- Beginnings: explorations with intentional marks (number & quantity)
Graphicacy
We use the term graphicacy to encompass all aspects of visual signs and representations that children use, including drawings, children’s own maps, early (emergent) writing and Children’s Mathematical Graphics. Communication is not only through speech, but also through graphical signs and marks that are embedded in the history of us all.
For a fuller description, see: Graphicacy
Scribble marks
These marks and signs often include intentionally made scribble-marks and dots.
• The term ‘scribbles’ is largely used by adults as a derogatory term, suggesting that the person making them, shows lack of care or interest.
• We identified scribble-marks (and sometimes multiple dots) as one of the earliest means children use to communicate their mathematical ideas.
• We use the term “scribble-marks” to refer to marks that adults would find difficult to interpret without the child’s verbal explanation.
• Within their pretend play, children often use scribble-marks as “shorthand” for writing, seemingly so that the course of their play is not interrupted.
Scribble-marks are the foundations of drawing, writing and mathematical notations.
| Charlotte’s “hundreds and pounds!” Charlotte (4 years, 2 months) was with her friend Jessica in the nursery. They had each selected a piece of paper and chosen coloured pens, holding as many as they could in each hand. As they excitedly covered their papers with numerous dots, Charlotte told her teacher, “Look! I’m doing hundreds and pounds!" She was making connections with the large quantity of dots she had made. Charlotte’s reference to ‘hundreds and pounds’ suggests a quantity that seems a great deal to her: both ‘hundreds’ and 'pounds’ fit into her thinking about a lot. Charlotte used spoken language to express what her marks suggested to her, attending to the link between her marks and the mathematical vocabulary of quantity in a general sense.
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"Fifty pounds please" Stacey (3 years, 2 months) was playing in the little house outside, pretending to serve food. Picking up a pen and notebook she asked her friend, “What do you like?” Her friend replied “Chicken Tikka please” as Stacey began to make circular scribble-marks, dots and scribble-marks in her notebook, she asked, “Chicken and chips?” adding “Fifty pounds please".” Stacey’s friend pretended to give her some money, and in turn, Stacey pretended to put it in her pocket. Stacey drew on her home knowledge of ordering a take-away meal, clear in her understanding that orders were written down, combined with her knowledge of asking for and taking orders and money.
meanings
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 | Sam and the calculator Bradley was playing with a calculator, making marks as he pressed buttons on the calculator. Sam (3 years, 6 months) watched Bradley making marks on paper and decided to do the same, pressing several buttons and each time making his own marks on a piece of paper.
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Weighing David During a small group time featuring kitchen weights and bathroom scales, David stood on the scales. Isaac (4 years, 5 months) used his under- standing of a variety of measuring units to talk about David’s weight. As he made circular scribble-marks on paper, Isaac explained,“David weighs 700 kilos, he’s 60 metres heavy". Next David (4 years, 1 month) stood on the scales, and looking at the dial he announced, “I’m 15, so I need to write it down". He made some letter-like signs (as numerals) on the whiteboard (not shown here).
quantities: Early explorations with marks: attaching mathematical meanings
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| "I spell 80354" Matt (3 years, 0 months) had just had his third birthday. At home he sat on the kitchen floor near his aunt who was writing postcards. Matt announced that he was "drawing". He rapidly covered many sheets of scrap paper with a range of marks, some which he named as ‘drawings’ and others were written messages, explaining the content of each. Showing this piece to his aunt, he ‘read’ it as, "My number's 1, 2, 3, 5, 6, 7, 8, and 11", later, (showing it to his Mum), "I spell 80354". This was the first time that he had attached any mathematical (numerical) meanings to any marks he had made. At home reading books, using the computer and writing are all daily family events and part of everyone’s experience. This example shows that Matt understands that marks can carry meanings and are sometimes be used to represent numerals. Perhaps he was thinking about a phone number he’d heard, recalling it as a reference point for his number-string. Talk about how to ‘spell’ may also be something he’d heard discussed with regard to spelling and writing his brother’s name, or his own.
marks: attaching mathematical meanings
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