Estudio de la estructura cognitiva de los alumnos de 9º y 12º cursos sobre el concepto de probabilidadla contribución de las Teorías de los Conceptos Nucleares y de los Conceptos Threshold

Abstract

Based on the Theories of Nuclear Concepts and Threshold Concepts, this thesis aims at understanding the cognitive structure of Portuguese students in years 9 (14-15 year-olds) and 12 (17-18 year-olds), concerning the notion of Probability. The mathematical object of this study � Probability � is part of the contents and a key element in the teaching processes of several countries, and is regarded as highly relevant in their curriculum policies as well as in the results of educational research. The adopted framework � the Theory of Nuclear Concepts � assumes that, as students progress through school, the structure of their knowledge becomes increasingly simpler, organized around a limited set of important notions � the Nuclear Concepts. On the other hand, the Threshold Concepts are ideas or notions that students initially consider complex or even problematic, but, when understood, become integrative and lead to change and significant learning. We intend also to investigate the possible relationship between these two theories. Methodologically, the inquiry of practising teachers, the examination of textbooks and the analysis of scientific articles as well as of Elementary and Secondary Education curricula were the basis for the definition of the terms /concepts / notions / examples to be applied, later on, in data collection. Then, in a first moment, 344 students were inquired and, in a second moment, 325. The software Goluca was used to collect the students� data, by resorting to graphical representations, in which the concepts appear as nodes and their relationships as line segments � Pathfinder Associative Networks (PFNETs). The PFNETs thus obtained led to the identification of the most relevant concepts in the students� conceptual framework � the Nuclear Concepts � as well as those notions which are not perfectly incorporated in the students� cognitive structure � the end-nodes � and also their respective organization. In addition, a comparative analysis of the various quantitative indicators of these representations according to Gender and Year Group was carried out. In the second moment of data collection a questionnaire was also applied, aiming to detect potential Threshold concepts. The findings reveal that the students� cognitive structure stabilizes over time and that the complexity of the PFNETs does not increase from year 9 to year 12. Female and male subjects do not show statistically relevant differences in most of the quantitative indicators. Finally, it was possible to demonstrate a statistically significant relationship between the Threshold Concepts, the Nuclear Concepts and the end-nodes of the PFNETs. It is our belief that, by making it possible to identify the most relevant concepts and the most important relationships in the students� cognitive structure, the Nuclear Concepts and Threshold Concepts Theories are useful tools to organize the teaching practice and a valuable and effective pedagogical framework, which should be taken into account in the teaching and learning processes of Probability.