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Welcome to the international Children's Mathematics Network

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Categories of graphical marks, signs and symbols:


Based on Peirce's categories (Buchler, 1955) and the findings of Maulfry's PhD (Worthington, 2021) led to a revision of our original categories - to:


  • Beginnings: early exploration with intentional marks (including dots 

        and scribble-marks): attaching mathematical meanings.


  • Indexical signs: drawing attention to, pointing to or indicating something, e.g., arrows.


  • Iconic signs: a resemblance between the appearance of a sign and its meaning.

         In their Mathematical Graphics children attach mathematical meanings to their marks, which may include wavy or zigzag writing-like lines; drawings; early emergent writing; letter- or numeral-like signs; crosses; ticks and tally-like marks. The iconic signs children use have some similarity with standard symbols and what they are representing.


  • Standard (formal) symbolic signs: including standard Arabic numerals and operators (such as '+' and '=') used in calculations.


       Buchler, J. (Ed.) Philosophical writings of Peirce. Dover.


       Worthington, M. (2021). The emergence and development of young children’s personal mathematical

      inscriptions: The evolution of graphical signs explored through children’s spontaneous pretend play

      [Doctoral Dissertation]. Vrije Universiteit, Amsterdam.