Abstract:

As it is well known, the best way to learn mathematics and consolidate the knowledge is practicing until getting confidence and ease in exercises resolution. Based on this opinion, method of Problem-Based Learning (PBL) appears to foster the effective development of logical-mathematical competence in the classroom. In this methodology, the students are a central part of the teaching-learning process, as they take the responsibility for taking decisions and searching for the most optimal solutions in order to find an answer to a given question. In this way the critical thinking is being improved, without using traditional lectures to explain all the types of concepts. A student feels more motivated and willing to plan different strategies of solutions to resolve given problems, being a professor one who rules these strategies to guide the student to the objectives established by the program.
This paper was carried out within the frame of the subject of mathematics as this is the fundamental subject for the science student, applying PBL methodology. This methodology helps to provide the student with the mayor autonomy and responsibility, losing the fear of facing new problems and to apply studied theory in the classroom in a practical and pleasant way. For this, various sets of problems were prepared that raise an initial challenge for the student, who are obliged to work on the subject from the very beginning as there are concepts that were not studied in other courses of secondary education such as trigonometry, derivatives, logarithms…etc. during first sessions the student looks for the tools with a help of a teacher that allow the student to think critically about the viability to find or not a solution for a given problem. Once the strategy is fixed, the next step is to solve the exercises firstly individually and after that through working in group that helps the students to obtain a new perspective for problems solving.
Furthermore, used methodology pretends to build knowledge on the basis of resolved problems, putting mathematics subject closer to the real life and offering a new vision to the students. The majority of secondary education students state that mathematics is essential for the life, however only few can explain the reasons why, situation that cannot be observed in other scientific technological subjects. In this way, basing a learning process on its practical side the student change the way to think about the subject and stop taking it as compound of arithmetic operations, to understand it as key subject for logical thinking and abstraction capacity development.
The results show that students who worked with this methodology during secondary education have less difficulty in the high school, adapting better to curriculum requirements of this educational stage that unlike Compulsory secondary education does not allow such liberty working with subjects units, because of the pressure of the admission test for the university. This is aim at providing the students with the maximum independence and responsibility for the studying, what helps them to know a scope of their opportunities and to get organized for the period of exams. In this way the student is obliged to work on a daily basis without accumulating large amount of information for the final exam and getting closer to the model of university education and labour market.

Keywords:

Problem-Based Learning (PBL), active methodologies, academic mathematics, interdisciplinarity.