Achievement emotions and academic performance: longitudinal models of reciprocal effects

TL;DR: The model was tested using five annual waves of the Project for the Analysis of Learning and Achievement in Mathematics (PALMA) longitudinal study, which investigated adolescents' development in mathematics, and showed that positive emotions positively predicted subsequent achievement and negative emotions negatively predicted achievement.

Abstract: A reciprocal effects model linking emotion and achievement over time is proposed. The model was tested using five annual waves of the Project for the Analysis of Learning and Achievement in Mathematics (PALMA) longitudinal study, which investigated adolescents’ development in mathematics (Grades 5–9; N = 3,425 German students; mean starting age = 11.7 years; representative sample). Structural equation modeling showed that positive emotions (enjoyment, pride) positively predicted subsequent achievement (math end-of-the-year grades and test scores), and that achievement positively predicted these emotions, controlling for students’ gender, intelligence, and family socioeconomic status. Negative emotions (anger, anxiety, shame, boredom, hopelessness) negatively predicted achievement, and achievement negatively predicted these emotions. The findings were robust across waves, achievement indicators, and school tracks, highlighting the importance of emotions for students’ achievement and of achievement for the development of emotions.

Summary

Introduction

• Specifically, longitudinal investigations suggested that K-12 students’ test anxiety and academic achievement reciprocally influence each other (Meece, Wigfield, & Eccles, 1990; Pekrun, 1992).
• In the following sections, the authors use Pekrun’s (2006; Pekrun & Perry, 2014) control-value theory of achievement emotions to derive a theoretical framework for the reciprocal causation of emotion and achievement.

Effects of Emotion on Achievement

• In the control-value theory, two dimensions describing human affect are used to distinguish types of emotions, namely valence (positive vs. negative or pleasant vs. unpleasant) and activation (activating vs. deactivating).
• Accordingly, these emotions are expected to positively influence students’ academic achievement under most task conditions.
• The opposite pattern of effects is proposed for negative deactivating emotions (boredom, hopelessness).
• These emotions are thought to reduce cognitive resources and task-related attention, to undermine both intrinsic and extrinsic motivation, and to promote shallow information processing.
• Moreover, they can facilitate the use of more rigid learning strategies, such as rote memorization.

Reverse Effects of Achievement on the Development of Emotion

• Achievement reciprocally influences the appraisals that are considered to be proximal antecedents of emotion.
• Students should enjoy learning when they judge themselves competent to master the learning task, provided they are interested in the material.
• Anxiety about an upcoming important exam should be high if students judge themselves incompetent to pass it.
• Competence and control are thought to influence both students’ momentary emotions within a specific situation and their habitual, re-occurring emotions, which are based on re-occurring appraisals and related control-value beliefs (for summaries of empirical evidence, see Daniels & Stupnisky, 2012; Pekrun & Perry, 2014).
• Similarly, since achievement has positive effects on control, and control has negative effects on negative emotions, it follows that achievement should have negative effects on the development of negative emotions.

Feedback Loops of Emotion and Achievement over Time

• Because emotions are posited to influence achievement and achievement, in turn, to influence emotion, the two constructs are thought to be linked by reciprocal causation over time.
• The existing evidence summarized above implies that negative activating emotions typically are aroused by failure and contribute to subsequent failure, suggesting that feedback loops should be positive for these emotions as well in the average student.
• At the start of secondary school, students are selected into one of three tracks, including lower-track schools , medium-track schools , and higher-track schools , based on their elementary school achievement.
• Given the stability of context, the authors expected relations between students’ trait-like emotions considered in this study and their achievement to be stable as well, with effects of these emotions on achievement, and effects of achievement on emotions, showing equivalence (i.e., developmental equilibrium) across each of the one-year intervals included.

Participants and Design

• The sample consisted of German adolescents who participated in the PALMA longitudinal study (Pekrun et al., 2007).
• All instruments were administered in the students’ classrooms by trained external test administrators.
• The sample comprised students from all three school types within the Bavarian public secondary school system as described earlier, including lowertrack schools (Hauptschule, 37.2% ), intermediate-track schools (Realschule, 27.1%), and higher-track schools (Gymnasium, 35.7%).

Measures

• Students’ emotions in mathematics were measured using the Achievement Emotions Questionnaire-Mathematics (AEQ-M; Pekrun, Goetz, Frenzel, Barchfeld, & Perry, 2011).
• The scores were also used to derive indexes for positive and negative affect factors combining positive and negative emotions, respectively (see Data Analysis section).
• Students’ achievement was assessed by their end-of-the-year grades in mathematics as retrieved from school documents and by standardized test scores.
• Demographic variables (gender and SES) and intelligence were included as covariates in the analysis.

Strategy of Data Analysis

• Structural equation modeling (SEM; Mplus, Version 7; Muthén & Muthén, 2012) was used to evaluate the reciprocal effects model.
• The emotion variables were modeled as latent constructs.
• Metric invariance additionally requires equal factor loadings, scalar invariance requires equal factor loading and intercepts, and residual invariance requires equal factor loadings, intercepts, and residual variances.
• To examine the robustness of the analysis, the authors replicated the cross-lagged analyses for emotion and achievement with the subsample of students who participated in the study from the beginning (N = 2,070).

Confirmatory Factor Analysis (CFA) for the Emotion Constructs

• To further examine the relations between emotions, item-based CFA models including the seven emotions were estimated.
• This was done separately for the five measurement occasions.
• The latent correlations between the emotion variables showed the same pattern as the manifest correlations (Table 1).
• The configural invariance models showed a good fit to the data, with CFI > .93, RMSEA < .03, and SRMR < .05 for all seven discrete emotion constructs (Supplemental Material, Table S3).
• As compared with these models, the loss of fit for the metric invariance models was CFI < -.004, RMSEA < .001, and SRMR < .006 for all models, indicating clear support for metric invariance for all of the emotions.

Reciprocal Effects Models of Emotions and Achievement

• The fit indexes provided support for the cross-lagged structural equation models for all seven emotions as well as positive and negative affect and across both measures of achievement.
• Factor loadings, path coefficients, and residual variances for the reciprocal effects models including grades are displayed in Table 3.
• In addition, positive paths emerged from each achievement outcome to the subsequent enjoyment and pride variables (all βs = .11, ps < .001).
• The findings were consistent across models for the seven discrete emotions, the combined positive and negative affect model, four time intervals, two different measures of achievement (grades, test scores), and the three school tracks while controlling for students’ gender, SES, and intelligence.

Reciprocal Effects Linking Emotion and Achievement

• The findings are congruent with previous evidence showing that emotions and academic achievement are correlated (Goetz & Hall, 2013; Pekrun & Linnenbrink-Garcia, 2014; Zeidner, 1998).
• These effects are in line with Pekrun’s (2006) control-value theory which posits that emotions influence learning and achievement outcomes.
• Previous research has produced mixed findings on the relation between students’ positive affect and their learning, with most studies reporting positive relations (see Linnenbrink, 2007) but some others null findings (e.g., Pekrun, Elliot, & Maier, 2009).
• This difference may relate to general asymmetries in the impact of negative versus positive states and events on human memory and action (see e.g., Baumeister, Bratslavsky, Finkenauer, & Vohs, 2001).
• The present research adds to this literature by showing that emotions other than anxiety share similar links with achievement.

Discrete Emotions versus General Affect

• It is noteworthy that the cross-paths were similar across different discrete emotions.
• As outlined in their reciprocal effects model, success is expected to generally increase perceived control, thus enhancing positive emotions, and failure is expected to decrease control, leading to negative emotions.
• Regarding effects of emotion on achievement, emotion theories such as the control-value theory (Pekrun, 2006) imply that the effects of some emotions (e.g., deactivating negative emotions such as boredom) may be more consistent than the effects of other emotions (e.g., activating negative emotions such as anxiety).
• Instead, the findings clearly indicate that the predictive effects of emotions on students’ long-term achievement were also similar across different emotions.
• This possibility is underscored by the robust findings for positive and negative affect documented in the present analysis.

Effects of Gender, Intelligence, and SES

• The findings on gender differences are consistent with previous evidence showing that girls report less enjoyment and more anxiety and shame in mathematics even if they perform as well as boys.
• As such, the findings suggest that girls exhibit a more maladaptive profile of math emotions, except for boredom.
• As expected, intelligence had substantial predictive effects on the achievement variables.
• Given that students’ mathematics achievement was included in the analysis, this finding suggests that higher general cognitive ability can help to reduce negative mathematics emotions, above and beyond any effects of students’ academic success in mathematics.
• Finally, SES also had positive, albeit weaker, effects on math achievement, suggesting that the family exerts an influence on students’ achievement, over and above any effects of cognitive ability.

Limitations, Suggestions for Future Research, and Implications for Practice

• The present study represents a significant advancement over previous research, because it documents reciprocal effects of emotion and achievement over time while controlling for general cognitive ability and critical demographic background variables.
• More research on the link between emotion and achievement as mediated by these cognitive and motivational mechanisms is needed to better understand students’ emotions and their relations with important school outcomes.

Figures

Figure 1. Basic structure of cross-lagged reciprocal effects models. Upper part: emotion and achievement. Lower part: positive affect, negative affect, and achievement. The models include cross-lagged effects, autoregressive effects, and directional paths from the covariates to emotion or affect and achievement at all waves. Correlations between the covariates and between residuals are not displayed.

Table 1 Alpha Coefficients and Pearson Product-Moment Correlations for Emotions and Achievement

Table 3 (continued)

Table 2 Reciprocal Effects Models for Emotion and Grades: Fit Indexes

Table 3 (continued)

Full text

Durham Research Online
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Citation for published item:
Pekrun, R. and Lichtenfeld, S. and Marsh, H.W. and Murayama, K. and Goetz, T. (2017) 'Achievement
emotions and academic performance : longitudinal models of reciprocal eects.', Child development., 88 (5).
pp. 1653-1670.
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https://doi.org/10.1111/cdev.12704
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T. (2017). Achievement Emotions and Academic Performance: Longitudinal Models of Reciprocal Eects. Child
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Running head: EMOTION AND ACHIEVEMENT
1
Paper accepted for publication in: Child Development
Achievement Emotions and Academic Performance:
Longitudinal Models of Reciprocal Effects
Reinhard Pekrun
Stephanie Lichtenfeld
University of Munich
Herbert W. Marsh
Australian Catholic University and University of Oxford
Kou Murayama
University of Reading
Thomas Goetz
University of Konstanz and Thurgau University of Teacher Education

Running head: EMOTION AND ACHIEVEMENT
2
Author Note
Reinhard Pekrun, Department of Psychology, University of Munich, Munich, Germany;
Stephanie Lichtenfeld, Department of Psychology, University of Munich, Munich, Germany;
Herbert W. Marsh, Institute for Positive Psychology and Education, Australian Catholic
University, Sydney, Australia, and Department of Education, University of Oxford, Oxford, UK;
Kou Murayama, Department of Psychology, University of Reading, Reading, UK; Thomas
Goetz, Department of Empirical Educational Research, University of Konstanz, Konstanz,
Germany, and Thurgau University of Teacher Education, Thurgau, Switzerland.
This research was supported by a LMU Research Chair grant awarded to R. Pekrun by
the University of Munich and four grants from the German Research Foundation (DFG) to R.
Pekrun (PE 320/11-1, PE 320/11-2, PE 320/11-3, PE 320/11-4). Parts of this paper were
presented at the annual meeting of the American Educational Research Association,
Philadelphia, PA, April 2014, and at the International Congress of Applied Psychology, France,
Paris, July 2014.
Correspondence concerning this article should be addressed to Reinhard Pekrun,
Department of Psychology, University of Munich, Leopoldstrasse 13, 80802 Munich, Germany.
E-mail: pekrun@lmu.de

Running head: EMOTION AND ACHIEVEMENT
3
Abstract
A reciprocal effects model linking emotion and achievement over time is proposed. The model
was tested using five annual waves of the PALMA longitudinal study, which investigated
adolescents’ development in mathematics (grades 5-9; N=3,425 German students; mean starting
age=11.7 years; representative sample). Structural equation modeling showed that positive
emotions (enjoyment, pride) positively predicted subsequent achievement (math end-of-the-year
grades and test scores), and that achievement positively predicted these emotions, controlling for
students’ gender, intelligence, and family socio-economic status. Negative emotions (anger,
anxiety, shame, boredom, hopelessness) negatively predicted achievement, and achievement
negatively predicted these emotions. The findings were robust across waves, achievement
indicators, and school tracks, highlighting the importance of emotions for students’ achievement
and of achievement for the development of emotions.
Keywords: achievement emotion, anxiety, academic achievement, mathematics
achievement, control-value theory

Running head: EMOTION AND ACHIEVEMENT
4
Research has shown that children’s and adolescents’ emotions are linked to their academic
achievement. Typically, positive emotions such as enjoyment of learning show positive links
with achievement, and negative emotions such as test anxiety show negative links (for
overviews, see Goetz & Hall, 2013; Pekrun & Linnenbrink-Garcia, 2014; Zeidner, 1998).
However, most of the available studies were correlational and do now allow any inferences about
the causal ordering of emotion and achievement over time. As such, it remains unclear how the
observed links should be interpreted. It is open to question if students’ emotions impact their
learning, if success and failure at learning influence the development of their emotions, if other
variables cause the association, or if several of these possibilities are at work. Given the need to
acquire knowledge about the antecedents of both students’ achievement and their emotions, this
is an issue of considerable theoretical and practical importance. To address this issue, the present
investigation went beyond merely observing correlations at a single point in time and attempted
to disentangle the temporal ordering of these constructs across multiple waves of data collection
and a developmental time span of several school years.
The investigation is based on a reciprocal effects model of emotion and achievement which
posits that the two variables reciprocally influence each other over time. This stands in contrast
to traditional unidirectional perspectives, which suggest that the link between emotion and
achievement is simply due to effects of emotions on students’ learning and performance. For
example, correlations between test anxiety and students’ achievement were interpreted as
indicating that anxiety impacts achievement, and test anxiety theories put forward various
suggestions about mediating mechanisms (e.g., cognitive interference, motivation; Zeidner,
1998, 2014). In a similar vein, in studies on affect and performance more generally, researchers
have been interested in the impact of moods and emotions on cognitive performance and created

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Running head: emotion and achievement 1 paper accepted for publication in: child development achievement emotions and academic performance: longitudinal models of reciprocal effects" ?

The model was tested using five annual waves of the PALMA longitudinal study, which investigated adolescents ’ development in mathematics ( grades 5-9 ; N=3,425 German students ; mean starting age=11. 7 years ; representative sample ). 

Q2. What future works have the authors mentioned in the paper "Running head: emotion and achievement 1 paper accepted for publication in: child development achievement emotions and academic performance: longitudinal models of reciprocal effects" ?

Nevertheless, several limitations should be considered when interpreting the study findings and can be used to suggest directions for future research. As such, although the present analysis used multi-wave longitudinal structural equation modeling and controlled for related variables and autoregressive effects, the possibility still exists that their findings are attributable to other variables that were not included in the study. To balance the benefits and drawbacks of different methodologies and make headway in this avenue of research, future studies should further pursue the approach taken herein while complementing this approach with experimental studies. Additionally, future research should explore if these findings generalize to emotions in achievement domains other than mathematics, 

Q3. What is the loss of fit for the metric and residual invariance models?

For positive and negative affect, the loss of fit was CFI < .008, RMSEA < .004,and SRMR < .005 for the metric, intercept, and residual invariance models, demonstratingsupport for invariance for these second-order constructs as well. 

Q4. What is the purpose of the proposed model of reciprocal effects?

In the proposed model of reciprocal effects, it is posited that effects of emotion on achievement are due to the influence of emotions on cognitive resources, motivation, and strategy use. 

Q5. What was the loss of fit for the metric and intercept models?

When constraining autoregressive effects, cross-laggedeffects, and factor residual variances to be equal across time intervals, the loss of fit was CFI <.003, RMSEA < .001, and SRMR < .003 for all of the models. 

Q6. What is the effect of doing well in school on students’ emotions?

More specifically, it appears that doing well in school can strengthen students’ positive emotions andreduce their negative emotions over time, whereas doing poorly in school undermines positive emotions and exacerbates negative emotions. 

Q7. What are the advantages of using grades as sources of students’ emotional development?

from the perspective of grades as sources of students’ emotional development, they could be seen as having almost perfectreliability---grades, rather than objective achievement, provide the feedback that shapes students’ perceptions of success and failure and any development based on these perceptions. 

Q8. What was the loss of fit for the metric invariance models?

The loss of fit for the scalarinvariance models was CFI < -.007,RMSEA < .004, and SRMR < .007 for all of theemotions, documenting that scalar invariance was supported as well. 

Q9. What are the dimensions of emotion that are used to describe human affect?

Using these dimensions renders four groups of emotions: positive activating (e.g., enjoyment, hope, pride), positive deactivating (e.g., relaxation, relief), negative activating (e.g., anger, anxiety, shame), and negative deactivating (e.g., boredom, hopelessness). 

Q10. What were the background variables included as covariates?

The background variables were included as covariates; for each of these variables, directional paths to all of the emotion variables and to all of the achievement variables were included. 

Q11. What scales were used to measure students’ emotions in math?

Participants responded on a 1 (strongly disagree) to 5 (strongly agree) scale, and the scores were summed to form the emotion indexes (Alpha range .86 to .92 across all scales and measurement occasions; see Table 1). 

Q12. What is the average influence of positive deactivating emotions on achievement?

notwithstanding individual differences regarding effects, the authors expect that the average overall influence of positive deactivating emotions on achievement is positive, and that the average overall influence of negative activating emotions is negative. 

Q13. What is the way to estimate missing values?

FIML has been found to result in trustworthy, unbiased estimates for missing values even in the case of large numbers of missing values (Enders, 2010) and to be an adequate method to manage missing data in longitudinal studies (Jeličič, Phelps, & Lerner, 2009). 

Q14. What is the effect of achievement on emotions?

Foreffects of achievement on emotion, this is to be expected, as success and failure are thought to impact the development of different positive and negative emotions in similar ways. 

Q15. What is the relationship between achievement and control?

Because emotions are posited to influence achievement and achievement, in turn, toinfluence emotion, the two constructs are thought to be linked by reciprocal causation over time. 

Q16. What is the significance of the present study?

The present study represents a significant advancement over previous research, because itdocuments reciprocal effects of emotion and achievement over time while controlling for general cognitive ability and critical demographic background variables. 

Q17. What is the relationship between perceived competence and control?

Perceived competence and control depend on students’ individual achievement history,with success strengthening control and failure undermining it.