Constantine Skordoulis et al. have written an article called “The system of coordinates as an obstacle in understanding the concept of dimension“. This article has recently been published online in International Journal of Science and Mathematics Education. Here is the abstract of the article:
The concept of dimension, one of the most fundamental ideas in mathematics, is firmly rooted in the basis of the school geometry in such a way that mathematics teachers rarely feel the need to mention anything about it. However, the concept of dimension is far from being fully understood by students, even at the college level. In this paper, we examine whether the Cartesian x-y plane is responsible for student difficulty in estimating the value of the dimension of an object, or is it only students misconceptions about dimension that lead them to a false estimation of the value of the dimension of various objects. A second question discussed in this paper examines whether the system of coordinates acts as an epistemological obstacle or whether it has only a didactical character.