Skip to main content
SpringerLink
Log in

Mathematical situations of play and exploration

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

The mathematical situations of play and exploration introduced here have been developed as an empirical research instrument for the longitudinal study “erStMaL” (early Steps in Mathematics Learning). They are designed as situations that allow children and a guiding adult to construct situation-related knowledge in common dialogue processes and in mutual conditions. In addition, the situations focus on the activity of the persons involved, as well as the meaning of artefacts as objects of different cultural worlds. Besides relevant theoretical aspects for the development of the mathematical situations of play and exploration, exemplary analyses are introduced to clarify the conceptual aims.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  1. The projekt “erStMaL”(early Steps in Mathematics Learning) is a longitudinal study in the field of early mathematical education. The project is established at the IDeA centre (Inidividual Development and Adaptive Education of Children at Risk). It is an interdisciplinary research center in the context of the LOEWE initiative of the federal state government of Hessen. LOEWE is a national initiative in the development of scientific and economic excellence.

  2. The indicated mathematical domains refer to educational standards of the Standing Conference of the Ministers of Education and Cultural Affairs of the Federal States of Germany (KMK) for the primary school, grade 4. In the “Principles and standards for school mathematics” of the National Council of Teachers of Mathematics (NCTM) the mathematical domains are formulated for overlapping grades.

  3. Transcript of the mathematical play and exploration situation “golden treasure”, data collection point T1 (legend: actions are in italics, < … happened at the same time, / …lifting the voice)

References

  • Acar Bayraktar, E., Hümmer, A.-M., Huth, M., Münz, & Reimann, M. (2011). Forschungsmethodischer Rahmen der Projekte erStMaL und MaKreKi [Research methodological frame of the project erStMaL and MaKreKi]. In B. Brandt, R. Vogel, & G. Krummheuer (Eds.), Die Projekte erStMaL und MaKreKi. Mathematikdidaktische Forschung am “Center for individual development and adaptive education” (IDeA) (pp. 11–24). Münster: Waxmann.

  • Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom. Artefacts and signs after a Vygotskian perspective. In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 746–783). New York: Taylor and Francis.

    Google Scholar 

  • Beardsley, G., & Harnett, P. (1998). Exploring play in the primary classroom. London: D. Fulton.

    Google Scholar 

  • Bodrova, E., & Leong, D. J. (2001). Tools of the mind: A case study of implementing the Vygotskian approach in American early childhood and primary classrooms. Genf: International Bureau of Education. Retrieved from http://www.ibe.unesco.org/publications/innodata/inno07.pdf [2011-03-15].

  • Brandt, B., & Höck, G. (2011). Ko-Konstruktion in mathematischen Problemlöseprozessen—partizipationstheoretische Überlegungen [Co-construction in mathematical problem-solving processes—participation-theoretical considerations]. In B. Brandt, R. Vogel, & G. Krummheuer (Eds.), Die Projekte erStMaL und MaKreKi. Mathematikdidaktische Forschung am „center for individual development and adaptive education“(IDeA) (pp. 245–284). Münster: Waxmann.

  • Bruner, J. (1985a). Vygotsky: A historical and conceptual perspective. In J. V. Wertsch (Ed.), Culture, communication and cognition: Vygotskian perspectives. Cambridge: Cambridge University Press.

    Google Scholar 

  • Bruner, J. (1985b). Nature and uses of immaturity. In J. S. Bruner, A. Jolly, & K. Sylva (Eds.), Play. Its role in development and evolution (pp. 28–64). Harmondsworth, Middelsey, England: Penguin Books Ltd.

    Google Scholar 

  • Clements, D. H., Sarama, J., & DiBiase, A.-M. (2004). Engaging young children in mathematics: Standards for early childhood mathematics education. Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Delors, J. (1996). Learning: The treasure within. Report to UNESCO of the International commission on education for the twenty-first century. Paris: UNESCO.

    Google Scholar 

  • Dinkelaker, J., & Herrle, M. (2009). Erziehungswissenschaftliche Videografie. Eine Einführung [Educationally videography: An introduction]. Wiesbaden: VS.

    Book  Google Scholar 

  • Fetzer, M. (2010). Objects as participants in classroom interaction. Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education in Lyon, 2009. 974–983. Retrieved from http://ife.ens-lyon.fr/publications/edition-electronique/cerme6/wg6-15-fetzer.pdf [2013-07-29].

  • Fthenakis, W. E., Schmitt, A., Daut, M., Eitel, A., & Wendell, A. (2009). Natur-Wissen schaffen. [Nature-knowledge producing] (Frühe mathematische Bildung, Vol. 2). Troisdorf: Bildungsverlag EINS.

    Google Scholar 

  • Henne, H., & Rehbock, H. (2001). Einführung in die Gesprächsanalyse [Introduction to conversational discourse analysis] (4. durchgesehene und bibliographisch ergänzte Aufl.). Berlin: Walter de Gruyter.

  • Hülswitt, K. (2006). Mit Fantasie zur Mathematik—Freie Eigenproduktionen mit gleichem Material in großen Mengen. [With imagination to mathematics—Free own productions with the same material in great quantities]. In M. Grüßing & A. Peter-Koop (Eds.), Die Entwicklung mathematischen Denkens in Kindergarten und Grundschule: Beobachten—Fördern—Dokumentieren (pp. 103–121). Offenburg: Mildenberger Verlag.

    Google Scholar 

  • KMK (Kultusministerkonferenz). (2004). Bildungsstandards im Fach Mathematik für den Primarbereich (Jahrgangsstufe 4). Beschluss der Kultusministerkonferenz vom 15.10.2004. [Educational standards in mathematics at the primary level (grade 4). Resolution of the standing conference of the ministers of education and cultural affairs (KMK)]. Retrieved from http://www.kmk.org/fileadmin/veroeffentlichungen_beschluesse/2004/2004_10_15-Bildungsstandards-Mathe-Primar.pdf [2011-03-15].

  • Krummheuer, G. (2011). Die empirisch begründete Herleitung des Begriffs der „Interaktionalen Nische mathematischer Denkentwicklung“(NMD) [The empirically grounded derivation of the concept "Interactional niche in the development of mathematical thinking" (NMT)]. In B. Brandt, R. Vogel, & G. Krummheuer (Eds.), Die Projekte erStMaL und MaKreKi. Mathematikdidaktische Forschung am „Center for Individual Development and Adaptive Education“(IDeA) (pp. 25–89). Münster: Waxmann.

    Google Scholar 

  • Krummheuer, G. (2012). Die Interaktionsanalyse. Methoden der Kindheitsforschung. [The interaction analysis. Methods of childhood research]. In F. Heinzel (Ed.), Methoden der Kindheitsforschung (2 vollständig überarbeitete Auflageth ed., pp. 234–247). Weinheim: Juventa.

    Google Scholar 

  • Mayring, P. (2007). Qualitative Inhaltsanalyse. Grundlagen und Techniken [Qualitative content anaylsis. Basic knowledge and techniques] (9th ed.). Weinheim: Beltz.

    Google Scholar 

  • Mayring, Ph. (2000). Qualitative content analysis. FQS 1(2), Art. 20. Retrieved from http://www.qualitative-research.net/index.php/fqs/article/view/1089/2386 [2012-08-02].

  • Montada, L. (2008). Fragen, Konzepte, Perspektiven [Questions, concepts, perspectives]. In R. Oerter & L. Montada (Eds.), Entwicklungspsychologie (6 vollständig überarbeitete Auflageth ed., pp. 3–48). Weinheim: Beltz.

    Google Scholar 

  • NCTM. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Nührenbörger, M. (2009). Diskursives Lernen im Mathematikunterricht - Interaktive Wissenskonstruktionen von und mit Kindern im jahrgangsgemischten Anfangsunterricht [Discursive learning in mathematics instruction - Interactive knowledge constructions of and with children in mixed age-group in elementary instruction]. In Beiträge zum Mathematikunterricht. Berichtband von der 43. Tagung für Didaktik der Mathematik in Oldenburg 2009 (pp. 111–114). Münster: WTM-Verlag.

    Google Scholar 

  • Oerter, R. (2011). Psychologie des Spiels. Ein handlungstheoretischer Ansatz [Psychology of the game. An action-theoretical approach] (2nd ed.). Weinheim: Beltz.

    Google Scholar 

  • Prediger, S. (2001). Mathematiklernen als interkulturelles Lernen—Entwurf für einen didaktischen Ansatz [Mathematics learning as intercultural learning—Design of an educational approach]. Journal für Mathematik-Didaktik, 22(2), 123–144.

    Google Scholar 

  • Sfard, A. (2002). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46, 13–57.

    Article  Google Scholar 

  • Sfard, A. (2008). Thinking as communicating. Human development, the growth of discourses, and mathematizing. New York: Cambridge University Press.

    Book  Google Scholar 

  • van Oers, B. (2002). The mathematization of young children’s language. In K. Gravemeijer, R. Lehrer, B. van Oers, & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 29–58). Dordrecht, Boston, London: Kluwer Academic Publishers.

    Chapter  Google Scholar 

  • van Oers, B. (2004). Mathematisches Denken bei Vorschulkindern [Mathematical thinking of preschool children]. In W. E. Fthenakis & P. Oberhuemer (Eds.), Frühpädagogik international. Bildungsqualität im Blickpunkt (pp. 313–329). Wiesbaden: VS Verlag.

    Chapter  Google Scholar 

  • Verenikina, I. M. (2003). Understanding scaffolding and the ZPD in educational research. In P. Jeffrey (Eds.), Conference Proceedings of AARE/NZARE Auckland: AARE. Retrieved from http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1695&context=edupapers. [2011-03-15]

  • Vogel, R. (2005). Patterns—A fundamental idea of mathematical thinking and leraning. Zentralblatt für Didaktik der Mathematik, 37(5), 445–449.

    Article  Google Scholar 

  • Vogel, R. (2011). “Muster erkennen”– eine mehrperspektivische Annäherung [“Pattern Recognition”- A multi-perspective approach]. In Beiträge zum Mathematikunterricht (pp. 859–862). Münster: WTM.

    Google Scholar 

  • Vogel, R. (2012). “weil ich größer bin …”—Kinder erklären Gewinnchancen [“because I‘m bigger …”—children explain odds]. Grundschule Mathematik, 32, 16–19.

    Google Scholar 

  • Vogel, R. (2013). Mathematical situations of play and exploration as an empirical research instrument. In C. Benz, B. Brandt, U. Kortenkamp, G. Krummheuer, S. Ladel, & R. Vogel (Eds.), Early Mathematics Learning—Selected Papers of the POEM 2012 Conference. New York: Springer. in press.

    Google Scholar 

  • Vogel, R., & Huth, M. (2010). “… und der Elefant in die Mitte”—Rekonstruktion mathematischer Konzepte von Kindern in Gesprächssituationen [“… and the elephant to the middle”—Reconstruction of mathematical concepts of children in conversation situations]. In B. Brandt, M. Fetzer, & M. Schütte (Eds.), Auf den Spuren Interpretativer Unterrichtsforschung in der Mathematikdidaktik (pp. 177–207). Münster: Waxmann.

    Google Scholar 

  • Vogel, R., & Jung, J. (2013). Videocoding—A methodological research approach to mathematical activities of kindergarten children. Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education in Antalya, 6−10 February 2013, in press.

  • Vygotsky, L. S. (1978). Mind in society. The development of higher psychological processes. Cambridge: Harvard University Press.

    Google Scholar 

  • Wells, G. (1999). Dialogic inquiry: Towards a sociocultural practice and theory of education. New York: Cambridge University Press.

    Book  Google Scholar 

  • Wippermann, S. (2008). Didaktische Design Patterns [Didactic design patterns]. Saarbrücken: VDM.

    Google Scholar 

  • Wippermann, S., & Vogel, R. (2004). Communicating didactic knowledge in university education – “Didactic Design Patterns” as Best Practices. In L. Cantoni & C. McLoughlin (Eds.), Proceedings of World Conference on Educational Multimedia, Hypermedia and Telecommunications 2004 (pp. 3231–3234). Chesapeake, VA: AACE.

    Google Scholar 

  • Wulf, C., & Zirfas, J. (2007). Ausblick: Lernkulturen im Umbruch. Zur Bedeutung von Ritualen und performativen Praktiken in Lernsituationen [Outlook: Learning cultures in transition. The importance of ritual and performative practices in learning situations]. In W. Ch, B. Althans, G. Blaschke, N. Ferrin, M. Göhlich, B. Jörissen, R. Mattig, I. Nentwig-Gesemann, S. Schinkel, A. Tervooren, M. Wagner-Willi, & J. Zirfas (Eds.), Lernkulturen im Umbruch. Rituelle Praktiken in Schule, Medien, Familie und Jugend (pp. 323–328). Wiesbaden: VS Verlag.

    Google Scholar 

Download references

Acknowledgments

This research was funded by the Hessian initiative for the development of scientific and economic excellence (LOEWE)

Author information

Authors and Affiliations

  1. Goethe University Frankfurt on Main, Center for Individual Development and Adaptive Education of Children at Risk (IDeA), Frankfurt on Main, Germany

    Rose Vogel

Authors
  1. Rose Vogel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rose Vogel.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vogel, R. Mathematical situations of play and exploration. Educ Stud Math 84, 209–225 (2013). https://doi.org/10.1007/s10649-013-9504-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-013-9504-4

Keywords

Search

Navigation