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Non-canonical Solutions in Children–Adult Interactions—A Case Study of the Emergence of Mathematical Creativity

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Early Mathematics Learning

Abstract

In research about mathematical creativity, seldom is the early childhood taken into account, although mathematical creativity already develops at preschool age (e.g., Becker-Textor, 1998; Krenz and Rönnau, Entwicklung und Lernen im Kindergarten. Psychologische Aspekte und pädagogische Hinweise für die Praxis (7th ed.), 1997). This chapter investigates mathematically creative solutions of kindergartners (in Germany children between 3 and 6 years attend the “kindergarten.”) who have social/emotional difficulties. Starting point is the longitudinal study MaKreKi (mathematical creativity of children), in which theories of mathematics education and psychoanalysis are amalgamated for the investigation of the development of mathematical creativity. In this chapter, two episodes of two children aged 4–5 years are presented, while they cope with a mathematical task. It focuses on the mathematically creative ideas emerging in the interaction between the involved children and the accompanying person and on how the children deal with the mathematical instructions given by the accompanying person.

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Notes

  1. 1.

    Hadamard has used introspection to describe mathematical thought processes. He developed the four-stage model of mathematical creative thinking: Preparation, incubation, illumination and verification (see Hadamard 1954).

  2. 2.

    http://www.idea-frankfurt.eu/. Accessed 6 Aug 2013.

  3. 3.

    http://www.idea-frankfurt.eu/en/research/research-domains/diagnostics-and-prevention/eva. Accessed 6 Aug 2013.

  4. 4.

    http://www.idea-frankfurt.eu/en/research/research-domains/resources-and-limitations-of-successful-learning/erstmal. Accessed 6 Aug 2013.

  5. 5.

    The following extract of René’s solution process refers to an analysis, which has already been published in German. For more details see Hümmer et al. (2011) and Krummheuer (2011).

  6. 6.

    Because of the difficulties conducting IQtests in early childhood, Nina has only participated in the performance test (and not in the verbal test). So these values have to be interpreted carefully.

  7. 7.

    In Germany the period of a marriage lasts 14 years on average, so many children like Nina live in a single-parentfamily.

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Acknowledgments

The preparation of this paper was funded by the federal state government of Hessen (LOEWE initiative).

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Authors and Affiliations

  1. Goethe-Univesity Frankfurt a.M. and IDeA-Center Frankfurt a. M., Frankfurt, Germany

    Melanie Münz

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  1. Melanie Münz
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Correspondence to Melanie Münz .

Editor information

Editors and Affiliations

  1. Institut für Mathematik, Martin-Luther-Univ Halle-Wittenberg, Halle, Germany

    Ulrich Kortenkamp

  2. Inst. für Schulpädaogik und Grundschuldidaktik, Martin-Luther-Universität Halle-Wittenberg, Halle (Salle), Germany

    Birgit Brandt

  3. Pädagogische Hochschule Karlsruhe, Institut für Mathematik und Informatik, Karlsruhe, Germany

    Christiane Benz

  4. FB 12 Informatik und Mathematik, Goethe Universität Frankfurt am Main FB 12 Informatik und Mathematik, Frankfurt am Maim, Germany

    Götz Krummheuer

  5. Fachrichtung 6.1 Mathematik, Universität des Sarlandes, Sarbrücken, Germany

    Silke Ladel

  6. FB 12 Informatik und Mathematik, Goethe Universität Frankfurt am Main, Frankfurt, Germany

    Rose Vogel

Appendix

Appendix

Rules of Transcription

Column 1

Serially numbered lines

Column 2

Shows when people are talking at the same time

Column 3

Abbreviations for the names of interacting people

Column 4

Verbal (regular font) and non-verbal (italic font) actions

/

Rising pitch

-

Even pitch

\

Falling pitch

… …

Breaks of 1, 2 or 3 s

(4)

Breaks of a specified time span

Bold

Accentuated word

S p a c e d

Spoken slowly

(word)

Unclear utterance

(remark)

Remark, offering alternatives to unclear utterances

 + 

The indicated way of speaking ends at this symbol

#

There is no break; the second speaker follows immediately

<

Indicates where people are talking at the same time

>

The next block of simultaneous speech is indicated by a change

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Münz, M. (2014). Non-canonical Solutions in Children–Adult Interactions—A Case Study of the Emergence of Mathematical Creativity. 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_9

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