A case study on the concept images and mathematical understanding of prospective secondary mathematics teachers? related with concept of `slope?

The purpose of this study is to investigate prospective secondary mathematics teachers? concept images and mathematical understanding of `slope?. It also examines the connections that prospective teachers? make among various representations of `slope?.The participants were five prospective secondary mathematics teachers enrolled in a Faculty of Education Department of Secondary Mathematics Education. Five prospective secondary mathematics teachers were chosen through a purposeful sampling technique and they voluntarily participated in this study. Data were obtained through interviews and participants? written work.Case study design is used as a research approach for this study. Each of the five prospective mathematics teachers? was studied as a distinct case and their data was analyzed individually. Content analyses were administered for data and each case was investigated individually. The analysis particularly focused on identifying participants? concept images and mathematical understandings as they answered interview questions during the interviews. The whole data was analyzed considering mostly Tall and Vinner?s (1981) framework of concept image and concept definition.The trigonometric and physical representations were the most dominant types of representations? of slope in the prospective teachers? mind. It is thought that prospective teachers? own high school and university education and daily life experiences affect their thoughts.With some of the interview questions, investigating the connections that prospective teachers? make among various representations of slope gives some information about their mathematical understanding about slope. If prospective teachers can transfer the data to the graphs in the questions, which require some mathematical operations, they make the connections among different representations of slope in a higher level.Finally, suggestions are made for both researchers and educators who want to work on this issue in the future.Keywords: Geometry Education, Geometric Concepts, Prospective Secondary Mathematics Teachers, Slope, Concept Definition, Concept Image, Mathematical Understanding.