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MATHEMATICAL MODELING IN THIRD LEVEL PROFESSIONAL COURSES IN PORTUGUESE SECONDARY EDUCATION: AN EVALUATION REFERENTIAL

S. Santos, T. Neto, M.J. Loureiro

University of Aveiro (PORTUGAL)
In Portugal, an effort to overcome the inexistence of a sufficient number of professional courses led to their implementation in national secondary schools (Portaria nº 550-C/2004, 21st of May, altered by Portaria nº 707/2006, 10th of August), complying with the European Council requirements: education and training systems need to adapt both to the demands of the knowledge society and to the need for an improved level and quality of employment (European Union, 2002).
New curricular programs and guidelines were established for Mathematics Teaching in Third Level Professional Courses (PCIII), whose central axis is the concept of competency. This reality increases responsibilities, particularly in the Curriculum Management for Mathematics (CMM), as the teacher is required to explore new didactic approaches and incorporate new knowledge, drawing mathematic education and the work context closer together.
This justifies the relevance of the CMM evaluation in PCIII, encompassing instituted management – with reference to curricular guidelines and to the Mathematics program, intentional management – where the Mathematics curriculum is understood, programmed and planned, and implemented management – classroom practice, where the following investigation question plays a central role: To what extent does the Mathematics Curricular Management in PCIII reflects the connection to situations-problem that promotes the development of competences aiming professional performance?
Mathematical Modeling (MM), particularly in PCIII, is a cross-program theme where situations-problem, connected with different professional fields, compose both the work methodology and a competence that should be developed in the students, who, in their professional performance, will face concrete and diverse case-problems, whose effective resolution relies on their ability to select suitable mathematical tools.
The aim of this paper is to present part of the evaluation referential, based in the theoretical and methodological assumptions of the Onto-Semiotic Approach (OAMKI) to Mathematical Knowledge and Instruction, focusing on MM and its process, as well as its interdisciplinary and intra-disciplinary connections. Its explanation will be substantiated in a situations-problem that will serve as a reference for each criterion and its respective indicator.
The nature of the question of research leads us to the “ecological dimension” of the reference that may provide answers on different levels: (1) curricular guidelines – elements of the curriculum that are attended after experiencing the situations-problem proposed, mainly its purposes, goals, nature and mathematical competences; (2) interdisciplinary connections – connections between the situation-problem and other themes of Mathematics to PCIII; (3) interdisciplinary connections - connections between the situation-problem and other subjects from the training plan and/or technical area of the PCIII; (4) conditioning factors – social, material or other factors that conditioned the situation-problem and substantiate the curricular management desired/implemented of Mathematics.