Posing problems and solving self-generated problems: the case of convergence and divergence of series

Abstract

The aim of the study was to examine how students generate problems about the concept of series, and how they evaluate and solve these problems. The difficulties experienced by the students while posing problems and their perceptions of the posing-evaluating-solving approach were also explored. In the first stage, 46 second-year university students posed problems for four tasks. In the second stage, which occurred a week after the first stage, the students evaluated their self-generated problems in terms of appropriateness to the tasks. The students who thought that they did not pose problems suitable for the tasks revised or reposed the problems, and then solved them by specifying the convergence or divergence of the series in the problems. The students also considered the impact of problem-posing implementation on their knowledge of the series. Findings showed that students’ difficulties led to unsuitable and unsolvable problems. The most prominent difficulties were using sequences instead of series and using convergent series instead of divergent series or vice versa. Moreover, providing the students with opportunities to evaluate and solve their self-generated problems at the end of the second stage was effective for the increase in the number of suitable and solvable problems.