The understanding of numeration in primary school

Bednarz, Nadine; Janvier, Bernadette

doi:10.1007/bf00305497

Cited by 29 publications

(12 citation statements)

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“…Ainsi l'analyse de la pratique de comptage et de vente de mangues ouvre une voix intéressante pour le travail sur la numération pouvant être fait avec les élèves au primaire. Nous avons en effet montré dans des études antérieures portant sur la compréhension de la numération par les enfants du primaire (Bednarz & Dufour-Janvier, 1982 toute l'importance du travail sur les groupements, qui ne peut être détaché d'un traitement des collections sur lesquelles on opère, et toute l'importance qu'il y avait à voir la pertinence de regrouper. Nos analyses montraient alors les limites des situations d'enseignement (mettant l'accent sur l'écriture et la lecture des nombres, indépendamment de toute signification et de toute pertinence à voir l'intérêt d'un tel système).…”

Section: Interprétation Et Discussionunclassified

Mathématiques de la vie quotidienne au Burkina Faso: une analyse de la pratique sociale de comptage et de vente de mangues

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Bednarz

2009

Educ Stud Math

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Mathematics teaching in Burkina Faso is faced with major challenges (high illiteracy rates, students' difficulties, and high failure rates in mathematics, which is a central topic in the curriculum). As evidenced in many of these studies, mathematics is reputed to be tough, inaccessible, and far from what students live daily. Students here look as though they are living in two seemingly distant worlds, school and everyday life. In order to better understand these difficulties and to contribute in the long run to a more adapted teaching of mathematics, we tried to document and elicit the "mathematical resources" mobilized in various daily life social practices. In this paper, we focus on one of them, the counting and selling of mangoes by unschooled peasants. An ethnographic approach draws on the observation of the situated activity of counting and selling mangoes (during harvesting) and on "eliciting interviews" of the involved actors. The analysis of results highlights a richness of structuring resources mobilized and distributed through this practice, related to what Lave (1988) call "the experienced lived-in-world" and "constitutive order." The mathematical resources take the form of "knowledge in action" and "theorems in action" (Vergnaud, Rech Didact Math 10(23): 1990), embedded in the social, economic, and even cultural structures of actors.Résumé L'enseignement des mathématiques au Burkina Faso fait face à des défis importants (haut taux d'analphabétisme, difficultés des élèves en mathématiques et taux d'échec important dans cette matière qui occupe une place centrale dans les programmes). Les mathématiques ont, comme le montrent plusieurs de ces études, la réputation d'être difficiles et inaccessibles, bien loin de ce que les élèves vivent au quotidien. Les élèves semblent ici vivre dans deux mondes qui apparaissent très éloignés l'un de l'autre, celui de l'école et de la vie quotidienne. Dans le but de mieux comprendre ces difficultés et de contribuer, à plus long terme, à un enseignement des mathématiques davantage adapté, nous avons cherché à documenter et expliciter les «ressources mathématiques» mobilisées dans différentes pratiques sociales de la vie quotidienne. Nous revenons plus spécifique-ment dans cet article sur l'une d'entre elles, le comptage et la vente des mangues par des paysans non scolarisés. Une approche ethnographique met à contribution une observation de l'activité de comptage et vente de mangues in situ (lors de la récolte des mangues) et des entretiens d'explicitation avec les acteurs impliqués. L'analyse des résultats met en évidence les éléments qui agissent comme ressources structurantes dans cette pratique, et qui relèvent de ce que Lave (1988) nomme «le monde expérientiel des acteurs» et «l'ordre constitutif». Les ressources mathématiques prennent la forme de «connaissances en acte» et «théorèmes en acte» (Vergnaud, 1990) imbriqués dans les structures sociales, économiques et même culturelles des acteurs.

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Section: Interprétation Et Discussionunclassified

Mathématiques de la vie quotidienne au Burkina Faso: une analyse de la pratique sociale de comptage et de vente de mangues

Traoré

Bednarz

2009

Educ Stud Math

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“…Different works of research have tackled the conceptual analysis of the numeration and the stages of development that the subjects go through in their learning (Bednarz & Janvier, 1982;Steffe & von Glaserfeld, 1985;DeBlois, 1996). Our aim has not been to characterize the notion of numeration and establish learning levels of the same thoroughly, but to unfold the network of semiotic functions implied when carrying out a specific task done by a pupil, revealing the system of rules that the child should progressively learn.…”

Section: Final Reflectionsmentioning

confidence: 99%

Why is the learning of elementary arithmetic concepts difficult? Semiotic tools for understanding the nature of mathematical objects

et al. 2010

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The semiotic approach to mathematics education introduces the notion of "semiotic system" as a tool to describe mathematical activity. The semiotic system is formed by the set of signs, the production rules of signs and the underlying meaning structures. In this paper, we present the notions of system of practices and configuration of objects and processes that complement the notion of semiotic system and help to understand the complex nature of mathematical objects. We also show in what sense these notions facilitate the description and comprehension of building and communicating mathematical knowledge, by applying them to analyze semiotic systems involved in the teaching and learning of some elementary arithmetic concepts. Natural numbers as equivalence classes of setsThe understanding of the nature of mathematical concepts is a complex question as is revealed in the following class episode. This extract of the interaction between a lecturer and a group of future primary education teachers shows the predominance in the lecturer of a formalist understanding of natural numbers which contrasts with the informal use of these numbers. As we shall see in the following section, from an educative point of view, it is necessary to assume a wider perspective of the nature of the numbers to that shown by this lecturer with this group of students.Does anyone know what a number is? 1The lecturer begins the class on "natural numbers" by saying: First we will work on the concept of number, the idea and then we will think about the language in which we are going to write it. What are numbers?; for example, What is number five? We are posed with a problem, we have been using numbers from a very early age. However, when we are asked what a number is, we have difficulty in answering. He asks the students: Does anyone know what a number is? One student replies, A sign that refers to a quantity. The lecturer asks again: What is number four? The students do not reply. The lecturer writes the symbol 4 on the board and says: This is no more than a sign. What would the idea behind this be, how could we define it? The lecturer answers the question himself: If I want to communicate what number four means we put examples of groups of four, like for example: four pieces of chalk, four fingers, four people, four chairs, etc. What these sets have in common is what we call the idea of being four. How do we work in Preschool and Primary Education?The numbers are first shown as tools; however as future teachers we are going to take them as an object of study.The lecturer continues the class by explaining the Logicist construction of the natural numbers as the elements of the quotient set determined on the set of finite sets by the relationship of equivalence or coordinability between sets.Two aspects are reported from this episode:-The lecturer's teaching strategy: The lecturer's questions are rhetorical since he is assuming the discourse weight. The initial reply given by the student ("a sign that refers to a quantity") is neither considered n...

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“…Of particular interest to our investigation is Steffe's work which has led to a model of children's counting types and to an analysis of children's concepts of ten (e.g., Boulton-Lewis and Halford, 1992;Steffe et al, 1988) and Bednarz and Janvier's (1982) investigations which developed an organized framework for grouping.…”

Section: Learning Within a Constructivist Contextmentioning

confidence: 99%

A model for nurturing and assessing multidigit number sense among first grade children

1994

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ABSTRACT. Based on a synthesis of the literature and on the results of a two-year teaching program working with young primary children, a framework was developed, refined and validated for nurturing and assessing multidigit number sense. The major constructs incorporated in this framework were counting, partitioning, grouping, and number relationships. For each of these constructs, four different levels of thinking were established which, in essence, reflected a "learning apprenticeship" for multidigit number sense. At each level, and across all four constructs, learning indicators were developed and matched to distinctive problem tasks that went beyond the four basic operations.The framework was validated through data obtained from six case studies of grade 1 children. The thinking of these children was assessed and analyzed on the problem tasks for the four constructs and four levels. While the students were at different levels, all but one showed striking consistencies across the four constructs. Moreover, no student was able to solve a problem at a higher level when they had not solved a lower-level problem in the same category. The present framework for multidigit number sense covers only the lower primary grades, but research and instruction would benefit from an extended framework across the elementary grades.

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The understanding of numeration in primary school

Cited by 29 publications

References 2 publications

Mathématiques de la vie quotidienne au Burkina Faso: une analyse de la pratique sociale de comptage et de vente de mangues

Mathématiques de la vie quotidienne au Burkina Faso: une analyse de la pratique sociale de comptage et de vente de mangues

Why is the learning of elementary arithmetic concepts difficult? Semiotic tools for understanding the nature of mathematical objects

A model for nurturing and assessing multidigit number sense among first grade children

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