Free Problem Posing Cases of Prospective Mathematics Teachers: Difficulties and Solutions

AbstractThe aim of this study is to evaluate free problem posing studies of prospective mathematics teachers about Ratio and Proportion Subject’, to determine the difficulties faced by the prospective teachers during problem posing process and to elicit suggestions regarding the experienced difficulties. For this purpose a data form was created by the researchers. This data form has three parts which were; i) The task of posing free problems, ii) The difficulties faced during problem posing process and iii) Suggestions for solutions of the difficulties. The data form was applied to 114 prospective primary mathematics teachers. During the analysis of the data regarding the first part of the data form, the following criteria were considered; i) Problem text (language and expression), ii) The compatibility of the problem with the mathematical principles, iii) The type/structure of the problem and iv) The solvability of the problem. In the analysis of the data obtained from the second and third parts of the form, content analysis was conducted and the program which is called as NVivo 10 was used. In conclusion, it was concluded that prospective mathematics teachers posed clear and understandable problems which were compatible with the mathematical principles in the form of exercise type and which can be solved by students. The difficulties faced during problem posing process determined as; lack of experience, lack of the content knowledge, not recognizing the cognitive levels of the students, lack of curriculum knowledge and difficulties in writing problem texts. The solutions which were suggested in the scope of this study were as the following; emphasizing problem solving and posing studies, in depth analysis of the curriculum, teaching special teaching methods in details and resorting to resources during problem posing process