Primary school students? difficulties associated with the resolution of non-routine problems

This study examines primary school students? difficulties associated with the resolution of non-routine problems. It also examines problem solving strategies that the participating students used when solving non-routine problems.The research employed a qualitative case study, and it was carried out with five 4th grade students in Fatoş Büyükkuşoğlu Primary School in Kayseri. After reviewing available literature about problem solving, seven non-routine problems were developed and used within this research. These problems were revised in accord with the experts? views. When developing the research tasks factors including students? cognitive abilities and grade levels were also taken into account. In this research seven problem solving strategies were considered and these include: Making a list, making a table, drawing a diagram, mathematical reasoning, writing mathematical sentences, working backwards, and guess and check.Data was collected through semi-structured interviews. The interviews were conducted out of class time. Each student was given the problems one by one and asked to solve them. Students? responses were tape-recorded and annotated field notes were taken. Students were given paper and pencil and encouraged to write down their answers if they wanted. Qualitative methods were used to analyse the data collected. Analysis was carried out on the transcripts of the students? interviews their written responses whilst the researcher?s annotated field notes were used as supplementary sources.The study indicated that students encounter difficulties in every stage of problem solving. These difficulties are associated with many factors and indicated themselves in the implementation of problem solving strategies. The participating students had difficulties in understanding the problem, and this resulted mainly from their deficiency in understanding the problem story ? the linguistic aspect of the problem. It is for this reason they could not proceed the following stages. It was observed that some students began to solve the problems before making a plan. During the implementation phase students difficulties resulted, mainly, from their lack of mathematical knowledge and their deficiency in using arithmetical operations. Students were inclined very much to check procedures and arithmetic operations rather than the meaning behind them. The study indicated also that students were more successful in using certain strategies such as making a list, drawing a diagram and mathematical reasoning than they did use the other strategies.Based on the research findings we suggest that students should be encouraged to use more than one strategy when solving non-routine problems. They should be taught thinking strategies that could enable them employ different strategies when solving mathematical problems. Students should be allowed to work on real life problems and the language used in the problem story should be familiar to the students. In closing it should be underlined that problem solving is a process-oriented activity; so, the teachers should give attention to the process of problem solving rather than to its product (the result of the problem).Key Words: Problem solving, problem solving strategies, nonroutine problems