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Early construction of number as position with young children: a teaching experiment

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Abstract

Our study is motivated by the importance of the number line in the visualisation of elementary properties of operations and numbers. For the number line to be an aid for visualisation, first it must be conceived as a coordinate system (origin, orientation and unit). This paper focuses on the construction of the concept of position on a line, and on the number as a means of remembering position, for pre-elementary school children aged 5–6 years. Using didactic design as a methodology, we conducted an experiment to observe how knowledge was constructed while carrying out a certain kind of task in a situation where position had to be designated. Our study shows that pupils, despite recognising number as a quantity, fail to apprehend number as something which represents position. They are, however, capable of understanding the characteristic elements of the number line in suitable situations. Our research suggests that it is possible to teach the use of ordinal numbers to young pupils.

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Notes

  1. In the rest of this paper we write ‘coordinate system’ but here we are dealing only with one dimension. We are aware that in English it is sometimes called a ‘number line’ but this term is not suitable for our paper, since we have to consider the question of the coordinate system (“repère” in French) and the use of numbers separately.

  2. http://www.education.gouv.fr/bo/2008/hs3/programme_maternelle.htm (Accessed 10 Oct 2013).

  3. For this figure, as for those that follow, we use the following key: A1 refers to class A, group 1 (customary mixed groups in each class, not corresponding to an academic level), the pupil’s first name, phase number; necklace 7 means that the coloured bead which the pupil had to reproduce was in 7th position from the knot. Since there is no colour in the printed version, the arrow means that one bead is different from the others.

  4. The only case which is not represented is the presence of the knot with the absence of the representation of the end of the necklace and the verticality.

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Authors and Affiliations

  1. ACTé, EA 4281, Université Blaise Pascal, Clermont-Ferrand, France

    Claire Margolinas

  2. IRIST EA 3424, Université de Strasbourg, Strasbourg, France

    Floriane Wozniak

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  1. Claire Margolinas
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  2. Floriane Wozniak
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Correspondence to Claire Margolinas.

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Margolinas, C., Wozniak, F. Early construction of number as position with young children: a teaching experiment. ZDM Mathematics Education 46, 29–44 (2014). https://doi.org/10.1007/s11858-013-0554-y

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