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Early Mathematics in Play Situations: Continuity of Learning

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Mathematics and Transition to School

Part of the book series: Early Mathematics Learning and Development ((EMLD))

Abstract

In recent years, many concepts for early mathematics education have been developed. Taking a closer look at these concepts, it can be seen that they differ considerably in pedagogical background and in quality. During the transition from kindergarten to school, it is extremely important to guarantee consistency and continuity in mathematical learning processes. All early mathematics education should be mathematically correct, ‘intellectually honest’ and ensure that children acquire the essential prerequisites for further mathematical learning. Additionally, mathematical learning should be designed according to children’s specific age. Based on scientific findings, this chapter specifies why early mathematics education in natural learning situations, like play activities, meets these requirements of subject- and child-orientation. Play situations can foster the development of mathematical learning in kindergarten and in school sustainably. Results of an intervention study about learning mathematics while playing traditional board games (n  = 95, average age: 4.8 years, control and intervention group) confirm this claim. The intervention shows significant effects. Video analyses of the play situations illustrate the findings and allow investigating in detail the role of the teachers and the mathematical learning processes which occurred during the play activities.

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Notes

  1. 1.

    Mensch ärgere dich nicht—Schmidt-Spiele.

  2. 2.

    Fang den Hut—Ravensburger.

  3. 3.

    Schätze sammeln—ZahlenZauberei, Oldenbourg-Schulbuchverlag.

  4. 4.

    Der Maulwurf und sein Lieblingsspiel—Ravensburger.

  5. 5.

    Da ist der Wurm drin—Zoch.

References

  • Anders, Y., Grosse, C., Rossbach, H.-G., Ebert, S., & Weinert, S. (2012). Preschool and primary school influences on the development of children’s early numeracy skills between the ages of 3 and 7 years in Germany. School Effectiveness and School Improvement: An International Journal of Research, Policy and Practice, 24(2), 195–211.

    Article  Google Scholar 

  • Anderson, A., Anderson, J., & Thauberger, C. (2008). Mathematics learning and teaching in the early years. In O. N. Saracho & B. Spodek (Eds.), Contemporary perspectives on mathematics in early childhood education (pp. 95–132). Charlotte: Information Age Publishing.

    Google Scholar 

  • Australian Association of Mathematics Teachers & Early Childhood Australia. (2006). Position paper on early childhood mathematics. http://www.aamt.edu.au/content/download/721/19509/file/earlymaths_a3.pdf. Accessed 23 Nov 2013.

  • Baroody, A. J., & Wilkins, J. L. M. (1999). The development of informal counting, number, and arithmetic skills and concepts. In J. V. Copley (Ed.), Mathematics in the early years (pp. 48–65). Reston: The National Council of Teachers of Mathematics.

    Google Scholar 

  • Bruner, J. (1999). The Process of education. London: Harvard University Press.

    Google Scholar 

  • Clements, D. H. (2004). Major themes and recommendations. In D. H. Clements & J. Sarama (Eds.), Engaging young children in mathematics. Standards for early childhood mathematics education (pp. 7–72). Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Cross, C. T., Woods, T. A., & Schweingruber, H. (2009). Mathematics learning in early childhood: Paths towards excellence and equity. Washington, DC: The National Academies Press.

    Google Scholar 

  • Dornheim, D. (2008). Prädiktion von Rechenleistung und Rechenschwäche: Der Beitrag von Zahlen-Vorwissen und allgemein-kognitiven Fähigkeiten. Berlin: Logos.

    Google Scholar 

  • Friedrich, G., & de Galgóczy, V. (2004). Komm mit ins Zahlenland. Eine spielerische Entdeckungsreise in die Welt der Mathematik. Freiburg: Christophorus, Herder.

    Google Scholar 

  • Fröbel, F. (1838). Ein Ganzes von Spiel- und Beschäftigungskästen für Kindheit und Jugend. Erste Gabe: Der Ball als erstes Spielzeug des Kindes. In E. Blochmann (Ed.), Fröbels Theorie des Spiels I. (2nd ed., pp. 16–38). Langensalza: Thüringer Verlagsanstalt.

    Google Scholar 

  • Fthenakis, W. E., Schmitt, A., Daut, E., Eitel, A., & Wendell, A. (2009). Natur-Wissen schaffen. Band 2: Frühe mathematische Bildung. Troisdorf: Bildungsverlag EINS.

    Google Scholar 

  • Fuson, K. C. (2004). Pre-K to grade 2 goals and standards: Achieving 21st-century mastery for all. In D. H. Clements & J. Sarama (Eds.), Engaging young children in mathematics. Standards for early childhood mathematics education (pp. 105–148). Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Fuson, K. C., Kalchman, M., & Bransford, J. D. (2005). Mathematical understanding: An introduction. In S. Donovan & J. D. Bransford (Eds.), How students learn: History, mathematics, and science in the classroom (pp. 215–256). Washington, DC: The National Academies Press.

    Google Scholar 

  • Gasteiger, H. (2010). Elementare mathematische Bildung im Alltag der Kindertagesstätte. Grundlegung und Evaluation eines kompetenzorientierten Förderansatzes. Münster: Waxmann.

    Google Scholar 

  • Gasteiger, H. (2012). Fostering early mathematical competencies in natural learning situations. Foundation and challenges of a competence-oriented concept of mathematics education in kindergarten. Journal für Mathematik-Didaktik, 33(2), 181–201.

    Article  Google Scholar 

  • Gasteiger, H. (2014). Professionalization of early childhood educators with a focus on natural learning situations and individual development of mathematical competencies: Results from an evaluation study. In U. Kortenkamp, B. Brandt, C. Benz, G. Krummheuer, S. Ladel, & R. Vogel (Eds.), Early mathematics learning. Selected papers of the POEM 2012 conference (pp. 275–290). Berlin: Springer.

    Google Scholar 

  • Hannula, M. M., Räsänen, P., & Lehtinen, E. (2008). Development of counting skills: Role of spontaneous focusing on numerosity and subitizing-based enumeration. Mathematical Thinking and Learning, 9(1), 51–57.

    Article  Google Scholar 

  • Hasselhorn, M. (2005). Lernen im Altersbereich zwischen 4 und 8 Jahren: Individuelle Voraussetzungen, Entwicklung, Diagnostik und Förderung. In T. Guldimann & B. Hauser (Eds.), Bildung 4- bis 8-jähriger Kinder (pp. 77–88). Münster: Waxmann.

    Google Scholar 

  • Hauser, B. (2013). Spielen. Frühes Lernen in Familie, Krippe und Kindergarten. Stuttgart: Kohlhammer.

    Google Scholar 

  • Huizinga, J. (1949). Homo ludens. London: Routledge.

    Google Scholar 

  • Hunting, R. P. (2010). Little people, big play, and big mathematical ideas. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education. Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia, (pp. 715–718). Fremantle: MERGA.

    Google Scholar 

  • Hunting, R., Mousley, J., & Perry, B. (2012). Young children learning mathematics. A guide for educators and families. Camberwell: ACER.

    Google Scholar 

  • Jordan, B. (2009). Scaffolding learning and co-construction understandings. In A. Anning, J. Cullen, & M. Fleer (Eds.), Early childhood education. Society and culture (pp. 39–52). London: Sage Publications.

    Google Scholar 

  • Kaufmann, L., Nuerk, H.-C., Graf, M., Krinzinger, H., Delazer, M., & Willmes, K. (2009). TEDI-MATH. Test zur Erfassung numerisch-rechnerischer Fertigkeiten vom Kindergarten bis zur 3. Klasse. Bern: Hans Huber, Hogrefe.

    Google Scholar 

  • Kortenkamp, U., Brandt, B., Benz, C., Krummheuer, G., Ladel, S., & Vogel, R. (Eds.). (2014). Early mathematics learning. Selected Papers of the POEM 2012 Conference. Berlin: Springer.

    Google Scholar 

  • Kunze, H.-R., & Gisbert, K. (2007). Förderung lernmethodischer Kompetenzen in Kindertageseinrichtungen. In BMBF (Ed.), Auf den Anfang kommt es an: Perspektiven für eine Neuorientierung frühkindlicher Bildung (pp. 15–117). Berlin: BMBF.

    Google Scholar 

  • Lee, J. S., & Ginsburg, H. P. (2009). Early childhood teachers’ misconceptions about mathematics education for young children in the United States. Australasian Journal of Early Childhood, 34(4), 37–45.

    Google Scholar 

  • Mashburn, A. J., Pianta, R. C., Hamre, B. K., Downer, J. T., Barbarin, O. A., Bryant, D., Burchinal, M., Early, D. M., & Howes, C. (2008). Measures of classroom quality in prekindergarten and children’s development of academic, language, and social skills. Child Development, 79(3), 732–749.

    Article  Google Scholar 

  • McConkey, R., & McEvoy, J. (1986). Games for learning to count. British Journal of Special Education, 13(2), 59–62.

    Article  Google Scholar 

  • Montague-Smith, A. (2002). Mathematics in nursery education (2nd ed.). Oxon: Routledge.

    Google Scholar 

  • National Association for the Education of Young Children (NAEYC). (2002). Early childhood mathematics: Promoting good beginnings. http://www.naeyc.org/positionstatements/mathematics. Accessed 23 Nov 2013.

  • Perry, B., & Dockett, S. (2010). What makes mathematics play? In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics eduction. Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia, (pp. 715–718). Fremantle: MERGA.

    Google Scholar 

  • Petermann, F., & Lipsius, M. (2011). Wechsler preschool and primary scale of intelligence III, German version. Frankfurt a. M.: Pearson Assessment.

    Google Scholar 

  • Peters, S. (1998). Playing games and learning mathematics: The results of two intervention studies. International Journal of Early Years Education, 6(1), 49–58.

    Article  Google Scholar 

  • Pramling, I., & Asplund Carlsson, M. (2008). The playing learning child: Towards a pedagogy of early childhood. Scandinavian Journal of Educational Research, 52(6), 623–641.

    Article  Google Scholar 

  • Ramani, G. B., & Siegler, R. S. (2008). Promoting broad and stable improvements in low-income children’s numerical knowledge through playing number board games. Child Development, 79(2), 375–394.

    Article  Google Scholar 

  • Rechsteiner, K., Hauser, B., & Vogt, F. (2012). Förderung der mathematischen Vorläuferfertigkeiten im Kindergarten: Spiel oder Training? In M. Ludwig & M. Kleine (Eds.), Beiträge zum Mathematikunterricht 2012 (pp. 677–680). Münster: WTM.

    Google Scholar 

  • Reusser, K. (2006). Konstruktivismus—vom epistemologischen Leitbegriff zur Erneuerung der didaktischen Kultur. In M. Baer, M. Fuchs, P. Füglister, K. Reusser, & H. Wyss (Eds.), Didaktik auf psychologischer Grundlage. Von Hans Aeblis kognitionspsychologischer Didaktik zur modernen Lehr- und Lernforschung (pp. 151–167). Bern: h.e.p. verlag.

    Google Scholar 

  • Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research. Learning trajectories for young children. New York: Routledge.

    Google Scholar 

  • Schweinhart, L. J., & Weikart, D. P. (1997). The high/scope preschool curriculum comparison study through age 23. Early Childhood Research Quarterly, 12(2), 117–143.

    Article  Google Scholar 

  • Sedlmeier, S. (2013). Würfelspiele als Möglichkeit zur Förderung mathematischer Kompetenzen in der Vorschulzeit—eine theoretische und praktische Auseinandersetzung. Unpublished thesis.

    Google Scholar 

  • Seo, K.-H., & Ginsburg, H. P. (2004). What is developmentally appropriate in early childhood mathematics education? Lessons from new research. In D. H. Clements & J. Sarama (Eds.), Engaging young children in mathematics. Standards for early childhood mathematics education (pp. 91–104). Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Siraj-Blatchford, I., Sylva, K., Muttock, S., Gilden, R., & Bell, D. (2002). Researching effective pedagogy in the early years. Norwich: Queen’s Printer.

    Google Scholar 

  • Starkey, P., & Klein, A. (2008). Sociocultural influences on young children’s mathematical knowledge. In O. N. Saracho & B. Spodek (Eds.), Contemporary perspectives on mathematics in early childhood education (pp. 253–276). Charlotte: Information Age Publishing.

    Google Scholar 

  • Stebler, R., Vogt, F., Wolf, I., Hauser, B., & Rechsteiner, K. (2013). Play-based mathematics in kindergarten. A video analysis of children’s mathematical behavior while playing a board game in small groups. Journal für Mathematik-Didaktik, 34(2), 149–175.

    Article  Google Scholar 

  • Sylva, K., & Nabuco, M. (1996). Research on quality in the curriculum. International Journal of Early Childhood, 28(2), 1–6.

    Article  Google Scholar 

  • Tietze, W., Schuster, K.-M., Grenner, K., Roßbach, H.-G. (2005). Kindergarten-Skala (KES-R): Feststellung und Unterstützung pädagogischer Qualität in Kindergärten. Berlin: Cornelsen Scriptor.

    Google Scholar 

  • van den Heuvel-Panhuizen, M. (2001). Children learn mathematics. A learning-teaching-trajectory with intermediate attainment targets for calculation with whole numbers in primary school. Utrecht: Freudenthal Institute.

    Google Scholar 

  • van Oers, B. (2004). Mathematisches Denken bei Vorschulkindern. In W. E. Fthenakis & P. Oberhuemer (Eds.), Frühpädagogik international (pp. 313–330), Wiesbaden: VS Verlag für Sozialwissenschaften.

    Chapter  Google Scholar 

  • van Oers, B. (2010). Emergent mathematical thinking in the context of play. Educational Studies in Mathematics, 74(1), 23–37.

    Article  Google Scholar 

  • van Oers, B. (2013). Challenges in the innovation of mathematics education for young children. Educational Studies in Mathematics, 84(2), 267–272

    Article  Google Scholar 

  • Vygotsky, L. (1978). Mind in society. Development of higher pedagogical processes. Cambridge: Harvard University Press.

    Google Scholar 

  • Wittmann, E. C., & Müller, G. N. (2009). Das Zahlenbuch. Handbuch zum Frühförderprogramm. Stuttgart: Klett.

    Google Scholar 

  • Wood, E., & Attfield, J. (2005). Play, learning and the early childhood curriculum. London: Sage Publications.

    Google Scholar 

  • Young-Loveridge, J. M. (2004). Effects on early numeracy of a program using number books and games. Early Childhood Research Quarterly, 19(1), 82–98.

    Article  Google Scholar 

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Correspondence to Hedwig Gasteiger .

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Gasteiger, H. (2015). Early Mathematics in Play Situations: Continuity of Learning. In: Perry, B., MacDonald, A., Gervasoni, A. (eds) Mathematics and Transition to School. Early Mathematics Learning and Development. Springer, Singapore. https://doi.org/10.1007/978-981-287-215-9_16

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