Semiotic aspects of cognitive development: Illustrations from early mathematical cognition.

Abstract

The premise of this article is that cognitive development involves both conceptual and semiotic achievements. From this perspective, the authors emphasize the distinctness of the semiotic issues and develop a differentiated appreciation of semiotic aspects of cognition, particularly in the field of elementary mathematical cognition. The authors provide semiotic analyses of the differences between counting, adding, and multiplying and of the conventional place-value sign system. The authors introduce the concept of the field of reference of a sign, the differentiation of the field into foreground and background, and the dynamics within the field of reference. Finally, the authors relate these ideas to the dynamics between two dimensions of semiotic relations: the sign-referent dimension and the sign-sign dimension.

The importance of non‐verbal skills in the acquisition of place‐value knowledge: Evidence from normally‐developing and language‐impaired children

“…without grasping the cardinal values involved). However, a pioneering study by Becker & Varelas (1993) suggested that children's place-value knowledge depends on conceptual grasp of the symbolic function of place as opposed to procedural understanding of the exchange of items. recitation of the verbal number sequence, is a necessary precursor to conceptual understanding, e.g.…”

Microgenetic Analysis of Group-Based Solution of Complex Two-Step Mathematical World Problems by Fourth Graders

“…The problem with this view is that it encourages children to perceive math as mere numbers and to prematurely jump from the referent to symbol (Lester & Garafalo, 1982;Schoenfeld, 1988). Moreover, the very symbol system itself, for example, the place value system, often impedes correct correspondence (Becker & Varelas, 1993). The key to success lies in learning to move fluidly between the system of math and the objects for which they stand, and this cannot happen well if the connections of meaning have been guessed at, or wrongly invented by the active child math user.…”

‘You Can't Have a Cake Unless It's Written Down’: Semiotic Activity and Authentic Learning in Play as a Potential Tool for Analysis

“…Meaning remains stable throughout the edifice of sense, no more than potentiality that finds diversified realisation in speech.' Vygotsky, 1934/62, p. 146 Young children need to do quite a lot of 'sense-making' to both establish and later break away from sign-object links in their meaningful establishment of symbolic activity, (see Becker and Verlas, 1993 for an interesting study of such links in early counting-on strategies). SEMIOTIC ACTIVITY AND AUTHENTIC LEARNING 51 A further and most important point which Van Oers and Wardekker make is that authentic learning is not something that happens to an individual it is something only that person can do for themselves.…”