The relations between concept knowledge related to the limits and continuity concepts in one variable functions and in two variables functions of prospective secondary mathematics teachers

The purpose of this thesis is to investigate whether there is a relationship between the concept knowledge related to the limit and continuity of prospective secondary mathematics teachers formed in one-variable functions and in two variable functions.In this research, quasi-experimental research method and a design based on timely test applications (pre and last test) on a single group were used. The reason for choosing this method is that it requires a data collection period of nearly a year to find responses to the research problems. The results of experimental study were presented here was carried out during the 2007-2008 / 2008-2009 academic years within a period of 10 weeks.The sample of this study is selected among the 1st, 2nd and 3. undergrade students of Mathematics Education Department of Education Faculty of a public university in Ankara. The first part of the research was conducted to 45 prospective secondary mathematics teachers who attending their first year at school during November-2007 and the second part were carried out by these 37 prospective teachers who participated in the first part of the research and they were in their second year, in December 2008.Additionally, to contribute the research, we addressed some open ended questions to totally 48 third-year students who took topology course for to get their views about the limit and continuity of any two real-variable, topologic and spatially recognized functions.The gathered data were analyzed by the ?content analysis? comprising the main patterns of the qualitative research including determination, coding and categorizing. Direct citations were presented in order to reflect the opinions of the individuals interviewed and observed.Inventories were formed about the specified topics by determining the minimum acquisitions that the students were required to get about the limit and continuity concepts of one-variable and multi-variable real functions in the studies. Nine criteria were examined in the inventory studies and it was determined whether there was a relationship between each of the overlapping competencies by comparing the competencies related to the limit and continuity of the one-variable functions of the prospective teachers and those of the multi-variable functions of the same candidates.During the research, results were found out about the concept images of the limit and continuity of the one-variable and bi-variable real functions of the prospective teachers by using the data, and interpretations were made. Interpretations were also made about the effects of the concept images the prospective teachers formed related to these concepts in the one-variable functions while configuring their concept images related to the limit and continuity of multi-variable functions, and the problems the participants faced during the processes of mathematical generalization and abstraction. Moreover, within the framework of the research findings, discussions were made along with the literature and some suggestions were presented both for the application and the educators and those who want to research about these topics.