Our brains are psychologically predisposed to prioritise stories. We remember them much more easily than information that lacks narrative. The idea of designing a curriculum and sequences of learning to tell a story gives us a framework for our decisions. If we are choosing between several options – in the order we teach something, the tasks we use or the methods we demonstrate – having an idea of the narrative we want to gradually reveal helps us to make those decisions.
Leslie Dietiker of Boston University describes the metaphor of ‘story’ for planning sequences of learning in a paper in which the aspects of story – characters, plot, actions, tension etc. – are used to think about what happens in the mathematics classroom. Dietiker (2015) tells us that when we sequence mathematical events, they are experienced by the ‘reader’ as a mathematical story. In our mathematical story, the characters could be numbers, algebraic terms, shapes and so on. The mathematical action is the activity of the ‘actor’: the pupil, the teacher or a third party described in a word problem. The setting of the story is where the mathematical events happen and could be any representation, model, or manipulative, such as a ratio table, Cartesian graph or algebra tiles. The story must have a plot that brings the pupils from what they already know to the new knowledge, sometimes with tension, sometimes with anticipation, and sometimes with a twist. Storytelling works as a metaphor for curriculum, a learning sequence within that curriculum and a lesson within that sequence.
If, for instance, we want our pupils to learn about prime numbers, then how to decompose a composite number into a product of its prime factors, before applying this prime factorisation in various contexts, we might tell a story a bit like this over a sequence of lessons.
- All positive integers (natural numbers) have factors.
- Some, like 24, have lots of factors.
- Most have factors in pairs.
- Some have an odd number of factors. These are the square numbers.
- The number 1 is a very special number, the only one that is a factor of all natural numbers.
- Some natural numbers have only two factors. These are special because the two factors are always themselves and 1. We call these prime numbers.
- There is only one even prime number. All the rest are odd.
- We can multiply prime numbers together to make other numbers. We will call this ‘composing’ prime numbers.
- Composing 2 and 3 gives 6. Composing 2, 3 and 5 gives 30. Let’s explore which numbers we can make by composing primes.
- Some natural numbers can’t be made by composing primes. These are the prime numbers.
- Every natural number (greater than 1, because 1 is special) is prime or can be composed from primes.
- We can take any natural number that is not prime and decompose it. We call this its ‘prime factorisation’.
- We can use this prime factorisation to discover all sorts of things about natural numbers.
- The highest common factor of pairs of numbers.
- The lowest common multiple of pairs of numbers.
- Whether they are square/cube/…
- The number of trailing zeros they have.
- …
The sequence here is a plot summary. It doesn’t begin to delve into how we tell the story – the questions we ask, the tasks pupils engage in, the problems we set, the solutions we explain, what we make explicit, what we ask them to think about for themselves. These are the considerations that make the story come alive. These are the things that a teacher does to make learning memorable, to help pupils become successful. These are the things that we cover throughout the rest of this book*.
* The book being Succeeding as a Maths Teacher, by Caroline Kennedy, Amie Meek, Emma Weston, and me. This post is an excerpt. Over the next few weeks I’ll share more excerpts, but if you can’t wait, you can always get it now – we think you’ll love it!
References
Dietiker, L. (2015), ‘Mathematical story: a metaphor for mathematics curriculum’, Educational Studies in Mathematics, 90, (3), 285–302.
The World Is Maths 