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 early 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.  Iconic signs are transitional, helping children move from scribble-marks towards standard abstract symbols. 

• 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.

References

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