eng Science and Education Publishing American Journal of Educational Research 2327-6150 2017-03-23 5 3 303 309 10.12691/education-5-3-11 EDUCATION20175311 article Vahid Borji vahid.borji@stu.um.ac.ir, Vahid_math@yahoo.com 1 Michael. Gr. Voskoglou 2 Department of Mathematics, Ferdowsi University of Mashhad, Iran Mathematical Sciences, School of Technological Applications, Graduate Technological Educational Institute of Western Greece, Patras, Greece This paper continues a research started in an earlier work on teaching/learning the polar coordinates in the plane with the APOS/ACE instructional treatment of mathematics. Based on the Genetic Decomposition developed in our previous work, we design here an ACE circle and we apply it for teaching/learning the polar coordinates to a group of students of an Iranian university. For testing the effectiveness of this application the results of the experimental group are compared to those of a control group, for which the polar coordinates were taught at the same semester in the traditional, lecture-based way. The conclusions drawn enable us to make some minor revisions to the initial design of our Genetic Decomposition. http://pubs.sciepub.com/education/5/3/11/education-5-3-11.pdf Cartesian and Polar Coordinates (PCO) and Curves APOS Theory Genetic Decomposition (GD) ACE Circle Mathematics Teaching