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APOS Theory

A Framework for Research and Curriculum Development in Mathematics Education

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  • © 2014


  • The first book on APOS Theory in Mathematics Education, written by the people who developed APOS Theory
  • Provides examples of curriculum development utilizing APOS Theory
  • Links research and teaching APOS Theory in a coherent manner
  • Describes relation of APOS Theory to Functions, Mathematical Induction, Discrete Mathematics, Linear and Abstract Algebra? and more

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About this book

In spite of the fact that APOS Theory has been used extensively in numerous scholarly publications, in the design of textbooks, and in teaching practice, there is no single references that contains all the relevant information about its components, and provides guidance about its application. The goal of this book is to present the main elements of APOS theory. It should be useful for researchers who work with, or would like to learn more about, this theoretical approach, people who are interested in the way which mathematical conceptions are constructed according to this theory, Mathematics Education researchers, graduate students in Mathematics Education, and Mathematics instructors.

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Table of contents (12 chapters)


“This book is clearly intended to persuade researchers to consider adopting an APOS-based approach. … the authors describe APOS theory as a Kuhnian paradigm, and set out to explain the paradigmatic questions, assumptions, and methods that within-paradigm researchers adopt. … In sum, for a reader interested in understanding APOS theory, this is an excellent book. It lays out APOS’s theoretical assumptions and standard research methods with clarity and precision, and it gives helpful examples of research conducted within the programme.” (Matthew Inglis, International Journal of Research in Undergraduate Mathematics Education, Vol. 1, 2015)

Authors and Affiliations

  • College of Education, Givat Washington Academic, Tel Aviv, Israel

    Ilana Arnon

  • Department of Mathematics, Ohio Dominican University, Columbus, USA

    Jim Cottrill

  • School of Education, University of Miami, Miami, USA

    Ed Dubinsky

  • Departamento de Matemática Educativa, Cinvestav-IPN, Mexico City, Mexico

    Asuman Oktaç

  • Escuela de Matematicas Edificio Camilo Torres, Oficina 201, Universidad Industrial de Santander, Bucaramanga, Colombia

    Solange Roa Fuentes

  • Departamento de Matematicas, Instituto Tecnologico Autonomo de Mexico, Col. Tizapan, San Angel, Mexico

    Maria Trigueros

  • Department of Mathematics, Ferris State University, Big Rapids, USA

    Kirk Weller

About the authors

Ed Dubinsky is a Visiting Adjunct Professor at the University of Miami, FL, USA. Dr. Dubinsky is considered the father of APOS Theory. Ilana Arnon is a lecturer of Mathematics Education for prospective middle school mathematics teachers at Givat Washington Academic College of Education, Israel. Jim Cottrill is an assistant professor of Mathematics at Ohio Dominican University, OH, USA. Asuman Oktaç  is a professor in the Department of Mathematics Education at CINVESTAV-IPN, Mexico. Dora Solange Roa is an associate professor in the School of Mathematics at the Universidad Industrial de Santander, Colombia. Maria Trigueros is a professor in the Department of Mathematics at Instituto Tecnológico Autónomo de México, Mexico. Kirk Weller is a professor and head of the Mathematics Department at Ferris State University, MI, USA.

Bibliographic Information

  • Book Title: APOS Theory

  • Book Subtitle: A Framework for Research and Curriculum Development in Mathematics Education

  • Authors: Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, Maria Trigueros, Kirk Weller

  • DOI:

  • Publisher: Springer New York, NY

  • eBook Packages: Humanities, Social Sciences and Law, Education (R0)

  • Copyright Information: Springer Science+Business Media New York 2014

  • Hardcover ISBN: 978-1-4614-7965-9Published: 05 August 2013

  • Softcover ISBN: 978-1-4899-9825-5Published: 27 August 2015

  • eBook ISBN: 978-1-4614-7966-6Published: 04 August 2013

  • Edition Number: 1

  • Number of Pages: XI, 254

  • Topics: Mathematics Education, Learning & Instruction

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