Abstract
In a longitudinal study about the development of mathematical thinking of children ages 4–6, a first comparative analysis of the participation patterns of one child over this period of time in different peer situations of mathematical play and exploration has been completed. The theoretical background and the accomplished results will be presented.
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Notes
- 1.
By the term “situational,“I refer to a differentiation that stems from Goffman (1963): “Work tasks that an individual performs while others are present he can sometimes perform equally well when alone. This aspect of activity may occur in situations but it is not of situations, characteristically occurring at other times outside situations. This unblushing part of reality I will refer to as the merely-situated aspect of a situated activity. … my only interest in such matters will be to be able to segregate them analytically from the component of situated activity that will concern us here; namely, the part that could not occur outside situations, being intrinsically dependent on the conditions that prevail therein. This part will be referred to as the situational aspect of situated activity” (p. 21 f.).
- 2.
This example stems from Brandt and Krummheuer (2015).
- 3.
For more details see Acar Bayraktar, Hümmer, Huth, Münz, and Reimann (2011).
- 4.
A group of two other colleagues and several research assistants conducted this project. For the part of the study that I especially was engaged in, I depended very much on the cooperation of Birgit Brandt, Rose Vogel, Anne Hümmer, Ergi Acar Bayraktar, Melanie Beck, Melanie Huth, and, specifically for recent comparative analyses, Marcus Schütte.
- 5.
I refer here to Bruner’s concept of “narrativity,” which he does not only see as an “expository act” but also as a rhetorical one (Bruner, 1990, p. 87). In this context he also introduces the notion “verisimilitude,” when he, for example, formulates “.. when reasons are used in this way, they must be made to seem not only logical but life like as well, for the requirements of narrative still dominate. This is the critical intersection where verifiability and verisimilitude seem to come together” (ibid, p. 94; also Bruner, 1996).
- 6.
- 7.
Here, the notion of “situation” “ refers to a common terminology of design research and differs from the concept of a “social situation” as used in Goffman’s definition of “situational” (see above).
- 8.
As an overview of all research activities, see Brandt, Krummheuer, and Vogel (2011) and the special issue “Alternative perspectives on learning mathematics in the early years” in the Educational Studies in Mathematics Volume 84, No. 2, October 2013.
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Krummheuer, G. (2018). The Genesis of Children’s Mathematical Thinking in Their Early Years. In: Benz, C., Steinweg, A., Gasteiger, H., Schöner, P., Vollmuth, H., Zöllner, J. (eds) Mathematics Education in the Early Years. Springer, Cham. https://doi.org/10.1007/978-3-319-78220-1_6
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