How to be Inventive When Teaching Primary Mathematics

Developing outstanding learners

Steve Humble

• Publisher: Routledge
• Year: 2015
• Print ISBN: 9781138843417
• eBook ISBN: 9781317550709
• Topic: Bildung
• Subtopic: Bildung Allgemein

Have you ever taken your children on a maths walk?

Are your pupils shape detectives?

How to be Inventive When Teaching Primary Mathematics is a pocket guide to inspire primary teachers to become confident, effective, imaginative teachers who enjoy teaching, and whose pupils enjoy learning. It is packed with exciting, creative, unexpected ideas, to help teachers and pupils open their eyes to the mathematical world around them. It gives teachers the tools to develop their own classroom activities and experiences, supporting learners as they move fluently between mathematical ideas and develop their ownership of mathematics: Take your pupils on a maths walk, meet dinosaurs, visit art galleries, learn your destiny number, create your first human graph in the playground and learn how to be an algebra magician.

Written by Steve Humble, expert teacher, teacher trainer and, as Dr Maths, advocate for the power and potential of mathematics, this friendly, stimulating guide offers a fresh, practical approach to teaching mathematics, based on the best research and practice, and years of experience in the field. Focussing on five key mathematical topics - number, geometry, measurement, statistics and algebra – it is structured in the form of a journey, introducing historical facts, ideas for innovative and inventive classroom activities and explorations of the key misconceptions for each topic.

How to be Inventive When Teaching Primary Mathematics will challenge you to think about your own beliefs and how they influence your practice, and help you understand how best to transform your teaching to stimulate children's emotions to improve knowledge, learning and enjoyment of the beauty of maths.

Chapter 1

Our mathematical world

If you can count your money, you don’t have a billion dollars.

J. Paul Getty

Opening your mathematical eyes in any town, city, village or countryside will allow you (and your students) to experience maths in a new way. Realizing that maths is not just a subject in school but is part of your everyday world gives you more ownership of that knowledge and allows you to see connections that otherwise you may never have associated with maths.

So what do I mean?

Look at the patterns of fields, hedges and lines of trees. How about street grid systems, bridges, buildings and paving stone patterns? Looking more closely at buildings we can often see lines of symmetry in windows, fire escapes and doorways.

Typically our surroundings have been constructed by our ancestors. They were using their logical minds following clear patterns that we can all ‘see’ but maybe never have.

Until now.

Around us are shapes such as triangles, rectangles and circles, as well as three-dimensional objects such as cuboids, pyramids and spheres. What is interesting is that these shapes are known as Euclidean shapes. They are named after a Greek mathematician, Euclid, who in about 300 BC wrote a series of books which classified all the geometrical properties of different shapes. Euclid created a blueprint that all mathematical architects have used ever since in the construction of the man-made world we live in. Not only may you find this interesting but so will your students.

So tell them.

The reason for telling them is that some of your pupils will be interested in history, people and the past, and maybe not so interested in maths (yes really). Talking about history in your maths lesson will offer a hook upon which to hang mathematics and draw in those students. Ownership of mathematics is also very important for children and adults so they can say: ‘this is my maths’. In art and English lessons it’s easy for children to have ownership: ‘this is my piece of art’ or ‘these are my thoughts in this essay’. It seems at first glance that in mathematics this is harder to do, if not impossible. I’m going to show you in this book that this is not true and children can have ownership of ‘their maths’.

FIGURE 1.1 Cauliflower fractals

The natural world follows a different blueprint that mathematicians have recently discovered. One such mathematician was Benoit Mandelbrot who wrote a famous book called The Fractal Geometry of Nature (1983). This world he discovered (along with other mathematicians) also has beautiful mathematical symmetries. The geometry of the natural world we now call ‘fractals’ and can be seen clearly in objects such as ferns and cauliflowers. If you take a part of a fern it looks like the whole fern; likewise each individual floret of a cauliflower looks like the whole cauliflower (Figure 1.1). This is called self-symmetry.

So why not take your class out for a mathematical walk in order to open your children’s mathematical eyes? What could be more exciting? It’s like a mathematical treasure hunt. The treasures are hidden all around us.

HOW TO PLAN AND ORGANIZE YOUR FIRST MATHS WALK

One way to open your students’ mathematical eyes is to take them on a maths walk.

Outdoor maths walks can supply further evidence of enhanced learning. They are meaningful, stimulating, challenging and exciting for children. Most important, these walks invite all students, irrespective of their classroom achievement level, to participate successfully in problem solving activities and gain a sense of pride in the mathematics they create. As youngsters discover real-world shapes, patterns, numbers, data, symmetry and reflections – to name just a few examples – their eyes open to the mathematics in their world. They become maths detectives – posing questions and solving problems as well as documenting and communicating their discoveries in multiple ways.

Teachers and parents value insights into children’s mathematical learning and the different ways that this learning can be fostered in the home, the local community and the school environment. Adults also appreciate seeing their youngsters totally immersed in learning. As one teacher said during a maths walk I was organizing, ‘I’ve seen my children ready to “pop” because they have been so excited about what they’ve discovered’.

A typical walk consists of a sequence of designated sites along a planned route where students stop to explore maths in the environment. Maths walks make mathematics come alive for children by engaging them cognitively, physically and emotionally.

First you need to think about what you want your students to see with their mathematical eyes. Plan this beforehand. Go for a walk at the weekend. See if you can find, for example, some fractal symmetry in nature and also some man-made symmetries.

Students and teachers alike can create walks that target a range of mathematical understanding. We can classify maths walks under four main categories:

• Student-created – Pupils from the same grade can design a walk for each other. Alternatively older children in the school can create a walk for their younger peers.

• Teacher-created – You yourself design the walk. Once the children have had an opportunity to answer the questions along the way you can encourage them to modify your walk to produce a new and improved version.

• Teacher-created and community – You not only design the walk for the children but now you include their families as well. These types of walks can explore the school surroundings, their homes and their local community environment.

• Teacher-created and peers – Now you have become an expert you can inspire the rest of your colleagues to try a maths walk for themselves. This will allow them to think about mathematics from a different standpoint involving the use of other subjects such as history and literature, something up until now they may not have considered.

When first creating a maths walk give some initial thought to its proposed purpose and the anticipated learning outcomes. For example, if children are undertaking a unit on shape and pattern, then the maths walk could focus on exploring various shape and pattern examples in the school buildings and in the grounds, e.g. let them become ‘shape detectives’.

Here are some useful starting questions upon which to base your initial discussion with the class:

• Find three objects where you can see one line of symmetry.

• Find an object with rotational...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• List of illustrations
• About the author
• Introduction
• 1 Our mathematical world
• 2 Starting points: number
• 3 More and more numbers
• 4 On the journey: measurement
• 5 Many paths to take: geometry
• 6 Ownership: statistics and probability
• 7 Almost there: algebra
• 8 Starting your own new journey
• Appendix
• Glossary
• References
• Index