In this article I present some results from a 5-year longitudinal investigation with young students about the genesis of embodied, non-symbolic algebraic thinking and its progressive transition to culturally evolved forms of symbolic thinking. The investigation draws on a cultural-historical theory of teaching and learning--the theory of…

In this response we address some of the significant issues that Tony Brown raised in his analysis and critique of the Special Issue of "Educational Studies in Mathematics" on "Semiotic perspectives in mathematics education" (Saenz-Ludlow & Presmeg, Educational Studies in Mathematics 61(1-2), 2006). Among these issues are conceptualizations of…

Before the advent of symbolism, i.e. before the end of the 16th Century, algebraic calculations were made using natural language. Through a kind of metaphorical process, a few terms from everyday life (e.g. thing, root) acquired a technical mathematical status and constituted the specialized language of algebra. The introduction of letters and…

Meaning is one of the recent terms which have gained great currency in mathematics education. It is generally used as a correlate of individuals' intentions and considered a central element in contemporary accounts of knowledge formation. One important question that arises in this context is the following: if, in one way or another, knowledge…

Investigates ways in which students use signs and endow them with meaning in their very first encounter with the algebraic generalization of patterns. Provides accounts of students' emergent algebraic thinking. Uses ethnographic qualitative methodology supported by historic epistemological research. Focuses on a discussion held by a small group of…

The cognitive significance of the body has become one of the major topics in current psychology. However, it is our contention that claims about the embodied nature of thinking must come to terms with the problem of the relationship between the body as a locus for the constitution of students' subjective mathematical meanings and the historical…

Describes theoretical points concerning the idea of semiotic means of objectification. Analyzes classroom activity by observing the interface between the spoken and the seen. Discusses the role of a category of linguistic terms related to actions of showing or pointing out something that constitute a key element in the mathematical discursive…

Examines the relationship between mathematical knowledge and social practices of the Renaissance. Suggests that all efforts to understand the conceptual reality and the production of knowledge cannot restrict themselves to language and the discursive activity, but that they also need to include the social practices that underlie them. (Author/KHR)

In this paper we deal with the problem of the genetic relationship between the sensual and the conceptual in knowledge formation. Transcript and videotape analyses of two small groups of a regular Grade 11 mathematics class shed some light on the dialectics between semiotic activity and artefact-mediated kinesthetic actions. The analyses point to…

Contrasts students' presymbolic and symbolic procedures in generalizing activities. Uses the semiotic-cultural theoretical approach and focuses on the role of body, discourse, and signs when students refer to mathematical objects. Identifies types of generalizations and discusses a specific kind of rupture in the ostensive gestures and…

In this paper we focus on the role of signs in students' perceptive processes underpinning the generalization of numeric-geometric patterns. Based on a videotaped Grade 9 classroom group activity undertaken by three students and framed by a cultural-semiotic theoretical perspective, we carry out a microgenetic analysis of an elementary form of…

In this paper we report an analysis of a teaching sequence in which Grade 11 students were asked to produce some graphs corresponding to the relationship between time and distance of a cylinder moving up and down an inclined plane. The students were also asked to carry out the experience using a TI 83+ graphic calculator equipped with a sensor,…