From Theory to Practice, and Back: Student Evidence Testing ZPD, APOS, CLT, and Constructivism in Mathematical Thinking Workshops

Abstract

University mathematics-support programs rarely test their theoretical foundations against student evidence, particularly in the Global South. This study addresses that gap by analyzing how students’ experiences in Mathematical Thinking Workshops (MTWs) at a South African university confirm, nuance, or challenge assumptions the Zone of Proximal Development (ZPD), Action–Process–Object–Schema (APOS) theory, Cognitive Load Theory (CLT), and constructivism. We conducted a qualitative secondary analysis of six focus-group interviews (n = 17), using abductive reflexive thematic analysis and an Assumption–Indicator–Evidence matrix that linked design rationales to student narratives. Student accounts strongly supported ZPD, with facilitation and peer norms fostering psychological safety and risk-taking, while also showing that equitable participation required explicit role-rotation routines. APOS-informed task sequencing enabled coordination across representations but operated recursively, with students calling for planned revisiting sessions to consolidate difficult ideas. CLT claims were affirmed where venue conditions and timing inflated extraneous load, highlighting the need for short debriefs and load-aware logistics. Constructivist activity fostered belonging, confidence, and more social views of mathematics but generated uncertainty when tasks ended without brief closure. We conclude by proposing context-aware refinements to these frameworks and outlining a replicable routine for testing educational theory through student evidence.