Picture books engage students through narrative that provides a context for learning. Within that context, teachers can build the language of mathematics and develop models for problem solving that students can apply to their learning in unfamiliar situations.
Pictures and words
Picture books provide children’s first experiences with problem solving. They sift through the information to try and make sense of the story and the world around them. The beginnings of problem solving in mathematics lie in searching for mathematical ideas within a narrative. It seems a natural progression to introduce picture books to the mathematics classroom.
The aim of Mathematics in K–10, NSW syllabuses for Australian curriculum, is for students to:
- be confident, creative users and communicators of mathematics, able to investigate, represent and interpret situations in their personal and work lives and as active citizens
- develop an increasingly sophisticated understanding of mathematical concepts and fluency with mathematical processes, and be able to pose and solve problems and reason in Number and Algebra, Measurement and Geometry, and Statistics and Probability
- recognise connections between the areas of mathematics and other disciplines and appreciate mathematics as an accessible, enjoyable discipline to study, and an important aspect of lifelong learning. Mathematics K–10 syllabus, NSW syllabuses for the Australian curriculum.
Where to start
Planning is vital to ensure that students can work towards the aims outlined above. Here are some ideas to get started:
- develop a good relationship with the teacher librarian to locate the most appropriate picture books
- know your students’ stage or age of learning to determine how a picture book is used – picture books support ‘’visualisation– that crucial bridge between concrete and abstract
- think about the teaching and learning cycle: What do they already know ... conceptually?
- backward map, break down concepts and begin from the appropriate starting point for your students.
Programming for the 21st century learner in mathematics
When programming, consider these points:
- the 4Cs – critical thinking, communication, collaboration, creativity
- the Quality teaching framework
- learning/teaching scaffolds
- the language of mathematics
- resources – What? Where? How?
Literacy of mathematics in the early stages
As a Mathematics K–6 Consultant in Northern Sydney Region (2008–2010), I first explored working with picture books in the mathematics classroom through a pilot project. The focus was to increase student engagement and improve student learning outcomes in number.
In collaboration with Stage 2 teachers in participating schools, learning sequences that targeted the literacy of mathematics were designed around a narrative with which the students were familiar. These were found in engaging picture books that were purpose written or incidentally presented mathematical ideas. Carefully structured scaffolds, which utilised Anne Newman’s ‘Error analysis’, also known as Newman’s prompts, (Newman, 1977) as a teaching and learning tool, supported students as they worked on problem solving tasks.
Evaluation of the project showed a high level of engagement by all students, particularly students who had struggled with mathematics in the past and had ‘switched off’. It also highlighted an increase in student communication, and the capacity to use a range of written strategies with success when solving word problems.
The open-ended nature of the tasks supported students at all levels of ability and their enjoyment of mathematics was clear. Quantitative data gathered on a fortnightly basis demonstrated an improvement in student learning outcomes. Qualitative data gathered from teachers over time demonstrated increased enjoyment in teaching mathematics and the capacity to meet the learning needs of their students.
The success of this project encouraged me to delve more deeply into the world of picture books as a teaching and learning resource in mathematics, and to develop tools to support teachers and students alike in linking literacy and numeracy in the classroom. I also wanted to go beyond the number strand and develop integrated units of work in all stages.
In 2011, I returned to the classroom and have continued to work with teachers across all stages using fabulous picture books such as Shaun Tan’s ‘The Lost Thing’, Nadia Wheatley’s ‘My Place’, Jeannie Baker’s ‘Mirror’, Jon Scieszka’s ‘Math Curse’and Jean-Luc Fromental’s ‘365 Penguins’. A recent favourite for younger students is Herve Tuillet’s ‘Press Here’.
Developing a context for learning
Most primary school teachers feel confident in the literacy classroom, but this is often not the case when it comes to teaching mathematics. Lessons in mathematics built around picture books offer a familiar learning environment for teachers and students.
Effective pedagogy from the literacy classroom can be transferred directly to the mathematics classroom. Teachers and students are comfortable with the notion of studying a whole text in the literacy classroom and then breaking it down into manageable chunks.
Picture books offer the opportunity to present mathematical concepts in the same way.
Reading with a ‘mathematical eye’, teachers can map out picture books and plan learning experiences that address the central themes of working mathematically. With a framework in place, teachers can plan one or two lessons to gain a sense of where their students are in terms of engagement, and meeting their learning needs, before planning an entire unit of work or teaching and learning sequence.
Lessons built around concepts and delivered through a whole class integrated approach to develop knowledge, skills and understanding (rather than built around a single activity, or addressing a single syllabus outcome) can bring about significant change in learning and teaching when embedded in the narrative of a picture book. Learning experiences that involve students in role play or drawing and making when working with picture books in a literary context, transfer easily to a picture book that presents mathematical ideas.
Many students face language issues in the mathematics classroom that impact significantly on their understanding of mathematical ideas, capacity to investigate problems and success in recording their learning.
Picture books offer the opportunity to incorporate active learning experiences in the mathematics classroom. As we already know, the discussion that flows naturally from exploring picture books supports language development. Taking on the role of certain characters to act out problems presented in a text, writing or drawing also provide a direct connection to the narrative and an opportunity to use language linked to mathematical ideas. Experiences like these facilitate the acquisition of mathematical terms and the everyday language needed to explain mathematical ideas.
Using picture books
Teachers can familiarise themselves with picture books to plan learning experiences to:
- introduce concepts
- consolidate concepts
- guide activities
- provide a springboard for problem solving
- contain the problems themselves
- provide a strong link between literacy and numeracy.
My place:position and data
‘My Place’, by Nadia Wheatley and Donna Rawlins,provided the springboard for learning experiences that introduced: informal and formal mapping, collection and representation of data, and writing and visual arts with a ‘mathematical flavour’to my Stage 2 class in 2011. This book provided a strong link between literacy and numeracy as seen in the final maps below. Emulating the writing style of Nadia Wheatley and the informal maps with ‘chatty’labels of Donna Rawlins, Year 4 students told the story of their first decade and mapped out their place– writing and visual arts sat naturally with mathematics.
All students were actively engaged in their learning and deepened their understanding of numeracy concepts through their connection to a rich narrative in a real world setting. Their work in HSIE at the time also focused on changes to their local area over time.
The following Stage 2 student work samples show learning experiences from the ‘My Place’ unit.
Through a scaffolded approach, writing has become an important part of our mathematics lessons. The key to success has been the opportunity for students to discuss mathematical ideas with a learning partner of like ability at planned intervals during each lesson and jointly constructing written responses before writing independently as each new concept is introduced. Talking and writing focus on the five working mathematically processes to support students at all levels of ability in deepening their conceptual understanding of mathematical ideas in all strands of mathematics.
Integral to this success has been the building of vocabulary walls linked to mathematical concepts. This means that, over a series of lessons, there is a language for students to draw on when they are talking and writing. Vocabulary walls can take many forms. My preference is to build them by writing on a whiteboard so the words are visible all the time. Using a different coloured marker, I draw a cloud around each word to make it stand out. Other teachers prefer an interactive whiteboard or laminated cards.
Visual arts: representing mathematical ideas
Picture books, like ‘The Lost Thing’by Shaun Tan, provide a wealth of opportunity to explore mathematical ideas through visual arts. In 2012, my Stage 3 class deepened their understanding of 2D and 3D space and built a sophisticated mathematical vocabulary to describe features and properties through their learning experiences in visual arts.
Again, linking maths and art is not new and there are many resources available to teachers to do so, but tapping in to visual images within a picture book provides another connection for problem solving and the opportunity for discussion and practical tasks to deepen conceptual understanding.
Examples of teaching and learning sequences
Sample lessons, planning scaffolds, teaching and learning sequences, and targeted assessment opportunities are available for working with each of these picture books:
- ‘Mirror’, ‘The Lost Thing’and‘My Place’ — problem solving: planning scaffolds — Early Stage 1, Stage 1, Stage 2 & Stage 3
- ‘365 Penguins’ — Working Mathematically, Whole Numbers, Addition & Subtraction, Multiplication & Division, Fractions and Decimals, Patterns & Algebra, Time, Chance — Early Stage 1, Stage 1, Stage 2 & Stage 3
- ‘Math curse’ — Working Mathematically, Whole Numbers, Multiplication & Division, Fractions & Decimals, Patterns & Algebra, Length, Time, Data — Stage 2 & Stage 3
- ‘My Place’ — Working Mathematically, Whole Number, Time, Position, Data — Stage 2 & Stage 3.
A final note
Just like our students when they create artworks, there are many ‘happy accidents’when working with picture books in a numeracy context. Begin with one lesson and see where it takes you and your students. So many ideas that integrate key learning areas and deepen student understanding of numeracy concepts will surface as you explore picture books with a ‘mathematical eye’.
References and further reading
Baker, J. 2010, Mirror = Mira’t, Walker, UK, 2010.
Fromental, J. & Jolivet, J. 2006, 365 penguins, Abrams, New York.
Join a reading adventure rap, NSW Curriculum and Learning Innovation Centre, NSW Department of Education and Communities, accessed 12 April 2013.
Newman, A. (1977) ‘Newman’s prompts’, Numeracy Skills Framework, NSW Department of Educaton, accessed 20 January 2018.
NSW Department of Education and Training 2003, Quality teaching in NSW public schools. Discussion paper, Professional Support and Curriculum Directorate, Sydney, NSW.
Partnership for 21st Century Learning 2011,Above and beyond: the story of the 4Cs, Fable Vision, accessed 20 January 2018.
Scieszka, J. & Smith, L. 2007, Math Curse, Viking, New York.
Tan, S. 2000, The Lost Thing, Lothian, Port Melbourne, VIC.
Tuillet, H. 2010, Press Here, Allen & Unwin, Crow’s Nest, NSW.
Wheatley, N. & Rawlins, D. 2012, My Place, Walker, Newtown, NSW.
Keywords: mathematics, literacy, numeracy, picture books, programming, K-6;
How to cite this article: McCredie, J. 2013, ‘Picture books: Engaging students in numeracy’, Scan 32(2)