C&C 49, 3-4 (2016)
|A. GAGATSIS, A. MONOYIOU, P. MICHAEL – CHRYSANTHOU. Major Aspects of Cypriot and Italian Preservice Teachers’ Conceptual Understanding of Function: an Interpretation in the Context of the Fundamental Educational thought|
MAJOR ASPECTS OF CYPRIOT AND ITALIAN PRESERVICE
TEACHERS’ CONCEPTUAL UNDERSTANDING
OF FUNCTION: AN INTERPRETATION IN THE
CONTEXT OF THE FUNDAMENTAL
Athanasios Gagatsis, Annita Monoyiou, Paraskevi Michael – Chrysanthou
In this study the concept of function is viewed from two different perspectives, the point wise and the coordinated perspective. In the point wise approach, a function is perceived of as linking x and y values: For each value of x, the function has a corresponding y value. In the coordinated approach, the students can “coordinate” two systems of representation, the algebraic and the graphical one. The present study investigates the relationship between the students’ approach to function and their performance to some major aspects of the conceptual understanding of functions; in particular, giving a correct definition and examples of the concept, recognition of the concept given in various representations, making conversions from one mode of representation to another and solving complex problems. The participants were 279 Cypriot and 206 Italian pre-service teachers who completed two tests on functions that were constructed for the needs of the present study. The collected data were analyzed using different types of quantitative statistical methods. The results showed that students who employed the coordinated approach demonstrated considerably higher performance at the various aspects of the understanding of function relatively to the students who used the point wise approach. Furthermore, within the coordinated approach group of pre-service teachers, problem solving was found to relate to all the other aspects of the conceptual understanding of function, whereas for the point wise group, the phenomenon of compartmentalization was detected in their responses to the tasks, which involved different mathematical reasoning and use of this concept. These findings are discussed and interpreted in light of the theoretical framework of mathematical work space (MWS) and of the practical significance of the fundamental educational thought.
Function, point wise approach, coordinated approach, semiotic representations, compartmentalization, mathematical work space, fundamental educational thought.
|Fernand Vandamme. JUSTICE, LAW AND APPLIED SCIENCE.|
JUSTICE, LAW AND APPLIED SCIENCE
Applied Science, Law, criminal law, Justice, dyssocials, wisdom, intelligence, harmony, conflict resolution, metaphor, enzymes, applied scientific justice, justice-audit, proteolytic actors.