Self-Efficacy, Emotions and Mathematics Achievement: Longitudinal Effects of Flipped Learning

Abstract

Background: First-year engineering mathematics courses present a critical academic challenge, often leading to a significant decline in student self-efficacy, a key predictor of retention and success. While flipped learning is a proposed solution, a lack of longitudinal research using robust comparison groups has limited our understanding of its true impact over time. This study addresses this gap by examining the interplay of a flipped learning model, self-efficacy, emotions, and achievement across a full academic year. Objectives: To longitudinally investigate how a student-centred flipped learning model influences the development of first-year engineering students' self-efficacy compared to a student-centred lecture-based model, and to examine the roles of emotional valence and mathematics achievement in this process. Methods: This quasi-experimental study involved 393 first-year engineering students at a Finnish university. Students were organised into a flipped learning intervention group and a lecture-based control group for four compulsory mathematics courses over the 2019–2020 academic year. Data on self-efficacy and emotional valence were collected at five time points and analysed, along with mathematics achievement scores, using multilevel modelling. Results: While an overall decline in self-efficacy was observed, the developmental pattern differed by group: the control group showed a steady linear decline, while the intervention group exhibited a non-linear trend of decline and pre-pandemic recovery. However, the flipped learning intervention significantly mitigated this overall decline, with the intervention group maintaining a consistently higher trajectory of self-efficacy. While this treatment effect was statistically significant, its practical effect size was small, a finding that aligns with prior meta-analyses in engineering disciplines. Positive emotions and higher achievement were positively related to self-efficacy for all students, but no significant interaction effects with the instructional model were found. Conclusions: Flipped learning can serve as a protective buffer against the erosion of student confidence in challenging first-year engineering mathematics courses. The findings suggest that the primary benefit of the model stems not simply from inverting instruction, but from the structured, collaborative social interactions that foster mastery experiences and peer support. Educators should prioritise these components to support students during their critical transition to higher education.