%0 Conference Paper %1 darford05a %A Radford, Luis %B Proceedings of the 2004 Annual Meeting of the Canadian Mathematics Education Study Group %D 2005 %E Simmt, E. %E Davis, B. %K body cognition cultural embodied learning mathematics mythesis semiotics social symbol tool %P 111-117 %T Body, Tool, and Symbol: Semiotic Reflections on Cognition %U http://laurentian.ca/NR/rdonlyres/48B42F02-5E4B-4C36-84AF-659631C367CE/0/bodytoolsymbol.pdf %X Although 20th century psychology acknowledged the role of language and kinesthetic activity in knowledge formation, and even though elementary mathematical concepts were seen as being bound to them (as in Piaget’s influential epistemology), body movement, the use of artefacts, and linguistic activity, in contrast, were not seen as direct sources of abstract and complex mathematical conceptualizations. Nevertheless, recent research has stressed the decisive and prominent role of bodily actions, gestures, language and the use of technological artefacts in students’ elaborations of elementary, as well as of abstract mathematical knowledge (Arzarello and Robutti 2001, Nemirovsky 2003, Núñez 2000). In this context, there are a number of important research questions that must be addressed. One of them relates to our understanding of the relationship between body, actions carried out through artefacts (objects, technological tools, etc.), and linguistic and symbolic activity. Research on the epistemological relationship between these three chief sources of knowledge formation is of vital importance for a better understanding of human cognition in general, and of mathematical thinking in particular. In the first of this paper, I discuss the roots of the reluctance in Western Thought to include the body in the act of knowing. In the second part, echoing current debates in mathematics education, I discuss, from a semiotic viewpoint, the importance of revisiting cognition in such a way as to think of cognitive activity as something that is not confined to mental activity. In the third part, I present a developmental overview of the theoretical foundations of my research program and of the research questions that my collaborators and I are currently investigating.

@inproceedings{darford05a, abstract = {Although 20th century psychology acknowledged the role of language and kinesthetic activity in knowledge formation, and even though elementary mathematical concepts were seen as being bound to them (as in Piaget’s influential epistemology), body movement, the use of artefacts, and linguistic activity, in contrast, were not seen as direct sources of abstract and complex mathematical conceptualizations. Nevertheless, recent research has stressed the decisive and prominent role of bodily actions, gestures, language and the use of technological artefacts in students’ elaborations of elementary, as well as of abstract mathematical knowledge (Arzarello and Robutti 2001, Nemirovsky 2003, Núñez 2000). In this context, there are a number of important research questions that must be addressed. One of them relates to our understanding of the relationship between body, actions carried out through artefacts (objects, technological tools, etc.), and linguistic and symbolic activity. Research on the epistemological relationship between these three chief sources of knowledge formation is of vital importance for a better understanding of human cognition in general, and of mathematical thinking in particular. In the first of this paper, I discuss the roots of the reluctance in Western Thought to include the body in the act of knowing. In the second part, echoing current debates in mathematics education, I discuss, from a semiotic viewpoint, the importance of revisiting cognition in such a way as to think of cognitive activity as something that is not confined to mental activity. In the third part, I present a developmental overview of the theoretical foundations of my research program and of the research questions that my collaborators and I are currently investigating.}, added-at = {2008-04-27T17:44:54.000+0200}, author = {Radford, Luis}, biburl = {https://www.bibsonomy.org/bibtex/20c9e54308e4e6f9830cccf245a476716/yish}, booktitle = {Proceedings of the 2004 Annual Meeting of the Canadian Mathematics Education Study Group}, editor = {Simmt, E. and Davis, B.}, interhash = {26c0c48bf1524fa0ba1175e503f4271a}, intrahash = {0c9e54308e4e6f9830cccf245a476716}, keywords = {body cognition cultural embodied learning mathematics mythesis semiotics social symbol tool}, pages = {111-117}, timestamp = {2008-04-27T17:45:49.000+0200}, title = {Body, Tool, and Symbol: Semiotic Reflections on Cognition}, url = {http://laurentian.ca/NR/rdonlyres/48B42F02-5E4B-4C36-84AF-659631C367CE/0/bodytoolsymbol.pdf}, year = 2005 }