Short-Term Relations Between Expectancies and Task Values in Math: A Random-Intercept Cross-Lagged Panel Approach

• In Event: Students' Expectancies and Values After the Transition to Higher Education: A Situated Perspective

Abstract

Purpose and Theoretical Framework
Recently, expectancy-value research has shown that short-term motivational declines in the very first weeks of college serve as a precursor to later academic struggles such as course dropout and poor exam performance (Benden & Lauermann, 2020). Furthermore, the situated expectancy-value theory (Eccles & Wigfield, 2020) suggests that these motivational beliefs can influence each other over time so that motivational declines in some beliefs (e.g., loss of confidence in one’s ability) can contribute to further declines in others (e.g., loss of interest). However, we lack evidence of such reciprocal associations at sensitive periods such as the beginning of college and using course-specific versus situation-specific assessments. In addition, analyses of cross-lagged associations over longer periods have failed to account for stable between-person motivational differences, which can bias the estimated cross-lagged associations (Hamaker et al., 2015).
Accordingly, we examine reciprocal links among college students’ expectancy-value beliefs in math-intensive courses, and we estimate both stable between-person motivational differences and cross-lagged predictive effects across the entire semester (course-specific assessments; RQ1) and the first weeks of the semester (situation-specific assessments; RQ2).

Methods
Data from five cohorts of students in gateway math courses in their physics, math teacher education, or math study program were available (N =773). Course-specific expectancy-value beliefs (Table 1) were assessed at the beginning (T1/Week 2), midpoint (T5/Week 8), and end of the semester (T6/Week 15). Situation-specific expectancy-value beliefs referencing students’ experiences with mandatory weekly worksheets were assessed in Weeks 3 to 5 of the semester (T2–T4).

Results
Random-intercept cross-lagged panel models (Figure 1) revealed that the random intercepts of expectancy and each task value facet were moderately-to-highly correlated, suggesting that students who generally had higher expectancies compared to other students also reported higher levels of intrinsic/utility values and lower levels of cost.
Furthermore, significant contemporaneous associations between students’ expectancy and task values emerged, for both the course-specific (RQ1) and the situation-specific (RQ2) assessments. Within a given time point, a positive deviation of students’ expectancies from their baseline corresponded to higher intrinsic/utility values and lower levels of cost.
Analyses of students’ course-specific assessments (RQ1) revealed significant autoregressive effects for expectancy and intrinsic/utility value, as well as significant cross-lagged effects of students’ expectancy on their intrinsic and utility values (Table 2). In contrast, using situation-specific assessments, we found little evidence of significant autoregressive or cross-lagged effects from one week to the next at the beginning of the semester (RQ2; Table 3).

Discussion
Results indicate that reciprocal effects between expectancies and task values depend on whether course-specific or situation-specific motivational beliefs are studied. Significant “motivational spillover effects” were found for students’ beliefs about their math course in general (i.e., course-specific expectancies drive changes in intrinsic/utility values across the semester). However, we found no evidence of such spillover effects from week to week suggesting that students’ experiences with their worksheets are relatively self-contained within a given week. These results underscore the importance of considering both the time lag and the type of assessment when examining reciprocal links between expectancies and task values.

Authors

• Daria Katharina Benden, TU Dortmund University

• Fani Lauermann, TU Dortmund University