An investigation of problem solving-posing abilities of secondary school students and their thoughts concerning problem posing by means of using methaphors

making the work much more important since it has been providing a significant gain from the time during the assessment of the problem posing activities. The way of problem posing activities by means of using questions with multiple selections have been investigated and the teachers have been provided with the template question forms in order to prepare problem posing tests, which are including questions with multiple selections, to obtain the required clues from the mathematical knowledge of their students. The other advantage of the research itself is to learn the comments of the students concerning the problem posing activities realized with the metaphoric thoughts. Both qualifying and quantifying research methods have been used in this work. Related problem posing and problem solving success tests, which are used as data collection tool, have been developed by the researcher. The comments of 4 mathematical teachers and 2 institute members, who are experts in the field of the mathematical education, have been taken during the development processes of the success tests. In addition, the Turkish language teachers have examined the tests in terms of grammatical and compositional aspects. Afterwards, a pilot work has been realized in order to test the reliability of the success test themselves. A semi-structured sentence has been presented to the students at the end of the work and they have been requested to complete this sentence by means of reflecting their metaphoric thoughts. Mann-Whitney U test for comparing two different independent variants and Wilcoxon point test for comparing two dependent variants have been used as quantifying methods for analyzing operations of the data. Fisher chi-square exact test and Yates corrected Chisquare test were used for determining the link between multiple problem solving and taking course, and multiple problem solving and giftedness. The aim of this research is to question whether the students who have been presenting solutions, which are more than one way of solution, to the problems are much more successful in problem posing activities when they have been compared with the other group of students who have not been presenting any alternative ways of solutions to the problems and to obtain the thoughts of the students concerning the problem posing activities by means of metaphors. The capabilities of both superior talented and normal talented students concerning the solving a mathematical problem by means of using various alternative solution ways that are more than one solution way have carefully been studied and their success degrees on problem posing activities have been compared with each other in the group in order to satisfy this requirement of aim. The success degrees on problem posing for the students who have been presenting various solutions, which are more than one solution way to a mathematical problem, have carefully been compared with the degrees of the other group of students who have not been presenting any alternative ways of solutions in this research. It has been tried to analyze the features of the students who have been presenting various solutions, which are more than one solution, to a mathematical problem and discover their thoughts concerning the problem posing activities. The problem posing activities of the students have been carried out by means of using questions with multiple selections. This situation has been one of the major reasons The metaphors created by students have been classified with a content analyzing provided from qualifying research methods. The favorite findings from the obtained results of the thesis work itself are that the superior talented students cannot totally present an alternative way of solution, students who are finding various solutions, which are more than one solution way, to the problems have much higher scores in problem posing success tests and the metaphoric thoughts in problem posing activities have much more positive effects on the normal talented students. Keywords: Mathematical problem posing, problem solving, problem solving with various solutions that are more than one solution, metaphoric thought and gifted student