Abstract
This chapter investigates children’s own constructions of recognizing or perceiving collections of objects. Identifying quantities of collections is a well-accepted content in early childhood education. Different ways of perception and determination of quantities of collections will be discussed because they shall contribute in different ways to the development of conceptual and procedural understanding of numbers. Firstly, different processes will be looked at which can be used for identifying quantities theoretically. The processes of perception, in particular the process of decomposing a collection into parts, will be focused on later. Questions will be asked about whether and how they decompose or structure collections of single objects into substructures or parts. On the basis of the results of the present study, conclusions will be drawn regarding how this ability can be supported and how children’s constructions must be considered as a basis for instruction in early mathematics education.
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References
Benz, C. (2010). Kindergarten educators and math. In M. M. F. Pinto & T. F. Kawasaki (Eds.), Proceedings of the 34th conference of the international group for the psychology of mathematics education (Vol. 2, pp. 201–208). Belo Horizonte: PME.
Benz, C. (2011). Den Blick schärfen. In A. Peter-Koop & M. Lueken (Eds.), Mathematischer Erstunterricht: Empirische Befunde und Konzepte für die Praxis (pp. 7–21). Offenburg: Mildenberger.
Benz, C. (2012). Attitudes of kindergarten educators about math. Journal für Mathematik-Didaktik. 33(2), 203–232.
Clements, D., & Sarama, J. (2009). Early childhood mathematics education research: Learning trajectories for young children (Studies in mathematical thinking and learning) (1st ed.). New York: Routledge.
Dornheim, D. (2008). Prädiktion von Rechenleistung und Rechenschwäche: Der Beitrag von Zahlen-Vorwissen und allgemein-kognitiven Fähigkeiten. Berlin: Logos.
Gaidoschik, M. (2010). Wie Kinder rechnen lernen—oder auch nicht: Eine empirische Studie zur Entwicklung von Rechenstrategien im ersten Schuljahr. Frankfurt a. M.: Peter Lang.
Gasteiger, H. (2010). Elementare mathematische Bildung im Alltag der Kindertagesstätte: Grundlegung und Evaluation eines kompetenzorientierten Förderansatzes. Münster: Waxmann.
Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge: Harvard University Press.
Gerster, H.-D., & Schultz, R. (2004). Schwierigkeiten beim Erwerb mathematischer Konzepte im Anfangsunterricht. Bericht zum Forschungsprojekt Rechenschwäche—Erkennen, Beheben, Vorbeugen. Pädagogische Hochschule, Freiburg. http://opus.bsz-bw.de/phfr/volltexte/2007/16/pdf/gerster.pdf
von Glasersfeld, E. (1987). Wissen, Sprache und Wirklichkeit. Braunschweig: Vieweg.
Lueken, M. (2010). The relationship between early structure sense and mathematical development in Primary School. In M. F. Pinto & T. F. Kawasaki (Eds.), Proceedings of the 34th Conference of the international Group for Psychology of Mathematics Education (pp. 241–248). Belo Horizonte, Brasil.
Mulligan, J. T. (2002). The role of sturcture in children’s development of multiplicative reasoning. In B. Barton, K. C. Irwin, M. Pfannkuch, & M. Thomas (Eds.), Mathematics education in the south pacific. Proceeding of the 25th Annual Conference of the Mathematics Education research Group of Australasia Inc. (pp. 497–503). Auckland: MERGA.
Mulligan, J. T., Mitchelmore, M. C., English, L. D., & Robertson, G. (2010). Implementing a pattern and structure awareness program (PASMAP) in kindergarten. 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. 797–804). Fremantle: MERGA.
Mulligan, J. T., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33–49.
van Nes, F. (2009). Young children’s spatial structuring ability and emerging number sense. Utrecht: All Print.
Resnick, L. B. (1983). A development theory of number understanding. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 110–151). New York: Academic Press.
Rottmann, T. (2006). Das kindliche Verständnis der Begriffe “die Hälfte” und “das Doppelte”. Theoretische Grundlegung und empirische Untersuchung. Hildesheim: Franzbecker
Schipper, W. (2009). Handbuch für den Mathematikunterricht an Grundschulen. Braunschweig: Schroedel.
Söbbeke, E. (2005). Zur visuellen Strukturierungsfähigkeit von Grundschulkindern: Epistemologische Grundlage und empirische Fallstudie zu kindlichen Strukturierungsprozessen mathematischer Anschauungsmittel. Hildesheim: Franzbecker.
Steffe, L. P., & Cobb, P. (1988). Construction of arithmetical meaning and strategies. New York: Springer.
Young-Loveridge, J. (2002). Early childhood numeracy: Building an understanding of part-whole relationships. Australian Journal of Early Childhood, 27(4), 36–42.
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Benz, C. (2014). Identifying quantities—Children’s Constructions to Compose Collections from Parts or Decompose Collections into Parts. In: Kortenkamp, U., Brandt, B., Benz, C., Krummheuer, G., Ladel, S., Vogel, R. (eds) Early Mathematics Learning. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4678-1_12
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