American Journal of Educational Research
ISSN (Print): 2327-6126 ISSN (Online): 2327-6150 Website: http://www.sciepub.com/journal/education Editor-in-chief: Ratko Pavlović
Open Access
Journal Browser
Go
American Journal of Educational Research. 2016, 4(16), 1149-1156
DOI: 10.12691/education-4-16-5
Open AccessArticle

Applying the APOS Theory to Study the Student Understanding of Polar Coordinates

Vahid Borji1 and Michael. Gr. Voskoglou2,

1Department of Mathematics, Ferdowsi University of Mashhad, Iran

2Mathematical Sciences, School of Technological Applications, Graduate Technological Educational Institute of Western Greece, Patras, Greece

Pub. Date: October 20, 2016

Cite this paper:
Vahid Borji and Michael. Gr. Voskoglou. Applying the APOS Theory to Study the Student Understanding of Polar Coordinates. American Journal of Educational Research. 2016; 4(16):1149-1156. doi: 10.12691/education-4-16-5

Abstract

A Genetic Decomposition (GD) is developed in this paper, in terms of the APOS instructional treatment of mathematics, for teaching and learning the polar coordinates. The design of the GD is based on the conclusions obtained by a written test and by oral interviews performed on a group of students of the Physics Department of the University of Neyshabur, Iran.

Keywords:
Polar and Cartesian Coordinates and Curves APOS Theory Genetic Decomposition (GD) Triad Mechanism of Schema Development

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Asiala, M., et al., A framework for research and curriculum development in undergraduate mathematics education, Research in Collegiate Mathematics Education II, CBMS Issues in Mathematics Education, 6, 1-32, 1996.
 
[2]  Clark, J.M., et al., Constructing a schema: The case of the chain rule, The Journal of Mathematical Behavior, 16(4), 345-364, 1997
 
[3]  Dubinsky, E. & McDonald, M. A., APOS: A constructivist theory of learning in undergraduate mathematics education research. In: D. Holton et al. (Eds.), The Teaching and learning of Mathematics at University Level: An ICMI Study, 273-280, Kluwer Academic Publishers, Dordrecht, Netherlands, 2001.
 
[4]  Piaget, J. & Garcia, R., Psychogenesis and History of Science, Translation by H. Feider, Columbia University Press, N.Y., !989 (the original work published in 1983).
 
[5]  Stewart, J., Calculus, 7th Edition, Brooks/Cole Cengage Learning, Mason, 2010.
 
[6]  Swinburne.edu, Grade Point Average Assessment, retrieved from http://www.swinburne.edu.au/studentadministration/assessment/gpa.html, on October 10, 2012.
 
[7]  Voskoglou, M. Gr., An application of the APOS/ACE approach in teaching the irrational numbers, Journal of Mathematical Sciences and Mathematics Education, 8(1), 30-47, 2013.
 
[8]  Voskoglou, M. Gr., Fuzzy Logic in the APOS/ACE Instructional Treatment of Mathematics, American Journal of Educational Research, 3(3), 330-339, 2015.