Modeling Complex Trajectories of Change: Using Freed Loading Latent Curve Modeling to Visualize Growth Trajectories in Math Interest

• In Event: Complexity in Motivation and Engagement Research: Evidence for Contextual Dynamic Patterns

Abstract

Objectives/Purpose.
To explore math interest growth trajectories for students participating in a personalized math interest intervention, utilizing conditional, freed loading latent curve modeling
Perspectives/Theoretical Framework.
Personalized Learning (PL) – or instruction tailored to suit students’ needs, preferences, and interests – has shown promise in improving students’ motivation and learning (Walkington & Bernacki, 2020). In particular, context personalization situates learning tasks in the context that is aligned with students’ interest (Walkington & Bernacki, 2014; Bernacki & Walkington, 2018). This approach draws on students’ prior knowledge about the problem context and promotes students’ situational interest for learning. Thus, context personalization has the potential to trigger and maintain students’ interest, instigating a positive trajectory of interest in a particular subject domain (Hidi & Renninger, 2006). This study examined students’ math interest trajectory as they participate in a personalized math intervention leveraging context personalization to align instruction with their interest in specific STEM careers.
Methods
Participants for this study include 135 middle school, 64 high school, and 252 community college students. Of these, 118 students were assigned to business-as-usual instruction, whereas 333 others were assigned to three varying personalized instruction conditions related to problem activities targeted and math topics covered (career problem posing, career problem solving, or popular culture problem posing).
Data Sources
Math interest data was collected at six time points before and after students engaged in the relevant math units within their course (i.e., 3 pre-unit and 3 post-unit measures; odd time points are pre-unit and even time points are post-unit). Online surveys were integrated within the learning management system for students’ math courses, facilitated via Qualtrics. Students responded to 4 items from the individual interest scale (Linnenbrink-Garcia et al., 2010), specifically tapping their value for math.
Results
Latent curve modeling was used to examine students’ math interest trajectories. Results showed that the conditional latent curve model showed satisfactory fit (Table 1, Model B) with experimental condition specified as a predictor of the slope parameter and grade level as a predictor of both the intercept and slope. However, investigations of resulting plots revealed that sample data showed fluctuations around the predicted curve corresponding to pre- and post- measurements. Additional models which allowed freed slope loadings for pretests (Model C) and for all timepoints (except first and last for scaling, Model D) showed significantly better fit, with significant χ2 tests supporting the least constrained model, p<0.05. Finally, multiple groups analysis supported the final model (Model E) which allowed the intercept and freed slope loadings to vary between the secondary and post-secondary groups. College students showed a more consistent increasing pattern of math interest whereas middle and high school students had a fluctuating pattern with regressed scores within units (i.e., lower than expected post-unit scores).
Significance
Complex longitudinal data as derived from intervention settings may not conform to a linear trajectory. In particular, pre- versus post-unit scores may show both between- and within- lesson fluctuations for some students. By proceeding with the assumption of linearity, we may miss informative patterns of how motivational factors like interest develops over time.

Authors

• Vanessa Wanchanit Vongkulluksn, University of Nevada - Las Vegas
  Presenting Author

• Matthew L. Bernacki, University of North Carolina - Chapel Hill
  Presenting Author

• Candace A. Walkington, Southern Methodist University
  Presenting Author

• Meghan J. Greene, University of North Carolina - Chapel Hill
  Presenting Author

• Taylor Darwin, Texas Tech University
  Presenting Author