Problem Solving, Reasoning and Numeracy Evidence of mathematical mark making This PowerPoint gives an overview of young children’s engagement with mathematics in the environment. There are some examples of adult led experiences but many more of children using the materials around them in ways that can give us insight into their developing mathematical thinking. Children’s own initiated play is prompted by adults awareness of how to set up the environment to encourage and support children’s mathematical experiences. Over the time of the project adults have learnt how to model using and thinking about maths in more challenging ways for children. As a result of developing greater opportunities for mathematical mark making across the learning environment we were led to see how closely tied these opportunities were with pre-writing. We became increasingly aware that mathematical thinking and understanding is at a higher level than expressed and/or written examples and that by observing children’s play with maths we were better able to see their understanding and development. Examples were collected of mathematical mark making but adults observed a lot of mathematical play shows children (before and alongside this written evidence) using 3D objects as though they were making marks with them e.g. representing numbers and making the beginnings of calculations. In other words the marks are there but not in their written form. They present through use of other materials and resources and this PowerPoint gives many examples of this. Histon Early Years Centre February 07

Numbers as Labels and for Counting Uses number names and number language spontaneously An adult drew a chalk number line outside and modelled walking up and down it playing with the numbers. Children used this in many ways. This child engaged in kinetic learning of 1-1 correspondence.

Developing sorting, matching and mark making in a play environment Open ended activity. This is how the child choose to sort select and arrange. Here is an example of 3D objects being used in ways similar to mark making. Grouping the objects and making them into ‘sets’ with marks to define them shows her ability to classify objects according to her own criteria. Time and again we see these concrete experiences have to happen before representing the objects as marks. Mark making on it’s own would not have shown this child’s ability to sort and classify. Using concrete resources shows a higher mathematical knowledge than children are able to show in mark making. From our observations we believe children continue to need these concrete experiences to represent their mathematical thinking for a long time both before and whilst they are developing their ability to represent through marks. Developing sorting, matching and mark making in a play environment

Uses some numbers and matches quantity correctly The children used the dominoes in different and unexpected ways. They shared their mathematical thinking and language. Here they matched the numbers they found on top of the same numbers. The child on the right has used squared paper. She coloured in chosen squares, counted them then checked by reading numbers on the keyboard. Here we can see the resource of squared paper and keyboard have been vital to this child's play. We learnt from this and provided more opportunities for mathematical play by including these kinds of resources in other areas inside and outside. Another enabling factor was her ability to combine resources. It sounds obvious, but making resources readily available on open shelves or in accessible drawers AND allowing children to gather resources together from different areas AND modelling this, will enable their mathematical development far better than pre- selecting everything.

saying and using them in a correct order Recognising numerals, saying and using them in a correct order The child on the left hasn’t begun to mark make with mathematical representations yet but uses magnetic numbers to show he is well able to recognise numbers and number order. His sequencing is the same as the child on the right who is able to represent his thinking on paper.

Pre-mark making skills Showing a curiosity about numbers and numerals Through these tactile experiences the child is feeling the number having pressed it into the dough.

Showing an interest by making arrangements with objects Again the children are using these large dominoes in unexpected ways. Children need to feel safe using things in different ways to be able to support their own play and thinking. Adults modelling using resources in different ways and feeding back to children about how clever they are to ‘make up that game’, helps them to move away from the idea that there is a ‘right way’ to use what we provide for them.

Making a number line with children is fun! Number lines using children puts them right at the heart of the maths! Counting up to three of four objects by saying one number for each item Making a number line with children is fun!

Recognise some numerals of personal significance This stocking has a house door with a number 11 on it so that Santa knows which house to come to The children had templates of stockings. This child drew the door of her house with her house number. The example shows how children will learn through materials they can personalise and that have meaning to them.

Using numbers by the same child within a few days of each other both inside and outside. Notice mirror writing. This child drew numbers on both squared paper and paving stones, both within a few days of each other.

Squared paper often interests children who are not keen to make marks Modelling writing registers and providing some templates etc leads children to use paper in different ways, often ways that link with real world purposes.

Adult modelling of mark making; then the child engages physically by jumping and counting. Other children mark make with chalk and brushes The children’s chalk lines mimic the adults modelling.

Show curiosity about numbers by offering comments and asking questions The first photo shows a child drawing the three bears in front of her, she illustrates their different sizes. The second photo shows a complex sorting and distribution of a group of objects in the child’s own small world play. There is no mathematical mark making but the maths is quite sophisticated. She pairs the people in the beds and then allocates one paper blanket for each pair. Again she combined resources , blocks, play people and paper, collecting what she needed from different areas.

Using mathematical tools for measuring and mark making Having maths resources readily available is essential. A ‘Maths tool kit’ is a good way of doing this. See Maths tool kit in the resources section of our website.

Know that numbers identify how many objects are in a set This child shows something so close to mark making, or perhaps one can call it mark making, just not on paper. There is a number 6 on the stamp and she makes 6 worms. These tactile experiences and being able to move the ‘worms’ around would have contributed significantly to her learning. Just as so much of young children’s learning is multi sensory so are their ways of counting and calculating numbers. Again we can see the understanding is there without having to see it written down.

Tallies We add templates, registers etc to role play inside and outside, along with clipboards or notepads. In the second photo an adult has modelled using a register and a child has made marks for who is present.

Show curiosity about numbers by asking questions and offering comments This child said her phone number and pressed the corresponding digits on the defunct phone Again providing appropriate resources allows children to transfer their home experiences. Here her maths supported and added meaning to her imaginative play.

Match, then compare the number of objects in two sets This child is comparing the two groups of objects and saying which has the most of each fruit. An adult’s open ended questions led the chid to compare and contrast. From this the adult was able to assess her knowledge.

Children using 10 in the bed song book, then problem solving and then being given squared paper to remember activity. During free play these children enacts 10 in a bed using teddies and a tray that they had collected. An adult added paper saying ‘how can we remember..’. Using the squared paper they marking the play on paper.

Say and use number names in a familiar context Matching of numbers, measuring with blocks, enclosing, and making a parking space with lots of parking tickets Developing enclosure schema

Begin to categorise objects according to properties such as shape or size Bowls and collections can lead to open ended activities of sorting and classifying.

Sorting objects, making choices and justifying decisions The resources were provided together here and led to colour matching, grouping and numbering.

Share objects into equal groups and count how many are in each group This child made a pattern then transferred it and made a new pattern lifting the tiles to the next tray and seeing the new pattern she could make from the old.

Shape, Space and Measure An adult set up a random collect of objects and asked children to choose 3 and how would they would remember their choice. Some drew around the objects, some looked at them and tried to remember them and others made marks to remember them.