Investigation of students' algebra learning and problem posing skills in a mathematics classroom supported by problem posing approach

The aim of this research is to determine the mathematical knowledge, process skills, problem qualities and problem posing strategies of students following the linear equations course supported by problem posing approach. This case study was conducted in seventh grade mathematical course related with linear equations topic with 20 students. 13 problem posing tasks during the course, 3 problem posing tasks for each learning outcome at the end of the course and clinical interviews were used as data collecting tools. Content analyse was used to determine students' mathematical knowledge and process skills, problem posing strategies. Problem posing evaluation rubric was developed to evaluate the problem qualities. Rubric consists of; clarity, mathematical accuracy, contextual originality, originality in terms of mathematical relationships, complexity level and pertinence to situation qualifications. Statistical tests were used to investigate whether the problem qualities differed on learning outcome and type of problem posing task. According to results, it was obtained that some of the students have sufficient knowledge, but besides this some of them had lack of conceptual knowledge and there was certain unsatisfactory skills among students. Problem posing points in contextual originality, originality in terms of mathematical relationships and complexity level qualifications increased significantly. Problem posing strategies were defined as; dependence to problem posing task, forming context, focusing on mathematical topics, emotional approach, integrating unrelated structure, adhering to question template and focusing on difficulty. As a conclusion, integrating problem posing approach into the lecture can be an effective way to improve mathematical knowledge, skills and problem qualifications.