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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 a subsequent revision of our original 2023 categories to:


  • Beginnings: early exploration with intentional 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, abstract) symbolic signs: including standard Arabic numerals and operators (such as '+' and '=') used in calculations.


Note: Children's Mathematical Graphics do not support a stage theory. Although all children begin with early exploration with intentional marks, some older children may use standard symbolic signs, whilst (at the same time) in their pretend play they may use scribble-marks, so as not to interrupt their play.


     All children use some forms of iconic signs as they move towards freely using standard symbols. These iconic signs are 'proto' signs that form a bridge to standand, abstract symbols.


'Proto', meaning pre; first; early forms; beginning; visual non-standard marks and signs to communicate something.


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