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http://repositoriodigital.ipn.mx/handle/123456789/11669| Título : | Estabilidad y cambio de concepciones alternativas acerca del análisis de funciones en situación escolar |
| Autor : | Dolores Flores, Crisólogo |
| Fecha de publicación : | 16-ene-2013 |
| Descripción : | In school practice, mathematics professors use cartesian graphics figural representations for teaching functions and analysis of its behavior. But there’s evidence of several conceptions which grow in the students minds regarding these representations which are unacceptable in mathematics (Wainer, 1992; Mc Dermot, Rosenquist, Van Zee, 1987; Dolores, 1998; Dolores & Guerrero, 2002; Dolores, Alarcón & Albarrán, 2003; Dolores, 2003). These questions have implications on teaching and learning process of the mathematics of variables. As for us, we assume these conceptions can be removed from students mind in order to approach them to acceptable conceptions by means of a systematic teaching process. In relation to such thought, this research has as a fundamental goal to analyze the stability and change of the students alternative conceptions regarding to the analysis of functions in particular instructional conditions. In a full context this work is based on the ideas which about the Thinking and Variational Language have come out from the group of researchers organized around the Educational Mathematics Latinoamerican Committee (CLAME). In a specific context it is built on the foundations of the alternative conceptions and intentional conceptual change. In our country several researchers carry out their projects focusing on the research line called Thinking and Variational Language which studies the link between the didactic systems, attending to a systematic approach which allows to include the four basic elements in the construction of knowledge: its epistemological nature, its sociocultural dimension, the cognitive frames and the models of transmission through teaching. Regarding to the alternative conceptions, as for Mevarech & Kramarsky (1997) children develop ideas about their world, they develop meanings for words used in science and create strategies to obtain explanations about how and why things behave the way they do. These categories of the children’s beliefs, theories, meanings and explanations make the basis for the use of the term students conceptions. When those conceptions struggle with the other accepted ones, the alternative conceptions then appear. On the other hand, from the didactic point of view, the alternative conceptions can not stay indefinitely in the students minds, they should suffer transformations as a consequence of the practice of instructional designs even though some researchers observe that some alternative conceptions are resistant to change and others are not. Regarding to the conceptual change Pozo (1996) think that: • It’s not enough to present the student a better explanatory model, we have to make him see what is better • With the purpose of helping student understand the superiority of the new theory it is fundamental to face him to conflictive situations which may become real challenges to his ideas. Xviii • Students alternative concepts are usually implicit. A first step to their modification will be to make them explicit though their use in concrete problems. Other additional element of the conceptual changes lies on the purpose of those changes. The intentional conceptual change involves the deliberate attempt of a person looking for a radical change from a conceptual system to another because they are captivated by the power of such new conceptual system, or because they perceive a deep defect on their present vision (Ferrari & Elik, 2003). From this perspective, under conditions of the real word the new and old concepts are influenced by moderators and mediators of the conceptual change. The mediators create the whole approach which someone has about a particular concept; moderators define the simplicity or difficulty the individual will have in order to change the present concepts. With the inventory of the past ideas it is easy to see how important is the relevant role that the study of students alternative conceptions on the topic of the analysis of functions. As research is developed with the purpose of removing these conceptions in order to substitute them in agreement with the scientific knowledge, we will have the chance to make even the way to the students in school period, so that when the time comes to face their own concept of the mathematics of change, they have the sufficient stability in their conceptions to be able to make the analysis of functions related to the accepted conceptions by the discipline. In order to reach the objective of this research we set out the design of the following methodological program: background inquiry, design of the activities of incidence and instruction which at the same time are: a diagnosis, a design of the departure conditions of the instructional designs and analysis of results; finally, to the light of these activities we made the analysis of stability or change of alternative conceptions to be studied, from which we conclude that: • The degree of stability of the different identified alternative conceptions is variable. • Some students seem to pay attention to the curve of the function and ignore the relationship of co–variation seen in Cartesian graphics. Therefore the lack of co– variational reasoning in them seems to be origin of the identified alternative conceptions. • Changes of the conceptions are not linear; they happened in different ways; there are advances and turn backs. |
| URI : | http://www.repositoriodigital.ipn.mx/handle/123456789/11669 |
| Otros identificadores : | http://hdl.handle.net/123456789/1188 |
| Aparece en las colecciones: | Doctorado |
Ficheros en este ítem:
| Fichero | Descripción | Tamaño | Formato | |
|---|---|---|---|---|
| valero_2003.pdf | 2.02 MB | Adobe PDF | Visualizar/Abrir |
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