This study employed a repeated cross-sectional design to investigate MA and PSA among undergraduate students enrolled in a Numerical Methods course across four successive cohorts from 2021 to 2024 at two Southeast Asian universities (see Figure 1). Each year involved independent cohorts from UTHM, Malaysia and UP, Indonesia. This design enables comparison of aggregated cohort-level trends over time while avoiding assumptions of individual-level change because the same participants are not repeatedly measured (Caruana et al., 2015).

A total of 139 undergraduate students participated across both institutions: 23 from UTHM and 116 from UP, with sample sizes differing by year (see Table 1). Inclusion criteria comprised the enrollment in the Numerical Methods course and consent to participate. Data with incomplete responses were excluded. The sample size imbalance was considered in the analysis to mitigate bias. To address unequal group sizes, Type III sums of squares were applied in factorial ANOVA, which provides adjusted estimates under unbalanced designs. Because the UTHM subgroup sizes within individual years were small (n = 5–7), year-specific estimates and interaction effects were interpreted as exploratory.

Ethical approvals were obtained from UTHM and UP institutional review boards. Data collection occurred during the scheduled class sessions for each cohort. In 2021 and 2022, data were collected remotely through supervised online assessments due to COVID-19 restrictions. In 2023 and 2024, a hybrid instructional model was implemented (Bozkurt & Sharma, 2020). Standardized administration instructions and timing protocols were used to ensure procedural consistency.

Data cleaning involved excluding incomplete cases and detecting multivariate outliers using Mahalanobis distance at p < 0.001. Descriptive statistics were computed for MA and PSA by university and year. A two-way factorial ANOVA (University × Year) was conducted treating both factors as between-subjects variables, appropriate for repeated cross-sectional data (Tabachnick & Fidell, 2013). Given the unequal and relatively small subgroup sizes, Type III sums of squares were applied, and effect sizes (partial η^²) with confidence intervals were emphasized alongside statistical significance to facilitate a more comprehensive interpretation of the findings. Pearson correlation coefficients were examined to assess the relationship between MA and PSA. Assumptions of normality, homogeneity of variance, and independence were verified and met.

This study aimed to investigate MA and PSA among undergraduate students enrolled in a transnational Numerical Methods course spanning four academic years (2021–2024) at UTHM and UP. Utilizing a repeated cross-sectional design, the study examined differences between institutions, temporal trends, and the interaction between contextual factors and instructional modalities during the COVID-19 pandemic.

Consistent with findings reported in the literature (Ashcraft & Ridley, 2005; Maloney et al., 2011), MA and PSA were inversely correlated, confirming that higher levels of anxiety are associated with decreased problem-solving performance. This relationship supports cognitive theories positing that MA consumes working memory resources critical to mathematical reasoning (Ashcraft & Krause, 2007). Such a negative relationship may impair mathematical learning progression (Ramirez et al., 2018).

The downward trend in MA scores observed at both institutions is particularly noteworthy in the context of Numerical Methods, a course widely recognized for its high cognitive demand and its reliance on both mathematical abstraction and computational reasoning (Quarteroni et al., 2007). The progressive reduction in MA across successive cohorts may reflect differences in cohort composition, learning experiences, or other unmeasured contextual factors. These findings are consistent with Bozkurt and Sharma (2020), who demonstrated that adaptive instructional modalities can meaningfully reduce mathematics anxiety in technically demanding courses, and Ramirez et al. (2018), who identified instructional support as a key moderator of affective responses to mathematics. Reviews of the literature indicate that MA affects learning motivation, self-regulation, and academic achievement in higher education contexts (Luttenberger et al., 2018).

Furthermore, the inverse relationship between the declining MA trend and the corresponding increase in PSA scores, as reported in Table 2, supports the theoretical framework underpinning this study. The pattern observed across both universities reinforces the well-established proposition that elevated mathematics anxiety functions as a cognitive inhibitor, constraining the working memory resources necessary for effective problem-solving in numerically intensive tasks (Ashcraft & Ridley, 2005; Hembree, 1990). Within the specific context of Numerical Methods education, where iterative procedures and algorithmic reasoning are central competencies, the reduction of MA may be a prerequisite condition for meaningful gains in problem-solving performance.

Collectively, the trends depicted in Figure 2 provide important cross-national evidence that mathematics anxiety in Numerical Methods courses follows a declining cohort pattern over time at both UTHM and UP. It also simultaneously highlights the persistent gap that warrants targeted comparative investigation between the Malaysian and Indonesian higher education contexts. At the higher education level, MA has been linked to lower course grades and higher dropout rates (Núñez-Peña et al., 2013).

The progressive improvement in mean PSA scores observed at both UTHM and UP across the four cross-sectional sampling points is a noteworthy finding that warrants careful interpretation within the broader theoretical and pedagogical context of Numerical Methods education. The upward trend at both institutions, when examined alongside the parallel decline in MA scores (see Figure 2), provides empirical support for the theorized negative relationship between affective inhibition and cognitive performance in mathematically demanding courses. Specifically, as successive cohorts of students at both universities reported lower mean MA, corresponding cohorts demonstrated higher mean PSA. This pattern is consistent with the cognitive interference model of MA proposed by Ashcraft and Ridley (2005), positing that anxiety occupies working memory resources otherwise available for complex problem-solving.

The substantially larger cumulative PSA gain observed at UP (7.3 points) relative to UTHM (3.3 points) may reflect a ceiling effect at UTHM, where initial PSA scores were already comparatively high (78.0 in 2021), constraining the margin for further improvement. Conversely, the lower baseline PSA at UP (55.2 in 2021) afforded greater room for measurable growth, consistent with regression-to-the-mean dynamics frequently observed in repeated cross-sectional educational research (Reichardt, 2002). The negative relationship between MA and mathematical performance has been documented as a global phenomenon, transcending cultural and national boundaries (Foley et al., 2017). The larger cohort-level increase in PSA at UP should be interpreted cautiously because baseline differences, cohort composition, and other unmeasured contextual factors may have contributed to the observed pattern. Nevertheless, the persistent and widening interinstitutional gap, increasing from 17.0 to 18.8 points across the study period, indicates that gains at UP, although substantial in relative terms, have yet to translate into comparable absolute performance levels with UTHM students. This observed disparity may be associated with unmeasured differences in student preparation, curriculum implementation, learning resources, and other institutional factors (Yusof & Tall, 1998). Overall, these findings indicate that despite positive affective and cognitive trends in both contexts, targeted interventions to strengthen foundational mathematical competencies and reduce anxiety in computationally intensive courses are needed to narrow the performance gap between Malaysian and Indonesian students.

Differences between UTHM and UP students in both MA and PSA were significant, with UP students exhibiting higher MA and lower PSA consistently across cohorts. This finding is in line with the contrasting educational systems described in the introduction: Malaysia’s centralized, government-supported system with bilingual instruction and technology integration (OECD, 2024; Padilla-Valdez, 2019) versus Indonesia’s decentralized system characterized by infrastructural and resource variability (OECD, 2019). These educational disparities may be associated with the observed differences, reflecting sociocultural and institutional influences on student affect and achievement (Beilock et al., 2010; Gutierrez, 2002). Observed differences between institutions should not be interpreted as direct effects of nationality, culture, or educational quality. Factors such as students’ prior mathematical preparation, socioeconomic background, curriculum implementation, access to technology, and academic support were not measured and may have contributed to the observed differences.

Temporal analyses revealed significant reductions in MA and concomitant increases in PSA over the four-year period, particularly pronounced among UP students. The observed cohort-level reductions in MA and increases in PSA coincided with changes in instructional conditions from online to hybrid delivery. However, the repeated cross-sectional design does not permit causal attribution of these patterns to instructional modality (Bozkurt & Sharma, 2020). The significant interaction effects between University and Year further suggest that institutional contexts may influence how students respond across cohorts to instructional changes. UP cohorts demonstrated greater improvements during the period in which instructional modalities transitioned toward hybrid learning. However, these changes should not be interpreted as causal effects of instructional modality because other institutional and cohort-related factors may have contributed. Such differential effects underscore the importance of tailored instructional and support strategies that account for institutional and cultural contexts (Bandura, 1997; Pajares & Miller, 1994).

The repeated cross-sectional design limits causal inference about individual trajectories but provides robust group-level insights into how MA and PSA evolve under varying contextual pressures. Future research employing longitudinal cohort designs would complement these findings by tracking intra-individual changes and disentangling within-person from between-group effects (Caruana et al., 2015). Additionally, qualitative studies exploring student perceptions and coping strategies may enrich understanding of the complex sociocultural dimensions underpinning MA.

Practically, reducing MA while enhancing PSA requires integrated efforts: improving institutional resources and technology, fostering positive cultural attitudes toward mathematics, and implementing pedagogical practices that build self-efficacy and problem-solving skills (Ramirez et al., 2018; Schoenfeld, 2017). Given the ongoing challenges posed by educational disruptions, hybrid or blended learning models combined with culturally responsive teaching hold promise for supporting diverse learner populations.

This study advances the understanding of MA and PSA in a Southeast Asian transnational context during a period of rapid pedagogical change. The findings highlight significant institutional and temporal influences on these constructs and underscore the need for contextually sensitive interventions to mitigate anxiety and enhance mathematical problem-solving capacities in higher education.