A Course-Embedded Rubric for Statistical Modeling in Vocational Undergraduate Mathematics: Student Performance, Scoring Quality, and Instructional Implications

Source abstract

Vocational undergraduate programs increasingly expect students to use probability and statistics to make decisions in workplace-like settings, yet instructors often lack practical tools for evaluating open-ended modeling work consistently and instructionally. This study developed and applied a course-embedded analytic rubric for statistical and probabilistic modeling in a required mathematics course. The rubric addressed six dimensions: contextual problem understanding, assumptions and data quality, model formulation, quantitative reasoning, validation and uncertainty, and vocational communication. Two authentic tasks, a manufacturing quality-sampling decision and a service waiting-time evaluation, were implemented, and 203 anonymized student submissions were scored. Two trained raters scored all submissions, with a third rater scoring a subsample to examine rater effects. Evidence from inter-rater agreement, many-facet Rasch measurement, and correlations with an independent transfer-oriented assessment evaluated scoring quality and educational usefulness. Results indicated good overall scoring consistency, ordered category functioning, small rater severity differences, and moderate-to-strong relations between rubric scores and transfer-oriented performance. Students performed more strongly on problem understanding, model formulation, and quantitative reasoning than on validation, uncertainty, and vocational communication. Beyond demonstrating scoring quality in a vocational setting, the study conceptualizes statistical modeling competence as a course-embedded, multidimensional, formative performance construct. This shows that rubric-based assessment can operationalize modeling not only as technical execution, but also as the coordinated integration of problem framing, quantitative reasoning, validation, and vocational communication. The findings suggest that a course-embedded rubric can serve as both a scoring tool and a practical framework for feedback, instructional adjustment, and curriculum improvement in vocational undergraduate mathematics.