Background Mathematical conceptual understanding is a critical competency for vocational students who must apply mathematics to authentic technical, industrial, and sustainability-oriented problems. However, comparisons of students’ mathematical thinking across regions, school specializations, and gender are often conducted without first establishing measurement equivalence, risking biased conclusions and inequitable educational decisions. This study examines whether vocational students conceptualize mathematics in the same way by validating a multidimensional measurement model and testing its invariance across key contextual and demographic groups. Methods A cross-sectional quantitative design was employed with 125 vocational high school students in Indonesia. Mathematical conceptual understanding was conceptualized as a four-dimensional latent construct comprising Conceptual Reasoning, Mathematical Representation, Problem Modeling, and Knowledge Transfer. Confirmatory Factor Analysis (CFA) was used to evaluate the factorial validity of the model. Multi-Group Measurement Invariance (MGI) testing was then conducted sequentially across region (Java vs. non-Java), school specialization (technical vs. non-technical), and gender (male vs. female) at configural, metric, and scalar levels. Results The four-factor model demonstrated excellent fit to the data and strong reliability and convergent validity. Configural and metric invariance were supported across all grouping variables, indicating a shared conceptual structure of mathematical understanding among vocational students. Full scalar invariance was not achieved; however, partial scalar invariance was established by freeing several context-sensitive items. Latent mean comparisons revealed meaningful contextual differences: students from Java scored higher in mathematical representation and problem modeling, while students in technical programs showed advantages in problem modeling and knowledge transfer. Gender differences were small across dimensions. Conclusions Mathematical conceptual understanding in vocational education is a multidimensional construct that can be measured fairly across diverse student groups. Although the underlying structure is invariant, learning outcomes are shaped by contextual factors such as regional resources and program specialization.
Mudi et al. (Thu,) studied this question.
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