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Standard symbolic operations with small numbers

Addition and subtraction


Standard symbolic calculations arise directly out of the preceding ones, children's previous knowledge and understandings combining to support simple calculations with small numbers and quantities.



Jax (5 years, 2 months) was adding grapes.

By using dots (an iconic form), reinforced by

the numerals '6' and '4' implies numerals or 

quantities. This can be read as "6 and 4 = ten",

Jax having written the initial 't' of ten.  


  • Taxonomy: children's own methods,

         symbolic operations with small numbers

  • Addition



                                                                                                   Numerals only

Peter (5 years, 9 months) (also adding

grapes) has used his own abbreviated

calculation, which, provided he reads it

to us, can be understood as "4 - 3 = 1".


  • Taxonomy: children's own methods, symbolic operations with small numbers    
  • Subtraction

More grapes: dots and numerals

Mary (5 years, 4 months) used a combination

of iconic and symbolic responses, with the

minus and equals signs implied, denoting "6,

minus / subtract 3 equals 3".


  • Taxonomy: children's own methods, 

​​​​​​​​​​​​​​         symbolic operations with small numbers  

  • Subtraction