Over time, young children develop their repertoires (or

   lexicons) of graphical signs, drawing on the signs that

   originate in different contexts of their early drawings, and

   using them to communicate their ideas through drawing,

   writing and Children's Mathematical Graphics. In this 

   section we focus on dots, crosses and zigzags.

Dots

"Hundreds and pounds!"                                                                     

Charlotte (3 years, 7 months), and her friend Jessica were drawing,

each selecting a piece of paper and coloured pens. Charlotte held

many pens in one hand, dotting the entire paper as she shouted 

excitedly,“Hundreds and pounds! Hundreds and pounds!" Her 

reference to 'hundreds and pounds' meant that she was making 

connections between the large quantity of dots: this seemed a lot

to her, and a hundred fitted in with her thinking about a lot: 'pounds'

also fits in with her sense of a large quantity.

   Tore and the shark

   Three-year-old Tore was  

   drawing excitedly on a

   whiteboard, explaining

   his marks as a "shark". It seems possible that his marks

   suggested to him the rapid movement of a shark moving

   through (or vigorously thrashing) in water. Perhaps the

   dots and short vertical lines suggested ‘teeth’, although

   without further explanation of course we cannot know.

"When there are three ticks you can go!"  

Oliver and Isaac (both 4 years of age), were playing car

parks, triggered by Isaac's recent experience of using an electronic card-reader with with his dad, in a city car

park. Issac made a number of signs to inform drivers, and Oliver decided to make his own sign, drawing dots and

writing letter-like signs, explaining,"These are ticks. When there are three ticks you can go, when are two you can't

go that way. I've made two ticks - that means you aren't allowed." Then pointing in the other direction,"People

allowed in that way." Whilst Oliver included dots, he did

not explain what he intended them to mean.

   Subtracting beans

   In this class of 5-6 year olds, the children were playing a

   subtraction game with beans and flower pots. They each

   chose personal ways to represent what they did,

   Francesca using dots to represent each bean, whilst at

the same time she decided to use a subtraction and an equals sign.

Jax adds grapes                                                                                     

Jax (4 years, 3 months) was adding quantities of grapes.    

She wrote numerals for the two amounts of grapes, then

drew dots to represent them, finally writing the 'T' of the

word 'ten'.

Crosses

 Jazper's gun and "flyer"

          Jazper (4 years, 11 months) explained "This           

          is my gun" (in the centre of the page). Then

          pointing to the 'cross' shape (top right), added,

          “and this is my flyer" (aeroplane). Beneath his

           drawings he wrote a series of letter- or 

           numeral-like signs.

"A plane flying above the world"                                Mohit (4 years, 8 months) used two different signs to  signify his meaning of aeroplanes; a cross to represent "a plane flying above the world", and in the lower left he drew the profile of a plane in flight.                                                                                    Crosses and zigzags                                                                In the Netherlands, Nadieh (5 years, 7 months), included   horseshoe shapes in her drawing to signify "birds flying",  birds more often represented in young children's drawings in  the west as a 'V', 'M' or 'W'. The people she drew have crosses for hands,  and the zigzag at the top represents the sky.    Note: compare Nadieh's birds with those that Sterre drew (below) in her drawing herself at the beach (with zigzags).

Sharing talk about crosses                                                   

Ayaan (4 years, 9 months) wrote two large crosses on                                 

a small whiteboard outside, talking about her symbols

with a friend. They were both clearly interesting in this

distinctive symbol, although we do not know what thier

intended meaning was.

       Shopping

       When playing shops, Nathan (4 years, 7 months) chose to

      write a 'shopping list'. He read his list as "carrots, potatoes

       and spaghetti."His mother explained that they always wrote

       a list before the family went to the supermarket. Nathan had

       drawn on his home cultural knowledge in his play at the 

       nursery.

"No! Keep out!"                                                                   

In the 'garage' play area outside, Mark (4 years, 2 months) was

playing in an area that was enclosed on three sides. He objected that several boys were riding their bikes and wheeled toys into

'his' corner, insisting"No!Keep out! You can't come here!"  Since

his verbal request failed to have the desired effect,  Mark chose

an alternative means to communicate, and fetching a stick of

chalk he drew many large crosses, and emphasising his message

once more by repeating his verbal instructions. Finally the other

boys 'heard' his message and moved away. 

     Shop closed

     Daniel (4 years, 9 months), had been playing shops and

     decided to make signs, to show when the shop was

     'open', and another to show when it was 'closed'. His

     teacher had noticed what he was doing, and Daniel

     explained, "It's closed now the shop is closed." His

     teacher asked how people would know it was closed,

     and pointing to the cross he explained, "Look here,

     see?  Closed. That means it's closed." Next he drew

     another smiling face, but this time without a cross,

     explaining, "Look, that means it's open." Then drawing

     a cross over the new face remarked, "Oh dear ... it's

                                                                                  closed."

The dice game                                                                    

In this mixed age class of 4-6 year olds, a group of

children were playing a dice game, playing in pairs

and rolling two dice together. This provided an

opportunity for them to represent the amount of dots
they got each time, (on one dice, or the total of two combined) - if they chose. Amelie (4 years, 1 month),

played this game during her third week at school. She

counted the dots out loud and was very animated as she

read the 'e' as an '8', and clearly knew the '4' of her age.

She used a combination  of marks, iconic signs and

standard symbols, 'plus' and equals symbols and some standard numerals with boxes around them. Since her teacher had not modelled boxes around numerals it seems likely that Amelie may have copied from her peers.

                            Adding dots on dice                                  

                          Anna (6 years, 3 months), was a good deal older

                          than Amelie. She chose to represent her

                          calculations (of the total number of dots on the

                          two dice), in the standard symbolic form. Whilst

                         Amelie had represented the dots in a highly

                         personal (unschooled) way, Anna used standard

                         numerals, and addition and equals signs. She chose

                         to draw a box around each calculation, a feature

                         she had copied from her peers.

Zigzags

Shadow of the flags

In the Netherlands, Sterre (5 years, 3 months), named the triangles

at the top of the page as "flags", and those she cut with pinking

shears at the foot of the page as"shadow of the flags."  She used

zigzags to represent the water (or waves) and "beach shoes",

adding short zigzags (like a letter 'M') to represent birds in flight.

Boat on water

     In Amsterdam, Aman (4 years, 7 months) used a stick she had

     found, to draw 'boats' in the sand outside, and completed each

     with a wavy (or zigzag) line, explained that this was "water. By

     combining the curved line line of the boat's hull with the wavy line,

     it appeared that Aman's intended meaning of 'boat-on-water':

     rather than combining two words, she combined two graphical

     signs to communicate her meaning.

Romy's staircase                                   

In the Netherlands, Romy (5 years, 5 months) drew a house,           

drawing several zigzag lines outside her house that suggested

staircases.

  Writing, and a caterpillar cake                  

  On one side of his paper(not shown), Nathan (4 years, 4  

  months), drew a horizontal line with zigzags over it,

  explaining that it was his "birthday cake." His mum had

  made a caterpillar-shaped cake for his fourth birthday

  party, the day before. Turning his paper, he repeated the

  same lines and zigzags, now referring to them as "writing."

Molly's birthday card                                                            

Molly made herself a birthday card, her zigzag 'writing' saying

Happy Birthday" followed by her name, and beneath it she

wrote a number '4' for her age.