Categories of graphical marks, signs and symbols:

The following categories are based on Peirce's categories (Buchler, 1955) and a subsequent revision of our original 2003 categories to:

• Beginnings: early exploration with intentional marks: attaching mathematical meanings.

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

      In their Mathematical Graphics children attach mathematical meanings to their graphical signs, which may include wavy or zigzag writing-like lines; drawings; early emergent writing; letter- or numeral-like signs; arrows; crosses; ticks and tally-like marks. The iconic signs children use share some similarity with standard (formal, abstract) symbols and what they represent.

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

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

Note 1: Children intentionally use their Mathematical Graphics to communicate their mathematical thinking to others.

Note 2: 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.

'Proto', meaning pre; first; early forms; beginning: these iconic signs are visual non-standard signs to communicate something. All children use some forms of iconic signs as they move towards freely using standard symbols. These signs act as a bridge to standard, abstract symbols.

References

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