Modeling Concrete and Virtual Manipulatives for Mathematics Teacher Training: A Case Study in ICT-Enhanced Pedagogies

Abstract

This feature paper explores the comparative pedagogical roles of concrete and virtual manipulatives in preservice mathematics teacher education. Based on a design-based research (DBR) methodology, this study investigates the effects of tangible tools (e.g., base-ten blocks, fraction circles) and digital applications (e.g., GeoGebra Classic 6, Polypad) on preservice teachers’ problem solving, conceptual understanding, engagement, and instructional reasoning. Data were collected through surveys (n = 53), semi-structured interviews (n = 25), and classroom observations (n = 30) in a Spanish university’s teacher education program. Key findings show that both forms of manipulatives significantly enhance engagement and conceptual clarity, but are affected by logistical and digital access barriers. This paper further proposes a theoretically grounded model for simulating manipulatives through ICT-based environments, enabling scalable and adaptive mathematics teacher training. By linking constructivist learning theory, the Technologically Enhanced Learning Environment (TELE) framework, and simulation-based pedagogy, this model aims to replicate the cognitive, affective, and collaborative affordances of manipulatives in virtual contexts. Distinct from prior work, this study contributes an integrated theoretical and practical framework, contextualized through empirical classroom data, and presents a clear plan for real-world ICT-based implementation. The findings provide actionable insights for teacher educators, edtech developers, and policymakers seeking to expand equitable and engaging mathematics education through simulation and blended modalities.