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Counting continuously

We use the term counting continuously to describe this early 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 number of children 

who would be eating. This number 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                                                               


Selling Flowers

Alice (4 years, 11 months) was playing in

the class's pretend play 'garden centre' and

was serving a customer who had just asked

for four flowers. Alice rapidly drew the 16

flowers in the pot, and then crossed out four

of  them. She then wrote    '16' and next to it

the total of '12' that remained.                                                                                                             


  • Taxonomy: early subtraction, counting


  • Early subtraction





                                                                              How old are you?

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