology, 23, 332-346. doi:10.1037/0012-1649.23.3.332
Ilies, R., & Judge, T. A. (2002). Understanding the dynamic relationships among personality, mood, and job satisfaction: A field experience sampling study. Organizational Behavior and Human Decision Processes, 89, 1119–1139. doi:10.1016/S0749-5978(02)00018-3
Inkinen, M., Lonka, K., Hakkarainen, K., Muukkonen, H., Litmanen, T., & Salmela-Aro, K. (2013). The interface between core affects and the challenge-skill relationship. Journal of Happiness Studies, 15, 891-913. doi:10.1007/s10902-013-9455-6
Jahng, S., Wood, P. K., & Trull, T. J. (2008). Analysis of affective instability in ecological momentary assessment: indices using successive difference and group comparison via multilevel modeling. Psychological Methods, 13, 354–375. doi:10.1037/a0014173
Kernis, M. H., Grannemann, B. D., & Barclay, L. C. (1989). Stability and level of self-esteem as predictors of anger arousal and hostility. Journal of Personality and Social Psychology, 56, 1013-1022. doi:10.1037/0022-3514.56.6.1013
La Guardia, J. G., Ryan, R. M., Couchman, C. E., & Deci, E. L. (2000). Within-person variation in security of attachment: A self-determination theory perspective on attachment, need fulfillment, and well-being. Journal of Personality and Social Psychology, 79, 367-384. doi:10.1037/0022-3514.79.3.367
Larsen, R. J. (1987). The stability of mood variability: a spectral analytic approach to daily mood assessments. Journal of Personality and Social Psychology, 52, 1195-1204. doi:10.1037/0022-3514.52.6.1195
Lee, W., & Reeve, J. (2012). Teachers’ estimates of their students’ motivation and engagement: Being in synch with students. Educational Psychology, 32, 727–747. doi:10.1080/01443410.2012.732385
Li, X., & Hedeker, D. (2012). A three-level mixed-effects location scale model with an application to ecological momentary assessment data. Statistics in Medicine, 31, 3192-3210. doi:10.1002/sim.5393
Malmberg, L.-E., Walls, T., Martin, A. J., Little, T. D., & Lim, W. H. T. (2013). Primary school students' learning experiences of, and self-beliefs about competence, effort, and difficulty: Random effects models. Learning and Individual Differences, 28, 54–65. doi:10.1016/j.lindif.2013.09.007
Malmberg, L.-E., Woolgar, C., & Martin, A. (2013). Quality of measurement of the Learning Experience Questionnaire for Personal Digital Assistants. International Journal of Quantitative Research in Education, 1, 275-296. doi:10.1504/IJQRE.2013.057689
Malmberg, L.-E., Pakarinen, E., Vasalampi, K., & Nurmi, J-E. (2015). Students’ school performance, task-focus, and situation-specific motivation. Learning and Instruction, 39, 158-167. doi:10.1016/j.learninstruc.2015.05.005
Marsh, H. W. (1989). Age and sex effects in multiple dimensions of self-concept: preadolescence to early adulthood. Journal of Educational Psychology, 81, 417-430. doi:10.1037/0022-0663.81.3.417
McConville, C., & Cooper, C. (1997). The temporal stability of mood variability. Personality and Individual Differences, 23, 161-164. doi:10.1016/S0191-8869(97)00013-5
Morin, A. J. S., Marsh, H. W., Nagengast, B., & Scalas, L. F. (2014). Doubly latent multilevel analyses of classroom climate: An illustration. The Journal of Experimental Education, 82, 143-167. doi:10.1080/00220973.2013.769412
Musher-Eizenman, D. R., Nesselroade, J. R., & Schmitz, B. (2002). Perceived control and academic performance: A comparison of high- and low-performing children on within-person change patterns. International Journal of Behavioral Development, 26, 540–547. doi:10.1080/01650250143000517
Muthén, L. K. & Muthén, B. O. (2012). Mplus statistical analysis with latent variables: User’s guide (Version 7). Los Angeles, CA: Muthén & Muthén.
Nett, U. E., Goetz, T., & Hall, N. C. (2011). Coping with boredom in school: An experience sampling perspective. Contemporary Educational Psychology, 36,49–59. doi:10.1016/j.cedpsych.2010.10.003
Nett, U. E., Goetz, T., Hall, N. C., & Frenzel, A. C. (2012). Metacognitive strategies and test performance: An experience sampling analysis of students’ learning behavior. Education Research International. Article ID 958319, 16 pages. [online] http://kops.ub.uni-konstanz.de/handle/urn:nbn:de:bsz:352-206102 (Accessed 12 April 2013).
Nurmi, J.-E., & Aunola, K. (1998). Observer Rating Scale of Achievement Strategies (OSAS). Unpublished measurement instrument. Jyväskylä: University of Jyväskylä, Finland.
Nurmi, J.-E., Hirvonen, R., & Aunola, K. (2008). Motivation and achievement beliefs in elementary school: A holistic approach using longitudinal data. Unterrichtswissenschaft, 36(3), 237–254. doi:10.3262/UW0803237
Pianta, R. C., & Hamre, B. K. (2009). Conceptualization, measurement, and improvement of classroom processes: Standardized observation can leverage capacity. Educational Researcher, 38, 109-119. doi:10.3102/0013189X09332374
Pianta, R. C., Belsky, J., Vandergrift, N., Hours, R., & Morrison, F. (2008). Classroom effects on children’s achievement trajectories in elementary school. American Educational Research Journal, 45, 365-397. doi:10.3102/0002831207308230
Ram, N., Chow, S.-M., Bowles, R. P., Wang, L., Grimm, K., Fujita, F., & Nesselroade, J. R. (2005). Examining interindividual differences in cyclicity of pleasant and unpleasant affect using spectral analysis and item response modeling. Psychometrika, 70, 773-790. doi:10.1007/s11336-001-1270-5
Reeve, J., Jang, H., Carrell, D., Jeon, S., & Barch, J. (2004). Enhancing students’ engagement by increasing teachers’ autonomy support. Motivation and Emotion, 28, 147-169. doi:10.1023/B:MOEM.0000032312.95499.6f
Roesch, S. C., Aldridge, A. A., Stocking, S. N., Villodas, F., Leung, Q., Bartley, C. E. & Black, L. J. (2010). Multilevel factor analysis and structural equation modeling of daily diary coping data: Modeling trait and state variation. Multivariate Behavioral Research, 45, 767-789. doi:10.1080/00273171.2010.519276
Rosenberg, M. (1965). Society and the adolescent self-image. Princeton, N J: Princeton University Press.
Schmitz, B. (2006). Advantages of studying processes in educational research. Learning and Instruction, 16, 433-449. doi:10.1016/j.learninstruc.2006.09.004
Schmitz, B. (2015). The study of learning processes using time-series analyses [Video file]. Available from http://www.education.ox.ac.uk/network-on-intrapersonal-research-in-education-nire/seminar-1/bernhard-schmitz/
Schmitz, B., & Skinner, E. (1993). Perceived control, effort, and academic performance: Interindividual, intraindividual, and multivariate time-series analyses. Journal of Personality and Social Psychology, 64, 1010-1028. doi:10.1037/0022-3514.64.6.1010
Schmitz, B. & Wiese, B. S. (2006). New perspectives for the evaluation of training sessions in self-regulated learning: Time-series analyses of diary data. Contemporary Educational Psychology, 31, 64 – 96. doi:10.1016/j.cedpsych.2005.02.002
Sheldon, K. M. & Elliot, A. J. (1998). Not all personal goals are personal: Comparing autonomous and controlled reasons for goals as predictors of effort and attainment. Personality and Social Psychology Bulletin, 24, 546-557. doi:10.1177/0146167298245010
Skinner, E. A., & Belmont, M. J. (1993). Motivation in the classroom: Reciprocal effects of teacher behavior and student engagement across the school year. Journal of Educational Psychology, 85, 571-581. doi:10.1037/0022-0663.85.4.571
Trull, T. J., Solhan, M. B., Tragesser, S. L., Jahng, S., Wood, P. K., Piasecki, T. M., & Watson, D. (2008). Affective instability: Measuring a core feature of borderline personality disorder with ecological momentary assessment. Journal of Abnormal Psychology, 117, 647-661. doi:10.1037/a0012532
Tsai, Y-M., Kunter, M., Lüdtke, O. & Trautwein, U. (2008). Day-to-day variation in competence beliefs: How autonomy support predicts young adolescents’ felt competence In H. W., Marsh, R. G., Craven, & D. M., McInerney (Eds.), Self-processes, learning, and enabling human potential: dynamic new approaches (pp. 119-143). Charlotte, NC:Information Age Publishing..
von Neumann, J., Kent, R. H., Bellinson, H. R., & Hart, B. I. (1941). The mean square successive difference. The Annals of Mathematical Statistics, 12, 153–162. doi:10.1214/aoms/1177731746
Walls, T. A., Barta, W. D., Stawski, R. S., Collyer, C, & Hofer, S. M. (2011). Time-scale dependent longitudinal designs. In B. Laursen, T. D. Little, & N. Card (Eds.), Handbook of developmental research methods (pp. 46-64). New York: Guilford Press.
Wilhelm, P., Perrez, M., & Pawlik, K. (2012). Conducting research in daily life. In M. R. Mehl, and T. S. Conner, (Eds.), Handbook of research methods for studying daily life (pp. 62-68). New York: Guilford Press.
Zhang, X., Nurmi, J-E., Kiuru, N., Lerkkanen, M.-K., & Aunola, K. (2011). A teacher-report measure of children's task-avoidant behavior: A validation study of the Behavioral Strategy Rating Scale. Learning and Individual Differences, 21, 690–698. doi:10.1016/j.lindif.2011.09.007
Zimmerman, B. J. (2000). Self-efficacy: An essential motive to learn. Contemporary Educational Psychology, 25, 82–91. doi:10.1006/ceps.1999.1016

Appendix 1. Hand-calculation of the mean square successive difference (MSSD)

This hand-calculation presents the values of Panel A in Figure 1. The columns below represent: time-point = 28 time-points for one individual. Note that the numeric values of intrT+1 are replicated in the intrT column, only one row below each corresponding intrT+1 value. This gives a 29th time-point; intrT+1 = intrinsic motivation at time-point T+1; intrT = intrinsic motivation at time-point T. This variable was created by lagging the intrT+1 variable one time-point step. Time-point T becomes a predictor of time-point T+1; Δ = difference between intrT+1 and intrT; Δ2 = squared difference between intrT+1 and intrT;  = missing data created by the lag.

Appendix 2. Mplus code for single construct model (intrinsic motivation)

TITLE: MSSD 28 June 2016 ;

DATA: FILE IS "C:\variability.txt" ;

VARIABLE: NAMES ARE
studid sequence lag_n
diff_t1 diff_t0
well_t1 well_t0 und_t1 und_t0
enj_t1 enj_t0 int_t1 int_t0 cho_t1 cho_t0
focus1 focus2 focus3 avoid1 avoid2 avoid3 ;
!enj=enjoyment, int=interest, cho=choice, t1 = time T+1, t0 = time T
USEVAR = enj_t1 int_t1 cho_t1 enj_var int_var cho_var ; !include three observed and three defined variables
MISSING ALL (-9) ;
BETWEEN enj_var int_var cho_var ; !defined variables are at level 2
CLUSTER = studid; !clustering by student DEFINE:
enj_va = (enj_t1 - enj_t0)**2 ; !squared difference of enjoyment
int_va = (int_t1 - int_t0)**2 ; !average squared difference of enjoyment
cho_va = (cho_t1 - cho_t0)**2 ;
!squared difference of interest
enj_var = CLUSTER_MEAN (enj_va) ; !average squared difference of interest
int_var = CLUSTER_MEAN (int_va) ;
!squared difference of choice
cho_var = CLUSTER_MEAN (cho_va) ; !average squared difference of choice
CENTER (grandmean) enj_t1 int_t1 cho_t1 enj_var int_var cho_var ; !grand mean centre level 2 indicators

ANALYSIS: TYPE = TWOLEVEL ;

MODEL:
%WITHIN%
w_intr BY enj_t1 (a)
int_t1 (b)
cho_t1 (c) ;
! w_ = state-construct (within-level)
! factor loadings of within and between indicators are equated between level

w_intr (var_w) ;
!estimate variance, and use for calculating new parameter
%BETWEEN%

b_intr BY enj_t1 (a)
int_t1 (b)
cho_t1 (c) ;
! b_intr = trait-construct

intr_var BY enj_var int_var cho_var ;
! variability construct

b_intr WITH intr_var ;
b_intr (var_b) ;
!estimate variance, and use for calculating new parameter

int_t1*.05 (br1) ;
! estimate error variance

MODEL CONSTRAINT:
br1 > 0 ; !br2 > 0 ;
NEW(var_comp);
var_comp = var_b / (var_b + var_w) ;
! calculate intraclass correlation of latent constructs

OUTPUT: STAND SAMPSTAT TECH1 TECH2 ;