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This research work presents the strategy called "PRODEHIMA", a teaching-learning strategy for mathematics based on the problem-solving method and technological means such as the mathematical applications MAPLE and DERIVE, with the purpose of obtaining significant improvements in the academic performance of students in the subject of Mathematics IV of the Faculty of Civil Engineering of the National University "Santiago Antúnez de Mayolo", during the 2006 - I academic semester. The study population consisted of 62 students from the faculties of civil engineering and agricultural engineering enrolled in the subject, of which 20 students from the faculty of civil engineering were chosen to form the experimental group, and 20 from agricultural engineering to form the control group. The study period covered the development of four didactic units of the subject. In the experimental group the PRODEHIMA teaching-learning strategy was applied, while in the control group the traditional teaching method was applied. It was found that the "PRODEHIMA" strategy significantly improved the students' academic performance.