Understanding the written number system: 6 Year-olds in Argentina and Switzerland

Abstract

ABSTRACT. Thirty children in Geneva, Switzerland, 15 middle-class children in Bariloche and 15 lower-class children from a semi-literate or illiterate milieu in Bariloche, Argentina, were tested. All children were aged 6 and attending public schools. Tasks were: (1) judging which of two bi-or tri-digit written numerals was the biggest, and explaining why; and (2) explaining the role played by the different digits in numerals such as 11, 12, 16, 17. Results show that children at these ages use various strategies in task I: they compare number of digits; read aloud the numerals and refer to number-string knowledge; treat bi-and tri-digits as the sum of their face value parts; and lastly, quite often take both face value and position of digits into account in a correct way. They, however, were not able to explain place-value. Most subjects gave "face value interpretations", while a few children account for the whole collection of chips and make part of the chips correspond to one digit, and the other part to the other digit. Differences in performance between the three types of children emerge.

Using calculators for assessing pupils’ conceptualization on place-value

“…Few children see the validity of doing and undoing groupings (partitioning) to solve multidigit number problems. Another difficulty connected to place-value is the case of seeing multidigit numbers as unitary collections [31]. It is a way of global correspondence between multidigits and numbers.…”

Estruturas multiplicativas e tomada de consciência: repartir para dividir

“…Diferentes trabalhos mostram como são complexas e precoces as realizações das crianças de dar significado às marcas de quantificação que encontram e que produzem em seu cotidiano. E diversos autores defendem duas dimensões indispensáveis a serem articuladas na educação matemática: a da produção, pelas crianças, de símbolos, de marcas para as quantidades, e a da sua própria interpretação dessas marcas, porque a transformação dos sistemas de escrita numérica só se faz por meio de sua interpretação pelo sujeito (Sinclair, 1990;Sinclair & Scheuer, 1993;Sinclair & Sinclair, 1986;Sinclair, Tièche-Christinat & Garin, 1994).…”

The roles of punctuation marks while learning about written numbers

“…The theoretical grounding for this research is provided by Piagetian and constructivist research that focuses on the one hand on unearthing children's spontaneous ideas about different phenomena, finding them to be guides not only for children's own ways of thinking but also for us as educators and researchers (e.g., Confrey 1991;Ferreiro 1986;Smith, diSessa, & Roschelle 1993Vergnaud 1988), and focuses on the other hand on children's construction of conventional symbolic systems, taken as cultural objects that children interact with on a daily basis and gradually reconstruct (e.g., Brizuela 2004;Ferreiro 1996;Ferreiro and Teberosky 1979;Sinclair 1988;Sinclair and Scheuer 1993;Sinclair andSinclair 1983, 1984).…”

“…The specific investigation described in this paper is inscribed within a line of research that has documented children's uses and understandings of written numbers and the written number system, such as that developed by Scheuer and Anne and Hermine Sinclair (e.g., Scheuer 1996;Scheuer, Merlo de Rivas, & Tieche-Christinat 2000;Sinclair 1988;Sinclair and Scheuer 1993;Sinclair et al 1983;Sinclair and Sinclair 1984;Sinclair and TiecheChristinat 1992). This research has shown that children's appropriation of written numbers is a constructive process, in which children develop their own ideas, which are many times surprising to adults.…”

“…Research has shown this appropriation process not to be automatic; it is a gradual process. There is a progression in the types of notations children use when they represent quantities (e. g., Hughes 1986;Sastre and Moreno 1976;Sinclair 1988;Sinclair and Scheuer 1993;Sinclair and Sinclair 1984). In appropriating the NWS, children need not only to appropriate the conventional forms for numbers, but also the logic that underlies the relationships among the written numbers in the system.…”