%0 Journal Article %1 Radford00 %A Radford, Luis %D 2000 %J Educational Studies in Mathematics %K CiHB CnE07 ILE algebraic approach cerme6 generalization ijceell06 ijtme2006 jls10 mathematics mathgamespatterns meanings means mythesis objectification of representation semiotic semiotic-cultural sequences sequences-esm sequences-ictmt7 signs social sociocultural symbolization thinking to vygotsky %N 3 %P 237-268 %T Signs and meanings in students' emergent algebraic thinking: a semiotic analysis %U http://laurentian.ca/educ/lradford/esm%202000.pdf %V 42 %X The purpose of this article, which is part of a longitudinal classroom research about students? algebraic symbolizations, is twofold: (1) to investigate the way students use signs and endow them with meaning in their very first encounter with the algebraic generalization of patterns and (2) to provide accounts about the students? emergent algebraic thinking. The research draws from Vygotsky?s historical-cultural school of psychology, on the one hand, and from Bakhtin and Voloshinov?s theory of discourse on the other, and is grounded in a semiotic-cultural theoretical framework in which algebraic thinking is considered as a sign-mediated cognitive praxis. Within this theoretical framework, the students? algebraic activity is investigated in the interaction of the individual?s subjectivity and the social means of semiotic objectification. An ethnographic qualitative methodology, supported by historic, epistemological research, ensured the design and interpretation of a set of teaching activities. The paper focuses on the discussion held by a small group of students of which an interpretative, situated discourse analysis is provided. The results shed some light on the students? production of (oral and written) signs and their meanings as they engage in the construction of expressions of mathematical generality and on the social nature of their emergent algebraic thinking.

@article{Radford00, abstract = {The purpose of this article, which is part of a longitudinal classroom research about students? algebraic symbolizations, is twofold: (1) to investigate the way students use signs and endow them with meaning in their very first encounter with the algebraic generalization of patterns and (2) to provide accounts about the students? emergent algebraic thinking. The research draws from Vygotsky?s historical-cultural school of psychology, on the one hand, and from Bakhtin and Voloshinov?s theory of discourse on the other, and is grounded in a semiotic-cultural theoretical framework in which algebraic thinking is considered as a sign-mediated cognitive praxis. Within this theoretical framework, the students? algebraic activity is investigated in the interaction of the individual?s subjectivity and the social means of semiotic objectification. An ethnographic qualitative methodology, supported by historic, epistemological research, ensured the design and interpretation of a set of teaching activities. The paper focuses on the discussion held by a small group of students of which an interpretative, situated discourse analysis is provided. The results shed some light on the students? production of (oral and written) signs and their meanings as they engage in the construction of expressions of mathematical generality and on the social nature of their emergent algebraic thinking.}, added-at = {2008-05-30T05:56:34.000+0200}, author = {Radford, Luis}, biburl = {https://www.bibsonomy.org/bibtex/2a7f6bb41ca7225520e0af94ab1bff1ff/yish}, citeulike-article-id = {493470}, comment = {"In the introductory note to his monumental Arithmetica, written ca. 250 AC, Diophantus of Alexandria mentions the discouragement that the students usually feel when learning what we now term ?algebraic techniques? to solve word-problems." Algebraic signs have a "dual life": one on hand they are signifiers, pointing to abstract mathematical objects and concepts, at the same time they are tools which allow us to perform actions. "In line 64, Anik rephrases with her own words the instructions about the message to be written. At the end of line 64, she hypothetically takes the role of the addressee (?You would have to explain really well why, I mean, how I would . . . ?). Interestingly, in this move, consisting in taking the place of others and which is essential in social understanding (Astington, 1995), she omits the linguistic expression conveying the generality, i.e., that the message must say what to do to know how many circles are in any figure. Instead, she takes a concrete figure ? Figure 120 ? as an example to talk about the general. To talk in general terms, they hence take a specific figure, which is Figure 12 from line 76 onwards. Notice, however, that Figure 12 (as well as the aforementioned Figure 120) is not among those made with colored plastic bingo chips that the students materially have in front of them. Thanks to its ?unmateriality?, Figure 12 fits the purpose of their reasoning about the general very well. Nevertheless, Anik and her group-mates are not really talking about the particular Figure 12, something emphasized by the hypothetical expression ?Let?s say? (line 76). This is why they are not strictly counting the number of circles in Figure 12. We may say hence that Figure 12 is not taken literally but metaphorically by the students. In discursively taking an absent albeit specific figure, they talk metaphorically about the general through the particular."}, interhash = {815103071ee85e177bad141d197837bb}, intrahash = {a7f6bb41ca7225520e0af94ab1bff1ff}, journal = {Educational Studies in Mathematics}, keywords = {CiHB CnE07 ILE algebraic approach cerme6 generalization ijceell06 ijtme2006 jls10 mathematics mathgamespatterns meanings means mythesis objectification of representation semiotic semiotic-cultural sequences sequences-esm sequences-ictmt7 signs social sociocultural symbolization thinking to vygotsky}, number = 3, pages = {237-268}, priority = {2}, timestamp = {2010-07-07T17:03:25.000+0200}, title = {Signs and meanings in students' emergent algebraic thinking: a semiotic analysis}, url = {http://laurentian.ca/educ/lradford/esm%202000.pdf}, volume = 42, year = 2000 }