An overview of research and advice about developing mathematical learning 0-5 years is provided in this online guidance from the University of Cape Town in South Africa. http://www.wordworks.org.za/wp-content/uploads/2017/01/More-than-Counting_web.pdf
Their definition of mathematics may be helpful. The booklet is freely available, very readable and packed with ideas for activities.
“What do we mean by mathematics?
Most people associate mathematics primarily with arithmetic – numbers and calculations.
The terms ‘numeracy’ and ‘mathematics’ are often used interchangeably but the term mathematics should be used to describe the broad subject area of mathematics concepts, skills and applications. Numeracy refers to the everyday uses of mathematics, and includes the ability to reason and to apply simple numerical concepts, such as addition and subtraction. A person with adequate numeracy skills can manage and respond to the everyday mathematical demands of life; in other words, numeracy is an essential life skill in the same way that reading and writing are.
Babies start to make sense of the world in mathematical ways from birth, recognising the difference between small numbers of objects and identifying familiar shapes and patterns in the environment around them. Toddlers and young children continue to develop early mathematics concepts in the early years, through for instance, ordering, matching and classifying objects, and developing and using ideas about shape, space, time and measurement. Although these concepts might not seem mathematical they are important emerging mathematical insights for the growing child. In addition, mathematics provides a powerful means for organising insights and ideas about the world in systematic ways that include describing and representing quantities, collecting information and problem solving.
Mathematics becomes most real and comprehensible for young learners when it develops out of everyday situations and experiences. Mathematical learning can be found and conveyed through many home and classroom activities, and facilitated by teachers, parents and carers in simple ways. In all early years settings, including the home, children can be helped to learn about mathematics through play (for instance, with blocks, sand and water), shared storybook reading, pretend or make-believe games, as well as through their participation in everyday routines and situations, such as going shopping or sharing sweets. Children can also make connections between mathematics and musical experiences, like rhythm and keeping time, and art, when they explore visual patterns or symmetry.
Structured mathematics learning for young children should therefore extend far beyond counting and number concepts, and also include introducing children to the concept areas (such as number, patterns, space, shape, measurement and data handling) and specialised language, which they will require for successful mathematics learning from Grade R onwards.” Page 5., Kuhne et al Much more than counting: supporting mathematics development from birth to 5 years University of Cape Town Schools Development Unit email: [email protected]
| Element | Knowledge/ Experiences/ Strategies/ (Evidence) |
| Background/ Theory | The 2030 agenda for sustainable development aspires to a world with Universal numeracy. Sustainable development goal 4 relates to inclusive and equitable education for all and includes the statement ‘ensure that all youth and a substantial proportion of adults, both men and women, achieve literacy and numeracy’ (United Nations, 2015). At the most fundamental level, literacy and numeracy constitute a foundation for developing higher-order cognitive skills, such as analytic reasoning, and are essential for gaining access to and understanding specific domains of knowledge (OECD, 2016). Too many adults lack the skills needed to face the challenges of globalisation. More than 200 million adults across OECD countries (about one in four) have low literacy or numeracy skills and 60% of them lack both types of skills (OECD, 2017). The EYFS recognises that creativity and critical thinking are important in all areas of learning and are as integral to mathematics as they are to painting or dance (DCSF, 2009a). The EYFS states that ‘mathematics involves providing children with opportunities to develop and improve their skills in counting, understanding and using numbers, calculating simple addition and subtraction problems; and to describe shapes, spaces, and measures’ (DfE, 2017, p.8). It is important in early years to combat the common perception that Maths is hard. Delvin (2000) explains that whilst we naturally use mathematical concepts in everyday situations e.g. cooking, crossing the road, to adapt and use these for abstract reasoning and provide logic for this is challenging. Maths is everywhere! (Skinner, 2011). Maths should not be constrained by an area of the environment moreover practitioners need to understand how maths permeates all spaces, indoors and outdoors, and use these accordingly. The Williams review (2008) recognised the importance of play-based learning of a mathematical nature in promoting mathematical development.
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| Numbers | Use number stories and number action rhymes to develop understanding of number and counting forwards and backwards Encourage children to match their fingers to the number Activity - put hands behind backs and count together, one, two, three, four, five. Bring out hands with five fingers standing – i.e. one whole hand Count group of objects in different layouts to develop concepts of sets and similar amounts Observing and identifying numbers in the environment e.g. buses, road signs, on food containers Explore money when shopping and in role play Use birthdays to understand simple numbers and share dates Use the language of counting and ordering in everyday situations e.g. climbing stairs, building blocks, getting dressed Play practical games that enable counting, adding and taking away, estimating Encourage children to ‘keep score’ when playing Use the sharing of food to discuss how many pieces Encourage mark making in number writing and representations Provide small world play from familiar stories, giving reasons for counting and encourages number talk Display numerals in purposeful contexts Provide number labels and number lines for children to use and refer to in their play Encourage number writing for a purpose in play e.g. football numbers, car registrations, taking the register Outdoor number hunt
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| Shape, space and measure | Pound (2009) analyses this aspect of development and suggests it includes four key categories, actions e.g. responding, sorting noticing changes, comparing; thinking processes e.g. logic, understanding variations, recognising similarities and differences, investigating things that challenge expectations; talking e.g. using relevant language and vocabulary and describing solutions; dispositions for learning e.g. enjoyment, curiosity Positional language games e.g. where is it?, where am I/ you? Provide a wide range of natural objects and materials that motivate children to match, sort and categorise Provide and encourage the use of standard and non-standard measures Heuristic play with containers and objects Opportunities to observe and explore patterns Cooking activities Opportunities to explore space with their bodies e.g. crawling in spaces Discuss times of the day e.g. morning, before snack time, 5 minutes time Shape hunts inside and outside
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Mathematical creativity (Tucker, 2014, p.4) | Using open ended questions and sustained shared thinking techniques Provide open ended resources (loose parts link) Ensure time and space for children to explore and extend their enquiry Allow children to leave out any play resources so they can re-visit them the following day and develop their thinking further Ensure that children have the opportunity to review their work and talk about their thinking using appropriate language Encourage children to make links between maths and other experiences Discover pattern in 2 and 3D art activities, playing musical instruments, using loose parts Imaginative role play and small world play
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Problem solving DCSF, 2009a | Use everyday activities and routines e.g. how many places do we need to set for lunch today, registration - how many more, less children are here today Counting lunch preferences and the most and least popular. Encourage children to create their own graphical representations of these figures (Williams, 2011) Allow children to be challenged in their thinking and scaffold as appropriate (Vygotsky, Bruner) Discuss problem solving strategies children have used and provide time for reflection Den building Provide a culture of enquiry where children’s own ideas are at the heart of planning Share and discuss children’s ideas of calculation strategies with them Make regular times for small-group discussions about children’s own personal mathematical problem solving
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