Andrew Day - The Numberverse : How numbers are bursting out of everything and just want to have fun

1. This and That Make Ten
   Number bonds and operations
2. The Real Deal
   Numbers, digits and numerals
3. 1, 2, 3, Lots
   The purpose and scope of numbers
4. Two Square Thoughts
   The nature of numbers
5. Base Jumping
   The decimal system and its alternatives
6. A Jump to the Left and a Step to the Right
   Place value
7. A Plus Point
   Addition and the beginnings of mathematics
8. Dont Drag the Tables
   Rote learning
9. The Cocky Chicken
   Mathematical knowledge and logic
10. Square Are They?
    Shapes and definitions
11. Prime Innit, Sir
    Prime numbers
12. Arch Angles
    Geometry in art
13. Less to Square
    Square numbers
14. This Land is My Land
    Area
15. Zero the Hero
    The history and development of our number system
16. Squintasticadillion and One
    High numbers and the invention of numerical terms
17. Beauty Secrets
    The golden section in art and nature
18. A Bit More Than Three
    Pi, and the perimeter and area of a circle
19. Inbetweeny Bits
    The concept of fractions
20. Half to You
    Fractions in everyday language
21. Action Fractions
    The practical application of fractions
22. Go Compare
    Percentage
23. Your Average Number
    Averages mode, median and mean
24. Our Street
    Geometry in the built environment
25. Sets Education
    Sets and the individuals number line
26. Stairs Into Space
    Estimating, reasoning and dividing
27. Bone Setting
    Algebra
28. Voyager
    Maths as universal truth

I didnt mean to get interested in maths. I wasnt even supposed to be doing it. What I normally do is visit schools and run philosophy sessions for an hour at a time. Doing philosophy with children doesnt mean telling kids the names of old dead men and what their theories were. We get children to philosophise themselves: to give reasons and compare ideas. We call these lessons enquiries. In our class enquiries we touch on, among other things, science, morals, religion, language and sometimes numbers.

Then one day a school asked me to show their staff how to use the philosophical approach with all subjects in other words, to turn lessons into enquiries, putting the children themselves at the heart of the lesson, with their curiosity driving it. This was daunting because I was training people more qualified and experienced than me. But at least I had an idea. So, with the help of some colleagues and the teachers themselves, I began to make some progress. That is how I ended up trying to create maths lessons.

Teachers are sometimes surprised to be told that philosophy and mathematics are closely related. They expect there to be links between philosophy and religion, psychology and literature, and there are, but philosophy has been practised by mathematicians, and vice versa, from the very beginning. In fact, Pythagoras, one of the earliest mathematicians, and perhaps the easiest one to name, was also a philosopher in the sense we understand it now.

As a philosopher, I had a grasp of some of the fundamental questions of what mathematics is. Admittedly, having not studied maths to a very high level it was impossible for me to follow the expert answers to those questions. But, as I explained to some of the teachers I met, not being good at something is sometimes an ideal position from which to teach it, because you can empathise with the students, whereas if you find something easy, your hardest task can be to see why someone else would fail to understand.

When I sat down to start, my first thought was that you would need to make mathematics practical to show how the things being taught are useful in everyday life. But, as I read the curriculum documents, I found constant references to children acquiring a sense of number in the abstract. They were supposed to gain an understanding of how the whole number system fitted together and the patterns that run through it. Good luck with that, I thought. I was sure children wouldnt be interested unless you found a practical application.

How wrong I was. I dont think Ive ever been more wrong about anything.

As soon as I set youngsters puzzles using pure numbers they leapt into them. And whats more, they had questions. And theories. Sometimes they were well wide of the mark, but because I didnt mind, neither did they. Time after time, I saw children trying to make more sense of what they already knew, and to connect it up to new ideas. To them, the most elementary bits of mathematics were open to question and nothing was taken as read. I persevered with the practical aspect as well, because I thought it was important, but it often took more effort to engage the children that way.