Between confidence and procedural flexibility in calculus

Abstract

Greater flexibility with procedures is known to be associated with greater conceptual knowledge of mathematics and vice versa. In parallel, a student’s emotional relationship to mathematics–i.e. their ‘affect’–is known to influence how they learn and perform in mathematics. For example, a confident student may engage more fully with mathematics, thereby improving their knowledge and skill acquisition and performance. What remains to be understood is the relationship between a student’s affect and their procedural flexibility. The results of this study indicate a positive, albeit moderate, correlation between a student’s confidence and their flexibility with calculus procedures. This reveals a potential avenue to improved mathematical understanding and performance: the symbiosis between confidence and flexible procedural knowledge.