Problem Posing. (c2015)

Abstract

Researchers argue that one of the main aims of mathematics education is to develop students’ abilities to solve a wide range of complex problems. Thus, advocates of the reformed movements in mathematics education constantly research various methods which ought to enhance the ability to be a good problem solver. The current research explores the effectiveness of using problem posing as a teaching strategy to enhance students’ problem solving abilities. It also tries to determine the effects of such a strategy on students with originally different achievement level. This is accomplished by using a mixed-method research design for data collection and analysis, consisting of an experimental study comparing two groups of grade-8 students, a control group and an experimental group. A pretest and a posttest are administered to both groups to determine the level of improvement after the study. The study evaluates the performance of students in these tests, according to a problem solving rubric which targets four main problem solving abilities: “understand a problem”, “use information appropriately”, “apply appropriate procedures/representation”, and “answer a problem”. On the other hand, clinical interviews are conducted with a selected sample consisting of three pairs from each group at different levels of achievement, then qualitatively analyzed to explore the effect of problem posing activities on students’ problem solving abilities. The study shows that students who were subject to problem posing activities demonstrated more improvement than students who were subject to the usual method of solving word problems. The researcher also concludes that the average- and high- math achieving students were the most affected by the problem posing activities. Students who were subject to the problem posing activities were more successful in problems that require logical thinking and reasoning. On the other hand, students in the control group were more successful in problems of procedural nature. Regarding the assessed problem solving abilities, the whole sample, and in particular the high-achieving group, revealed a significant improvement in the ability to “understand a problem”. The study concludes with recommendations for further research on the use of problem posing strategies at the intermediate level, with larger samples and more time dedicated for the implementation.