Abstract:
When we look at the theoretical relationships between the three types of geometry,
we find that the most primitive type is topology and that both Euclidean and projective
geometry are derived from this earlier type. Therefore, Piaget described the first
stage or level of understanding geometry as topological understanding. In this study,
the geometric thinking conditions of mathematics teacher candidates were examined
and what they think about the topology course was determined by surveying their
opinions about the undergraduate courses. The participants of the study consisted
of 36 teacher candidates studying in the Mathematics Department of the Faculty
of Science attached to a university in Turkey. The findings of the study revealed
that none of the teacher candidates used topological thinking to solve the questions
in the data collection instrument. Those candidates who considered topology as an
abstract course did not associate topology with geometry. A thorough understanding
of the meaning of topology and topological thought is an advantage to young
children as well as college-age
students; improving mathematics curricula on this
topic, particularly at the graduate level, will ensure that all future teachers are appropriately
trained for their future responsibility of educating others. We believe that it
is necessary to give Topology and topological thought the place they deserve in the
educational process.
