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Gallery 8: Children's graphic symbols and texts in self-initiated contexts

    © Copyright M. Worthington & E. Carruthers 2012

Where adults value and support children’s own mathematical notations, and where tools and resources for graphicacy are available throughout the setting (indoors and out), children will freely and spontaneously communicate their mathematical thinking using their own signs and representations.

Tim (4 years 1 month) was in the garden, lifting some old fence posts onto a trolley. He spent a lot of time transporting them to another area. His teacher joined him, wondering how many logs he had moved. Tim was too engrossed in what he was doing to reply immediately, but later took a clipboard and pen from the basket outside, drawing circular shapes and other signs across the top of this page. Tim’s teacher watched as he counted the shapes he’d drawn (from left to right) and his teacher asked if she might write the numbers he had said.

When he reached ‘eight’ Tim returned to the beginning to check, counting each shape in turn as he touched them, then continuing to 25 (missing a few of the teen numbers). Next Tim drew four long longs, commenting ‘They’re very lo-o-ong.’ Beneath the first ‘long log’ he wrote some letter-like signs, reading ‘This says ‘do not move my logs and do not park here’. Tim’s experience of physically lifting and moving his logs clearly had an impact, and his decision to represent and communicate this thinking revealed some of his mathematical thinking.


  • Written number and quantities: representing quantities that are counted; early written numerals

Occasionally a picture-story book will trigger some mathematical explorations, in this instance, counting and addition. The teacher had read the story ‘One is a Snail, Ten is a Crab’ (2006) by Pulley Sayre, A., Sayre, J. and Cecil, R. The children were very excited by this and wanted to find creatures to calculate their own chosen total.

Shimae decided to ‘find out what 100 is’. She wrote the number ‘100’ and as she progressed, counted the legs of each creature she drew. After a while she said that so much counting was difficult, and an adult counted with her, Shimae noting the total she counted each time. When she reached 100 she wrote ‘6 spidr 3 insec 1 pursn a well (whale) 1 pig.’.

Other children explored different quantities, allowing them all to differentiate according to the number they felt able to deal with. Harrison (not shown) had chosen to work out which creatures to select so that their feet would total 11. He began by explaining, ‘I don’t know how to draw spiders, so I’m just going to do the legs.’ Next he drew two additional legs, saying ‘one person’, and then counted them all: ‘One, two, three, four… ten’. Now I just need one more – it’s a snail. There! That’s eleven altogether.’
The children used a range of ways of representing, such as Jamie’s written response below:

Jamie also chose ‘100’, ‘because that’s massive!’ He wrote ‘9 peeple’ and then used his fingers to count in twos, writing ‘1 optpus 2 spiders, admitting ‘This is getting hard now. I know! I can write it down each time and count on!’ When he neared his total he added ‘9 spiders’, then crossed it out and wrote ‘8’, explaining ‘Nine makes too many legs – so I had to take one off to make the right amount.’

Children love to challenge themselves, and analysing thousands of children’s examples we have never found a child who planned to work on something that was too easy: they either match what they do to their understanding, or stretch themselves to go beyond what they have previously done.


  • Written number and quantities: representing quantities that are counted

  • Calculations: children's own methods: counting continuously; separating sets

Popular signage
Young children readily absorb environmental signage that matters to them. In the two examples below, the children have represented the double golden arcs of ‘M’ for ‘McDonalds’ as they try out writing a familiar letter symbol.

Isaac’s ‘M’ for MacDonald’s when playing ice cream vans outside his home, in his dad’s van.

David’s repeated ‘M’ for MacDonald’ in a notebook.


  • Explorations with gestures, words, artefacts, marks, symbols and signs.

  • GRAPHICACY: writing

As early years practitioners it’s easy to assume ‘writing’ and mathematical notations belong on paper, but young children show us so many locations where they want to communicate through marks and symbols. Shereen drew and wrote following graphics on the front of some drawers.
Figure 1 Figure 2

Shereen drew a house with a long path, some people and letters (figure 1) and four girls and some letters (figure 2). In figure 3 Shereen wrote the numerals 1 – 9 and drew several stars.

Children’s free and spontaneous graphics enable them to explore the various visual systems that interest them, including written and mathematical symbols and signs.

Figure 3



  • Explorations with gestures, words, artefacts, marks, signs and symbols

  • GRAPHICACY: writing and children’s mathematical graphics

Letter or numeral-like - or exploring alphanumeric signs?
Between the ages of 3 – 4 years some children begin to represent the appearance of writing, using separate graphical signs that seem to imitate the appearance of letters or numerals.

Figure 1. Elizabeth was writing notes in the minibus, explaining ‘It says dear my friend Emma, come back soon dear Elizabeth.’ She included the first two letters of her name, with other signs that resemble letters, and captured what she knows of the conventions of communicating by letter (i.e. ‘Dear my friend Emma’ and ‘Come back soon’).

Figure 2. The early writing of children whose first language uses a different alphabet, also shows that they have captured something of the appearance of the written letters of their language (as here, in Arabic) Ayaan did when writing her name.

Children begin to explore and think about the similarities and differences between alphanumeric signs (i.e. letters of the alphabet and numerals) but this is not at all straightforward, and sometimes leads to numerals within written text, or letters in the place of numerals. These are not mistakes, but children working hard to understand the differences.

Figure 3 shows Elizabeth’s list of children in her group who had arrived that morning. She appears to have written several letter-like signs and a numeral ‘3’. There was no indication that she had counted three children.


  • Meaning making in socio-cultural contexts

  • Explorations with gestures, words, artefacts, marks, signs and symbols

  • GRAPHICACY: writing and children’s mathematical graphics

Writing and Mathematics
  • Exploring Symbols

Elizabeth’s self-initiated mathematical graphics (nursery)

Sitting next to a friend in the gazebo, both children wrote in large diaries. Elizabeth wrote a line of numerals across the top of one page, adding a box-like grid, an arrow and a flower beneath. She read her combination of ‘1’s and ‘5’s on the right-hand page as teen numbers, beginning to represent and understand two digit numbers in a pattern. Ernest (2006) argues that it is easy to underestimate the considerable achievement it is for children to learn place value and use it with confidence.

Ernest, P. (2006). A semiotic perspective of mathematical activity: the case of number. Educational Studies in Mathematics, 61(1), 67-101.


  • Numerals as labels.

The Mathematics
  • Place value

Children’s graphics: Shereen (Nursery)

Valuing, understanding and assessing children’s graphics
It would be easy to assume that figure A was made by an older child (or by the same child when older) - than that shown in figure B. However, Shereen made both, figure A three months earlier that figure B, and showing the influence of the context in which they were made.

A. 8th January: child-initiated writing. B. 17th March: pretend play.

Figure A: Shereen had borrowed her teacher’s notebook to write in. She referred to the numerals in circles as ‘buttons’ (possibly relating to buttons on a calculator or computer), reading them as ‘1, 2, 3, 4’. Then writing the letters at the top of the page, read them as ‘drawing’.


  • graphicacy: writing;

  • children’s mathematical graphics: numerals as labels.

Figure B was written in the course of Shereen’s pretend play with a friend, playing shops. Shereen read her list, ‘Cheeseburger, apples, tomato. Cheese, chicken, rice, sugar, mango juice. I’m writing chocolate bar’.


  • graphicacy: writing;

  • children’s mathematical graphics: early explorations with marks, signs and symbols.

Children often use scribble-marks for writing in their pretend play, perhaps to avoid interrupting the flow of their play. At these times their marks appear to be an indication of writing rather than an attempt to write letters. Shereen used a wide range of letters of the alphabet and numerals in a range of contexts throughout the year, interspersed with scribble-marks in some play contexts.

Children’s graphics: (Nursery)

CONTEXT: Shereen 4 years 6 months – drawing at home.

Shereen explained: ‘I looked out of the window. I saw a butterfly, ladybird, snails, mountain and a dog asking for its food’.

Children’s visual texts reveal their use of circles, dots, straight and curving lines, zigzags, squares, arrows, spirals, grids and other graphical marks and symbols such as those identified by Machón (2013) and Matthews (1999). They appear to often embellish their drawings with symbols, or to practice them, often including letters or numerals (alphanumeric signs) in a similar way. In this example Shereen’s drawings, symbols and signs comprise straight and curved lines, ‘U’ forms, a grid, arcs, dots and a triangle. She included letters (she did not say what they meant), the numeral ‘8’, spirals and a cross in her drawing. This burgeoning symbol and sign use between the ages of three and four years extends children’s existing graphical inventories.

Taxonomy: graphicacy: drawing, maps, writing

  • Early explanations with marks, signs and symbols.

* See below for reference.

Machón A (2013) Children’s Drawings: The Genesis and Nature of Graphic Representation. Madrid: Fibulas Publishers.

Matthews, J. (1999). The Art of Childhood and Adolescence: The Construction of Meaning. London: Falmer Press.

Children’s graphics: David and Isaac in the Nursery

CONTEXT: small group at ‘quiet time’, exploring the bathroom scales.

The children contextualise their mathematical graphics as they draw on their existing knowledge. For example David stood on the bathroom scales, and looking at its numbers said, ‘I’m 15, so I need to write it down’ and made some letter- and numeral-like signs on the whiteboard.

Using his understanding of a variety of measuring units, Isaac made rapid scribble-marks on paper saying, ‘David weighs 700 kilos, he’s 60 metres heavy’ (opposite).

The children appeared to sometimes use scribble-marks as ‘placeholders’ to denote specific meanings [notable within their pretend play], ‘suggesting that such rapidly made marks allow the course of play to proceed uninterrupted’ (Worthington and van Oers 2016b). * Children may also use scribble-marks to signify writing, an alternative to wavy or zigzag lines.


  • Early explanations with marks: attaching mathematical meanings.

CONTEXT: in the nursery - David, 4 years, 2 months: self-initiated drawing and mathematics.

Before he left to go to the forest with his peer group, David drew a ‘spider’.

He represented each leg, counting 1 - 15 in sequence, and then ’17, 18, 19, 20, 25.’ He then proceeded to enclose the legs with a spider web. Next he blacked out the spider’s face saying, ‘It’s all the flies on his face’.

David counted almost continuously, some of the many spider’s legs he had drawn.


  • Representing quantities that are counted.

CONTEXT: child-initiated graphicacy - at home
Elizabeth’s brother had been playing on his electronic ‘Super Mario’ game and Elizabeth decided to make her own. After representing the screen on the inside of her folded card, she added numerical buttons to press.

Playing pretend technologies is very popular with young children (see for example,
Worthington, 2010).


  • Numerals as labels

CONTEXT: in the nursery - Shereen, playing with pens

Shereen and Verast sat at opposite ends of a small table, each with a small notebook and felt-tip pen. Verast made purple marks and holding her notebook up said ‘That’s mashed potato.’ Shereen made marks with a red pen, held it up and announced ‘That’s fire.’

Young children sometimes attach meanings to their early marks after they have made them and in this instance, Shereen’s rapidly made marks appeared to suggest the flames of a fire to her. Shereen’s marks also characterise what Matthews (1999) refers to as ‘action representation’.

Such marks also offer semiotic potential (i.e. the possibility of signifying something other than the marks themselves), children often making a connection between the appearance of their marks and something they know in the real world. Worthington (2009) observed that young children’s symbol and signs in drawing points to a ‘natural history’ of their use that underpins all abstract symbolic languages.


  • Making meaning in social pretend play and imagination – graphicacy.

Matthews, J. (1999). The Art of Childhood and Adolescence: The Construction of Meaning. London: Falmer Press.

Worthington, M. (2009) Fish in the water of culture: signs and symbols in young children’s drawing. The Psychology of Education Review, Vol. 33, No. 1, March 2009.

CONTEXT: Maps and plans: pretend play and imagination

Triggered by Isaac’s interest in maps, Isaac and David created a large plan of a road layout.

Making lines Isaac announced, ‘These are roads crossing other roads’. He then drew a square with a series of lines, ‘These are arrows to say ‘go this way’.’ He drew another square on another part of the paper, ‘This is the car park gate; the square on the outside means it’s shut.’ The following day Isaac ‘opened’ the gate by making the two horizontal lines [across it]. Together they created imaginary accidents and problems with the vehicles such as crashes. David’s helicopter rescued the people (little wooden play people), while Isaac stood them all up in a crowd ‘to watch’. Pointing, Isaac explained, ‘here’s where you can park your lorries for 2 hours while you sit on the beach'. Then David referred to the charge for the car park: ‘We’re going to have signs to say what the speed limit is’.

This example is particularly interesting for its evidence of the boys’ abstract thinking through their explorations with symbols. For example drawing a square to signify the gate to the car park, Isaac ‘opens’ it the following day by adapting his symbol. Isaac also uses arrows to indicate direction. He uses spoken words to signify the meanings of his symbols: ‘these are arrows to say ‘go this way’; the square on the outside means it’s shut.’

This ability to invent and adapt symbols and signs stands the children in good stead when they later work on mathematical operations. Worthington and Carruthers refer to children’s use of arrows as ‘narrative actions’ (2003). Children sometimes choose to use arrows to indicate the operation of adding or subtracting items (Hughes 1986), some also using them in place of the symbols for ‘add’ or subtract’, (Carruthers and Worthington 2006; 2005). Poland et al. describe arrows as one of a number of ‘dynamic schematisations’, which children use to signify transformation, movement or change: they argue that such symbols should be given emphasis in early childhood since they underpin ‘most mathematical activities’ (2009: 310).


  • Explorations with symbols

CONTEXT: Child-initiated play

Attaching meanings to marks and communicating through graphics in pretend play

Oliver, Isaac and David have attached stickers on fences with zigzag marks and other marks and symbols, during their play in the sand area (at first no explanations). Then Isaac uses sticky labels and marks to act as ‘buttons’, sticking them all around the fence.

We can’t always know the meanings of all young children’s marks and symbols but their proliferation is exciting and shows their ease with communications through graphicacy.

Taxonomy: Making meaning in child-initiated play

  • Early explorations with marks: attaching meanings

CONTEXT: Child-initiated play

Exploring symbols

Nursery: Shereen - 4 years 4 months

In the forest, the children arrived at a curious shelter, with a wooden pallet in the doorway. One of the boys thought an elephant lived there. Other children joined them, and Shereen watched as the children went inside.

Drawing elephants on her hands Shereen added tally-type marks as she counted children going into a shelter and counting the marks on her hand up to 10. Afterwards she showed everyone the marks on her hand.

Triggered by this impromptu imaginary discussion in the forest, Shereen decided to count, using tally-type marks to represent the ten children who entered the shelter. Young children use a range of marks to tally items they count: sometimes children invent their own tally marks when they see a need, and some use vertical lines that may have been introduced to them by an adult.

Both are equally valid, and it is important that young children have opportunities to freely choose and experiment with their own marks should they wish to do so (rather than only being shown one way).

Taxonomy: Making meaning in child-initiated play

  • Explorations with symbols

  • Representing quantities that are counted

CONTEXT: Exploring symbols

Nursery: Elizabeth - 3 years 7 Months

Elizabeth wrote symbols on paper: ‘I can’t tell you what I’m drawing. It’s a map. It’s a treasure map to find treasure in the sand pit, but not at nursery, at home in my sand pit. Where I signed, that is the buried treasure’ (pointing to an ‘x’ on the paper). ‘I can’t tell you anything because it’s a secret!’

Finding another sheet of paper Elizabeth began to make similar symbols. Pointing to them she explained,’ that says my name. That’s James’s name and his second name and his third name. James’s second name is Thomas. My mummy had also got a second name called Elizabeth. My daddy also has a second name. I think it’s Roy.’

In both examples many of Elizabeth’s graphic symbols appeared letter- and numeral-like, with the addition of crosses. In the second example she enclosed each symbol, and then drew a box around all of them. According to Machón this period of experimentation and expansion of graphic symbols ‘is undoubtedly the most important in the entire graphic development’ [emphasis added], (2013: 95).

Machón A (2013) Children’s Drawings: The Genesis and Nature of Graphic Representation. Madrid: Fibulas Publishers.

Taxonomy: Making meaning in child-initiated play

  • Explorations with symbols

CONTEXT: Exploring symbols

Nursery: Ayaan - 4 years 2 Months

1. ‘A cat, here’s a cat. He’s got this’ (making another cross) ’she said. Her teacher wondered if she was thinking of a cat’s whiskers, when drawing red lines.

2. Ayaan was outside with a friend - Ayaan drawing large crosses on a whiteboard. She didn’t say what they were.

3. Ayaan watched as Tariq wrote a ‘T’ for ‘Tariq’, and then getting her own paper she made crosses on it (but without commenting on her marks).

4. Ayaan wrote these signs, reading them as her name. Perhaps she was combining the appearance of some Arabic letters with crosses.

Over a period of several days, Ayaan explored the versatility of graphical symbols, using crosses to signify various meanings.

Children’s increasing interest in the power and role of graphic symbols at this age supports their early writing and mathematical development, whilst cultural knowledge such as initial letters and names may also influenced by learning to write in another alphabet.

Taxonomy: Making meaning in social pretend play and imagination.

  • Exploration with symbols

CONTEXT: Imaginative Story and Football Scores

Nursery: Oliver - 4 years 0 Months

Oliver spent a long time on the whiteboard - ‘This is a dragon with lots of baddies.’ He drew large circular lines, explaining, ‘The dragon is fighting the baddies!’

Then he rubbed this out while talking to Remi and Emma about teams and football scores. Oliver listened and seemed to share understanding of football and scores. He made his own marks to represent the goals in an imaginary football game. Each mark that Oliver made related to a football score in their fantasy football game. Remi’s marks contrasted with Oliver’s, and included some letter-like symbols and scribble-marks.

Taxonomy: Making meaning in social pretend play and imagination.

  • Narrative drawing

  • Exploration with symbols

CONTEXT: spontaneous imaginative story-making - exploring symbols

The dragon story: nursery 3 - 4 years - Remi, David and Faith

Remi and David created their own story about a fire-breathing dragon using marks and drawings. Faith joined in, making signs to ‘block the dragon’; ‘These are checks (crosses) it means the dragon can’t go there. These are ticks – the people can go that way but not the dragon.’ Faith extended this, drawing long lines all over the whiteboard: ‘It stops the dragon coming. It like a jail!’

Faith’s symbols were an integral feature of her story telling, and graphical signs and symbols such as these are central to understanding and using the symbolic language of mathematics.

Taxonomy: Making meaning in social pretend play and imagination.

Written number and quantities:

  • Exploring symbols

CONTEXT: free play

The World Cup - Oliver 4 years 2 months

Oliver’s teacher Emma explained that this photo is from the time of the football world cup, which Oliver's parents and many families in the locality were watching and supporting. The nursery had invested in many different balls and goal posts that were eagerly taken up by the children.

Emma said, ‘These are Oliver's graphics in response to people scoring in the goal. He named the scorers after teams: England and Africa, England and Bristol. During this week, England had crashed out of the world Cup losing to Germany, this had served as great disappointment to supporters, creating a source of further discussion among the children’.

Taxonomy: Making meaning in social pretend play and imagination.

Written number and quantities:

  • Early explorations with marks: attaching mathematical meanings

  • Representing quantities that are not counted

  • Exploring symbols

CONTEXT: free play - exploring symbols

The power of writing: Amy and Tiyanni - 4 years

Young children’s ability to make sense of signs used in writing and other ‘literacies’ depend a great deal on their ability to freely use graphical signs in meaningful contexts for their own purposes of communication. In this example, Tiyanni and Amy were play together with the big blocks.

Amy’s writing
Amy explained their construction as ‘a trap’ and fetching a large envelope, she rapidly wrote a series of circles in rows from left to right. Amy described this as ‘writing’, explaining ‘it’s to say how to build a trap.’

Amy used circles as signs she knew (and perhaps considered to be writing-like): she was aware of the directionality of writing in our culture and attached to them the meaning she wanted to communicate to Tiyanni.

Taxonomy: Making and communicating meanings in social pretend play - graphicacy (drawing, maps and writing)

Tiyanni’s message
Closely watching Amy as she wrote, Tiyanni remarked admiringly, ‘You’re good at writing!’ Tiyanni went to fetch a large envelope too and drew a spiral and an enclosed shape, ‘reading’ them as ‘Please Tiyanni remember to bring some fruit!’ - something she’d heard staff in nursery say.

Tiyanni focused her attention on Amy’s facility with ‘writing’ perhaps impressed by Amy’s confidence and fluency.

Maintaining her interest in writing as a means of communication and completely ignoring Amy’s explanation of ‘how to build a trap’, Tiyanni wrote her own message with signs available to her and then read it to Amy.

Reflections on learning
Tiyanni seldom uses signs to communicate within her pretend play and this episode suggests powerful learning. It also demonstrates a significant point in young children’s learning - when they understand the relationship between signs and meanings, and take their own steps to communicate their personal thinking.

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