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

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.