The Numberverse: How Numbers are Bursting Out of Everything and Just Want to Have Fun
Andrew Day, Peter Worley
Format: PDF / Kindle (mobi) / ePub
The Numberverse will take you on a journey into the world of numbers, which are everywhere: over our heads, under our feet, and all around us. This book is designed especially for people who do not like math, so if you are one of those who find math boring, hard, annoying or pointless then this book is for you to enjoy.
First we'll look at stuff you find all around you. Numbers are in the walls and in church arches. In pine cones and petals. Continue looking and numbers will start jumping out at you, patterns will appear before your eyes, and you will see the secrets of The Numberverse opening up to you. And it doesn't stop there. Would you like to know the history of zero and what people did before zero was invented? How did people get along without fractions and percentages before they were invented? Do we even need them, anyway?
It's all in The Numberverse, and you will understand every word of it if you can understand what you are reading now. It's true: if you can count, and you are curious, well, then you have all the knowledge you need for the journey.
You can't expect to pluck a new topic out of the ether if it seems completely unrelated to any previous knowledge you might have, and the same goes for your students. For primary and secondary teachers to use with children aged 7-13 years, The Numberverse takes you through a series of thought experiments, activities, stories and histories which build the foundations for a deep understanding (and maybe even love!) of math. If math has always been a closed book to you, now is the time to turn to the first page. Also note: there are no tests anywhere in this book.
talking aloud, you focus almost completely on positive reinforcement. The term ‘positive reinforcement’ comes from the 1930s behaviourist school of psychology. Their founder, B. F. Skinner, and his followers believed that almost any behaviour could be produced in almost any human or animal by using positive and negative reinforcement – in other words, reward and punishment. If you are trying to train a pigeon to do a somersault, you give it a nasty electric shock when it stands still (that’s
to them. Trust that when one child starts to do what you want, your positive reinforcement will be picked up by other pupils, and soon more of them will work it out for themselves. In the same way, get children to commit to contradictions or errors by repeating them. So, you would say: So are you saying that because the four 2s add up to 8, there are eight numbers on the board? A lot of the time this will trigger a rethink in the speaker, but not always. And even if not, you have now made it
children to be socially isolated because they think other children are not up to their level, so the need to explain themselves and the opportunity to do so are good for them. 1 My colleague Peter Worley coined the term ‘iffing’ for this technique – see The If Machine: Philosophical Enquiry in the Classroom (London: Continuum, 2010), p. 35 for his explanation. It is actually a specific way of anchoring the group to the original question, but a very important and powerful one. A Jump to the
things make certain other things happen in certain circumstances, other times they don’t. This problem was burrowed into by the Scottish philosopher David Hume. Hume was fat, funny and believed in very little indeed. Famously, he expressed doubts about induction, which is our basic way of learning about the world. What is induction? It is what we have just been thinking about. So, if I prick myself with a pin, I find that it hurts. From this I draw the conclusion that if I prick myself with a
and providing all kinds of ideas, many of which I may have unwittingly passed off as my own in subsequent conversations. Alison Sharp and Kirstin Fisher at Ravenscroft School for pushing me so far out of my comfort zone that it disappeared behind me in the distance. Also, the teachers there for allowing me into their classrooms and giving me the benefit of their own experience. All the children and teachers I have worked with over the last few years who have shown me where these ideas were