Advancing Undergraduate Mathematics Education through APOS Theory: Conceptual Development, Reasoning, and Teaching Innovations

Guest Editors

Benjamin Tatira1

¹ Senior Lecturer in Mathematics Education, Walter Sisulu University, SOUTH AFRICA

Rationale

Understanding how undergraduate students construct advanced mathematical knowledge remains a central challenge in mathematics education research. Across many countries, students continue to experience difficulties with calculus, linear algebra, mathematical proof, abstract algebra, functions, and other university-level mathematics courses. These challenges are often characterised by procedural approaches, fragmented understanding, and limited mathematical reasoning.

APOS (Action–Process–Object–Schema) theory has emerged as one of the most influential constructivist frameworks for investigating conceptual development in undergraduate mathematics. Since its introduction by Dubinsky and colleagues, APOS theory has informed a substantial body of international research on learning, teaching, curriculum design, and technology-enhanced mathematics education. Recent developments involving digital learning environments, dynamic mathematics software, artificial intelligence, and increasingly diverse university populations create new opportunities to extend APOS research in meaningful ways.

This special issue will provide an international platform for advancing theoretical, empirical, and pedagogical research on undergraduate mathematics education through APOS theory and related constructivist perspectives.

Scope of the Special Issue

The special issue welcomes high-quality empirical, theoretical, methodological, and review papers that investigate undergraduate mathematics teaching and learning through APOS theory. Contributions may focus on conceptual understanding, mathematical reasoning, proof, abstraction, schema development, instructional design, technology integration, teacher education, and comparative international studies. The issue particularly encourages studies that connect APOS theory with contemporary developments in mathematics education, including digital technologies, artificial intelligence, equity, multilingual contexts, and curriculum innovation.

Aims

The special issue aims to:

  • advance theoretical developments and applications of APOS theory in undergraduate mathematics education;
  • examine students’ conceptual development across advanced mathematics topics;
  • investigate mathematical reasoning, proof, abstraction, and schema construction;
  • explore instructional interventions informed by APOS theory;
  • examine the role of technology and artificial intelligence in supporting conceptual learning;
  • promote comparative and cross-cultural studies across diverse educational systems;
  • strengthen international collaboration among researchers in undergraduate mathematics education.

Suggested Topics

Topics include, but are not limited to:

  • APOS theory and conceptual understanding
  • Learning of calculus, linear algebra, abstract algebra, real analysis, and differential equations
  • Mathematical proof, justification, and reasoning
  • Genetic decompositions and instructional design
  • Technology-enhanced APOS learning environments
  • GeoGebra, computer algebra systems, and digital mathematics tools
  • Artificial intelligence and conceptual learning
  • Transition from secondary to tertiary mathematics
  • Undergraduate students’ abstraction and schema development
  • Preservice mathematics teachers’ advanced mathematical knowledge
  • Comparative APOS studies across countries
  • Mixed methods and qualitative approaches in APOS research
  • Extensions, critiques, and integrations of APOS theory

Expected Contribution

The special issue will make three important contributions to mathematics education research.

First, it will synthesise contemporary APOS research across diverse mathematical domains and international contexts.

Second, it will highlight innovative teaching approaches that promote deep conceptual understanding rather than procedural learning.

Third, it will provide evidence-based insights for improving undergraduate mathematics teaching, curriculum development, teacher education, and technology integration internationally.

The issue will particularly encourage collaborative and comparative studies involving researchers from multiple countries and institutions.

References

Dubinsky, E., & McDonald, M. A. (2001). APOS: A constructivist theory of learning in undergraduate mathematics education research. In D. Holton (Ed.), The teaching and learning of mathematics at university level (pp. 275–282). Kluwer Academic Publishers.

Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Roa Fuentes, S., Trigueros, M., & Weller, K. (2014). APOS theory: A framework for research and curriculum development in mathematics education. Springer.

Submission Guidelines

All submissions undergo a thorough double-blind peer-review.

Submission Process

  1. Visit https://www.editorialpark.com/ejmste and log in (or create an EditorialPark account if you do not have one).
  2. Click the “Submit New Manuscript” button.
  3. Under the “Issue Type” section, select “Special Issue”.
  4. Select “Advancing Undergraduate Mathematics Education through APOS Theory: Conceptual Development, Reasoning, and Teaching Innovations” from the special issue list and submit your manuscript.

Key Dates

Submission Deadline: January 31, 2027

First review decisions: March 31, 2027

Revised manuscripts due: April 30, 2027

Final decisions: May 31, 2027

Expected Publication: June 30, 2027

Contact

Should you have any questions, please do not hesitate to contact us at ejmste@ejmste.com.