The emergence and development of young children’s personal mathematical inscriptions: The evolution of graphical signs explored through children’s spontaneous pretend play

Maulfry Dobromila Worthington

Research output: PhD ThesisPhD-Thesis - Research and graduation internal

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Abstract

Abstract The aim of this research is to trace the emergence of children’s notations they use to communicate mathematical ideas in their pretend play and other social contexts, to identify cultural and social influences and how these contribute to children’s developing semiotic modes and to their mathematical thinking. The trajectories of children’s signs are traced, showing their relationship with other multimodal literacies and the role of grammaticisation (usage-based language acquisition). New analysis shows how young children’s beginnings with intentional marks move via transitional signs to formal numerals and operators. For the first time the relationship between young children’s informal signs and those of the standard signs of the established mathematics culture is shown, the children’s marks and signs developing over time to reveal their advancing mathematisation. This research is based on a Vygotskian, cultural-historical perspective and informed by a social- semiotic perspective of young children’s appropriation, creation and understanding of symbolic tools, with consideration of their communicative potential (Vygotsky, 1978). It builds on previously conducted research by Carruthers and Worthington (2006), (during almost two decades) with children from 2 – 8 years of age, showing how children’s own symbols and visual representations support their developing understanding of the abstract symbolic ‘written’ language of mathematics. Using longitudinal, ethnographic case studies of children of 3-4 years of age, I have gathered data in an inner-city maintained nursery school in the south west of England. The study focuses especially on children’s free and spontaneous social pretend play. Data include written observations, photographs of the children’s play and graphicacy and original examples; scrapbooks with visual data from the children from home and nursery; field notes made during research visits; notes from informal discussions and interviews with the teachers, and home visits including informal discussions with children and parents. Analysis is supported by means of ‘computer assisted qualitative data analysis software’ (CAQDAS) with the advantage of more systematic and objective analysis of the textual data and a high degree of validity and reliability. Analysis of the visual data is within an interpretative paradigm drawing on research into multimodality and cultural features. The findings add to our understanding of the ways in which children explore, make and communicate meanings through signs and texts to support their symbolic development of mathematics over time. They reveal the importance of social contexts for learning, and that children who had developed a rich lexicon of graphic signs were at an advantage in representing their mathematical thinking, and were more likely to use standard symbols. They show also that those children who had developed the most extensive lexicons of graphical signs, were also those who spontaneously wrote Arabic number symbols (SWANS). They also demonstrate the power and potential of children’s rich pretend play, contributing to a deepening understanding of children’s mathematics and their natural and meaningful beginnings of the symbolic language of mathematics. Above all, the findings of this thesis show their interdependence on the culture, values and beliefs of the headteacher and teachers of the early years’ setting.
Original languageEnglish
QualificationPhD
Awarding Institution
  • Vrije Universiteit Amsterdam
Supervisors/Advisors
  • van Oers, Bert, Supervisor
  • Dobber, Marjolein, Co-supervisor
Award date10 Nov 2021
Place of PublicationAmsterdam
Publisher
Print ISBNs9789464216168
Publication statusPublished - 10 Nov 2021

Keywords

  • mathematical signs
  • children's mathematical graphics
  • socioculturalism
  • semiotics
  • nursery school
  • pretend play
  • children's social literacies
  • multimodality
  • language acquisition
  • mathematisation.

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