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Natural language as a tool for analyzing the proving process: the case of plane geometry proof

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Abstract

In the field of human cognition, language plays a special role that is connected directly to thinking and mental development (e.g., Vygotsky, 1938). Thanks to “verbal thought”, language allows humans to go beyond the limits of immediately perceived information, to form concepts and solve complex problems (Luria, 1975). So, it appears language can be studied as a cognitive process (Chomsky, 1975). In this investigation, I study language as a means for making the cognitive process explicit. In particular, I analyze the role of the verbalization produced by pairs of students solving a plane geometry problem. The basic idea of my research is that, during the resolution process of a plane geometry problem, natural language can play roles beyond that of communication: Natural language can be seen as a tool for supporting students’ cognitive processes (Robotti, 2008), and, at the same time, it can also be seen as a researchers’ tool which allows us to shed light on the evolution of students’ cognitive processes. With regard to language as researchers’ tool, I show how natural language (in our case, students’ verbalization during resolution of a plane geometry problem) can be used by the researcher to make explicit, to study, and to describe the development of the students’ cognitive processes during the resolution process. To this end, I present a model I have developed that allows us to identify, in students’ verbalization, different phases of their cognitive processes.

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Notes

  1. “l’ensemble théoriquement infini de toutes les entités en dehors de la langue…. Par essence, l’activité langagière s’articule à l’extralangage [en définissant] des espaces dotés de deux type de pertinence: la pertinence référentielle, c’est-à-dire la capacité à devenir un " contenu représenté " de l’activité langagière, et la pertinence contextuelle, c’est-à-dire la capacité de contrôler ou gérer le déroulement même de l’activité langagière.” (p. 26)

  2. “le degré de fiabilité que possède ce qui est énoncé dans la proposition : le contenu d’une proposition apparaît évident ou certain ou seulement vraisemblable, ou plausible, ou simplement possible, ou impossible ou encore absurde…” (Duval 1995a, b p. 21)

  3. “est le fait que la proposition énoncée est soit vraie soit fausse. A la différence de la valeur épistémique, la valeur logique d’une proposition ne dépend pas de la seule compréhension de son contenu mais elle résulte de procédures spécifiques de vérification ou preuve” (Duval 1995a, b p. 220).

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  1. DiDiMa srl, spin off ITD-CNR, Genova, Italy

    Elisabetta Robotti

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  1. Elisabetta Robotti
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Correspondence to Elisabetta Robotti.

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Robotti, E. Natural language as a tool for analyzing the proving process: the case of plane geometry proof. Educ Stud Math 80, 433–450 (2012). https://doi.org/10.1007/s10649-012-9383-0

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