A SOLO Taxonomy-based rubric for assessing conceptual understanding in applied calculus

Assessing conceptual understanding in mathematics remains a persistent challenge for educators, as traditional assessment methods often prioritize procedural fluency over the complexity of connections between mathematical ideas. Consequently, these methods frequently fail to capture the depth of students’ conceptual understanding. This paper addresses this gap by developing and applying a novel rubric based on the Structure of Observed Learning Outcomes (SOLO) Taxonomy, designed to classify student responses according to demonstrated knowledge capacity and cognitive complexity. The rubric introduces transitional levels between the main SOLO categories and includes provisions for evaluating unconventional solutions, enabling a more nuanced assessment of student work based on knowledge depth and integration. The rubric was constructed through an analysis of the conceptual knowledge components required to solve each problem, validated by expert review, and guided by criteria aligned with SOLO level classifications. It also incorporates qualitative feedback to justify each SOLO level assignment. Using this rubric, the study analyzed responses from 57 first-year undergraduate students—primarily chemistry and computer science majors at a private university in the Philippines—to test items on linear approximations and the Extreme Value Theorem. Interrater reliability was established through weighted Cohen’s kappa coefficients (0.659 and 0.667 for the two items). The results demonstrate the rubric’s capacity to differentiate levels of conceptual understanding and reveal key patterns in student thinking, including reasoning gaps, reliance on symbolic manipulation, and misconceptions in mathematical logic. These findings underscore the value of the SOLO Taxonomy in evaluating complex and relational thinking and offer insights for enhancing calculus instruction. By emphasizing the interconnectedness of mathematical ideas, the study highlights the potential of conceptually oriented assessments to foster deeper learning and improve educational outcomes. Furthermore, the rubric’s adaptability suggests its applicability beyond calculus, supporting a broader shift toward concept-focused assessment practices in higher education.