Catherine Attard outlines how picture books can be used for mathematics.
Student engagement with mathematics has been a concern to educators for many decades. One of the reasons students disengage is the challenge to see the relevance and application of mathematics within meaningful contexts. One effective way to improve student engagement in the primary classroom is through the use of picture books. They provide interesting contexts for mathematics and make maths lessons fun, engaging, and creative, while integrating important literacy skills. They also lend themselves to the working mathematically processes that are the core of our mathematics curriculum – problem solving, reasoning, communicating, understanding and fluency.
Rather than promoting simple content-based mathematics, picture books provide important opportunities for students to extend beyond computation through to problem solving, and even further, to mathematical investigation. Have you ever considered using picture books in your mathematics lessons to provide an interesting and creative context for mathematical exploration and investigation?
Promoting problem solving and investigation
Mathematical investigations move beyond problem solving, yet are not ‘project work’. They are inquiry-based and support a constructivist approach to learning in which learners actively construct their own knowledge through reflection on physical and mental actions.
The idea of investigation is fundamental both to the study of mathematics itself and also to an understanding of the ways in which mathematics can be used to extend knowledge and to solve problems in very many fields.
Cockroft, 1981, p. 250
During investigation-based work, learning is placed within a purposeful context that requires students to engage in mathematics by combining content knowledge with higher order thinking skills and creativity. Investigations provide insights into the work of mathematicians and mathematics as a career, as well as providing opportunities for students to adapt, modify, and build on prior knowledge (National Council of Teachers of Mathematics, 2000).
Children’s picture books can provide a rich context from which to begin mathematical investigations. They provide opportunities for students to incorporate creativity into mathematics while creating links across other subject areas. Using literature as a stimulus for open-ended investigation can provide each student in the class an opportunity to achieve success, regardless of mathematical ability, by creating a rich, shared context. There are many picture books that lend themselves to mathematical investigations – some are written with that purpose in mind, and others are books that were not intended for use as a stimulus for mathematics, but naturally lend themselves to mathematical exploration. Marston (2010) identifies three different types of mathematical picture books:
1. Explicit – books purposefully written for teaching and learning in the mathematics classroom, for example, ‘Counting on Frank’ (Clements, 1990) and ‘How Big is a Foot?’ (Myller, 1991)
2. Perceived – books with incidental mathematical concepts as perceived by the teacher, such as, ‘Goldilocks and the Three Bears’
3. Embedded – books that have embedded mathematical ideas but are written to entertain rather than specifically for teaching and learning, like ‘Uno’s Garden’ (Base, 2013).
A good book to use as a stimulus for mathematical investigations is one that builds intrigue and excitement in the mathematics classroom. It may also include the use of humour, which is important if you want to engage young learners needing support. A popular picture book is ‘Math Curse’ (Scieszka & Smith, 2007), which describes a young child who gets a ‘math curse’ after his teacher, Mrs Fibonacci, says ‘you know, you can think of almost anything as a math problem’. This book encourages readers to see mathematics in almost everything they do, from waking up in the morning to catching the bus to school, and sharing cup cakes with the class. Throughout the book, the authors have placed interesting mathematical challenges mixed with lots of humour.
The best way to begin a mathematical investigation is to read the book, and then brainstorm possible mathematical questions that could be explored. Once students have had a chance to share their ideas, it is up to the teacher to facilitate how the investigation should progress. Students can form groups and select an area to investigate, or they can conduct an individual investigation that could be teacher guided. Perhaps a group could select more than one area to investigate.
From problem solving to problem posing with ‘Math Curse’
What is the purpose of getting students to pose mathematical problems? First of all, the problems give us good insight into whether students recognise mathematical situations, and whether they understand where, how, and what mathematics is applied in day to day situations. An added bonus is that the students are highly engaged because they have ownership of the mathematics they are generating, the topics they choose are of interest to them, and stereotypical perceptions of school mathematics are disrupted.
The following are examples of student work from a Year 3 classroom. In this classroom, the teacher read Math Curse to the students before challenging them to create their own class maths curse. The children took their own photographs and, working in small groups, they came up with a range of mathematical problems and investigations, which they then gave to other groups to solve.
- If there are 31 people in the class (10 boys and 21 girls) and all of them have hair that is 30cm long. Half of the boys cut 10cm off their hair, the other half cut 20cm off their hair. How long is the class’s hair now altogether? How long was it before? How much hair has been cut altogether?
- Check your friend’s hair. Estimate how long it is when it is out, how long it is when it is in a ponytail, and how long it is when it is in a braid. List some different ways you could check if your estimate is accurate? What are the potential problems with your methods?
- I’m 9 years old. I had really long hair for 6 years, then I cut it. How long did I have short hair for?
- I have 5 friends that are girls and 2 friends that are boys. All 5 girls have hair length of 50cm. The boys both have different lengths of hair. The first boy has 30cm of hair, the second has 25cm of hair. What is the difference between the first boy and the girls and the second boy and the girls?
1. Write down the dates of important celebrations. If you add all the dates together, what is the value of their numbers?
2. How many days are there in 6 years?
3. If everyone’s birthday occurred every three years (starting the year you are born) what years would your birthday fall on?
4. If Lisa and Jane went on a holiday every 2 months, how many holidays could they take in a year?
5. If you could rearrange the seasons, what months would you choose to be Spring? Why?
6. What is the most popular letter in the days of the months?
7. Why do you think there are 4 seasons in a year?
The students who wrote the examples above completed a structured written reflection following the sequence of designing and solving each other’s maths curses. Here are some of the reflection prompts and a sample of responses:
1. What did you enjoy about today’s learning?
‘Working with my team.’
‘Working at the problems for a long time and then finally getting them after a long, hard discussion.’
‘Solving questions that my friends wrote.’
‘I felt challenged and I learnt more about what maths is.’
‘Working with my group, choosing our own questions and learning something new.’
‘I liked the chess card the best because we had to solve it together and use problem solving.’
‘Having a go at tricky questions even if I got them wrong.’
2. Did you learn anything new?
‘How to work things out in different ways.’
‘Working in groups helps you learn more skills.’
‘Not every question uses just one skill like addition, division, multiplication or subtraction.’
‘When I am challenged I learn more.’
‘Maths is not always easy.’
‘How to work together.’
‘Everyone in the group has different responses so we needed proof to figure out the right one.’
3. What surprised you about this task?
‘It surprised me how hard my own questions were.’
‘I got a shock! We had to research to solve some problems, Adam even taught me how to add a different way.’
‘It was hard but if we put our brains into gear we could figure it out.’
‘I was able to play while doing maths.’
Using picture books as a stimulus for these types of activities has multiple benefits for students. Contextualising the mathematics using students’ interests highlights the relevance of the curriculum, improves student engagement, and makes mathematics meaningful, fun and engaging!
References and further reading
Base, G. 2013, Uno’s garden, Penguin Books Australia, Sydney.
Clement, R. 1990, Counting on Frank, Collins, Sydney.
Marston, J. 2010, ‘Developing a framework for the selection of picture books to promote early mathematical development’, in C. Hurst, B. Kissane, & L. Sparrow, (eds) Shaping the future of mathematics education, proceedings of the annual conference of the Mathematics Education Research Group of Australasia, MERGA, Fremantle WA.
Myller, R. 1991, How big is a foot?, Yearling, New York.
National Council of Teachers of Mathematics 2000, Principles and standards for school mathematics, NCTM, Reston, VA.
Scieszka J. & Smith, L. 2007, Math curse, Viking, New York.
How to cite this article: Attard, C. 2017, 'Teaching mathematics through picture books', Scan, 36(4), pp. 6-10