Picturebooks 8 – Sum it up!

I feel I need to begin this article with a confession: Carol Vorderman I am not. When I was preparing to begin my teacher training, I worried about how I could convey enthusiasm and enjoyment in creating an enriching mathematical environment, when I myself had such few memories of interest in maths as a child. After perhaps my first day of placement, however, I knew I needn’t feel anxious about the children’s willingness to learn: ‘number time!’ can generate as much excitement in three- to five-year-olds as ‘storytime!’ or ‘glitter time!’.

Reading professor Richard Skemp’s comparison between instrumental mathematics (which centres on rote learning, memory, rules and correct answers) and relational mathematics (which focuses on establishing connections, applying concepts to other problems) made me realise that the former needs to be enhanced by the latter. It also helped me understand the importance in early maths of:

• creativity
• problem solving
• cross-curricular applications of mathematical concepts to real-world settings
• gradual challenges and increases in complexity.

Providing these after and alongside a firm grounding in the rules and ‘right answers’ of any particular concept are just some of the exciting and playful aspects of maths to which every child should have access, and which every teacher should enjoy delivering.

Inspired by the Reggio Emilia approach, by which teachers play the role of co-learners in the classroom alongside the children, I pondered what role I could play as a guide and resource to my enthusiastic mathematicians. By finding high-quality picturebooks with numeracy and mathematical concepts at their heart, I knew I could play to my strengths as a practitioner. I learned from authors and illustrators who really understood how to make maths meaningful and exciting per Skemp’s relational model, and how to truly embed this approach in my practice and in my setting by absorbing maths into the arena in which I felt comfortable: storytime.

MATHS THROUGH STORIES

Dr Vince Trakulphadetkrai, a lecturer in primary mathematics education at the University of Reading, is the founder and principal investigator of Maths Through Stories – an ‘international research consortium investigating various aspects of integrating story picturebooks…in mathematics teaching and learning’.

Dr Trakulphadetkrai’s website (www.mathsthroughstories.org) is a treasure trove of resources, including book recommendations, suggested lesson plans and academic evidence for the benefits of sharing and teaching maths through stories.

Shape, space and measure

What needs to be stressed as settings start to adopt the revised EYFS is that concepts relating to ‘Shape, space and measure’ should remain an important part of any early years maths curriculum – as evident in Dr Trakulphadetkrai’s website.

Controversially, the Government removed the Early Learning Goal of ‘Shape, space and measure’ from its proposed framework and failed to reinstate it following a consultation, in which many early years experts voiced their strong opposition to the move.

The Government did, however, amend the education programme, which now states, ‘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’.

See box for some of the early years picks from Maths Through Stories.

DEVELOPMENTAL SIGNIFICANCE

Early years expert Linda Pound, in her essential Supporting Mathematical Development in the Early Years, notes that evidence from a wide range of studies indicates that children even younger than six months old can ‘demonstrate that numerosity (or the number of objects in a set) is more important than the objects themselves’.

One example that she cites is that of a baby ‘preferring to look at three toy buses when shown a picture of three teddy bears, than at the two teddies placed in front of them’.

The picture of early mathematical development this suggests is a complex one, Pound continues. ‘Visualising and symbolic representations of numbers develop interdependently,’ she notes, ‘suggesting that various areas of the brain work together to develop number understanding’.

‘Variations in experience,’ Pound suggests, are important in ensuring this development. Alongside the use of illustration and props for developing numerosity should be the repetition of rhymes and rhythmic songs, which stimulate babies and very young children’s propensity to seek out patterns.

Returning to illustrated baby books, like Xavier Deneux’s simple, beautiful 123 and Counting, is one such way to introduce visual representation alongside the repetitive pattern that comes with reading and re-reading a favourite text aloud. For older children, there is nothing to stop practitioners sharing maths-minded picturebooks at storytime – Quentin Blake’s Cockatoos, Eileen Browne’s Handa’s Henand even Inga Moore’s Six Dinner Sid all spring to mind as wonderful stories that provide ample opportunity for counting, mathematical language and conceptual illustrations of their application.

However, the use of picturebooks for sharing and really exploring mathematical concepts is perhaps best suited to small group reading.

As Pound points out, ‘With all that has been said about the difficulties of the specialist use of language in mathematics and the emphasis which needs to be placed on thinking (which for little children is frequently spoken), it is plain that large-group sessions should be used sparingly… Opportunities to communicate ideas with the support of adults and other children, visual materials which give children some additional clues about the topic under discussion and a group size which allows children sufficient time to contribute will all help.’

I can think of little better opportunity than sharing a story with a small group to illustrate a tricky mathematical concept – providing a space in which children feel comfortable in engaging with a well-known, familiar resource, and confident in discussing an interesting concept via how it works within the setting of a story.

BEYOND STORYTIME: EMBEDDING MATHS

Mathematical picturebooks needn’t only live in the library corner, and be taken out for small-group work – choose some texts that illustrate mathematical concepts to live in, or occasionally visit, your maths area. Perhaps these could change to match weekly topics, and needn’t only be copies of Five Little Ducks!

Using props in relation to a story is an excellent way for children to explore often abstract concepts in a concrete way, using the stimulus of a familiar story as a scaffolding structure and launching pad for creative experimentation and exploration. Birds or animal counters (instead of cockatoos!) and a doll’s house, alongside a copy of Quentin Blake’s book from morning storytime, could inspire some really enriching creative mathematical play and deep conceptual experimentation.

Small-world figures and Bear Hunt props (either from a story sack for Michael Rosen and Helen Oxenbury’s picturebook classic, or home made) could be equally at home in the maths corner as the language corner – the positional language of ‘over’, ‘under’, ‘through’, ‘in’ and ‘out’ are central concepts in a thorough understanding of shape and space.

The same can be done with Ed Bryan’s Goldilocks and the Three Bears– available in picturebook paperback as well as via interactive app – with differently sized props for measuring size and matching.

One of my favourite maths-rich picturebooks is Emily Gravett’s Orange, Pear, Apple, Bear. The story’s increasingly complex pattern-making is great fun and begs to be recreated, explored and understood thoroughly through independent play with props (which, again, needn’t only be fruit or bears!).

There are a number of excellent mathematical picturebooks for readers older and more experienced than those in the early years – such as the Sir Cumference series by Cindy Neuschwander and Wayne Geehan.

Such heavily wordy stories like these wouldn’t be appropriate for sharing at storytime. However, their engaging illustrations of more advanced iterations of the concepts children in the early years will be just beginning to explore shouldn’t make them off-limits for the library corner in a Reception classroom well-equipped for differentiation and challenge.

Picturebooks for older children can inspire younger readers who can’t yet access them completely to ‘look over the garden fence’ – and realise that there is a bigger world waiting for them to which their learning and development will give them access in time.

The literacy gap between children from literature-rich home environments and those who encounter quality texts only at school can itself only begin to be closed when those stimulating, expansive home environments can be recreated in the classroom or setting – something of benefit across all areas of learning and curriculum.

MATHS THROUGH STORIES WEBSITE: recommendations

Number recognition

One by Kathryn Otoshi – One comes along and shows the warring colours how to stand up, stand together, and count. See also Zero and Two by the same author.

One Thing by Lauren Child – Lola takes on numbers in everyday life and bends them to her endearing and unique will.

Two is for Twins by Wendy Cheyette-Lewison and Hiroe Nakata – A look at things that come in pairs from bicycle wheels to a bluebird’s wings.

Filthy Franny and the Four Faery Fleas by MW Penn and Mike Linton – Franny doesn’t like to take baths, so when she wishes for a Faery Godmother, Faery Fleas turns up instead.

Sidney the Silly Who Only Eats 6 by MW Penn and Sarah Tommer – King Sidney only eats 6 until the chef puts his foot down.

One-to-one correspondence

Crash! Boom!: A Maths Tale by Robie H Harris and Chris Chatterton – Elephant wants to build something as tall as himself.

Seaweed Soup by Stewart J Murphy and Frank Remkiewicz – Turtle has made enough soup for everyone but it looks awful and smells worse!

Abu Ali Counts His Donkeys by Dorothy Van Woerkom and Harry Horse – When Abu Ali stops to count the nine donkeys that he has bought, he can count only eight. When he counts again, there are nine. Can his friend Musa solve the mystery?

Count Off, Squeak Scouts! (Mouse Math) by Laura Driscoll and Deborah Melmon – Mouse Albert makes his first trip to the attic and is determined to bring home a special souvenir.

The Right Place for Albert (Mouse Math) by Daphne Skinner and Deborah Melmon – Albert heads to the People Kitchen for the first time, in search of crumbs, treats and goodies.

Counting forwards and backwards

5 Little Ducks by Denise Fleming – A fresh take on the classic nursery rhyme

Alfie’s Numbers by Shirley Hughes – A counting journey with Alfie and Annie Rose, who make two and there’s four in Alfie’s family.

One to Ten and Back Again by Nick Sharratt and Sue Heap – Two friends list their very different favourite things: one girl called Sue to ten cakes for tea, and then all the way back down to one yellow moon.

Ten in the Bed by Penny Dale – A subtle variation on the traditional nursery song.

Have You Seen My Dragon by Steve Light – A boy travels uptown and down, searching for his friend.

Shape, space and measure

Inch by Inch by Leo Lionni – A small, green inchworm is proud of his measuring skills. But can he measure a nightingale’s song?

Circus Shapes by Stuart J Murphy and Edward Miller – The elephants form a circle and the monkeys a square. Now the challenge is to find all the circles, squares, triangles and rectangles.

Mouse Shapes by Ellen Stoll Walsh – What can you make with one oval, two circles, and eight triangles? Just ask three clever mice.

Balancing Act by Ellen Stoll Walsh – Two little mice balance on a see-saw until a frog and other friends come along. When a big heavy bird then arrives, it’s time to watch out!

Mouse is Small by Mary Murphy – Animals, and the pages of the book, increase in size from a mouse, to a tortoise, zebra and elephant.

+ 10: MORE FAVOURIE MATHS-RICH PICTUREBOOKS

Counting: A Child’s First 123 by Alison Jay – Follow the dreams of a sleeping girl and meet favourite folk and fairy tale characters as you journey from one to ten and back again.

One Leaf Rides the Wind by Celeste Davidson Mannis, illustrated by Susan Kathleen Hartung – A counting book that reveals the pleasure and tranquillity of the Japanese garden, while introducing haiku (short form) poetry.

Pezzettino by Leo Lionni – Pezzettino (‘little piece’) thinks, ‘I must be a piece of somebody. I must belong to someone else.’

The Doorbell Rang by Pat Hutchins – Ma has made enough cookies for her two children. Then the doorbell rings – and rings.

A Pair of Socks by Stuart J Murphy, illustrated by Lois Ehlert – A striped sock searches the house for its mate.

Centipede’s 100 Shoes by Tony Ross – A centipede has sore feet and decides to give his shoes away.

What’s the Time, Mr Wolf? by Annie Kubler – Follow the ever-hungry Mr Wolf and Little Wolf through the hours in their day, from waking up to all-important dinner time.

Round is a Mooncake: A Book of Shapes by Roseanne Thong – A little girl’s urban neighbourhood becomes a discovery ground for all things round, square and rectangular in this lyrical picture book.

One Duck Stuck by Phyllis Root, illustrated by Jane Chapman – Ever larger groups of animals try to help a duck stuck in a slimy marsh.

One is a Snail, Ten is a Crab by April Pulley Sayre – Crabs, dogs, insects and snails offer their feet for counting in silly, surprising combinations, from one to 100.