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Hidden Message 2: Mathematical ability is like having a magic eye or knowing a secret language
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In another picturebook about Katherine Johnson - ‘A Computer Called Katherine’ - the protagonist sees numbers up among the stars. Similarly, in ‘Nothing Stopped Sophie,’ a young Sophie Germain sees numbers vibrantly appearing out of thin air, superimposed over scenes of the French Revolution (opening 4). Although this might be a reasonable way to represent the thought processes of someone doing math in a picturebook, it might leave readers with the mistaken impression that talented mathematicians are people who literally see formulae floating around them.
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For other picturebook personae, mathematics functions like a decoder ring for translating or decrypting the language of the universe. For Einstein, numbers “were a secret language for figuring things out” (Berne & Radunsky, 2013, opening 9). The idea that math is akin to language is not problematic on its own. The issue is with the exclusive nature of languages if one does not speak them and believes one cannot learn them. For a child struggling with math anxiety, it could be frustrating to see that mathematics is a language understood easily by its conversant speakers but is incomprehensible to outsiders. Although the language of math is openly taught in classrooms, it is a language many learners struggle to use fluently. We can easily imagine children feeling inspired by Katherine Johnson, but also saying “I never see numbers floating in the air, so I guess I’m not a math person.”

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Hidden Message 3: Mathematics is about doing calculations quickly
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Twelfth century mathematician Fibonacci tells us that when he was just a boy, his teacher “wrote out a math problem and gave us two minutes to solve it. I solved it in two seconds” (D’Agnese & O’Brien, 2010, opening 2). Early in ‘The Great Math Tattle Battle,’ readers are told that Harley Harrison “could figure out forty-five plus thirty-nine faster than you could spell ‘Mississippi’” (opening 1). Harley’s mathematical experiences render him as mathematically capable because he is fast and does not make mistakes. His spot at the top of the class is only jeopardized when he produces an incorrect answer and becomes vulnerable to Emma Jean encroaching on his turf.

For both Harley and Fibonacci, the focus is on the result rather than the process of making sense of a problem at hand. This hidden message reflects the tendency to overemphasize manipulation of numbers over relational thinking about mathematical ideas, which precludes (slower) processes of taking ownership of mathematical ideas through reasoning.

In ‘Counting on Katherine: How Katherine Johnson Saved Apollo 13’, readers encounter the message that mathematical ability translates to experiences of speed and correctness. When the Apollo 13 spacecraft was in peril, Katherine “did flight-path calculations, quickly and flawlessly, to get the astronauts home safely” (opening 13). ‘The Girl with a Mind for Math: The Story of Raye Montague’ contains similar messages about mathematical speed and heroism: “Would it take her a month? Maybe weeks for success? Well, it took CALCULATIONS (and tons of caffeine), but Raye finished in HOURS … just over EIGHTEEN! (opening 22). ‘YOU DID IT!’ they cheered, and her boss had to say that her quick mind for math had in fact saved the day” (opening 24).
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Perhaps the goal of reading these and other picturebooks with children is to celebrate and normalize the contributions of Black women mathematicians. That is an admirable goal in and of itself! However, if the objective is to inspire children to view themselves as mathematically capable, it is counterproductive to insinuate that mathematical ability is based solely on innate speed and flawlessness. While speed and accuracy are important skills that need to be developed, having automatization take center stage is counterproductive to developing positive mathematical identities among young learners

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Hidden Message 4: Mathematical ability is associated with social awkwardness
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Few children yearn to be ostracized by their peers. However, one common message children receive about mathematics is that when you decide to devote time and energy to its pursuit, you may become a pariah, or at least socially awkward. This message is reinforced by numerous picturebooks. In ‘The Great Math Tattle Battle’, Harley Harrison and Emma Jean are the only two children shown to be interested in math. They are represented as being extremely annoying to their classmates. Eight centuries earlier, Fibonacci also annoyed his classmates, and later the townspeople of Pisa (D’Agnes & O’Brien, 2010).

In some picturebooks, characters find themselves with a choice to make: pursue mathematics or have friends. As a child, Albert Einstein “didn’t want to be like the other students. He wanted to discover the hidden mysteries of the world” (Berne & Radunsky, 2013, opening 6). Why is Einstein’s choice presented as mutually exclusive? Did studying mathematics preclude him from being like other kids? In the case of other picturebook personae, such as Ada Byron Lovelace, “numbers were her friends” (Wallmark & Chu, 2015, openings 7 and 16) and for Paul Erdös, “numbers were his best friends” (Heiligman & LeUyen, 2013, p. 11). Later, he made human friends when he met others who loved mathematics (p. 14). 
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We are concerned these picturebooks could leave young readers thinking, “I don’t want to be good at math because I don’t want to annoy people or be lonely.”

Can you imagine a city, an island, a world where numbers live together and mathematical operations become stories?
 
This is the basic idea of a new series of mathematical stories in Italian language by Germano Pettarin, an Italian professor of mathematics and computer science (and Jacopo Olivieri, his co-author). The books are published by Einaudi Ragazzi publishing house.
 
The idea of ​​books that propose mathematics as a story, using numbers as characters who talk, interact with each other, get angry, etc., is a novelty in the field of books with educational purposes for children here in Italy. Often the numbers are just elements of the stories, not the protagonists.
 
In these stories, numbers, operations, geometric figures come to life, and the rules of mathematics and geometry become the pretext for inventing places (e.g., the Pacifric Ocean, the Cifradi Archipelago), characters (e.g., the general Abacone or the unpredictable Pi Greek), or paradoxical situation (e.g., world without zeros and without circles). In a word, to tell stories where numbers and polygons all play together, argue, argue always following the rules of mathematics in a fun and playful way. Each with its own characteristics: One wants to be the leader, Three the perfect number, Zero unable to follow the rules: it does not divide, does not increase the result of the sums, etc.
 
Indeed, in his most recent story: numbers get sick, a pandemic between numbers, solved by a prodigious mathematical vaccine.
 
They are all stories that try to talk about maths to children and teenagers in fun and enjoyable way.
 
 
Inspirations for writing mathematical stories
 
The idea of ​​writing illustrated books on the intricate world of mathematics stems from the proposal of the publisher who, by the way, has always had a disgust towards mathematics. We would like to overcome the distrust that is found towards mathematics with books for children who have not taken the blows that lead to hatred of mathematics.

The publisher asked for books that explained the more particular concepts of mathematics to attract interest in this subject, in a colloquial and fun way. Children's books are good because you can express concepts, even difficult ones, in a simple way: the examples and images with which they are presented are effective not only for the little ones, but also for adults.

All treated in a non-notional way. Mathematics is a difficult subject for many, useless to go around it, with its round and square brackets, square roots and commas in the most unlikely places, elevations to surprising powers. It's hard to believe how you can have fun talking about it and even studying it. Especially if it is proposed in a rigid and repetitive way. In these novels it is approached from another point of view: mathematics as fun, discovery.
 
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About the series

The medium of oral story allows children flexibility to think playfully about mathematical ideas. In this blog post, I discuss a range of pedagogical benefits of thinking mathematically through storytelling. This piece has three aims: to characterise some of the qualities of oral mathematical storytelling; to consider the satisfaction and surprise the approach can bring; and, to promote this creative pedagogical tool.
 
Story and oral story
Story as an oral tradition is a powerful medium for thinking and one which is often neglected as part of young children’s learning experiences (Allison, 1987; Booker, 2004; Bryant, 1947; Egan, 1988; Walker, 1975). Children respond favourably to mathematical ideas contextualised in a meaningful way in story contexts (Schiro, 2004; Van den Heuvel-Panhuizen & Van den Boogaard, 2008). Where story and mathematics connect, there is scope to think mathematically through the story context.
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Oral story is the art of expressing verbally, real life or fantasy, without a written text. The concept of storying is described by Wells (1987, p.194) as “constructing stories in the mind”, which he positions as one of ‘the most fundamental ways of making meaning’. Oral mathematical story is telling a story with the intention of constructing mathematical meaning. Reading a book is interpreting a text in a shared way, whereas telling a story is a personal performance (McGrath, 2015). With oral storytelling, the storyteller is free from text; needs to be spontaneous; has a closer connection with their audience; and has a personal consciousness (Schiro, 2004).
 
To develop skill at oral mathematical storytelling, a three-step model is helpful. The proposed model draws on Corbett’s Talk for Writing (2008) where educators commit to the creative opportunity oral storytelling brings as they develop a personal pedagogic tool (Corbett, 2006; 2007; Palmer & Corbett, 2003). The three steps: imitation, innovation and invention which equip children with prerequisite story-writing skills, can be remodelled for oral mathematical storytelling. Oral story authors can start by retelling a published story without the picture book (imitation); then change something about the original story (innovation); and, create original oral mathematical stories (invention). The storyteller orchestrates words, gestures and simple story related materials as mediational tools (Carlsen, 2013).

What if?
This question prompts wondering, promotes possibility thinking, and, taps into the remarkable capacity of children to think playfully. What happens to the mathematical idea if we change the story? Or what happens to the story if we change the mathematical idea? For example, in ‘Goldilocks and The Three Bears’, what if there were four bears instead of three? What if there are two similarly aged small bears (twins)? What if Goldilocks is out with a friend from her village, how will they share the porridge? In mathematical oral storytelling, the ‘What if?’ question is key to thinking playfully about mathematics. 

Constructing a story with children 
‘Penguin’, is a story constructed between a teacher and a small group of Reception class children using cut-out coloured fish (see Figure 1). First, a summary of the story:
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Once upon a time there was a little penguin. His mum said to him ‘Go to the magical pond and catch ten fish for our tea.’ He walked a bit, and he walked a bit, and he walked a bit, and he walked a bit, until he got to the magical pond that glistens and shines. ‘Today we have orange and lemon flavoured fish’, the pond says. Penguin fished, and fished and fished until he caught ten delicious fish for tea. But on bringing the catch home, the family eats the fish and is still hungry and so Penguin has to return to the pond with the lemon and orange flavours and find different ways to catch ten fish …
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Figure 1: A Reception class teacher keeps number compositions for ten in view so that children think of other possibilities.

Different storytelling’s of ‘Penguin’ uncover ideas about: eleven possible number compositions for the number 10; conservation of number with different arrangements of fish on the carpet; a different sized fish feeding the family for longer; the division of a large fish; and tessellation as cut-up pieces are reunited. The commutative property of addition is made visible by using different coloured fish, for example, 10 is represented as 4 strawberry and 6 blueberry, and 6 strawberry and 4 blueberry flavours.
 
An outcome of the action of not placing all the same coloured fish together, is thinking about pattern. For example, Adam arranges 7 lemon and 3 orange fish carefully setting out (in this order) 5 lemon, 2 orange, 2 lemon and 1 orange fish. Equivalence between his 7 lemon flavours, composed of five and two; his 3 orange flavours composed of two and one, and a previous arrangement of 7 lemon and 3 orange fish, is realised.
 
Mathematical storytelling is characterised by conversations rich with higher order questioning which consequently allow children’s negotiation and generation of mathematical understanding. A teacher describes this pedagogical approach as: “a living interactive relational experience which is creative, exciting and unknown” (McGrath, 2019, p. 305). Naik (2013) refers to a “space between the known and the unknown where true creativity can thrive”; participants in the oral story project take a creative risk with their mathematical storytelling.
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Story as a medium provides meaningful, memorable, metaphorical contexts which help children think about and articulate mathematical ideas. After hearing ‘Penguin’, a child, for example, retells the story using the coloured fish with remarkable precision. She creatively adapts the story to fit with different characters, extends the story to try the number composition for 11 rather than 10, offering an imaginative twist at the end (see Figure 2). The transcript of this child telling 'Penguin' can be accessed here, and the accompanying audio file can be accessed under the Support Material section here.  ​

Figure 2: A child retells ‘Penguin’ arranging the cut out coloured fish in a way which requires further thinking.

 
Satisfaction and surprise
The imitative storytelling activity of children provides surprising insight about their mathematical capabilities. A child considered of lower ability explains a story contextualised idea of counting in multiples and in doing so challenges assumptions about her ability: “When you counted in twos you missed one out, so it’s like a pattern” (McGrath, 2014, p.67). During the oral story project, quiet children surprise their teachers with their mathematical storytelling confidence. (Children as kings and queens of oral mathematical storytelling is documented in McGrath (2015)).  
 
Oral mathematical story challenges educator perception of themselves and enhances their professionalism: “I have grown in confidence, from a teacher who stuck to traditional tales, to being able to create my own stories based on mathematical concepts, confidently telling them with just a simple story map as a prompt” (McGrath,  2014, p. 140). The impact of children sharing storytelling with their parents at home is noted by a teacher in McGrath (2019, p. 293): “[…] to be able to go home and be a storyteller…I just think that when children take their learning home…it gives you such a positive feeling as a teacher”.
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The possibilities
Oral mathematical story represents a hybrid of pedagogical approaches in that it is a traditional idea combined with modern practice. This alternative pedagogical approach opens up a new discourse which legitimatises a different way of teaching mathematics. As an integrative approach to implementing literacy and mathematics curricula, it is characterised by professional surprise and satisfaction. However, opportunity for oral mathematical story rely on a culture of creative choice.

References
Allison, C. (1987). I’ll tell you a story, I’ll sing you a song: A parents’ guide to the fairy tales, fables, songs, and rhymes of childhood. Dell Publishing.

Booker, C. (2004). The seven basic plots: Why we tell stories. Continuum.

Bryant, S. C. (1947). How to tell stories to children and some stories to tell. George G. Harrap and co. Ltd.

Carlsen, M. (2013). Engaging with mathematics in the kindergarten. Orchestrating a fairy tale through questioning and use of tools. European Early Childhood Education Research Journal, 21(4), 502-513.

Corbett, P. (2006). The bumper book of storytelling into writing Key Stage 1. Clown Publishing.

Corbett, P. (2007). Developing creative writing skills Available at: http://www.learning-works.org.uk/index.php?id=566  (Accessed: 30 October 2020).

Egan, K. (1988). Teaching as storytelling: An alternative approach to teaching and the curriculum. Routledge.

McGrath, C. (2014). Teaching mathematics through Story: A creative approach for the early years. Routledge.

McGrath, C. (2015). Mathematical storyteller kings and queens: An alternative pedagogical choice to facilitate mathematical thinking and understand children’s mathematical capabilities. In S. Chinn (Ed.) The international handbook for mathematical difficulties and Dyscalculia (pp. 369-382). Routledge.

McGrath, C. (2019). Oral story: A pedagogical tool encouraging children’s mathematical thinking. PhD thesis. University of Plymouth [Online]. Available at: https://pearl.plymouth.ac.uk/bitstream/handle/10026.1/13717/2018McGrath10163476phd_full.pdf?sequence=1&isAllowed=y (Accessed: 30 October 2020).

Naik, M. (2013). ‘Mathematics. In R. Jones and D. Wyse (Eds.), Creativity in the Primary Curriculum (2nd ed., pp. 33-49). Routledge.

Palmer, S. & Corbett, P. (2003). Literacy: what works? The golden rules of primary literacy and how you can use them in your classroom. Nelson Thornes.

Schiro, M. (2004). Oral storytelling and teaching mathematics: Pedagogical and multicultural perspectives. SAGE.
Talk for Writing (2008). Presented by P. Corbett [DVD]. DCSF Publications.

van den Heuvel-Panhuizen M. & van den Boogaard, S. (2008). Picture books as an impetus for kindergartners’ mathematical thinking. Mathematical Thinking and Learning, 10(4), 341-373.

Walker, B. (1975). We made a story. Garnet Miller Ltd.

​Wells, G. (1987). The meaning makers: Children learning language and using language to learn. Hodder and Stoughton.
 

​When you think about math picture books, do you think about counting and shapes? I did.

Do you think about diverse characters and rich, satisfying stories? I didn’t.

But then Marlene Kliman, a math expert at STEM non-profit TERC, reached out to Charlesbridge, the independent publishing company where I work as an editor. Marlene proposed an alternative perspective on what math picture books can and should be. What if a math picture book could explore important math topics beyond counting and shapes? What if it could feature characters who reflect the diversity of our world? And what if it told a story that young children would want to read again and again? Such a picture book could have the power to change a child’s life.

​Naturally Charlesbridge said yes. We partnered with TERC to develop Storytelling Math, a new series of board books and picture books that bring together math, diversity, and the power of story.
 
What types of math?
There are many wonderful counting and shapes books out there, but math is more than that. Young children need exposure to a rich array of math topics, such as patterns, categorizing, and spatial reasoning. As Marlene puts it, “Research has shown that facility with math topics like these is critically important for young children’s school success in all subjects.” Storytelling Math introduces important but often overlooked math topics to young children and helps them build a foundation for later understanding.

In What Will Fit? by Caldecott and Newbery Honor winner Grace Lin, Olivia visits a farmers’ market and searches for something to fill her basket. As Olivia tries to fit an apple, then a zucchini (courgette), and finally a pumpkin in her basket, she builds her spatial sense. We use spatial sense every day, when we read a map, pack a car trunk, and put our shoes on the correct feet. Spatial sense is also crucial in every subject, including math, science, and reading.

Each Storytelling Math book includes hands-on activities for kids and grown-ups to explore math together. After reading What Will Fit?, parents can ask children to help pair socks or mittens and talk through their reasoning: “How can you tell these two are a pair?” Conversations like these can help children become stronger, more confident mathematical thinkers.

​Drawing from their research article titled ‘Integrating Mathematics and Children’s Literature for Preschoolers with Disabilities’ published in the Journal of Early Intervention, the authors - Dr. Katherine B. Green (University of West Georgia) and Drs. Peggy A. Gallagher and Lynn C. Hart (both Professor Emerita, Georgia State University), have put together this short and easy-to-read blog post for interested teachers and parents. We hope you will find the information stimulating.
 
School-entry mathematical knowledge, specifically the knowledge and understanding of numbers, is the strongest predictor of later academic achievement (Claessens et al., 2009). Researchers have found that preschoolers are developmentally ready for mathematics (Balfanz et al., 2003) and that there is key foundational content that young children should master before they can understand more complex mathematical content (National Association for the Education of Young Children & National Council of Teachers of Mathematics [NCTM], 2002). One of these broad content areas is that of Number and Operations, the focus of this research. The NCTM (2006) noted that the domain of number and operations for preschoolers includes the development of number sense, understanding whole numbers, concepts of correspondence, counting, cardinality, and comparison.

​Math and Young Children with Disabilities
While there has been a recent increase in research on mathematics and young children, there is a scarcity of research related to young children with disabilities and mathematics. This research is critical since, as noted, early mathematical knowledge is a predictor of later academic achievement (Claessens et al., 2009). In early childhood special education, researchers agree that most children learn best with a combination of explicit instruction and naturalistic learning, particularly children who are at risk or have disabilities (Wolery & Hemmeter, 2011). One way to intervene using a more naturalistic approach is to integrate mathematics and children’s literature.
 
Integrating Mathematics and Shared Storybook Readings
 In instruction that integrates mathematics and children’s literature, the literature becomes a context within which to think about the mathematics, and the mathematics can be taught and constructed naturally within the context (Van den Heuvel-Panhuizen & Van den Boogaard, 2008). Using children’s literature as a context for mathematics problems and situations provides opportunities for children to actively construct mathematical ideas and promote critical thinking by providing a forum to ask questions, elicit discussion, and make personal connections (Anderson et al., 2004; Haury, 2001). Through active construction of mathematical knowledge, children develop new mathematical ideas, structures, and schemas (Elia, Van den Heuvel-Panhuizen, & Georgiou, 2010). Empirical research supports the premise that mathematics can be effectively integrated within children’s literature during shared storybook readings (Hojnoski et al., 2014; Skoumpourdi & Mpakopoulou, 2011; Van den Heuvel-Panhuizen & Iliada, 2011).
 
Shared storybook reading is a common and well-documented research practice in preschool classrooms (Dynia & Justice, 2015). The majority of the research literature for children with disabilities focuses on children with mild to moderate language impairments (e.g., Colmar, 2014; Van Kleeck et al., 2006; Voelmle & Storkel, 2015). Shared storybook reading is effective in improving children’s expressive and receptive language skills, mean length of utterances (MLU), and literal and inferential language skills (Colmar, 2014;  Voelmle & Storkel, 2015). It is also effective in improving preliteracy skills, such as alphabet knowledge, concepts of print, alliteration, identification of initial sounds, name writing, and rhyming skills (Justice et al., 2015; Pile et al., 2010).

Our Study 
The purpose of our study was to examine the effects of an intervention that integrated mathematics instruction within children’s literature on the early numeracy skills of preschoolers with disabilities. The specific research question was, is there any difference in the math skills of preschoolers with disabilities who received a shared storybook reading intervention with related math activities and those of preschoolers with disabilities who received only a shared storybook reading?
 
We studied 50 children, ages 3 to 5 years, designated as having a developmental delay. The children all participated in preschool special education classrooms in one school district in a southeastern state in the U.S. We randomly divided the 10 preschool classrooms into two groups. Children in the intervention group read one children’s storybook three times per week for two weeks with related math activities introduced over the two week period. Three storybooks were read in all for a total of 18 sessions. For each lesson, this group spent approximately 5 to 10 minutes on the storybook reading and approximately 10 to 15 minutes on math instruction related to the storybook. Books used were The Snowy Day (Keats, 1962), Goldilocks and the Three Bears, and The Very Hungry Caterpillar (Carle, 1987). Children in the comparison group received the same small group storybook sessions, but there were no math questions or elaborations provided during the sessions.
 
We assessed all children before and after the intervention on the Test of Early Mathematics Ability, Third Edition (TEMA-3; Ginsburg & Baroody, 2003) and the Individual Growth & Development Indicators Early Numeracy (IGDIS-EN; Hojnoski & Floyd, 2004). The TEMA-3 is a norm-referenced instrument designed to measure the mathematical knowledge of children ages 3 to 8 years old, whereas the IGDIS-EN is a curriculum-based measure used to assess young children’s number sense including quantity comparison, one-to-one correspondence counting, and oral counting.
 
The Results
The results showed that the integration of mathematics and children’s literature had positive and significant effects on the intervention groups’ total mathematical ability scores on the TEMA-3, quantity comparison skills, oral counting, and one-to-one-counting correspondence on the IGDIS-EN.
 
The researchers believe that it is important to be intentional and purposeful in selecting the storybooks, and to consider which book(s) might best elicit particular math skills. It is interesting to consider the beginning number sense skills targeted in this intervention. For instance, the children in the intervention group were noted to experience significant gains in the Quantity Comparison task. The skill of recognizing which of two groups have “more” objects is one of the most fundamental and early developing numeracy skills (Chu et al., 2013), and, as discovered, a most natural concept to incorporate in math-focused storybook readings. For example, two of the targeted storybooks had several pictures throughout the book that naturally allowed for discussion of which page or object had more. The Snowy Day had some pages with more snowballs or snowflakes than other pages. The caterpillar in The Very Hungry Caterpillar ate more fruits on different days of the week. Quantity comparison was addressed in lesson activities and easily targeted during the storybook readings. Counting skills, too, were intentionally modeled and encouraged throughout the intervention. For example, in The Very Hungry Caterpillar, the researchers pointed, counting the fruit after reading each page. The children were then encouraged to count objects by touching each item as opportunities occurred during the instruction. Counting skills proved to be an easily integrated mathematics skill when reading all three target storybooks.
 
Integrating mathematics instruction and children’s literature allowed researchers to not only provide a shared storybook reading using quality literature within a short time frame, but also within a limited budget. The materials were specifically designed so that teachers may use the intervention in their own classrooms, with costs kept to a minimum. The manipulatives used were materials that most teachers already have in their classrooms (i.e., counting/sorting bears or snapping cubes), as were the books.
 
Implications
Providing mathematics interventions for children with disabilities is of immense importance, as researchers have found that children with disabilities who lag behind peers in math skills may experience less growth and slower gains than peers without disabilities (Lambert et al., 2014). Within a 20-minute intervention per day, three times per week for six weeks, two content areas were targeted: storybook reading and mathematics, with books and materials readily found within the preschool classrooms. Integrating the mathematics instruction and children’s literature provides a shared storybook reading to the children using quality children’s literature while encouraging the construction of early numeracy concepts. Implications for teacher preparation programs include focusing on the strategy of teaching early math skills through children’s literature. Parents could also implement many of the ideas and activities in their homes, as well, by reading the storybooks and creating fun and engaging games and mathematics activities with their children.
 
References
Anderson, A., Anderson, J., & Shapiro, J. (2004). Mathematical discourse in shared storybook reading. Journal for Research in Mathematics Education, 35, 5-33.

Balfanz, R., Ginsburg, H. P., & Greenes, C. (2003). The big math for little kids early childhood mathematics program. Teaching Children Mathematics, 9, 264-268.

Carle, E. (1987). The very hungry caterpillar (Rev. ed.) Philomel Books.

Chu, F. W., vanMarle, K., & Geary, D. C. (2013). Quantitative deficits of preschool children at risk for mathematical learning disability. Frontiers in Psychology, 4, 1-10. doi:10.3389/fpsyg.2013.00195

Claessens, A., Duncan, G., & Engel, M. (2009). Kindergarten skills and fifth-grade achievement: Evidence from the ECLS-K. Economics of Education Review, 28, 415-427.

Colmar, S. (2014). A parent-based book-reading intervention for disadvantaged children with language difficulties. Child Language Teaching & Therapy, 30, 79-90.

Crehan, K. D. (2005). Review of the Test of Early Mathematics Ability–Third Edition. In R. A. Spies & B. S. Plake (Eds.), The sixteenth mental measurements yearbook. Buros Institute of Mental Measurements. Retrieved from http://www.buros.org

Dynia, J. M., & Justice, L. M. (2015). Shared-reading volume in early childhood special education classrooms. Reading Psychology, 36, 232-269.

Elia, I., Van den Heuvel-Panhuizen, M., & Georgiou, A. (2010). The role of picture books on children’s cognitive engagement with mathematics. European Early Childhood Education Research Journal, 18, 125-147.

Haury, D. (2001). Literature-based mathematics in elementary school. ERIC digest (ED No. 464807). ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Hojnoski, R. L., Columba, H. L., & Polignano, J. (2014). Embedding mathematical dialogue in parent-child shared book reading: A preliminary investigation. Early Education and Development, 25, 469-492.

Hojnoski, R., & Floyd, R. (2004). Individual Growth and Development Indicators of Early Numeracy (IGDIS-EN). Early Learning Labs.
Justice, L. M., Logan, J. R., & Damschroder, L. (2015). Designing caregiver-implemented shared-reading interventions to overcome implementation barriers. Journal of Speech, Language, and Hearing Research, 58, S1851-S1863.

Keats, J. E. (1962). The snowy day. Viking Press.

Lambert, R. G., Kim, D. H., & Burts, D. C. (2014). Using teacher ratings to track the growth and development of young children using the Teaching Strategies GOLD® assessment system. Journal of Psychoeducational Assessment, 32, 27-39.

National Association for the Education of Young Children & National Council of Teachers of Mathematics. (2002). Early childhood mathematics: Promoting good beginnings. A joint position statement of NAEYC and NCTM. Retrieved from http://www.naeyc.org/files/naeyc/file/positions/psmath.pdf

National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence. NCTM.

Pile, E. J., Girolametto, L., Johnson, C. J., Chen, X., & Cleave, P. L. (2010). Shared book reading intervention for children with language impairment: Using parents-as-aides in language intervention. Canadian Journal of Speech-language Pathology & Audiology, 4, 96-109.

Skoumpourdi, C., & Mpakopoulou, I. (2011). The prints: A picture book for pre-formal geometry. Journal of Early Childhood Education, 39, 197-206.

Van den Heuvel-Panhuizen, M., & Iliada, E. (2011). Kindergartener’s performance in length measurement and the effect of picture book reading. ZDM Mathematics Education, 43, 621-635.

Van den Heuvel-Panhuizen, M., & Van den Boogaard, S. (2008). Picture books as an impetus for kindergartners’ mathematical thinking. Mathematical Thinking and Learning, 10, 341-373.

Van Kleeck, A., Woude, J. V., & Hammett, L. (2006). Fostering literal and inferential language skills in head start preschoolers with language impairment using scripted book-sharing discussions. American Journal of Speech-language Pathology, 15, 85-95.

Voelmle, K., & Storkel, H. L. (2015). Teaching new words to children with specific language impairment using interactive book reading. SIG 1 Perspectives on Language Learning and Education, 22, 131-137.

​Wolery, M., & Hemmeter, M. L. (2011). Classroom instruction: Background, assumptions, and challenges. Journal of Early Intervention, 33, 371-380.
 
​

 Our study
To gain a better understanding of how parents choose counting books for their children, we administered a survey to roughly seven hundred parents of children between two-and-a-half and four years old (Gaylord et al., 2020). Our initial predictions were that parents of boys may prefer counting books that include tactile features (i.e., books with a touch-and-feel component), whereas parents of girls may prefer books that include a narrative. We also suspected that parents’ education level may influence the books parents choose to read with their children, given previous studies suggesting a link between parents’ education level and the activities parents choose to participate in with their children (Stipek et al., 1992).
 
To determine which features parents preferred, we asked a series of forced-choice and open-ended questions. For the two sets of forced-choice questions, parents saw two different counting books and were asked which one they would prefer to read with their child and why. Unbeknownst to parents, one of the pairs pit a book with tactile counting features against a book without tactile counting features. The other pair pit a counting book with a narrative against a counting book without a narrative. For the forced-choice questions, the books that were presented were randomly selected from a larger set of ten possible books for that category (e.g., a given parent saw one of ten possible tactile books pitted against one of ten possible non-tactile books). By randomizing which books parents saw across a larger set of books that shared the same feature, our results are not tied to any one book, but are more likely to be representative of the feature more broadly. We also asked parents to rate, in general, how important four different factors were whenever they choose a counting book to read with their child: enjoyment, challenge, tactility, and presence of a narrative.
 
Overall, we did not find evidence of any consistent associations between preferences for certain features and child gender, but we did find an association between parent education level and their choice of counting book. When asked to select a counting book either with tactile features or without tactile features, parents with lower education levels were more likely to both pick a book with tactile features and mention the tactile features of the book when justifying their selection. Parents with a graduate-level education rated tactility as less important when considering counting books than parents with a bachelor’s degree or less. When asked to select a counting book either with a narrative or without a narrative, parents with higher education levels were more likely to both pick a narrative book and mention the narrative when justifying their selection. Parents with at least a bachelor’s degree also rated the level of challenge of the counting book as a more important factor than parents with less than a bachelor’s degree. Overall, parents of all education levels reported that enjoyment was the most important factor when selecting which counting book to read. Across these questions, it is clear that parents are picking books they think their children will enjoy, but it is also apparent that parents from different education backgrounds take different approaches to deciding which counting books they want to read with their children.
 
What else do parents consider?
A follow-up examination of the open-ended responses further indicated the factors affecting parents’ book choices (O’Rear et al., 2019). In general, parents were more likely to pick a book based on the illustrations of the book (42.8% of parents) than on the mathematical content (24.1% of parents). Of the responses that mentioned mathematical aspects of the book, 77% mentioned whether or not it would be helpful for children’s counting, compared to 29% who mentioned the way the numbers were represented within the book (e.g., “provides various ways of visualizing the same number”).
 
Take-home points
Overall, these findings suggest that the math content of the book is not a driving factor in parents’ selection of counting books. Instead, parents value the perceived enjoyment of the book and the book’s illustrations. Moreover, parents from different backgrounds differ in what they view as important in selecting counting books. Research has shown that counting book reading can promote children’s conceptual understanding of counting (Gibson et al., 2020; Mix et al., 2012; O’Rear & McNeil, 2019; Petersen et al., 2014). An important next step is to determine how best to design counting books to elicit a focus on the important mathematics concepts within the book in a way that parents and children find appealing.
 

References    
 
Gaylord, S. M., O’Rear, C. D., Hornburg, C. B., & McNeil, N. M. (2020). Preferences for tactile and narrative counting books across parents with different education levels. Early Childhood Research Quarterly, 50, 29-39. https://doi.org/10.1016/j.ecresq.2018.07.010
 
Gibson, D. J., Gunderson, E. A., & Levine, S. C. (2020). Causal Effects of Parent Number Talk on Preschoolers’ Number Knowledge. Child Development. https://doi.org/10.1111/cdev.13423
 
Mix, K. S., Sandhofer, C. M., Moore, J. A., & Russell, C. (2012). Acquisition of the cardinal word principle: The role of input. Early Childhood Research Quarterly, 27(2), 274-283. https://doi.org/10.1016/j.ecresq.2011.10.003.
 
O’Rear, C. D., & McNeil, N. M. (2019). Improved set-size labeling mediates the effect of a counting intervention on children’s understanding of cardinality. Developmental Science, 22, e12819. https://doi.org/10.1111/desc.12819
 
O’Rear, C. D., Gaylord, S. M., Hornburg, C. B., & McNeil, N. M. (2019, March). Features that Affect Parents’ Preferences for Different Counting Books [Poster presentation]. Biennial Meeting of the Society for Research in Child Development (SRCD), Baltimore, MD.
 
Petersen, L., McNeil, N., Tollaksen, A., Boehm, A., Hall, C., Carrazza, C., & Devlin, B. (2014). Counting practice with pictures, but not objects, improves children’s understanding of cardinality. Proceedings of the 36th Annual Meeting of the Cognitive Science Society, 2633-2638. Quebec City, Canada.
 
Powell, S. R., & Nurnberger-Haag, J. (2015). Everybody counts, but usually just to 10! A systematic analysis of number representations in children’s books. Early Education and Development, 26, 377-398. https://doi.org/10.1080/10409289.2015.994466
 
Stipek, D., Milburn, S., Clements, D., & Daniels, D. H. (1992). Parents' beliefs about appropriate education for young children. Journal of Applied Developmental Psychology, 13, 293-310. https://doi.org/10.1016/0193-3973(92)90034-F.
 
Ward, J. M., Mazzocco, M. M., Bock, A. M., & Prokes, N. A. (2017). Are content and structural features of counting books aligned with research on numeracy development? Early Childhood Research Quarterly, 39, 47-63. https://doi.org/10.1016/j.ecresq.2016.10.002.

Booked on math overview
In Mouse Count by Ellen Stoll Walsh, children follow the adventures of a group of mice and a snake in the meadow. The rhythm of the story and illustrations follows a glissando giving the story an easy to follow musical quality. Children are immediately engaged, and the short story can easily be re-read as children count forwards and backwards along with the adventures of the mice. A natural extension is to act out the countdown as a snake attempts to find the mice.

Parents and teachers understand firsthand the power of stories for children’s development of language and early literacy. Fewer make use of stories and read-aloud activities for the development of early numeracy and mathematical thinking despite the emerging body of work that explores the effects of interactive read-alouds on mathematics teaching and learning (Casey, Ekrut, Ceder, & Young, 2008; Clarke, 2002; Jennings, Jennings, Van den Heuvel-Panhuizen, & Iliada, 2011; Van den Heuvel-Panhuizen, Elia, & Robitzsch, 2016; Young-Loveridge, 2004). In the Mouse Count, preschool aged children learn to count forwards and backwards to ten. The Mouse Count is an example a story picture book used in the ten-week micro curriculum--Booked on Math­­--our team developed to support early numeracy and mathematical thinking. In this curriculum, students and teachers completed one read-aloud and associated lesson per week (10 total).  Each lesson is composed of a story to be read-aloud, activities to reinforce the key concepts, and extension activities students and parents can do at home to reinforce learning.
 
Supplementary lesson plans
Supplementary lessons included in the Booked on Math­­ micro-curricula follow an inquiry-based “5E” lesson framework developed by Bybee et al. (2006) where students engage with a challenging situation, then explore what the concept means, explain the new knowledge they gained through exploration, elaborate by applying this knowledge in a novel situation, and finally evaluate by reflecting on their learning. We design easy to follow lesson plans that support student learning through the 5E framework with Get Ready, Engage, Investigate, Discuss, and Extend cycle. There is a Make it Work at the end that supports students with varied skill development. Click here is the lesson plan and activities for Mouse Count.
 
During the micro-curricula development, we selected books from the National Association for the Education of Young Children's (NAEYC) recommended book list and other research-based early childhood curricula (e.g., MyTeachingPartner Mathematics and Science) that have demonstrated increases in student learning outcomes in pre-kindergarten mathematics and science classrooms through randomized controlled trials (Kinzie et al., 2014). Book readings were also chosen to reflect the four primary domains tested in the Teaching Strategies GOLD (TS GOLD) assessment. Mathematical domains include: (1) number concepts and operations; (2) spatial relationships and shapes; (3) comparison and measurement; and (4) patterns. These domains align with state standards for pre-kindergarten in most states (Neuman & Roskos, 2005). The full Booked on Math curriculum and TS Gold domain coverage by book reading is listed below:
 
Our study
We piloted Booked on Math in a pre-kindergarten center in the United States with seventy children (approximately 48 months old on average) across three classes. Teachers found the lesson plans easy to follow and were able to integrate Booked on Math into regular classroom activities. To test Booked on Math, some classes used the curriculum while the other teacher taught using their usual lessons. To measure the impact of the program, the school tested the children using the TS Gold assessment (The Center for Educational Measurement and Evaluation, 2011)—a typical preschool assessment of student learning in the United States—before and after Booked on Math. We found statistically significant differences in the areas of (1) quantifies, (2) shapes, and (3) spatial relationships on the TS Gold assessment after Booked on Math.
 
The three TS Gold areas that yielded statistically significant results for Booked on Math are both conceptual and visual in nature. Our hypothesis is that the book readings, associated images, and activities may have helped young students develop a stronger conceptual understanding in these constructs (in particular with the constructs of spatial relationships and shapes) when compared to the traditional teaching methods. This result is consistent with previous research that suggests an overreliance on auditory teaching methods (e.g., lecture or listening alone) are problematic for most learners and present significant barriers for visual-spatial learners.  
 
Recommendations and next steps 
We believe Booked on Math will help teachers—especially with those who have math anxieties or who spend little time teaching early numeracy—easily integrate mathematical thinking and concepts into their pre-kindergarten classrooms. The recommended extension activities can support parental involvement at home and increase communication between parent and teacher about early numeracy. Given the fact that many parents read to their children at home, Booked on Math presents an opportunity to support students’ early numeracy development through an the read-alouds they already do.  
 
There is increasing evidence that read-alouds help develop early mathematical in preschool children. Booked on Math helps to extend the value of these readings by engaging students, teachers, and parents in reinforcing these key concepts in a systematic fun way. The 5E framework and lesson plan format can be adapted to other books as teachers identify new readings. 
 

References

Bybee, R. W., Taylor, J. A., Gardner, A., Van Scotter, P., Powell, J. C., Westbrook, A., & Landes, N. (2006). The BSCS 5E instructional model: Origins and effectiveness. Colorado Springs, Co: BSCS, 5, 88-98.
 
Casey, B., Erkut, S., Ceder, I., & Young, J. M. (2008). Use of a storytelling context to improve girls' and boys' geometry skills in kindergarten. Journal of Applied Developmental Psychology, 29(1), 29-48.
 
Jennings, C. M., Jennings, J. E., Richey, J., & Dixon-Krauss, L. (1992). Increasing interest and achievement in mathematics through children’s literature. Early Childhood Research Quarterly, 7, 263-276.
 
Kinzie, M. B., Whittaker, J. V., Williford, A. P., DeCoster, J., McGuire, P., Lee, Y., & Kilday, C.R. (2014). MyTeachingPartner-Math/Science pre-kindergarten curricula and teacher supports: Associations with children's mathematics and science learning. Early Childhood Research Quarterly, 29(4), 586-599.
 
McGuire, P., Himot, B., Clayton, G., Yoo, Monica, & Logue, M. E. (2020). Booked on math: Developing math concepts in Pre-K Classrooms using interactive read-alouds. Early Childhood Education Journal. https://doi.org/10.1007/s10643-020-01073-1
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Neuman, S. & Roskos, K. (2005). The state of state’s pre-kindergarten standards. Early Childhood Research Quarterly, 20(2), 125-145.
 
The Center for Educational Measurement and Evaluation (2011). Teaching Strategies GOLD Assessment System Technical Summary. The University of North Carolina at Charlotte.
 
Van den Heuvel-Panhuizen, M., & Iliada, E. (2011). Kindergartener’s performance in length measurement and the effect of picture book reading. ZDM Mathematics Education, 43, 621-635.
 
Van den Heuvel-Panhuizen, M., & Van den Boogaard, S. (2008). Picture books as an impetus for kindergartners’ mathematical thinking. Mathematical Thinking and Learning, 10, 341-373.
 
Young-Loveridge, J. (2004). Effects on early numeracy of a program using number books and games. Early Childhood Research Quarterly, 19, 82–89.
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​Using storytelling to teach mathematics
The teaching of mathematics through the use of stories has emerged in recent years as a modern and effective method of teaching. Teachers can use stories to introduce, explain and discuss mathematical concepts in a memorable way. Integrating storytelling within mathematics teaching develops literacy skills and promotes mathematical language (Wiburne & Napoli, 2008). Storytelling helps teachers to create a dynamic and interactive learning environment that supports students to make sense of mathematical vocabulary (Bintz & Moore, 2002).
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The use of storytelling in teaching mathematics can spark students’ interest, reduce their anxiety, engage them in the educational process (Zazkis & Liljedahl, 2009) and provide an alternative explanation of a mathematical concept. Storytelling supports memory, provides learning motivation (Van den Heuvel-Panhuizen, Boogaard Doig, 2009) and improves analytical skills.

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Our study
The main purpose of our study was to investigate the role that the use of storytelling can play in teaching fractions to third grade students. The study sample consisted of 76 third graders (8-9 years old), who attended two primary schools in Greece. This sample was divided into experimental (n=38) and control (n=38) group.

The same teacher applied the teaching program to both groups (experimental and control group). Students of both groups followed the same curriculum for the teaching of fractions (Lemonidis, 2017) and had the same textbook (student book and workbook), which was created by the researchers in accordance with the principles and objectives of the particular curriculum.

When introducing a new mathematical concept to the experimental group, the teacher was reading a teaching story to students while the pictures accompanying the text were displayed. Then, a brief discussion on the content of the story took place in the classroom, while the students were working on math activities related to the story and learning objectives. The teacher was reading the story in an interactive way that fostered communication to accomplish the goal of meaningful student engagement (Courtade, Lingo, Karp, & Whithey, 2013). The Students were encouraged to strategically and purposefully interact with both the teacher and the content of the story. This reading experience requires students to be active participants than passive listeners (National Early Literacy Panel, 2008). Subsequently, students explored mathematical concepts through the processing of textbook activities (student book and workbook).

When introducing a new mathematical concept of fractions to the control group, the teacher used manipulative materials. The students worked with objects, area models, fraction strips and number lines to explore fraction concepts. Subsequently, the students approached mathematical concepts through the processing of textbook activities (student book & workbook).
 

The story
The story, written by the researchers, is entitled "Journey to the Land of Fractions" and includes seven parts. Each part was a target-focused story, namely, it was in accordance with the curriculum objectives. The protagonist of the story is “Takis, the little fraction” a fractional unit (1/8).

Takis fails his school exams and his value decreases as teachers add units to his denominator. Takis feels very disappointed and decides to leave the City of Fractional Units and not return, unless he increases his value. Two whole numbers, 3 and 5, help him overcome obstacles and manage to increase his value. Thus, a fascinating adventure begins, through which students observe the properties of fractions, watching the story's plot unfold.
 

The results
The results showed that the use of storytelling had a positive effect on students’ achievement in fractions, as the experimental group performed significantly better than the control group in post - test. This test was developed by the researchers and included 10 activities and problems that were in line with the teaching objectives of the intervention. These activities were referring to: a) The part-whole interpretation of fraction, b) Placing fractions on number line diagram, g) Creating and manipulating fraction representations and e) Comparing fractions.

Students who benefit most from the use of storytelling were the medium and low achieving students. The use of storytelling had a positive effect on mathematical skills, such as comparing fractions, finding equivalent fractions, creating and manipulating representations and problem solving.

The use of storytelling in teaching mathematics allowed students to approach mathematical concepts in a learning environment with rich stimuli that contributed to conceptual understanding of mathematical concepts (Capraro & Capraro, 2006; Van den Heuvel-Panhuizen, Boogaard, & Doig, 2009). Representations that students created through the use of the stories enriched their mathematical understanding. The students had the opportunity to transform the ideas presented through the stories into their own personal representations. Transforming an idea includes processes, such as rethinking, re-creating and reconstructing it in a new form (Whitin & Whitin, 2001).

As the development of mathematical concepts took place along with the story evolution, students had the opportunity to understand “What is fraction”, how its value changes, and what they should consider when comparing two fractions with a common numerator or common denominator. Subsequently, students could transfer this knowledge to solving problems with similar content.
The results from this study suggest that careful selection of a story and its targeted inclusion in teaching can support students’ understanding of mathematical concepts. Storytelling provides students with a meaningful context in which they can communicate and discuss the mathematical ideas inherent in the text. Students’ learning is more successful when material is presented in a way that is meaningful to them (Price, 2009). The context story provides students an opportunity to develop meaningful knowledge of concepts and processes through investigation rather than memorizing (Carparo & Carparo, 2006). Teachers and parents can use picture books as a way to introduce children to mathematical concepts in a meaningful and applicable way.

 
References

Bintz, W. P., & Moore, S. D. (2002). Using literature to support mathematical thinking in middle school. Middle School Journal, 34(2), 25–32.

Capraro, R. M., & Capraro, M. M. (2006). Are you really going to read us a story? Learning geometry through children’s mathematics literature. Reading Psychology, 27(1), 21–36.

Courtade, G. R., Lingo, A. S., Karp, K. S., & Whitney, T. (2013). Shared story reading. Teaching mathematics to students with moderate and severe disabilities. Teaching Experimental Children, 45, 34–44.

Lemonidis, Ch. (2017). In the trajectory of the rational. Kyriakidis Publications, Thessaloniki, Greece. [in Greek].

National Early Literacy Panel. (2008). Developing early literacy: Report of the national early literacy panel. Washington, DC: National Institute for Literacy.

Price, R. R. (2009). Using children’s literature to teach mathematics. Quantile.

Van den Heuvel-Panhuizen, M., Boogaard, S., & Doig, B. (2009). Picture books stimulate the learning of mathematics. Australian Journal of Early Childhood, 34(3), 30–39.

Wilburne, J. M., & Napoli, M. (2008). Connecting mathematics and literature: An analysis of pre-service education school teachers’ changing beliefs and knowledge. IUMPST: The Journal, 2, 1–10.

Whitin, P., & Whitin, D. (2001). Using literature to invite mathematical representations. In A. A. Cuoco (Ed.), The roles of representation in school mathematics (2001 yearbook of the National Council of Teachers of Mathematics, pp. 228–237). National Council of Teachers of Mathematics.

Zazkis, R., & Liljedahl, P. (2009). Teaching mathematics as storytelling. Sense Publishers.
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Drawing from their research article, titled 'Shared book reading to promote math talk in parent–child dyads in low-income families' which is published in Topics in Early Childhood Special Education journal, the authors - Dr. Nicole M. Hendrix (Emory University), Prof. Robin L. Hojnoski (Lehigh University) and Dr. Kristen Missall (University of Washington) – have put together this short and easy-to-read blog post for interested teachers and parents. We hope you will find their blog post interesting.

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Differences in early mathematical skill and knowledge develop prior to formal schooling, with some children entering kindergarten with greater skills and knowledge than others. Children from lower-income backgrounds, dual language learners, and children with disabilities may be at increased risk for entering school with limited mathematical skills and knowledge (e.g., Hojnoski et al., 2017; National Mathematics Advisory Panel, 2008). Because early mathematical skills and knowledge are related to long-term achievement in both reading and mathematics (Duncan et al., 2007), it is important to provide rich mathematical experiences for young children in their natural environments.
 
Math in the home
The home mathematical environment includes activities, materials, and interactions that support development of mathematical skills and knowledge. Different opportunities to learn in the home environment lead to differences in children’s skills and knowledge. The home learning environment varies widely across families (e.g., DeFlorio & Beliakoff, 2015; Levine et al., 2011), which has implications for school-based learning (Berkowitz et al., 2015; Kleemans et al., 2012). Variability may be due, in part, to gaps in understanding about skills and knowledge young children should develop as well as activities that can support mathematical development in the home. Given the busy lives of many families, it is useful to consider whether mathematical interactions can occur during more common routines, such as shared book reading.
 
During shared book reading, adults can support children’s learning through rich language experiences that go beyond the words on the pages (Towson et al., 2017). Adults can engage children in talking about key vocabulary and concepts embedded within the book, guiding children’s conceptual understanding and language skills through interactive dialogue. Because interactions during shared book reading are related to the content of the book, books can be strategically selected to promote certain types of interactions and learning.

Math in preschool
​​It is critical that young children are provided with experiences that foster mathematics skills (Ginsburg et al., 2008). A child’s classroom provides an opportunity to engage in mathematical learning experiences and build foundational mathematics skills (National Council of Teachers of Mathematics, 2013; NAEYC/NCTM, 2010). Young children often learn through direct instruction, observation, and engaging in games and other mathematics-related tasks (LeFevre et al, 2009; Sonnenschein et al., 2016), but learn best when instruction occurs in situations that children find engaging (NAEYC/NCTM, 2010; Pomerantz & Grolnick, 2017; Sonnenschein et al., 2016; Stites & Brown, 2019). While engaging child-centered opportunities for non-mathematics learning abound in preschool classrooms, mathematics exposure is often more limited (Ginsburg et al., 2008). Children spend an average of only 24 minutes a day with access to mathematics activities versus 77 minutes for literacy (Piasta et al., 2014).
 
Our study
Given this lack of exposure, and the importance of mathematical opportunities, we need to investigate often overlooked areas for mathematics learning. Classroom libraries have long been seen as effective ways to promote literacy development, especially when teachers take an active interest in supporting children’s use of it (Neuman, 1999). This research, along with what we know about reading storybooks with mathematical concepts to improve learning  (Hassinger-Das et al., 2015), indicates that the classroom library should not be left out when looking for ways to support young children’s mathematics learning.
 
We recently surveyed 150 preschool teachers in the USA about the types of books in their classroom libraries and the availability of mathematics-related story books for the children they teach. While we focused our study on preschool classrooms, the information provided likely applies to elementary classrooms as well due to the frequent presence of libraries in these settings. The majority of the teachers who responded to our study indicated they have a classroom library (98%) that they encourage children to use throughout the day during times like free choice and transitions, with children on average spending 10-30 minutes a day exploring books in the library. While most teachers indicated having a well-used library, we found that over 81% of teachers’ classroom libraries contained significantly fewer math books than other types of books. Many teachers reported mathematics storybooks and materials were kept for use in the math center, which are often not as freely available to students as the library.

​Context
Using strategies of interdisciplinary lessons with university preservice mathematics teachers (UPMTs) can often enliven lessons in ways that UPMTs oftentimes do not expect. In our mathematics education classes, we engage our UMPTs through children’s literature-based mathematics lesson activities. One such lesson activity was having UMPTs who are preparing to teach in the elementary or middle school classroom create mathematics lessons based on popular children’s literature. The literature did not have a mathematics theme but our UPMTs developed a mathematics activity incorporating the theme, plot, and or characters in the book. (For complete details on the research-based project, see Wheeler and Mallam (2020)). University faculty can view the activity and replicate it with their UPMTs. Elementary and middle school classroom teachers can view the literature and lessons and modify them to meet the mathematical needs of their K-8 students ​(5-14 year olds).

References

Adler, D. (2016). Don’t throw it to Mo. Penguin Young Readers.

National Governors Association Center for Best Practices, Council of Chief State School Officers (2010). Common Core State Standards for Mathematics. National Governors Association Center for Best Practices, Council of Chief State School Officers. www.corestandards.org/assets/CCSSI_Math%20Standards.pdf

Ray, M. L. (2011). Stars. Beach Lane Books.

Stein, M. K., Smith, M. S., Henningsen, M., & Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. Teachers College Press.

​Wheeler, A., & Mallam, W. (2020).  Examining type and quality of preservice teachers' lessons  based on children's literature.  International Journal on Teaching and Learning Mathematics, 3(1), 1-11. doi: 10.18860/ijtlm. v3i1.9206

​With 114 entries from 22 schools across six countries to judge, the Cindy Neuschwander Award* is very competitive this year. In this interview, 15-year-old Ayal Kaffman, the Award's winner, tells us a bit about himself, his inspiration for his winning maths story picture book entry (titled '​The Tale of Daisy Rabbit and the Autumn Festival') and his message for secondary school maths teachers and students globally.  


*The Cindy Neuschwander Award (12-15 years old category) and the Stuart J. Murphy Award (8-11 years old category) represent the two age categories of MathsThroughStories.org's Young Mathematical Story Author (YMSA) competition​. The competition is the world's first international mathematical story writing competition. 
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​With schools in many countries now being shut indefinitely in an effort to stop the coronavirus outbreak, many parents are increasingly worried about what they can do to support their child’s learning at home over the next few weeks and possibly months. One subject in particular that many parents need help with is maths. While some children may have already been given maths worksheets by their teachers to work on, it will likely be a matter of days before they start to lose their interest in having to routinely solve pages and pages of maths problems. Here at MathsThroughStories.org, we believe that the use of storytelling could serve as an effective maths learning strategy while keeping your child firmly engaged in their maths learning. What’s more – this strategy is not limited to just pre-school children, but is applicable to those in primary (elementary) schools and beyond too.
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Which stories and how to access them?
 
We have previously explained what we mean by maths stories in our earlier blog post, and how storytelling (particularly the picture book format) could help to enrich maths learning in another blog post, so we won’t be repeating them here, though we would encourage you to read these blog posts as well if you have not done so already. The focus of this blog post is more practical in nature, specifically how parents go about choosing which maths story picture books they could use and how to access them.
 
Concerning the former, our non-profit MathsThroughStories.org website contains the world’s largest database of recommendations for maths stories (500+). For your convenience, these recommendations are sorted firstly by maths topics, and then by age groups. You can find our Recommendations page here.
 
To access these books, you can either purchase them on-line (using platforms like Amazon) or find free videos of people reading many of these books on YouTube. We have partnered up with KidTime StoryTime, a YouTube channel, who works hard to get proper permission from publishers to record videos of them reading various story picture books including the many titles that are also on our Recommendations database. To access these videos by KidTime StoryTime, click here. There are also several other YouTube videos of people reading maths story picture books. However, as many of them have not sought permission from publishers to record videos of themselves reading these stories in their entirety, we would not be able to officially and publicly recommend them here, but “if you look, you shall find”.
 
If where you live is not under a lockdown, then you may also find some of our recommended maths story picture books in your local bookstores or public library.
 
It is also worth briefly noting here that all the maths story picture books on our Recommendations database are in English language. That said, many of these books have also been translated by their publishers to several other languages. If you want to use these maths story picture books in non-English languages, some of them do exist, but you will need to do a bit of detective work on Google to find them or simply directly contact relevant publishers. An example below is of ‘A Mousy Mess’ (Driscoll, 2014) with a maths focus on sorting and classifying skills. The story has been translated to Chinese and Spanish. (We will talk more about this story later in this blog post.)
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​How to use stories to enhance your child's maths learning?
 
Many well-written maths story picture books can almost “do the teaching” to young readers themselves without the support of teachers and parents. However, if your children are too young to read independently, then of course you will need to support them with the reading if a printed copy of the story books is used. If the YouTube video version is used, then your children can listen to the stories being read to them.
 
However, you should not limit your role to being just a reader. You can do more to help your child get the most out of their maths stories, for example, by asking a series of questions to draw their attention to the maths elements in the story or by providing resources to facilitate their maths learning based on the story.
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• Concerning the former (i.e. asking questions), we would suggest you giving your child an opportunity to read the story purely for pleasure the first time, and then to go over the story again the second time with the mathematical lens on. The kind of questions you can ask your child can be formulated in a way to foster their mathematical reasoning or to extend their mathematical thinking. To illustrate these examples, let’s use the the ‘A Mousy Mess’ story again. This is a story about a young mouse named Albert, his sister Wanda and their friend Leo who come out to play with a child’s toys before Albert accidentally knocks over the toys out of their different containers. Panicked, they quickly think of different ways to put these toys back to their containers so the people would not know that they had been there. Initially, some toys are sorted by their colour, while others are sorted by their shapes and sizes. Then, Albert finds a “big blue round roll-y ball” which can go into more than one pile. This prompts the mice to rethink about how best the toys should be sorted and organised. To foster your child’s mathematical reasoning, you could ask them why the “big blue round roll-y ball” could go into more than one pile or group. To extend their mathematical thinking, you could give them a few other everyday objects for them to try to sort them into one of the groups (or a combination of the groups). Moreover, you could also ask them to come up with their own sorting criteria (e.g. texture, price, etc.).
• Concerning the latter (i.e. providing resources), once your child has read or listened to the story, you could then ensure that your child has access to a wide range of everyday objects for them to try to sort them out into groups, that is to provide opportunities for your child to interact with concrete materials to give them a solid foundation that could subsequently lead them to the development of more advanced abstract thinking about classification (e.g. sorting numbers into odd and even numbers; sorting numbers into prime numbers and square numbers; sorting 2D shapes based on the number of vertices [angles], etc.).

 
The MathsThroughStories.org website has several ideas on what questions could be asked and what resources could be used to maximise maths learning opportunities. These ideas are drawn from story-based maths lessons taught by experienced teachers in different countries around the world and you can access them for free here.
 
 
Catering for the maths learning needs of older students
 
Maths story picture books for older students
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It is crucial to stress that the use of maths story picture books is not for pre-school children only. There are several well written maths story picture books that cater to the learning needs of older primary (elementary) school students and secondary school students, for example, most titles in the Sir Cumference series as well as ‘What's Your Angle, Pythagoras?’ (Ellis, 2004) and ‘One Grain of Rice’ (Demi, 1997) which can be used to introduce the Pythagorean theorem and exponential growth respectively. Again, several other age-appropriate titles can be found on our Recommendations page.

Older students creating their own mini maths story picture books

​Another way to enhance maths learning through storytelling for older students is by getting them to create their own mini maths story picture books (e.g. just 5-10 pages). It is worth highlighting here that we are not talking about just “writing maths stories”, but for them to actually “create maths story picture books”, that is for them to carefully think about how to visually illustrate abstract maths concepts via their page illustrations too. By contextualising and visualising abstract maths concept (i.e. through coming up with a relevant context/storyline and page illustrations respectively), we argue that it could foster students’ conceptual understanding in maths concepts. Just because a child knows, for example, that 5 x 4 equals 20 does not necessarily mean that they conceptually understand what the concept of multiplication means. In one of our on-going research projects, many 8-9 years-old children in the study when asked to come up with a word problem to represent, for example, 5 x 4, they would write something like: “If Jim has 5 sweets, and his mum gives him 4 more sweets, how many sweets does Jim have altogether?” Learning maths in a way that also helps to develop one’s conceptual understanding is thus crucial.
 
A few simple steps to help your child develop their very own mini maths story picture books:
 
1) decide on which maths topic to focus on in their story (e.g. multiplication);
2) ask them to think of a problem or a crisis in which having the knowledge of that topic could help to meaningfully solve that problem / crisis;
3) think of settings and characters;
4) think of how that maths topic could be visually represented in their page illustrations; and
5) bring all of these ideas together using our suggested maths story template which is downloadable here.
 
If you would like to learn more about enhancing maths learning through creating maths story picture books, read another one of our blog posts on this topic here. In 2019, the MathsThroughStories.org project launched the world’s first international maths story writing competition for young maths learners, and you can find examples of winning and shortlisted maths story picture books from the 2019 competition here. One particular example of maths story picture books we like from the 2019 competition is by Harriet, an 11-years-old pupil from the UK, and her story is titled 'Mindfulness through Maths'. You can read her story here. (Details of the 2020 competition can be found here.)

​In my previous blog posts, I have explained what mathematical story picture books (MSPBs) are, and their key features that could help to enhance pupils’ mathematics learning. In this blog post, I will attempt to convince you to see that pupils should be encouraged not just to read MSPBs, but also to create them.  

​The idea of getting pupils to develop their mathematical understanding through creating their own MSPBs is an innovative mathematics learning strategy that I have been trying to highlight to mathematics teachers (and curriculum developers) in the UK and abroad.
 
Here, I am not talking about asking pupils to create a full-feature 30-page MSPB in one lesson. As a mathematics learning activity, pupils can simply be asked to create their own mini MSPB with just 10 pages (or so) whereby, for example, the first 2 pages set the scene and the problem to be solved by the characters; the next 6 pages can feature three variations (or attempts) in which the characters try to use their mathematical knowledge to solve the problem; and the story can come to a close on the last two pages.
 
 
Why should it matter?
 
When pupils create their own MSPBs, they need to carefully think about the storyline, which requires them to consider practical and meaningful applications of the mathematical concept in question. In brief, they need to contextualise abstract mathematical concepts. Additionally, as the focus is on presenting the stories in the picture book format, pupils also need to actively think about page illustrations, and how best to communicate abstract mathematical concepts and situations visually to their readers. As previously highlighted in my other blog post, not only could learning mathematics through storytelling benefit pupils mathematically, it could also develop their language and creative writing skills and make possible a great cross-curricular teaching and learning opportunity. Equally important, the approach would allow pupils to see mathematics in a different light – one that is less test-driven, and more fun and imaginative. This is crucial especially if we want to improve pupils’ perceptions of the subject.
 
The preliminary findings of my pilot research with 8-9 years old Year 4 (Grade 3) pupils on the effectiveness of this mathematics learning activity is promising. Specifically, the results indicate that pupils in the intervention class (i.e. those that were asked to create MSPB on multiplication) had better conceptual understanding on multiplication (as measured through the study’s test) than their peers in the comparison class who learned multiplication the normal way (e.g. worksheets and textbooks, etc.). This pilot study was very small in scale, so I am spending this academic year to scale up the study to include over 1,300 pupils across 24 primary schools in the south east of England. Updates of this study will be posted on the project’s webpage here.
 
From a distance, having pupils create their own MSPB might look like a cute, fun activity. However, when you carefully examine this approach, you see just how pedagogically powerful it can be. I am surprised this approach has not been used more often, because it costs nothing in terms of resources – just a few sheets of A4 paper, a pencil and a splash of imagination!
 
This mathematics learning activity can also save you time! For example, if the concept in focus is multiplication, you could start the day with your maths lesson by getting your pupils to consider which everyday situations having knowledge about multiplication can help solve problems, and how the concept can be represented visually. Later in the literacy lesson, you could get your pupils to come up with the plot, characters and setting. You could also get them to work on their draft writing paying attention to things like grammar. After lunch, in the art lesson, you could get them to work on page illustrations, and putting their MSPB together. Before home time, the pupils could read their MSPB with the help of a visualiser to their peers. This one activity can be meaningfully integrated across different curricular subjects throughout the day. What’s more – you would have just one set of works to mark. 

​What’s next?
 
If you are inspired by this blog post, I hope you will give this pedagogical approach a go in your future maths lessons! You do not need to ask your pupils to create a MSPB in every single lesson throughout the school year: all I am asking is for you to consider, for example, adopting this approach at the end of each maths topic unit where pupils can use this opportunity to consolidate their learning of that topic unit. 
 
Moreover, I hope you will encourage your pupils to take part in MathsThroughStories.org’s Young Mathematical Story Author (YMSA) competition, which is an annual international competition set up to encourage young mathematics learners (8-15 years old) from around the world to embed their mathematics learning in a meaningful and engaging context through creating their own MSPBs. More details of this competition can be found here and you can find winning and shortlisted entries from the 2019 competition here. 

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​​The idea of using mathematical story picture books (MSPBs) to enrich mathematics learning is not a new idea. In fact, it has been around for almost three decades, particularly in the early years setting. What is less common is using MSPBs to enrich mathematics learning beyond the early years level. I have been arguing - and will continue to argue - that the approach could also benefit mathematics learning of older pupils. Specifically, I would argue that the use of MSPBs could: foster pupils’ conceptual understanding through multi-representation of mathematical concepts, variation of mathematical situations and the use of common misconceptions as a teaching point; develop language skills; and foster engagement with mathematics learning.

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Foster conceptual understanding through multi-representation
 
We can all (hopefully) agree that we do not teach mathematics so that our pupils become a human calculator, that is someone who is good at churning out correct mathematical answers but without conceptually understanding the concept behind it.
 
As part of one of my research projects, when Jack (pseudonym), a 9-year-old pupil, was asked by me what 20 ÷ 5 equals to, he was able to give me the correct answer (4) almost instantly. Then, when he was asked to (contextually) represent 20 ÷ 5 using a word problem, this is what he came up with: “Spanish Yoda had a can of Coke and a bag of bananas and apples and paint. How much did it cost her? Coke: £1.00. Bag of bananas: £2.00. Apples: £8.00. Paint: £9.00. Total £20.00”. How Jack’s word problem is related to 20 ÷ 5 remains a mystery.
 
What Jack demonstrates here is a classic example of pupils whose procedural fluency (i.e. the mechanic aspect of mathematical learning) in relation to division is good, but have yet to fully grasp what the concept means conceptually.
 
As many mathematics education scholars have argued, in order to demonstrate conceptual understanding in mathematics, pupils must be able to represent mathematical concepts in different ways using different representations (e.g. contextualisation, visualisation, etc.). Here, I would argue that key features of MSPBs, such as narrative and page illustrations, make learning mathematics conceptually effective as pupils get to learn mathematical concepts through these different representations. 

Take ‘Divide and Ride’ (Murphy, 1997), for example. This is a story about a group of eleven friends who want to go on carnival rides. Some of these rides have two-people seats, others have three- and four-people seats. As these seats have to be filled up before each ride can begin, the children constantly have to work out how to group themselves. Due to 11 being a prime number, there is always, at least, one person being left out (a remainder), and additional children are consequently invited to join their group to fill up the seats for each ride. Through the storyline, children can visually see how division works and what a remainder means in real life. This helps children to contextualize the concept. Additionally, not only do the illustrations depict division through images of children filling up the seats, they also include a mathematical model at the bottom of each page to represent the divisional situation in a different way as well as corresponding numerals to help children connect visual representation with symbolic representation.

​Theoretically speaking, the more children are able to make meaningful connections between different representations of mathematical concepts, the more conceptual understanding they are demonstrating. Thus, effective mathematical story picture books carefully look at how these different representations can be combined seamlessly throughout the story.
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​​Foster conceptual understanding through variation
 
Another key strength of teaching mathematics using MSPBs is the development of pupils’ conceptual understanding in mathematics through what I refer to as the variation of mathematical situations that are often found in well-written MSPBs. To explain this concept, take ‘Bean Thirteen’ (McElligott, 2007) as an example. The story follows two crickets, Ralph and Flora, who have collected twelve beans to bring home for dinner. When Flora decides to pick one more bean (i.e. Bean Thirteen), Ralph is convinced it will bring bad luck. No matter how many friends they invite to try to share the 13 beans equally, it is always impossible.
 
Situation 1: 13 beans to be shared between 2 crickets (Ralph and Flora) resulting in 1 remaining bean (6 beans each)
Situation 2: 13 beans to be shared between 3 crickets (Ralph, Flora and 1 friend) resulting in 1 remaining bean (4 beans each)
Situation 3: 13 beans to be shared between 4 crickets (Ralph, Flora and 2 friends) resulting in 1 remaining bean (3 beans each)
Situation 4: 13 beans to be shared between 5 crickets (Ralph, Flora and 3 friends) resulting in 3 remaining beans (2 beans each)
Situation 5: 13 beans to be shared between 6 crickets (Ralph, Flora and 4 friends) resulting in 1 remaining bean (2 beans each)
 
In this example, while the number of crickets varies, the number of beans is invariant (kept the same). Through this variation of mathematical situations, rich mathematical investigations are made possible. Pupils can be asked, for example, to continue the pattern to prove that 13 cannot be divided evenly by any other numbers except for 13 itself (and hence demonstrating the meaning of prime numbers in the process). I argue that such variation of mathematical situations is crucial to foster pupils’ conceptual understanding in mathematics.

​Another example of variation of mathematical situations can be found in ‘Fractions in Disguise’ (Einhorn, 2014). This story focuses on the concept of equivalent fractions and it is about how George Cornelius Factor (who happens to share the same acronym, GCF, with – wait for it – the greatest common factor!) invents a machine, called ‘Reducer’ to help him find a very sought-after fraction (5/9) that has been stolen from a fraction auction, and has been disguised as another fraction by the villainous Dr. Brok. While at Dr. Brok’s mansion, GCF uses his Reducer machine to reveal the true form of a range of fractions (e.g. 3/21 is really 1/7; 34/63 is already in its true form; 8/10 is really 4/5, and so on) before he comes across 35/63 which is later revealed as the 5/9 fraction he has been looking for.

Through such variation of mathematical situations, both ‘Bean Thirteen’ and ‘Fractions in Disguise’ make it possible for their readers to take their time to digest the new mathematical concept they are learning by providing them with several mathematical situations or examples to show them what is and what is not prime numbers and equivalent fractions, for example. The goal is that once they have seen enough examples of what is and what is not prime numbers and equivalent fractions, they will arrive at their own definition (and hence understanding) of these concepts themselves. Authors of well-written mathematical stories think carefully about what kind of variation their story needs that could help scaffold students’ learning of a mathematical concept in question. ​

​Develop language skills 
 
From my earlier research (Trakulphadetkrai, Courtney, Clenton, Treffers-Daller, & Tsakalaki, 2017) and those of others, it has been found that children’ mathematical abilities are linked to their language abilities. What is exciting is how recent research (e.g. Hassinger-Das, Jordan, & Dyson, 2015; Purpura, Napoli, Wehrspann, & Gold, 2017) have also found the positive impact of using stories when teaching mathematics concepts to young children on the development of their language abilities particularly their vocabulary knowledge. Why not kill two birds with one stone? Why not teach mathematics using MSPBs to develop both pupils’ mathematical and language development at the same time?

 
Engagement through emotional investment 
 
Another key advantage of teaching mathematics using MSPBs is that pupils arguably do not see MSPBs in the same way that they see, for example, mathematics textbooks or worksheets with word problems after word problems to be solved. They are more likely to view MSPBs as something that they can be emotionally invested in, and something that they can enjoy interacting with over and over again either together with the whole class or in their own time at their own pace. Research (e.g. McAndrew, Morris, & Fennell, 2017) has recently found that the use of stories in mathematics teaching can help to foster children’s positive attitude towards the subject.

​Final words
 
Teaching mathematics using MSPBs should not only be found in Nursery and Reception classes. This creative, cross-curricular and research-informed mathematics teaching and learning approach should too be utilised by teachers teaching at the primary school level and beyond.

​If you want to explore our 500+ recommendations for MSPBs that can be used to cover 40+ mathematical concepts, please head to our Recommendations here, and if you want to see examples of how MSPBs can be integrated as part of your mathematics teaching, see some of our examples here. 

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References
 
Einhorn, E. (2014). Fractions in Disguise. Watertown, MA: Charlesbridge. 
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Hassinger-Das, B., Jordan, N. C., & Dyson, N. (2015). Reading stories to learn math: Mathematics vocabulary instruction for children with early numeracy difficulties. Elementary School Journal, 116(2), 242–264.​
 
McAndrew, E. M., Morris, W. L., & Fennell, F. (2017). Geometry-related children’s literature improves the geometry achievement and attitudes of second-grade students. School Science and Mathematics, 117(1-2), 34-51.
 
McElligott, M. (2007). Bean Thirteen. New York, NY: Penguin's Putnam Publishing Group.
 
Murphy, S. J. (1997). Divide and Ride. New York, NY: HarperCollins.
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Purpura, D. J., Napoli, A. R., Wehrspann, E. A., & Gold, Z. S. (2017). Causal connections between mathematical language and mathematical knowledge: A dialogic reading Intervention. Journal of Research on Educational Effectiveness, 10(1), 116-137.
 
Trakulphadetkrai, N. V., Courtney, L., Clenton, J., Treffers-Daller, J., & Tsakalaki, A. (2017). The contribution of general language ability, reading comprehension and working memory to mathematics achievement among children with English as additional language (EAL): An exploratory study. International Journal of Bilingual Education and Bilingualism. DOI: https://doi.org/10.1080/13670050.2017.1373742
 
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​The ‘story’ in mathematical story picture books
 
Defining stories can be difficult. Haven (2007) attributes this difficulty to the fact that stories are “so interwoven into the fabric of our lives and minds that we can’t step far enough away from our storied world to view stories objectively” (p. 10). Nevertheless, attempts to define the concept have been made. For example, Bruner (2002, pp. 16-17), a leading scholar in the field of educational psychology and narrative, argued that a story must involve a cast of characters who have:

The way stories involve not only characters but also some sort of a struggle or a problem for the characters to solve lends itself perfectly for mathematics teaching and learning whereby characters find themselves having to use their mathematical knowledge and skill to solve a problem that they face in the story. An example of mathematical stories, defined in this way, include ‘A Mousy Mess’ (Driscoll, 2014). This is a story about a young mouse named Albert, his sister Wanda and their friend Leo who come out to play with a child’s toys before Albert accidentally knocks over the toys out of their different containers. Panicked, they quickly think of different ways to put these toys back to their containers so the people would not know that they had been there. Initially, some toys are sorted by their colour, while others are sorted by their shapes and sizes. Then, Albert finds a big blue round roll-y ball which can go into more than one pile. This prompts the mice to rethink about how best the toys should be sorted and organised. The story encourages young readers to think of other ways the toys can be sorted to help Albert, Wanda and Leo solve the problem. 

​However, we know from experience that not every story necessarily has to have a struggle or a problem for characters to solve. Take the much-loved ‘Handa’s Surprise’ (Browne, 2014) as an example. Set in a village of the Luo tribe in south-west Kenya, this story is about a girl, Handa, who wants to surprise her friend, Akeyo, with seven delicious fruits. Handa put the fruits in a basket, which itself sits on Handa’s head. Along the journey to see Akeyo, seven different mischievous animals take the fruits one by one from the basket without Handa knowing, until there is nothing left. As she is walking past a tangerine tree, lots of tangerines fall onto the basket on top of Handa’s head (presumably very gently and very quietly!). By the time she sees Akeyo, Handa is herself surprised to see lots of tangerines in the basket instead of the seven different fruits she picked for her friend. In this story, there are certainly characters and a storyline (regardless of how simple it is), but no problems nor struggles for Handa to solve, and yet this story provides a meaningful context for young readers to learn a range of mathematical concepts, such as subtraction. 

Stories can thus be defined more liberally as any narratives that simply have a storyline and a character(s). While such characterisation might seem painfully obvious to some, it is crucial to make explicit these key components of a story. This is particularly important as not every picture book has a story. Let’s take, for example, ‘One is a Snail, Ten is a Crab’ (Sayre & Sayre, 2003). While this book is very useful in helping young children learn to count and add through a series of illustrations of people and animals with different number of legs (e.g. “1 is a snail. 2 is a person. 3 is a person and a snail.”), it is not a mathematical story in that it contains no plots or storylines. It is a concept book with some lovely illustrations and some texts. That said, this should not necessarily be interpreted as concept books are inferior to mathematical story picture books. The key message here is simply that it is important that we all have a precise language to communicate with one another on what it is that we are referring to.

Here at MathsThroughStories.org, our focus is on mathematical story picture books, as opposed to concept books. The reason for this is that we strongly believe that the story component has the potential to make mathematics learning experience much more engaging and could be particularly useful for developing students' reading comprehension ability and vocabulary knowledge. I talk a bit more about these two points in my other blog post here. 

In summary, mathematical story picture books (or MSPBs) are here referred to as picture books that contain a narrative relating to mathematical ideas or applications. 

​Types of mathematical story picture books
 
Story picture books that are used to enhance mathematics teaching and learning can have either an explicit or implicit mathematical focus.
 
Story picture books with an explicit mathematical focus can be quite easy to spot as they often have mathematical terms in their title as well as recommendations for relevant mathematics learning activities which can usually be found at the end of the book. Many of them are also often found as part of a mathematical story series. For example, ‘A Mousy Mess’ (Driscoll, 2014) that we have come across in the previous section is part of Kane Press’s Mouse Math series (20 titles altogether). Other series include: HarperCollins’s MathStarts series (63 titles), Scholastic’s Hello Math Reader series (40 titles), and Kane Press’s Math Matters series (42 titles). These series are perfect for Early Years and Key Stage 1 children. There are also Charlesbridge’s Math Adventure series (16 titles) and Sir Cumference series (10 titles), which are great for Key Stages 2 and 3 pupils (7-14 years old).
 
However, stories that are great for mathematical teaching and learning do not have to have an explicit mathematical focus. In addition to ‘Handa’s Surprise’ (Browne, 2014) that we have already seen in the previous section, another example of story picture books with an implicit mathematical focus include ‘The Doorbell Rang’ (Hutchins, 1986). Nowhere in this story picture book did the author claim it to be written for mathematics teaching and learning, and yet the narrative lends itself nicely to mathematical investigations as shown here.

Quite often, the teachers who have what I refer to as mathematical lens, or the ability to identify meaningful opportunities for mathematics teaching and learning in story picture books with an implicit mathematical do not need to rely on explicit mathematical story picture books. Such ability can be particularly useful for teachers working in a class or a school that may not be able to afford to buy new picture books with an explicit mathematical focus. With the mathematical lens on, teachers can use any of their existing story picture books and turn them into a mathematics teaching and learning resource.
 
 
Final words
 
Regardless of how explicit or implicit the mathematical focus is, mathematical story picture books can be a powerful mathematics teaching and learning tool for the reasons outlined in my other blog post.

​If you want to explore our 500+ recommendations for mathematical story picture books that can be used to cover 40+ mathematical concepts, please head to our Recommendations section here, and if you want to see examples of how mathematical story picture books can be integrated as part of your mathematics teaching, see some of our examples here. 

Please use the Comments section below if you would like to discuss some of the ideas presented in this blog post. 
 
 
References
 
Browne, E. (2014). Handa’s Surprise. London, UK: Walker Books.

Bruner, J. (2002). Making stories: Law, literature, life. Cambridge, MA: Harvard University Press.

Driscoll, L. (2014). A Mousy Mess. New York, NY: Kane Press.

Haven, H. (2007). Story proof: The science behind the startling power of story. Westport, CT: Libraries Unlimited.

Hutchins, P. (1986). The Doorbell Rang. New York, NY: Mulberry Books.

​Sayre, A. P. & Sayre, J. (2003). One is a Snail, Ten is a Crab. London, UK: Walker Books Ltd.