Designing Cognitively Engaging and Relevant Mathematics Questions for Lifelong Learning

Abstract

Mathematics assessment questions influence students' perceptions of mathematics and their capacity for lifelong learning. This position paper argues that test items should be relevant to students' cognitive level, cognitively engaging enough to promote deep thinking, and sufficiently clear to avoid unnecessary confusion. Using the associative and commutative properties as a case study, the paper analyses how the item (x+y)(2m-n) - 2(x+y) can create avoidable cognitive load when students must infer implicit regrouping and subtraction as addition of a negative. Pilot classroom data from 62 SHS 2 students indicated that 71% rated the wording as confusing, 64% reported knowing the mathematics but becoming stuck during problem setup, and statistical tests confirmed that perceived confusion was systematic, with a large effect size (d = 1.08). Qualitative responses showed that students struggled mainly with commutativity, subtraction patterns, and mismatch between the prompt and previously learned examples. The paper presents five confusingversus-clear algebra and geometry examples, integrates classroom evidence with relevant assessment-design literature, and provides a ten-point clarity checklist for teachers. The findings suggest that clear wording, explicit notation, and appropriate scaffolding help students demonstrate mathematical understanding more validly and support the development of reasoning, transfer, and lifelong learning habits.