Types of mathematical difficulties experienced by secondary school students in problem solving

Throughout the history of scientific knowledge development, we can find a wide variety of difficulties that, although potentially error-prone, have contributed to the advancement of science. This study was conducted with the aim of identifying pupils’ performance and the difficulties in solving types of mathematical problems contextualized to the quadratic function and constitutes a descriptive-quantitative study. The data were obtained from 304 secondary school students in two regions of Chile, using a problem-solving test. According to the results, the greatest difficulties were found in the complexity of mathematical objects and mathematical thinking processes, surpassing the difficulties associated with teaching processes with which they were compared. With regard to the types of problems defined according to their nature and context, the lowest performance was obtained in non-routine problems and the highest was found in routine problems and those of a fantasist and purely mathematical nature. The results provide information for future research and encourage changes in school practice, which should take into account overcoming difficulties by eliminating them or by exploring their potential.