Bridging Procedural Fluency and Proof-Based Reasoning: A Case Study of Undergraduate Mathematics Majors

Abstract

Undergraduate mathematics majors frequently demonstrate strong procedural skills in solving equations, applying formulas, and manipulating symbolic expressions. However, research has shown that these students struggle in the area of transition from procedural fluency to the construction of mathematical proofs. This quasi experimental study employed a non equivalent control group, pre test/post test design to examine the relationship between procedural fluency and proof construction ability in 180 second year mathematics majors across six Nigerian universities in the south-west region. The experimental group (n = 120) received a twelve weeks scaffolded intervention (proof templates, guided inquiry, peer critique, metacognitive questioning); the comparison group (n = 60) received conventional instruction. Baseline scores showed strong procedural fluency (experimental: M = 82.0%, SD = 11.2; comparison: M = 80.4%, SD = 10.8) but poor proof construction (experimental: M = 38.0%, SD = 14.8; comparison: M = 37.2%, SD = 14.1). No significant baseline differences existed between groups (procedural: t(178)=0.92, p = .36; proof: t(178)=0.35, p = .73). A moderate positive correlation between procedural fluency and proof construction was found (r = .48, p < .01). Following the intervention, the experimental group demonstrated statistically significantly greater improvement in proof construction than the comparison group (F(1, 177) = 34.28, p < .001, partial η² = .16). The scaffolded intervention revealed a significant effect compared to conventional instruction alone. These findings suggest that instructional design can address the gap between procedural fluency and proof based reasoning, though causal claims require randomised designs. Keywords: Proof construction, Procedural fluency, Undergraduate mathematics majors, APOS theory, Scaffolded instruction. Journal Reference Format: Amao, F.A., Oladapo, D.I. & Ilo, U. C. (PhD). (2026): Bridging Procedural Fluency and Proof-Based Reasoning: A Case Study of Undergraduate Mathematics Majors. Journal of Behavioural Informatics, Digital Humanities and Development Research. Vol. 12 No. 1. Pp 51-66. https://www.isteams.net/behavioralinformaticsjournal. dx.doi.org/10.22624/AIMS/BHI/V12N1P4