(image: Esther O'Connor)
This blog has been written based on some guidance I put together with the Reception and Y1 teacher in mind. It is aimed to both support and stimulate you in thinking about the mathematics we offer our youngest children, now, and going forward as the schools return. We hope that what follows could also be useful to focus discussions with KS1 colleagues, maths leads, SLT and head teachers to support decision-making for September 2021 regarding provision and transition issues and how best to support their children mathematically.
Here I have gathered together in one place a number of articles, short videos, podcasts and websites on early maths that I have referred to in other blogs and elsewhere. I hope it helps.
Firstly, some important prerequisites.
What I have taken into account first and foremost in curating these materials, is children’s mathematical well-being for future learning. In other words, what matters most is:
building young children’s confidence,
their willingness to have a go,
their mathematical self-esteem and enjoyment; and
establishing firm relationships between the adults in school and families.
For supporting families with home learning, ‘Learning Trajectories’ (an amazing US site) has a useful area here: https://learningtrajectories.org/index.php/pages/sub_page/32
And I have written this article on supporting maths learning at home: https://www.famly.co/blog/helen-williams-maths-at-home
It is important to remember that The Characteristics of Effective Learning (CoEL) – with the additional word “teaching” - remain statutory for all 7 areas of learning in the new EYFS Framework, which comes onstream in September 2021: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/974907/EYFS_framework_-_March_2021.pdf
playing and exploring (engagement)
active learning (motivation);
and
creating and thinking critically.
These epitomise well-being in all areas of learning and must be taken into account when planning mathematical teaching episodes. In particular, ‘creating and thinking critically’ lends itself to nurturing mathematical reasoning.
(image: Esther O'Connor)
Early mathematics is not about ‘catching up’. Rather, it is about being aware that missing reception and pre-school experience will not be plugged quickly, or by moving too fast. It is additionally important after the year we have all experienced to remember that all reception learning is based on the three Prime Areas of the EYFS:
· Personal, social and emotional development
· Communication and language; and
· Physical development,
and that mathematics can be built around these prime areas, as we have indicated in the tasks below. Not all maths can - or indeed should - be done sitting at a table!
Reception must continue to be built on established and effective early years practice, the Early Childhood Mathematics Group (ECMG) is a good place to go for guidance on this: https://earlymaths.org . It is important that reception experiences flow into year 1 for well beyond the first few weeks of year 1. This should apply at all times but particularly so this coming year. This means that reception and year1 staff need to discuss how to make mathematical transition as positive and smooth as possible, and for year 1 to be as like reception as possible; rather than the other way around.
For example, R and Y1 considering jointly:
which mathematical teaching experiences have been successful in R and that we can repeat (and build on) in Y1)?
what were the particular features of these successful episodes?
how might we best exend and deepen these experiences over time, in R, and then during Y1?
how are our taught mathematical experiences in R successfully moved into continuous provision?
how can we continue to use continuous provision in Y1 to build our children’s mathematical independence and to cement and deepen their understanding?
how can we continue an emphasis on the CoETL through R and into and throughout, Y1 and into Y2 (and beyond)?
This 2020 short article (the list of authors takes longer to read than the article itself!) by, Sullivan, Bobis, Downton, Feng, Livy, Hughes, McCormick and Russo, is an interesting read in relation to all ages of pupil returning to school mathematics: https://www.researchgate.net/publication/341168177_Threats_and_Opportunities_in _Remote_Learning_of_Mathematics_Implication_for_the_Return_to_the_Classroom
Ideas of what to do in school
My article here summarises recent developments in our understanding of what is important in early years mathematics: https://impact.chartered.college/article/mathematics-in-early-years/
It is helpful to think of early mathematics as being based on six ‘Big Ideas’, all of which are equally important:
Counting and Cardinality
Comparison
Composition
Pattern
Shape and Space
Measures
The educational programme for mathematics within the 2021 statutory Framework encompasses all of these as well as mentioning the ‘weft’ of teaching; how children feel about their mathematics:
“Mathematics
Developing a strong grounding in number is essential so that all children develop the necessary building blocks to excel mathematically. Children should be able to count confidently, develop a deep understanding of the numbers to 10, the relationships between them and the patterns within those numbers. By providing frequent and varied opportunities to build and apply this understanding - such as using manipulatives, including small pebbles and tens frames for organising counting - children will develop a secure base of knowledge and vocabulary from which mastery of mathematics is built. In addition, it is important that the curriculum includes rich opportunities for children to develop their spatial reasoning skills across all areas of mathematics including shape, space and measures. It is important that children develop positive attitudes and interests in mathematics, look for patterns and relationships, spot connections, ‘have a go’, talk to adults and peers about what they notice and not be afraid to make mistakes.”
(DfE 2021:10)
Sometimes it is difficult for those not trained in or with a background in child development and early years education to recognise what is actually going on mathematically when they observe a R or Y1 group of learners. The early years area of the NCETM site https://www.ncetm.org.uk/in-the-classroom/early-years/ is a good starting point for finding issues to discuss with colleagues about what is important in early years maths. This podcast interview with Viv Lloyd of NCETM and Dr Sue Gifford is a good listen on how to support young children to develop their mathematical thinking: https://www.ncetm.org.uk/resources/52709
The Erikson Early Math Collaborative is a rich source for understanding early maths and for ideas for maths teaching based firmly in research: https://earlymath.erikson.edu. The “Why early math?’ tab outlines their list of the ‘Big Ideas’ in early maths, which overlap with the six above. Their “Idea Library” tab contains lots of ideas for developing maths from ordinary day-to-day tasks at home: https://earlymath.erikson.edu/ideas/
COUNTING AND CARDINALITY
(image: Esther O'Connor)
Watch this three minute video on counting: https://earlymath.erikson.edu/movement-counts/ This task takes into account physical development and communication (two of the three Prime Areas). It is informing to hear what the teacher is listening for and how she pulls out the mathematics elements of the activity.
Cardinality (number sense) is the ‘how many-ness’ of a number, and subitising is key in developing this sense. Doug Clements explains subitising here: https://www.researchgate.net/publication/258933161_Subitizing_What_Is_It_Why_Teach_It You will find many ideas for developing young children’s conceptual subitising on the Erikson site.
It takes children 3-4 years to fully develop their understanding of the all the connections between quantities and numbers. Many and varied experiences in a wide range of contexts (outside, role play, dice games etc.) need to be provided over time for children to explore to cement their understanding. For example: a wide range of opportunities to count out a small number of discrete physical objects from a larger quantity, varying these in type, size and colour, (counting items on a worksheet or PPT slide just won’t do), counting movements, counting sounds (eg: coins dropping into a piggy bank), counting continuous quantities (eg: spoonfuls of sand); and so on. We cannot assume that if children can count reliably to 10, they can count above 10. The ‘teen’ numbers are the hardest to learn in English, as they are irregular.
COMPOSITION
(image: Esther O'Connor)
How numbers are made from other, smaller, numbers – the necessary precursor for any calculating.
https://earlymath.erikson.edu/the-hoop-game-simple-tossing-game/ Listen to how the adult helps the children attend to the composition of the total (in this case 3 and later, 5). This task could easily take place outside, and played with as a continuous provision maths task, with the adult intervening at times to build on the children’s understanding of how a small number is composed. It could be bigger and involve water! Keeping the number of throwing items constant and talking about the ‘outside’ as well as the ‘inside’ amounts helps the children focus on composition. If this task is introduced without controlling the total number to throw each time, rather than working on understanding the composition of one amount (total), the children will be practicing their cardinal knowledge by counting how many they score ‘inside’ each turn, and maybe finding a way to record this informally.
PATTERN
(Image: Sue Gifford)
This short article by Dr Sue Gifford explains why pattern awareness is so important to develop: https://nrich.maths.org/13362
The important thing to draw children's attention to is the 'unit of repeat' in a repeating pattern (read Gifford and her colleagues on this here: https://www.atm.org.uk/write/MediaUploads/Journals/MT271/30-34_Helen_Thouless,_Sue_Gifford,_Karen_Moses_and_Ruth_James.pdf
On the “Maths with Parents” site: https://mathswithparents.com (you will need to register) watch this 3’ video on building repeating patterns, and how the adult draws the child’s attention to seeing and saying the unit of repeat: https://explore.mathswithparents.com/KWeb?startTime=1589902627338#slctd
More pattern tasks can be found here: https://earlymath.erikson.edu/why-early-math- everyday-math/big-ideas-learning-early-mathematics/big-ideas-of-pattern-number- pattern/
SHAPE AND SPACE
(image: Simon Gregg)
“A number of studies have also shown that these abilities are not innate but teaching young children spatial skills actually improves their maths, including their number understanding and general thinking skills.”
Dr Sue Gifford explains here clearly why shape and space are so important in mathematical development: https://nrich.maths.org/14544
Doing jigsaws is an undervalued area of early years. Make time for regular, collaborative jigsaw play, discussing how we choose the pieces, their similarities and differences and why and how they fit or don’t fit. Cards or packages can be cut up to make cheap jigsaws.
Lego and Duplo play is as useful for extending mathematical language and visualisation as expensive (and wonderful) large wooden block play.
Outside, children can be encouraged to plan and build large with crates, pipes and boxes, and to describe and maybe even to draw what they see from different viewpoints.
The DREME site https://prek-math-te.stanford.edu here gives ideas for exploring shape and space through story books: https://dreme.stanford.edu/news/5-great-picture-books-learn-about-shape-space Remember, you can find many of these books read aloud on YouTube if you don’t have access to the hard copy.
The ECMG have drawn up a comprehensive developmental trajectory full of ideas for supporting children’s spatial awareness from birth to 7 years of age here: https://earlymaths.org/spatial-reasoning/
MEASURES
(image: Maeve Birdsall)
Measures is applied number; number in context, and for that reason, very important. If we think of how pre-school children first meet number outside school, it is often in a measures context (their age, their height, distance, ‘sleeps’, etc). Interestingly, Davydov (Russian psychologist, 1930 -1998) maintained that number should be first introduced in a measures context:
“Using this approach to teach number focuses on the impact unit has on the
count or measure.”
In other words, the small spoon takes more spoonfuls than the ladle to fill the bucket with sand.
Gradually, we can begin to extend children’s vocabulary when making comparisons from “big” and “small”, to “a little bigger / taller/ fatter than”; “about the same length as..”; “a lot heavier than..” and so on.
The early years section of the Nrich site is a rich resource for ideas https://nrich.maths.org/early-years
and their ‘wrapping parcels’ task is good for discussion about size and shape and also accuracy – how accurate do we need to be for this to be successful? (All measure is to some degree inaccurate): https://nrich.maths.org/13535
In this video from the Erikson site, building two block towers leads to using something to indirectly make a comparison of height. Observe how the practitioner asks questions in order the children decide how to do this: https://earlymath.erikson.edu/measuring-a-block-tower-in-kindergarten//
https://learningtrajectories.org is an excellent site (you will need to register) to dig into all the many stages of development (the “trajectories”) in the various areas of maths. It is a site to dip into when unsure about how to build on what our children know.
Finally
Here is Ofsted’s definition of teaching from both the School Inspection Framework (https://www.gov.uk/government/publications/school-inspection-handbook-eif/schools-inspection-handbook-for-september-2021 para 333) and Early Years Inspection Framework (https://www.gov.uk/government/publications/early-years-inspection-handbook-eif/early-years-inspection-handbook-for-ofsted-registered-provision-for-september-2021 para 182) both applicable from September 2021 .
This would be useful printed out and displayed in every reception class and handed to every visitor:
“Teaching should not be taken to imply a ‘top down’ or formal way of working. It is a broad term that covers the many different ways in which adults help young children learn. It includes their interactions with children during planned and child-initiated play and activities: communicating and modeling language, showing, explaining, demonstrating, exploring ideas, encouraging, questioning, recalling, providing a narrative for what they are doing, facilitating and setting challenges. It takes account of the equipment that adults provide and the attention given to the physical environment, as well as the structure and routines of the day that establish expectations. Integral to teaching is how practitioners assess what children know, understand and can do, as well as taking account of their interests and dispositions to learn (characteristics of effective learning), and how practitioners use this information to plan children’s next steps in learning and to monitor their progress.” (Ofsted 2021)
What else?
Another useful and inspiring site: https://creativestarlearning.co.uk - maths outdoors for all ages.
And really finally – don’t think getting outside and playing ball is nothing to do with maths – read this article (Giles, Shire, Hill, Mushtaq, Waterman, Holt, Culmer, Williams, Wilkie, Mon-Williams 2018) where ‘interceptive timing’ is related to maths success! http://eprints.whiterose.ac.uk/127194/1/Giles_Wilkie_PsycSci_IT_Maths_Manuscript _finalformat.pdf
Enjoy every small mathematical moment with your children and most importantly, HAVE A VERY WELL DESERVED SUMMER BREAK.
Helen's book on playful mathematics will be published in March 2022 by SAGE.