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January 2012 |
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Jazper - 3 years, 6 months.
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Images and ideas often
appear to combine in ways that can seem unlikely to
adults. For example, pointing to different features
in his drawing, Jazper explained ‘Red lorry, blue
car and road’ then added ‘lots of eyes.’ Jazper’s
drawing seemed to combine elements of both a drawing
and a map (perhaps too with an unspoken narrative).
In rich learning cultures, children use graphical
representations to communicate for a variety of
purposes - including imagination, pretend play and
everyday contexts. Such rich experiences help them
come to see that they can also use their marks and
symbols to explore and communicate their
mathematical thinking.
Making meanings in
imagination and symbolic play: drawings / maps |
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December 2011 |
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Stacey’s café
This lovely example demonstrates a
highly significant aspect of young children’s
development, as they begin to use graphical marks
and symbols to communicate a range of ideas and
purposes, including their mathematical thinking.
Stacey
(3 years, 2 months) was playing in
the little house outside.
Picking up a pen and notebook she
asked her friend, ‘What do you like?’
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Her friend replied ‘Chicken Tikka
please’ and as Stacey began to make circular marks,
dots and other marks she asked ‘Chicken and chips?’
adding ‘Fifty pounds please.’ Her friend pretended
to give her some money, which Stacey put in her
pocket.
Stacey drew on her home knowledge of
ordering a take-away meal, clear in her
understanding that orders were written down in the
restaurant and integrating her understanding of
asking for and taking orders, and money.
Written number and
quantities: early explorations with
marks - attaching
mathematical meanings |
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November 2011 |
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Nursery – Rio’s
parking tickets
Rio (2
years, 2 months)
Rio was playing outside
with his friends: they were talking about parking,
and Rio spontaneously made himself some parking
tickets, drawing scribble-marks on gummed labels.
Written number and
quantities: early explorations with
marks |
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October 2011 |
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Nursery - a
spontaneous ball game
Henry, Joe and Thomas:
4 years, 4 months - 4 years 7 months.
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These are just two of
the many graphical signs that these boys generated
during the course of their game. These abstract
symbols have personal meaning for the children
within the context of their play and support their
developing understanding of the power of graphical
symbols. |
'This means you lose' |
'This means you double lose' |
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Written number and
quantities: explorations with symbols |
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September 2011 |
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Max’s card-girl
(reception)
Max cut two tiny
rectangles of paper and joined them at the top so
that he could open and shut them. Drawing a face on
the uppermost piece he announced that his artefact
was a ‘card-girl’.
Although we might regard
this as either a ‘drawing’ or a ‘card’, this hybrid,
multimodal artefact suggest it could be moved and
played with as a prop in Max’s imaginative play, as
a small puppet or person.
We all make meanings in
multiple and complex ways and when considering young
children’s meanings, it can be helpful to think
beyond single definitions such as ‘drawing’,
‘writing’ or ‘models’.
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Multimodal meaning
making: combining paper model and drawing
(with potential for movement and voice - as a puppet
or toy) |
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August 2011 |
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Caravans at snack
time (nursery) |
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At snack time
Harry (4 years, 5 months), initiated a
conversation about his experience of staying in a
caravan. Since some of the children had not stayed
in a caravan, Harry decided to represent the one
he’d stayed in to help them understand what they
were like. He showed the ‘two wheels’ and wrote the
‘long number’ on his caravan ‘12148’.
Written number and
quantities: representing quantities that are
counted; early written numerals; numerals as labels.
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Finnian (4
years, 1 month), wanted to represent the caravan
he’d stayed in too. He showed that there were many
caravans on the site where he’d stayed, and that
they were all very close together. The caravan he
drew at the top of the whiteboard show him, standing
on the sofa and looking out of the window.
Written number and
quantities: representing quantities that are
not counted |
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July 2011 |
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Kyran’s drawing of
his mummy (nursery)
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Commenting on this
drawing, Kyran said‘ she’s got funny hands!’
Developing from the
‘generational structures’ that John Matthews
identified (1999), children are influenced by signs
that have strong visual impact and distinct cultural
uses in their culture. They make choices and
decisions about the symbols they use to encode and
communicate specific meanings and some of these
become signs that others understand and accept.
It appears that some of
the most powerful signs that young children use
include zigzags, crosses and arrows. |
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Other examples include
children who used crosses to represent an aeroplane;
to emphasize ‘No! Keep out!’; to signify ‘shop
closed’; to identify someone who has lost in a ball
game; as kisses on a birthday card and to signify
items on a shopping list.
In communicating
mathematical ideas, individuals used crosses to
identify peers’ choices (data handling); to cross
out items (denoting subtraction) and later as an
addition sign. This flexibly also supports
understanding of standard abstract signs such as ‘x’
(as a letter and as a multiplication sign); letter
‘T’ and ‘t’ and the numeral ‘4’.
Kyran -
making meanings with marks: explorations with
symbols
See also:
Gallery 4: CM
Graphics of Past Months |
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May 2011 |
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Early bi-literacy:
‘bi-literacy’ refers to children and adults who
combine their first and second languages when
writing. Drawing and writing are aspects of
semiotics that also use abstract symbols. |
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Lay Hau Yun’s home
language is Cantonese. This example shows how she
represented her name twice, first as a zigzag line
(top left) as many young children do in English, and
then on the right, in Cantonese characters. On
another occasion whilst playing, she was writing
numbers as she counted, beginning ‘1’ and ‘2’ and
following this with the written Cantonese character
三 for ‘3’, integrating her knowledge of both written
languages.
Emergent writing:
explorations with symbols |
See also:
Gallery 5:
Beginnings in Play |
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April 2011 |
Written number and
quantities: early written numerals; numerals
as labels; explorations with symbols; representing
quantities that are not counted |
Finnian’s age
(nursery)
Finnian was aware that he was younger and smaller in
stature than the other children in his group.
Taking a pen Finn emphasized his exact age on a
nearby whiteboard explaining ‘I’m not three
and a half! I’m three and three quarters…
Look. This is how you write ‘three and a half’ [the
line of symbols at the very top] and this is how you
write ‘three and three quarters’!’ [the remaining
symbols in the centre and lower down].
Not
only had Finnian used symbols to explore fractions,
he understood (and used) symbols to persuade. |
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March 2011 |
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Amelia's Shopping
List
In the nursery Amelia
was playing shops, busy organizing things and
chatting happily to her friends. As she made marks
and letter-like symbols she said, ‘Chocolate
biscuits, rice pops, sausages’.
Amelia appeared to be
listing foods she liked to eat and that her mummy
bought when they went together to the supermarket.
Written number and
quantities: Attaching meanings to marks
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February 2011 |
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In the nursery Oliver
was exploring rulers and set squares with his
friends. One of the children used a ruler to draw a
triangle and then pivoted the set square, using it
as a template to get the shape he wanted. Oliver
used the rulers to measure the length of the table,
lining them up carefully in a straight line and then
using them to draw across the table. Others enjoyed
freely drawings across the length of the large sheet
of paper. The
children used a great deal of mathematical language
as they chatted about their lines, shapes and
drawings, developing their understandings of
measurement and shape. Their free play enabled them
explore aspects of measurement in open-ended ways.
Written number and
quantities: early explorations with marks;
representing quantities that are not counted |
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January 2011 |
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Shakkai’s Dad
Shakkai
laughed as he showed his friend that he’d drawn his
dad with ‘4 eyes’, then decided that he’d draw
another, saying, ‘I’m going to add another eye.
Look! He has 5 eyes now!’ and the boys laughed and
laughed about Shakkai’s drawing.
Written number and quantities: representing
quantities that are counted.
Calculations - children’s own methods:
counting continuously. |
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December 2010 |
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Liana’s ‘picture for my mum’
Young
children’s drawings are an important aspect of
graphicacy. Liana’s drawing began as a story might:
‘it’s a rainy day’ to set the scene, continuing as
Liana listed items ‘Here’s a small flower, here’s a
bigger flower. This is a scarecrow; a house; a
balloon and an apple’.
We can
also see that naming items appeared to be important
aspect of this, so it almost represents a list or
inventory. |
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November 2010 |
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Mason’s Spy Gadget |
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Intrigued by new media, new
technologies and popular culture, Mason was now a
champion of ‘21st century’ play and this
example shows how he also drew on his knowledge of
password protection and access, numbers and writing.
Mason watched Leola who was cutting a piece of card,
and finding a piece of yellow card, he also folded
and snipped similar cuts around its perimeter. Next
he wrote letters and numerals, reading 'sk’
‘714bp10’ and, lifting it to his face, explained
it was ‘a spy gadget… 'sk' is ‘to keep the
password safe. To switch it on you have to say
'714bp10'’. I asked if there was a way to switch
his 'spy gadget' off and picking it up he replied
excitedly 'Yeah! You have to read it backwards!'
promptly reading, '10
pb417'. |
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October 2010 |
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Nathan’s astronaut -
nursery
 Nathan
was in the art area, exploring an idea of his own.
Taking a white envelope Nathan tucked coloured paper
beneath the flap of the envelope, securing it with
masking tape. He explained that the coloured paper
was an astronaut, and the envelope was his suit: the
tape allowed the astronaut to undo his suit (the
flap of the envelope) and climb out of the space
suit.
Nathan accompanied his spoken explanation with
actions, moving his model rapidly above his head in
a trajectory to ‘the moon’; saying ‘blast off!’ and
making a whooshing sound as, in his
imagination, the rocket left earth.
Although the meaning of Nathan’s astronaut was not
immediately accessible to adults, the artefact he’d
made and his words and vocal sounds combined with
his actions and explanation to make symbolic
meanings. |
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September 2010 |
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One is a snail, ten is a
crab
After
sharing the delightful picture story book One is a
Snail, Ten is a Crab with the children in her
combined nursery and reception class (4-5 year
olds), the teacher suggested that the children
choose their own number and work out which
combination of creatures’ legs would total their
chosen number.
 Tyrees
burst out ‘I know why 10 is a crab, because it’s got
10 legs – see, 1, 2, 3, … 10.’ Then added, ‘I know,
9 could be an octopus and a snail.’ He explained he
was going to work out which ‘800’ and reaching for
some paper wrote ‘800’, after a while explaining
that he had 4 crabs and 4 snails ‘that’s 10, 20, 30,
40 and 4 more – 44! That’s not the 800 – I need
loads more so I think I’ll do more crabs ‘cos
they’ve got most legs.’
He
continued to draw ‘There, I done 6 more crabs.
That’s 10, 20, 30, 40, 50, 60 and 40 – there’s 100
and 4 more snails – that’s 104.’ Pausing, Tyree
decided ‘I don’t think I’m going to do any more
because it’s too big. I need 6 more so I can do 6
snails, or a dog and 2 snails, or 3 people – but I’m
just going to do a fly because that has 6 legs.’
Calculations: children’s own written methods:
counting continuously, separating sets, counting
with larger quantities
Their
teacher described this as a real ‘eye opener’: this
was the first time she had tried to support
children’s use of their own graphics to support
their mathematical thinking. She regarded the
children’s self-challenges and their individual
problem solving as remarkable. |
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May
2010 |
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James is
a young four-year old and in his first term at
school. Registers have personal meaning to young
children as they think about their peers and
identify each, enacting the teacher’s role. At
nursery and school writing ‘registers’ is often a
preoccupation in children’s play.
In this instance James has used a range
of letter-like signs, written from left to right. He understands
that writing in our alphabetic script uses different letters and has
thought about some of their features. He also includes short
zigzags, perhaps encoding his sense of the appearance of cursive
‘writing’, or capturing the movement of an adult’s hand as she
writes, |
James - 'Seeing who's
here'
Imagination and
symbolic play: making meaning with marks for
writing
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March 2010 |
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Megan: “A very
big fast roller coaster!”
Megan is in the reception class (the
first year of school in England). This was the first of three
drawings Megan drew at home about fairground rides, including a
Ferris wheel and ‘a runaway train’.
Megan’s drawing suggests the route the
roller coaster took, its undulating and rapid movement and shows its
many seats. Megan told her mum ‘This is a very big fast roller
coaster!’ Her mother explained ‘Megan was thinking about how much
she’d love to go to a funfair again’.
Megan recalled some of the different
rides with excitement and used the drawings as a means of persuading
her family that they should take her again.
Communicating meanings through
graphicacy
Children use their graphics for a wide range of communicative
purposes, to sometimes face and explore anxieties and to feel in
control or to develop, negotiate and justify their sense of
belonging (in their family and peer group).
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They reveal how new
media, technologies and popular culture exert
influence on both their feelings and their
representations and – as in Megan’s example – they
show how children also use their graphics to
persuade.
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February 2010 |
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Max
(Nursery)– ‘Yoda’s house
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Max drew on his personal interest of the ‘Star Wars’
films in his representation of ‘Yoda’s house’.
Although he didn’t give any explain for the details
he had drawn, his drawing suggests a plan or a map,
with various featured identified by their location
on the page and their relationship with each other.
The outer green circle suggests that Max was
thinking about the inside of Yoda’s house,
and the different arrangements and shapes (of lines
and other abstract symbols) suggest that he used
them to convey very specific meaning).
Max included an arrow pointing inwards (lower
right). Our research has shown that arrows play a
distinct role in children’s own early calculations.
see:
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Carruthers, E. and Worthington, M. (2008)
'Children's mathematical graphics: young
children calculating for meaning' in I.
Thompson, (Ed.) (2008) Teaching and Learning
Early Number, Maidenhead: Open University
Press, (2nd ed.).
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December 2009 |
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Daniel's Sign
'Shop Closed'
In the nursery, Daniel had been playing
shops and decided to make a sign to show when the shop was ‘open’
and another to show that it was ‘closed’. His teacher had noticed
what he was doing and Daniel explained:
Daniel: It’s closed now, the café is
closed
Adult: How do I know it’s closed?
Daniel: Look here, see? Closed, that means it’s closed.
Daniel pointed to his drawing of face
crossed out on chalk board and rubbing it out he drew a smiling face
without a cross:
Daniel: Look! Open that means its
open now... Oh dear...
Drawing a cross over his drawing of a
face he explained 'it’s closed'.
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Young children use
crosses in a variety of contexts to signify
different meanings in drawings: they also use them
to stand for writing. This flexibility of sign-use
is highly significant in supporting children as
their understanding of the abstract written language
of mathematics evolves. |
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November 2009 |
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Nathan's 'Writing'
See also:
Aman’s boat |
Children sometimes also
use a particular symbol to mean one thing in one
context, and then use it to mean something different
in another context. For example, on one side of his
paper (not shown) Nathan drew a horizontal line with
zigzags as his ‘birthday cake’ (his mum made a
‘caterpillar’-shaped birthday cake for his 4th
birthday). Turning his paper over, he repeated the
same lines and zigzags (figure 4) now referring to
them as ‘writing’.
Other children may use
zigzags to signify fierce animals (e.g. crocodiles,
monsters); lightening; water or stairs. They are
generalising about a graphical sign and also
understand that they can be used flexibly. You may
like to look out for lines, crosses and other
symbols in children’s graphics (e.g. drawing,
writing, maps and mathematics).
For more examples,
see: Worthington. M. (2009) 'Fish in the water of
culture: signs and symbols in young children’s
drawing', Psychology of Education Review Volume 33,
Number 1, March 2009. |
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October 2009 |
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Felix's Marks
Felix (4 years 1
month) used pens to make these busy marks. Afterwards he explained
it was ‘night-time’.
Young children
often attach their own meanings to their graphics after
noticing something in their marks and representations.
The pedagogical
feature that appears to contribute most to imaginative, symbolic
play (and to their understanding of symbolic marks and
representations) is adults’ interest in children’s meanings
(Worthington, 2009, paper submitted for PhD) –
unpublished. |
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