A quantitative research of 10th year students's conceptions on geometric locus concept by using the Ck¢ model

At the beginning of the research, one of the models is called cK¢ model, whichexplains how learning process is becoming, resources related to the topic were scanned andthen following this procedure the project was prepared. In the literature, there are lots ofresearches, concerning conceptions in general, an conceptions, created by students, inparticular. A comprehensive identification of the conceptions is important to understand, ofwhat proportion of the learning have been achieved, and of what proportion of the learninghave not been achieved. Diagnosing conceptions is very important and also a conception isnot an observable element. Observable elements are operators used by students, the problemsolved, the language used to express them and theoretical control structures. For therealization and durability of the learning, it is necessary for it, to consider these observablefacts. The cK¢ model also enables such an identification of the student conceptions. Thestarting point of the cK¢ model is the Theory of Didactical Situations, created by the Frenchmathematics educator Guy Brousseau, between the 1970?s and 1990?s. The aim of the Theoryof Didactical Situations is to study learning in didactical situations in the mathematicaldomain and the student being modelled as an epistemic subject. The cK¢ model, is the kindof model, which tries to explore how the learning process realizes, by accepting thehypothesis that problematic situation are the main resource of the information.In this research, a work sheet has been prepared by the researcher and the researcher?sadvisor, as an instrument of data collecting, for the 10th year students. The work sheet hasbeen prepared for exploring the 10th year students? conceptions, concerning the ?geometriclocus? concept, according to the cK¢ model.The research has been conducted with 6 groups, each of which composes of 2 students(i.e. 12 students in sum), who are getting their education in Ankara, in a private establishment,preparing students for various exams. The questions that take place in the work sheet, havebeen analyzed by the researcher and the researcher?s advisor. The data that obtained from thestudents, have been analyzed, according to the cK¢ model. These analyzes have beencompared with the mathematical analyzes that were conducted by the researcher and theresearcher?s advisor, and they have been interpreted. As results of this comparison, it has beenobserved that these students have not well constructed their conceptions of ?geometric locus?,they have some misconceptions and they use these misconceptions, without thinking on it. Ithas also been concluded that, the conceptions of the students, concerning the ?geometriclocus?, are being made, intuitively. In this research, the significance of students? conceptionsand the significance of the analyzes that is conducted according to the cK¢ model, inexploring in what degree, the taught content has been internalized by the student, has alsobeen seen thanks to hat model, comments of wider perspective, concerning the concepts thatare being taught and learned, have been able to be made, by the researcher. Besides, withinthe limits of the research findings, suggestions are made for both this study and for researchwho want to work on this issue in the future.