‘Raising the quality of teaching and learning within the area of children’s development that leads to written calculation’.

Case-studies from some of the settings involved in the Cambridge Nursery Mathematics Learning Network (2005 – 2007)

Note: descriptions in assessment sections of each child’s example in italics relate to the taxonomy

Charlotte: 4 years 3 months

Context: After some children had shown an interest in watching the class teacher filling in the register, squared paper had been put into the mark making area.

Observation: Charlotte began making mark in the squares of the paper. She then began to select children’s name cards and copy the names from them into the squares down the left side of the page. After a while, she said, “I just need three more, then all the boxes will be full. She then showed the complete page to the teacher and said “That’s so I know who to invite to my party”.

Assessing the child’s mathematical graphics: Charlotte was able to make one mark to represent each child. She knew how many more she needed to fill the spaces. She understood the purpose of her marks.

Charlotte represented quantities that are counted to help her think about how many children she was inviting to her party.

Helen: 3 years 8 months

Context: Helen was at the easel alongside a friend, drawing with large marker pens.

Observation: Helen spent a long time drawing with her friend. She repeatedly made crosses and was heard to say ‘I think I’ve made hundreds of kisses. How many do you think you have made?’ She accompanied the drawing and the kisses with other mark making.

Assessing the child’s mathematical graphics: Helen used iconic marks to represent quantities that are not counted to help her think about a large quantity of ‘kisses’ that she had drawn.

Isla: 4 years 4 months

Context: Isla was playing at a table with paper, pens, numbers and ‘compare bears’ with a friend during a free play session.

Observation: Isla concentrated for a long time as she made all these marks and chatted to her friend. She looked up and seeing the practitioner said, ‘I’m writing lots of numbers. I’m teaching all the children how to write their numbers because I already know how to write numbers and they might not know’.

Assessing the child’s mathematical graphics: Isla understands that numerals can be represented with individual symbols and enjoyed exploring her understanding through use of her own early written numerals.

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Julie: 4 years 3 months

Context: Julie had chosen to play in the ‘baby clinic’ role play areas. An adult had been playing alongside the children modelling ways of recording the ‘babies’ weight and height.

Observation: Julie weighed her baby on the scales and made a mark on her booking sheet in the appropriate space; she repeated this after using a tape measure to check the baby’s length. When she wrote the baby’s age she said ‘6’ and made 6 distinct tally marks (iconic).

Assessing the child’s mathematical graphics: Julie understands that quantity (representing mass) and numerals can be represented with symbols.

She used her own early explorations with marks and represented quantities that are counted to represent her personal meanings as she weighed her baby.

Angus: 4 years

Context: Angus had chosen to play in the graphics area alongside his friend Ben during a free play session.

Observation: Angus found two travel cards and wrote three numbers on each card. He said ‘Look, these are my scratch cards’. The adult asked him which numbers he had written and he replied ‘One, one, zero’.

Assessing the child’s mathematical graphics: Angus made personal mathematical meaning about the scratch cards he had come across at the shops, representing his numerals as labels.

Raymond: 4 years 2 months

Observation: Raymond chose to go into the office area saying, ‘I need to write a shopping list because after Nursery I’m going to Tesco with my Mum to do lots of shopping’. He selected a piece of squared paper then proceeded to write his shopping list and explained, ‘I have a lot of different things to buy.’ When asked what they were he stated, “Look! Lots of things, and I have put my name at the top of the list.” This showed his awareness of large quantities of items.

Assessing the child’s mathematical graphics: representing quantities that are not counted, Raymond explored his own meanings about buying ‘lots of things’.

Ella: 3 years 8 months

Context: Ella was playing inside in a small group of 4 girls

Observation: Ella had selected a clipboard, pencil and paper from Assessing the child’s mathematical graphics shelf. She then picked up a tape measure, went over to Alice and said, “What’s your size?” She used the tape measure, holding it against Alice, to measure her, and then made letter-like marks on her paper to show what she had measured.

Carol: 4 years 5 months

Context: Carol wanted to count the children sitting in her group at snack time, (the key worker had been modelling different forms of representation during the previous couple of weeks.)

Observation: Carol chose to draw faces to represent the girls present and circles for the boys. After drawing the pictures she then also chose to add numerals. She counted the number of items in each group and wrote the total.

Assessing the child’s mathematical graphics: using pictographic and symbolic marks, Carol represented quantities that are counted to support her understanding of how she might represent the children who were having snacks.

Isabel: 4 years

Context: In the model making area where there is a wide range of materials and resources from which to choose.

Observation: Isabel selected a flat box and cut it with scissors so that it opened up with a lid. She glued various smaller items onto it.

She then spent about ten minutes writing numbers over the inside of the box, explaining “I’m making a computer”.

Assessing the child’s mathematical graphics: Isabel knows computer keyboards need numbers and wrote some numerals on the computer she made.

She used numerals as labels to complete her computer.