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* Counting continuously

      We use the term counting continuously to describe this stage of children’s early representations of calculation strategies – both addition and subtraction. Though not directly taught, Hughes (1986, p.35) suggests that it is self-taught.



The breakfast cafe

     The children were preparing for a 'breakfast cafe'.

Alison (5 years, 1 month) was counting the children in

her group and each child's toy, ignorer to work out the total

who would be eating. The number from her group would

then be added to the others in her class (with their


      Alison counted both children and toys, representing

them as string of numerals. When self-checking she found

that she had too many numbers, and drew brackets around

those she did not  need (15, 16 and 17).The final number

in her count represented her total. The hand she drew

may denote addition, although we cannot be sure in this



  • Taxonomy:  Calculations - children's own methods, counting continuously
  •    Early addition                                                               


     Alice (4 years, 11 months) was playing in the class's 

'garden centre' and was serving a 'customer' who had

asked for 4 flowers. Having done so, she rapidly drew

16 flowers and crossed out four of them, then wrote

the numbers '16' and next to it, the remaining total of '12'.  


  • Taxonomy: early subtraction, counting continuously
  • Early subtraction





                                                                              Baylee just had her 5th birthday, and

wanted to find out the ages of the other

children in her class. After writing the

numbers 1 - 10, she began to add ticks

beneath the ages various children had


     When she showed her teacher, she

pointed to the ticks beneath the '2' and

the '7' (there were no children of these ages 

in her class). She explained that her brother

was 7 years of age, and her friend's sister

was 2. Then she asked her teacher her age,

and writing '35' at the top of her paper, gave

it a tick. Finally she counted the ticks for

each age, finding that '5' had the most ticks.


  • Taxonomy: counting continuously
  •  Data handling