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APOS Theory

A Framework for Research and Curriculum Development in Mathematics Education

  • Book
  • © 2014

Overview

Authors:
  1. Ilana Arnon

    1. College of Education, Givat Washington Academic, Tel Aviv, Israel

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  2. Jim Cottrill

    1. Department of Mathematics, Ohio Dominican University, Columbus, USA

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  3. Ed Dubinsky

    1. School of Education, University of Miami, Miami, USA

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  4. Asuman Oktaç

    1. Departamento de Matemática Educativa, Cinvestav-IPN, Mexico City, Mexico

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  5. Solange Roa Fuentes

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

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  6. Maria Trigueros

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

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  7. Kirk Weller

    1. Department of Mathematics, Ferris State University, Big Rapids, USA

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  • 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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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Introduction

    • Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, María Trigueros et al.
    Pages 1-4

  3. From Piaget’s Theory to APOS Theory: Reflective Abstraction in Learning Mathematics and the Historical Development of APOS Theory

    • Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, María Trigueros et al.
    Pages 5-15

  4. Mental Structures and Mechanisms: APOS Theory and the Construction of Mathematical Knowledge

    • Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, María Trigueros et al.
    Pages 17-26

  5. Genetic Decomposition

    • Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, María Trigueros et al.
    Pages 27-55

  6. The Teaching of Mathematics Using APOS Theory

    • Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, María Trigueros et al.
    Pages 57-91

  7. The APOS Paradigm for Research and Curriculum Development

    • Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, María Trigueros et al.
    Pages 93-108

  8. Schemas, Their Development and Interaction

    • Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, María Trigueros et al.
    Pages 109-135

  9. Totality as a Possible New Stage and Levels in APOS Theory

    • Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, María Trigueros et al.
    Pages 137-150

  10. Use of APOS Theory to Teach Mathematics at Elementary School

    • Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, María Trigueros et al.
    Pages 151-174

  11. Frequently Asked Questions

    • Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, María Trigueros et al.
    Pages 175-187

  12. Conclusions

    • Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, María Trigueros et al.
    Pages 189-195

  13. Annotated Bibliography

    • Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, María Trigueros et al.
    Pages 197-226

  14. Back Matter

    Pages 227-254
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Keywords

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.

Reviews

“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: https://doi.org/10.1007/978-1-4614-7966-6

  • 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: 978-1-4614-7965-9

  • Softcover ISBN: 978-1-4899-9825-5

  • eBook ISBN: 978-1-4614-7966-6

  • Edition Number: 1

  • Number of Pages: XI, 254

  • Topics: Mathematics Education, Learning & Instruction

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