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Everyday pedagogical practices in mathematical play situations in German “Kindergarten”

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Abstract

This study describes situations in German daycare facilities (Kindergarten) in which the development of mathematical thinking in children is specifically encouraged through examination of common play objects. Using micro-sociological methods of analysis, the mathematical potential of such interactions between teacher and child is elaborated within the framework of everyday pedagogical practices (Bruner, 1996) and instructional models (Rogoff; Mind, Cult Activ 1(4): 209–229, 1994). It is also considered which concepts of mathematics may be important in these interactions.

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Notes

  1. In this study, I refer only to the curriculum of Hesse, “Bildung von Anfang an” [Education from the beginning] (Hessisches Sozialministerium & Hessisches Kultusministerium, 2012), as the empirical study erStMaL is carried out there. In this curriculum, mathematics is grouped as a domain with natural sciences and engineering.

  2. The German word “Spiel” includes free play, role plays, dice games or other rule-based games, matches, etc.

  3. In Germany, “Kindergarten” is an institution for children from ages 3 to 6. “Kindergarten” is not a compulsory institution of education and is separated from primary school. In this study, I will use “Kindergarten” to remind the reader of this German kind of institution. “Kindergarten teacher” will be used for the pedagogical staff in this institution.

  4. The project erStMaL (early Steps in Mathematics Learning) is part of the research activities of the “Center for Individual Development and Adaptive Education” (IDeA) located in Frankfurt am Main, Germany. It is funded for 6 years, beginning in July 2008. See, for more information: http://www.idea-frankfurt.eu/homepage/idea-projects/projekt-erstmal.

  5. Nevertheless, the idea of “pervasive learning through observation and listening-in” (Rogoff, Paradise, Arauz, Correa-Chávez, & Angelillo, 2003) in the concept of “intent participation” (ibid.) bears resemblance to this imitative learning. However, intent participation is linked to realization of shared endeavor (Rogoff et al., 1996, 2003) and beyond plain imitation.

  6. Transcripts for the situations can be found in the Appendix. In the following reconstructions, additional information before or after the sequences, indicated in the transcripts, are used.

  7. In the following figures, colors will be referred to by the initial letters.

  8. Numbers in angle brackets refer to the numbered lines in the transcript.

  9. Following the developmental hierarchy of repeating patterns, this symmetrical approach by reversing the sequence comes earlier to awareness than the use of the continuation of the pattern in the given order (Rustigian, 1976; cited in Threlfall, 1999, p. 23; cf. Garrick et al., 1999, p. 11).

  10. She is using a strategy that does not apply to the whole repeated sequence, but to the relation of adjacent items. Thus, the procedure of patterning could be done by remembering the relations: after red, I have to take yellow (cf. Threlfall, 1999, p. 21).

  11. Dora is one of the few Kindergarten teachers whom we observed several times. Thus, we can assert that this pedagogical orientation is typical for her, despite a specific mathematical domain and the material: she always initiates task-structured ways of interaction in the observed situations.

  12. In Germany, HABA is a well-known manufacturer of predominantly wooden toys, which is widespread in day-care facilities (as well as in middle class families).

  13. Zilly uses the German word “Spitze”, which is colloquial language for the vertices of a star.

  14. Sometimes, cookies which are cut into triangles or diamonds are called “Spitze”.

  15. This adjustment included a focus on the Euclidean properties of the tiles, but this aspect was not verbalized in the interaction.

  16. This again is an implicit focus on the Euclidean properties of the tiles.

  17. From a mathematical point of view, only a specific rule determines the continuation. Since in this example the repetition is only indicated by a first recurring sequence item, here there are indeed other just as meaningful continuations. Thus, she “teaches” repeated sequences as a special kind of pattern—but without paying attention to the sequence as a whole.

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Acknowledgments

I would like to thank all the participating children and nursery teachers. This research was funded by the Hessian initiative for the development of scientific and economic excellence (LOEWE).

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    Birgit Brandt

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Table 3 The trancripts of the situations
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Brandt, B. Everyday pedagogical practices in mathematical play situations in German “Kindergarten”. Educ Stud Math 84, 227–248 (2013). https://doi.org/10.1007/s10649-013-9490-6

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