APOS Theory

A Framework for Research and Curriculum Development in Mathematics Education

Authors: Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Roa Fuentes, S., Trigueros, M., Weller, K.

  • 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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Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-1-4614-7966-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-1-4614-7965-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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.

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.

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)


Table of contents (12 chapters)

  • Introduction

    Arnon, Ilana (et al.)

    Pages 1-4

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

    Arnon, Ilana (et al.)

    Pages 5-15

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

    Arnon, Ilana (et al.)

    Pages 17-26

  • Genetic Decomposition

    Arnon, Ilana (et al.)

    Pages 27-55

  • The Teaching of Mathematics Using APOS Theory

    Arnon, Ilana (et al.)

    Pages 57-91

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-1-4614-7966-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-1-4614-7965-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
APOS Theory
Book Subtitle
A Framework for Research and Curriculum Development in Mathematics Education
Authors
Copyright
2014
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-7966-6
DOI
10.1007/978-1-4614-7966-6
Hardcover ISBN
978-1-4614-7965-9
Edition Number
1
Number of Pages
XI, 254
Topics