How often do you progress from problem solving to investigation-based work in your mathematics classroom? Have you ever considered using children’s literature in your mathematics lessons to provide an interesting and creative context for mathematical exploration?
“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).
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. 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 literature 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 children’s 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:
- Explicit: books purposefully written for teaching and learning in the mathematics classroom, e.g. Counting on Frank (Clements, 1990) or How Big is a Foot? (Myller, 1962);
- Percieved: books with incidental mathematical concepts as perceived by the teacher e.g. Goldilocks and the Three Bears; and
- Embedded: books that have embedded mathematical ideas but written to entertain rather than specifically for teaching and learning e.g. Uno’s Garden (Base, 2013)
A good book to use as a stimulus for mathematical investigations is one that builds intrigue and excitement in your classroom. A good book will also include humour, whch is important if you want to engage reluctant learners. One of my favourite children’s books is Math Curse (Szieska & 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…”. The 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.
Here is are some websites that list children’s literature suitable for use in mathematics teaching and learning:
Base, G. (2013). Uno’s garden. Sydney: Penguin Books Australia
Clement, R (1990). Counting on Frank. Sydney: Collins
Marsten, J. (2010). Developing a Framework for the Selection of Picture Books to Promote Early Mathematical Development. In C. Hurst, B. Kissane, & L. Sparrow (Eds). In Shaping the future of education. Proceedings of the annual conference of the Mathematics Education Research Group of Australasia. Fremantle WA: MERGA
Myller, R. (1962). How big is a foot? New York: Bantam Doubleday Dell Publishing Group
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM
Szieska J., & Smith, L. (1995). Math Curse. New York: Penguin