Happiness/Joy Mediates The Effect of Story Problem Difficulty on Arithmetic Strategy Sophistication in Kindergarten

• In Event: Emotions and Emotion Regulation in Mathematics: New Insights Into Antecedents And Outcomes

Abstract

Objectives

A corpus of research validates the Control-Value Theory of Achievement Emotions (CVTAE; Pekrun, 2006), which was built on analysis of survey responses of upper-primary+ students. In [Grant Blinded], we centralize the achievement emotions of kindergarten children. We use automatic facial coding software to generate the intensity of nine emotions to examine how they relate to arithmetic accuracy and problem-solving strategies. Here, we investigate the direct and indirect relationships between the mathematical context, the achievement emotion of happiness/joy, and arithmetic outcomes.

Theoretical Framework

Through the CVTAE, happiness/joy is an activating, positive state, and has been linked to early mathematics (Lichtenfeld et al., 2023). Additionally, the broaden-and-build theory (Fredrickson, 2013) postulates that happiness/joy expands the range of thoughts and potential actions. Thus, momentary fluctuations in happiness/joy could impact problem-solving behaviors and strategy development in early mathematics. We hypothesize happiness/joy will mediate the influence of story problem structure on arithmetic strategy sophistication.

Methods

We coded the arithmetic problem-solving behaviors of 40 kindergarten students and generated the intensity of their emotions through FaceReader9. The coding procedures are detailed in (Blinded, 2024; 2025). Emotion data generation will be completed during Fall 2025.
Explanatory Variable: Story-Problem Structure is composed of three structures, listed from least to most difficult: Result Unknown (RU), Difference Unknown (DU), and Start Unknown (SU) (Clements and Sarama, 2021).
Mediator: Happiness/Joy intensity is generated through a FaceReader9 analysis of facial muscle groups; accuracy and generalizability are discussed in [Blinded, 2025].
Outcome: Strategy Sophistication is binarized: 0 = “Counting Strategies” (e.g., counting all/on) and 1 = “Fluency”, where known combinations were a component of the problem-solving strategy (e.g., derived combinations).

Analytic Approach

The intensity of happiness/joy is a curve over time within each student’s attempts to solve a story problem. Accordingly, our mediator is a function and our models fall into the family of functional mediation (Coffman et al., 2023; Lindquist, 2012), implemented using the funmediation R package.

Results

The proof-of-concept sample represents 15% of the final sample (6/40 students) generating 1004 problem-solving attempts, median duration=28.97 seconds. Happiness/joy facial expressions were on average most intense, followed by sadness, boredom, interest, and confusion.
Figure 1 depicts average curves of happiness/joy within a problem-solving attempt. Figure 2 depicts the mediation. Relative to RU attempts, SU and FD feature more pronounced U-shaped happiness curves. The direct effect of SU was significant (Odds Ratio 95% CI = 1.18, 2.75): students were more likely to use fluent strategies on SU vs RU attempts. There was an inconsistent indirect effect of SU vs. RU attempts (Odds Ratio 95% CI = 0.60, 0.99; 41% of total effect mediated). Additionally, the deployment of fluent strategies for SU problems was more likely when students expressed more intense initial happiness/joy.

Significance

Hypothesis confirmed; additionally, the indirect effect indicates students who resist the dip in happiness/joy, characteristic of difficult problems, especially early in the attempt, are more likely to use sophisticated strategies. This preliminary evidence aligns with the broaden-and-build theory: positive emotional states promote and maintain flexible exploratory behaviors that benefit arithmetic strategy development.

Authors

• Traci Shizu Kutaka, University of Virginia

• Pavel Chernyavskiy, University of Virginia

• Julia Pfeiffer, University of Virginia