This research is developed to describe the factors that are related to the difficulties that students present in solving mathematical problems. It studies and offers strategic proposals and heuristic methods to enable students to solve mathematical problems. The research is justified because of the poor performance and difficulties presented by students at university and high school levels to focus and to solve specific and general problems effectively. We, also, observe that teachers frequently have limitations in providing strategies and procedures to the students that could help them in the process of solving problems.
Solving a problem implies tasks that require the process of thinking that are complex and not simple routine activities. Problems usually are new situations that require creative and innovative responses. To achieve the objective of the research the following methodological scheme was employed: 1. Design and validation of a survey to explore the strenghts and weaknesses of the students. 2. Apply the survey to a population of high school and university students with the objective of collecting data and information. 3. Analyze the results obtained from a population of 60 students surveyed to gather information concerning and related to the factors considered as the difficulties students have in solving mathematical problems. 4. Present the final results.
The results of the survey indicated the need to offer didactic and methodological orientation to students, to teachers and to authors of textbooks for mathematical problem solving. For this purpose we propose a manual of cases and problems illustrating the factors identified as difficulties that will be encountered in the solution of problems by students and teachers. This reaserch will foster analytical thinking.