HOTS in Calculus Assessment: Examining the Gap between Student Capacity and Assessed Practice

Abstract

The development of Higher-Order Thinking Skills (HOTS) is a critical objective in undergraduate mathematics education, particularly in calculus, which serves as a gateway to STEM disciplines. However, standard assessments often privilege procedural fluency over conceptual depth. This exploratory case study investigates how specific assessment task designs can elicit and evaluate HOTS, specifically transfer, critical thinking, and problem-solving among first-year calculus students. Guided by Brookhart’s assessment theory and Lithner’s framework of Creative Mathematical Reasoning, the study adopts a qualitative task-based interview approach with students from mainstream calculus modules at a South African university. Findings from online assessments and follow-up interviews show a substantial reliance on Algorithmic Reasoning, where students demonstrated procedural competence but struggled with the Creative Mathematical Reasoning required for interpretation and interdisciplinary transfer. The study argues that to bridge the gap between "knowing how" and "knowing why," assessment tasks must be explicitly designed to disrupt rote formula application and require justification