The 25 February 2009 defended his doctoral thesis, based on theoretical notions of EOS, entitled:
Coneixement The significant constructio mathematicism a l'ESO a sociocultural perspective des d'
The author is Marta Sundays, being directed by Dr. Montserrat Benlloch and Àngel Alsina and presented at the University of Vic (Catalonia, Spain).
SUMMARY:
enough is a fact known to see a clear distance between the bases of the LOE educational psychology, focusing on socio-constructivist perspective and what happens in the classroom itself today, and more specifically in the classroom Mathematics of the ESO. And is that despite the law, mathematics teachers tend to make explanatory class, examples and exercises, and stand little to let students build collectively and individually, the mathematical meaning. With the intent to influence this problem, in the framework of the thesis (Domingo, 2004) designed protocols were developed from this point of view, for the introduction of new mathematical content to students in 3rd and 4th of ESO, which then there are two important consequences: it increases the motivation and comprehensive memory of the students.
As part of the thesis is considered necessary to analyze the protocols from the point of view more qualitative, where several elements to look like the type of discourse (speech prolèptic), the type and degree of interaction between students and between teacher and students, the adequacy of the protocol to the curriculum, the way how to treat the error, and other factors affecting the protocols are "valid" from the point of view of Mathematics Education. This new perspective brings us closer to the socio-constructivist perspective of human learning, as pointed Coll (1993): If from constructivism learning is seen as an active process of the pupil through which he can build, enhance and diversify their knowledge of to the various contents from the meaning and the meaning he attributed the socioconstructivism incorporates the idea that cognitive development is a process that goes from the outside world into the inner world social, individual. Seeking an objective tool that allows us to validate our materials, and from a current literature review, we find the contributions of the approach ontosemiotic (EOS) of Godino, Font and Wilhelmi (2006), analysis of any teaching-learning content mathematicians.
In this context, the search query is configured as follows: "Under the socio-constructivist perspective, the degree of suitability educational program has the didactical transposition of mathematics content to THAT? ". Based on the final question, have finalized the following objectives: 1 .-
Analyze a program protocol didactic transposition of mathematical content at ESO (Domingo, 2004) from self-observation and make appropriate improvements, obtaining a improved protocol.
2 .- To evaluate the degree of suitability or epistemic mathematics improved protocol.
3 .- To assess the degree of cognitive adequacy of the improved protocol.
4 .- To evaluate the degree of suitability interactional improved protocol.
5 .- To evaluate the degree of suitability mediational improved protocol.
6 .- To assess the degree of emotional appropriateness improved protocol.
7 .- Assess the level of environmental soundness of the improved protocol.
Other studies carried out from the EOS (Godino and Tanner, 1994; Font and Godino, 2006; Godino, Contreras and Font, 2006; Godino, Font and Wilhelmi, 2006; De Amore and Godino, 2006; Godino, Font, Wilhelmi and Castro, 2007; Godino, Bencomo, Font and Wilhelmi, 2006) have proposed five levels or types of analysis for a process of mathematical study: analysis of the types of problems and systems of practices (meaning systemic), development of configurations of objects and processes mathematical analysis of the educational paths and interactions, identification of system and meta-rules that condition and enable the study process (policy dimension) and, finally, evaluation of educational adequacy of the study process. The first four levels are tools for teaching descriptive - explanatory, that is used to understand and respond to the question "What is happening here and why?", While the fifth aims to improve the functioning of the study process .
As part of this work we concentrate on the fifth floor, because we want to evaluate an approach to implementing the classroom. After applying the methodology provides Castro (2007), and from the context of action research, our results indicate that the level of educational adequacy of the protocol is high.
the analysis in particular each of the objectives relating to the different degrees of fitness, we have drawn some conclusions about the possible relationship between these and those with the sociocultural perspective of human learning, which allows us to supplement and enrich a little under Notional defined
- It is necessary that the teacher has a good education to obtain a high degree of suitability math, interactive, mediational and emotional.
- It is necessary that the teacher has a good understanding of reality and context of the center, as well as students, to encourage cognitive and ecological suitabilities.
- A high degree of interactional adequacy, supports and helps the activity happens on a sociocultural perspective. Necessary, but must be analyzed as the interaction.
- A high degree of emotional adequacy, supports and helps the activity happens on a sociocultural perspective.
- A high degree of emotional fitness, promotes and helps to make learning meaningful.
- The use of manipulative material is also positive from the age of 12.
- The use of manipulative material increases the degree of motivation, and retruque increases the degree of emotional fitness, encouraging, then, again, that the activity happens on a sociocultural perspective.
- The fact of working in groups, increases the degree of motivation, and retruque, increases the degree of emotional fitness, encouraging, then, again, that the activity happens on a sociocultural perspective.
With the survey we conducted we have found that the distance is much smaller, but you have to continue to investigate and make concrete proposals to assist it in mathematical terms, to tend towards zero. And, as they say Chamoso and Rawson (2004) "At certain times of the day difficult road of education, we wonder if students are able to perform some activity and organizing and thinking to achieve an adequate response. It seems very clear that they will always be given the opportunity to do so ... "(p. 38)
