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Contribution to the Topic Group 27, ICM 11, Mexico

The following web address, http://tsg.icme11.org/document/get/391

can download the contribution made by,

John D. Godino, Mauro Rivas, Walter F. Castro and Patricia Konic

to Topic Group 27 of the ICMI 11, "Mathematical Knowledge for Teaching" with the title,

AND epistemic ANALYSIS OF AN ARITHMETIC COGNITIVISM - Algebraic PROBLEM SOLUTION

Abstract:

We analyze the solution of a problem proposed on the context of a mathematics methods course for in-training primary teachers, by applying some notions of the “onto-semiotic approach” to mathematics knowledge. The generalization of the arithmetic statement given to students involves the use of algebraic reasoning, giving way to the study of the relations between arithmetic and algebra, as well as the relations between empirical and deductive argumentation. The solution of elementary problems and the epistemic-cognitive reflection on the objects and meanings used during the solution is proposed as a means to overcome a limited students’ conception on the nature of mathematics, usually reduced to its conceptual and procedural aspects.

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Article published in Educational Studies in Mathematics "

  was published online the article,  
 
  Font, V. & Contreras, A. (2008). The problem of the particular and Its 
   relation to the general in mathematics education.    
 Educational Studies in Mathematics .   (DOI: 10.1007/s10649-008-9123-7)  
 
  that can be downloaded from the  
 
    http://www.springerlink.com/content/u8441071121170p1/  
 
   
  Abstract Research in the didactics of mathematics has Shown the  importance of the    
   problem of the particular and its relation to the general in teaching and    
   learning mathematics as well as the complexity of factors related to them.    
   In particular, one of the central open questions is the nature and diversity    
   of objects that carry out the role of particular or general and the    
   diversity of paths that lead from the particular to the general. The    
   objective of this article is to show how the notion of semiotic function and    
   mathematics ontology, elaborated by the onto-semiotic approach to    
   mathematics knowledge, enables us to face such a problem.  
 

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Multidisciplinary Seminar on Communications

On Thursday April 10, 2008 was held at the Universidad del Valle (Cali, Colombia), in the framework of the Inter-institutional Ph.D. in Education, the seminar entitled, Can ontosemiotic approach in applying the various Science Education?, conducted by JD Godino.

SUMMARY:

ontosemiotic Approach (EOS) is a theoretical framework that has emerged within the mathematics education with the purpose of expressing different points of view and theoretical notions about knowledge mathematical teaching and learning. To this end we adopt a global perspective, taking into account the various dimensions involved and the interactions between them. In particular, it proposes an epistemological model of mathematics based on anthropological assumptions / sociocultural ( Bloor, 1983; Chevallard, 1992, Radford, 2006 ), a mathematical model of cognition - on bases semiotics (Eco , 1976; Hjelmslev, 1943; Peirce, 1931-58) and an instructional model - on socio-constructivist bases ( Ernest, 1998; Brousseau, 1998 ), a systemic model - green (Morin, 1977) linking together the previous dimensions and the biological background, material and sociocultural (Maturana and Varela, 1984) in which activity takes place of study and mathematical communication.

The set of tools that make up the theoretical models mentioned, and its application to various studies have been published in several papers available on the website of the research group "Theory of Mathematics Education" of the University of Granada: http://www.ugr.es/local/jgodino . A summary of the EOS is presented in Godino, Batanero and Font (2008).

As indicated, the EOS is supported and financed by contributions from various disciplines and technologies involved in human cognition, such as epistemology, psychology, sociology, semiotics, ..., and the efforts and contributions of many researchers that address the issues of dissemination and knowledge development in educational contexts. In this conference - conference, after presenting a brief summary of the origin, objectives and components of the EOS, we aim to address the following issues:

• How budgets EOS are, or not specific mathematical knowledge?
• what extent the theoretical tools offered by the EOS can be applied to other subject areas?
• What commonalities and complementarities between the EOS and other theoretical models used in research in Teaching Special and General Didactics?

References:

Bloor, D. (1983). Wittgenstein. A Social Theory of Knowledge . London, UK: The Macmillan Press.

Brousseau, G. (1998). teor The didactic situations . Grenoble: La Pensée Sauvage.

Chevallard, Y. (1992). Fundamental concepts in didactics: perspectives brought by a approache anthropological. Research in Mathematics Education, 12 (1), 73-112.

Eco, U. (1976). Tratado general semiotics. Barcelona: Lumen.

Ernest, P. (1998). Social constructivism as a philosophy of mathematics . New York, NY: SUNY.

Godino, JD Tanner, C. and Font, V. (2007). The onto-semiotic approach to research in mathematics education. DMZ. The International Journal on Mathematics Education, 39 (1-2), 127-135. [Expanded and updated version available online: http://www.ugr.es/local/jgodino ].

  Hjelmslev, L. (1943). Prolegomena to a Theory of Language (1971). Madrid: Gredos.      

  Maturana, H. and Varela, F. (1984).   The tree of knowledge. Debate, 1996.      

  Morin, E. (1977).  The method I, the nature of nature  (1986). Madrid: Cátedra.    

  Peirce, CS 1931-1958. Collected Papers  . Vols. 1-8, C. Hartshorne, P. Weiss and AW Burks (Eds.). 
 
 Cambridge, MA: Harvard University Press.    

Radford, L. (2006). The anthropology of Meaning. Educational Studies in Mathematics, 61, 39-65