Children develop a really clear understanding of mathematical concepts and an acquisition of skills through experiencing practical activities. They develop their mathematical language by hearing practitioners use it appropriately, by learning to use it themselves, and by exploring ways of recording their mathematical understanding, whether it be with a picture, a construction or a movement. The initial stages of finding out about shape include the understanding of proximity (how close together objects are) and separation (how far apart they are).Young children very often enjoy taking things apart, putting them together, arranging and re-arranging objects, and it is through these practical activities that they form their first concepts of shape and space. They use their senses to investigate colour, texture and features of objects such as those with holes in, for example, a slotted spoon, an airflow ball, a tennis racquet, or a colander. They explore items with flat surfaces, curved surfaces, solid shapes, shapes that bend or twist, and many settings create interesting interactive displays for the children to explore each concept separately. Discussing differences between items (size, shape, texture, flexibility) encourages close observation and development of appropriate vocabulary. Children find looking for differences much easier than looking for similarities! Saying “What can you tell me about these two shapes?", or “Can you tell me one thing that is different about these shapes?” will, at first, be difficult for the children to answer but with practice, they will find these open-ended questions easier to tackle. Children need to be encouraged to see shapes around them, eg windows, cereal packets, baked bean tins, or a suitcase. We can help children to develop their understanding of shape by asking open-ended questions, such as “How else can the pieces fit?” or “Where else can this piece go?” or “What other ways will this piece fit into that piece?” Questions such as “What if….?” encourage children to try out different ideas, for example “What if you turn it around? What if you turned it over? What if you bent/twisted it?” If practitioners describe what it is the children are doing, or what they themselves are doing, children will learn to express themselves in similar ways, As Nicola Call states, One of the most effective methods of enriching and accelerating learning is called “pole-bridging”. Pole-bridging is talking your thoughts aloud, describing what you are doing as you are actually doing it (2003; p.85) So by saying things like “If I put this red brick on top of the biggest blue box, …”, we are giving children the very tools they need to link language to their experience. Sorting and classifying 3D shapes usually comes before knowing the names; babies and very young children like to stack cylinders on top of each other, discovering that flat ends can stack easily. We, as practitioners, need to use mathematical vocabulary constantly and consistently, as the children grow older; “The ends are round and flat aren’t they? They are called circles”. In this way, children begin to learn about the properties and names of 2D shapes. Language such as flat, curved, round, points, corners and edges will help children to learn about shapes which roll, stack or slide. They will learn that certain shapes are not suitable for stacking purposes, for example, cones, pyramids and spheres. Seeing the nets of 3D shapes is always a fascinating experience, particularly if we provide activities where they dismantle familiar objects such as cereal boxes, and flatten them. Allow them plenty of opportunities to construct and deconstruct the boxes, by carefully taking them apart at the seams. Posting boxes manufactured for very young children are perhaps the first toys where children are encouraged to match a 3D shape with its 2D hole. Children need opportunities to explore lines which are straight, curved, looped, zigzag, thick and thin, long and short. Drawing around objects helps children to understand the concept of shape enclosure. Tracing around objects on paper, in the sand tray or in shaving foam, printing with solid shapes and using sewing cards are all good activities for children to engage with lines. Learning about lines through the use of computer games, programmable toys and art packages allow children to explore forward, backward and turning movements, and to investigate creating and manipulating shapes, infilling with colour. Most settings offer a huge variety of activities for children to learn about 2D shapes; making pictures with gummed paper shapes, mosaic tiles, magnetic shapes, fuzzy felts, jigsaw puzzles are used alongside appropriate mathematical language. Children like to sort and name 2D shapes, including everyday shapes like moons, stars, animals and transport shapes, and they take satisfaction in creating pictures which tessellate (shapes that fit together with no gaps, eg a regular hexagon). Observing familiar objects from different viewpoints is a wonderful activity for young children; encourage them to use a digital camera to photograph objects in your setting from above, below, and from a sideview. Massive scope for the use of positional language! And don’t forget, your movement or PE session is the perfect arena for the use of positional language. In role play or small world play, we can reinforce the children’s learning by asking “Can I buy the tin of beans from the top shelf please?” or “Is the teddy hiding behind the tree?” Investigating reflection and symmetry with the use of mirrors is an activity young children like to take part in. Cutting out pictures of faces, minibeasts, butterflies, flowers, etc., cutting them in half, and encouraging the children to make the other half with a mirror is a nice activity, as is cutting symmetrical pictures in half for matching activities. The ubiquitous blot painting on folded paper is usually a winner too! Helping children to use mathematical language correctly Model correct language regularly and frequently, by describing what the children are doing as you work alongside them, eg “Ah, you made the car go straight ahead and then turn left around the corner”. Encourage the children to talk to adults and to each other about what they are doing. Value children’s spontaneous language, eg “My shape has three pointy bits”. Extend what children have said in different ways, eg “Yes, it’s got three corners”. Set up activities that encourage children to describe and explain, eg “How do you know it is the box/ball/piece of string inside the bag?” Provide opportunities for children to estimate, predict, and hypothesise, “Will that lorry hold one more brick?” or “How many cubes can you hold in your hand?” What does the EYFS Practice Guidance tell us? The guidance states that settings should "develop mathematical understanding through all children's early experiences" (2007; p.62). So, how do we, as practitioners, plan for learning and teaching in this area of the curriculum. Firstly, we need to bear in mind the following: Effective learning involves children enjoying mathematical learning because it is purposeful. Effective learning is learning which is consolidated and extended through games, and gives children opportunities to practice their mathematical skills and knowledge. Effective learning involves children being confident and enthusiastic to join in with or talk about mathematical activities. Effective teaching requires practitioners who help children to see themselves as mathematicians, and develop positive attitudes and dispositions towards their learning. Effective teaching requires practitioners making good use of opportunities to talk mathematically as children play or take part in normal daily activities Effective teaching requires practitioners encouraging children’s mathematical development by intervening in their play Effective teaching requires practitioners developing children’s thinking by showing an interest in methods, not just solutions (requests such as “Tell me how you made your model” (Curriculum Guidance for the Foundation Stage, 2000, p.70-72) To ensure that our settings provide the rich environment the children need, staff need to be give time together to discuss how to support the children in their mathematical learning. We need to be looking at the resources and activities provided, and deciding upon the language practitioners can use alongside these to encourage the children to be confident mathematicians. What language do we need to be using? The following list contains the mathematical language that we should be modelling for the children. Frequent exposure will encourage the children to use the vocabulary themselves. Counting and recognising numbers Number Zero, one two…. to twenty and beyond Zero, ten, twenty, ….to one hundred None How many? Count, count up to, count on, count back (from, to) More, less How many times? Pattern, pair Guess, estimate Nearly, about the same as Just over/under Too many/few, enough/not enough Comparing and ordering numbers More, larger, bigger, greater Fewer, smaller, less Compare, order Size First, second….fifth Last Before, after, next, between Adding and subtracting Add, more, and Make, total, altogether Take away, leave How many are left? Exploring patterns, shape, and space Shape, pattern, repeating pattern Flat, curved, straight, round, corner Face, side, edge, end Hollow, solid Sort, make, build, draw Circle, square, rectangle (oblong) star Cube, pyramid, sphere, cone, cylinder, cuboid Bigger, larger, smaller Over, under, above, below Top, bottom, side On, in, outside, inside, around In front of, behind Front, back Before, after, beside, next to Opposite Between Left, right Up, down Forwards, backwards, sideways Along, through, towards, away from Move, slide, roll, turn, stretch, bend Assessing children for mathematical learning in shape and space How do we know what our children can do? We need to observe them closely in their play, and we also need to know what we are looking for. The following is not a list to be checked off for each child, but some ideas of things to look out for when you observe your children. The child: Can identify same and different Sorts consistently according to one/two criteria Can describe different reasons for sorting Uses vocabulary to describe colour, texture or other features of shapes Describes differences between shapes Describes similarities between shapes Fits pieces together and takes them apart Can describe model using some shape or positional vocabulary Use movement vocabulary to describe properties of 3D shapes (roll, slide, stack, balance) Can describe simple properties of 2D or 3D shapes Can recognise faces of 3D shapes Can name simple 2D and 3D shapes Can rearrange and reshape modelling materials Makes lines in a variety of ways. Follows instructions which include positional language Can describe an order using words such as first, next, last, etc. Can make line patterns Can copy a pattern Can extend a pattern Can explore reflection and symmetry Children learn mathematical concepts by doing, then by doing and hearing, and then by doing and saying. As Foundation Stage practitioners, we must not feel pressured to get the children writing numbers, etc too quickly; we can provide evidence of quality mathematical learning through observation notes and through photographs of the children engaged in their everyday play, exploring mathematical concepts and being supported in their learning by knowledgeable practitioners. Bibliography Curriculum Guidance for the Foundation Stage (DfEE, 2000) Practice Guidance for the EYFS (DfES, 2007) Call, N. (2003) The Thinking Child Montague-Smith, A. (2002) Mathematics in Nursery Education
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