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This content is taken from the Cambridge University Press's online course, Teaching Probability. Join the course to learn more.
1.1

## Cambridge University Press

Skip to 0 minutes and 5 seconds Welcome to our FutureLearn course on teaching probability. My name is David Spiegelhalter. Probability is important - none of us know what is going to happen in the future and probability provides a structure and language for analysing the uncertainty we all face. Every day we hear about the risks that might come from our environment or our behaviour, what the weather might be tomorrow, how the climate might change in the future and we have to decide whether to take out insurance or even what medical treatments to accept. So some understanding of probability is a vital skill for dealing with everyday life, apart from it being fascinating in its own right. But probability is not generally well taught in schools.

Skip to 0 minutes and 50 seconds It can be reduced to an abstract, algebraic level which has little to do with realistic applications. Also the curriculum often jumps very quickly from obvious things, such as a one in six chance of getting a six when throwing a die to combining probabilities which is much more complex than is generally given credit for. I’m often asked why people find probability unintuitive and difficult and I reply that after years working on the topic I finally concluded that probability can be unintuitive and difficult, unless it is taught in a clear and transparent way. This course introduces ideas that should help with that teaching. Hello, my name’s Jenny Gage I taught probability in UK schools during my career as a classroom teacher.

Skip to 1 minute and 40 seconds I never felt I did it particularly well. Then some 15 years ago I went out to South Africa to teach teachers who had never studied probability, it was new on their curriculum at that time. They had enormous problems with the way we do it here, which is what I took with me - the coins, the dice, the cards. In particular they couldn’t get their heads round the 6 on the die not meaning 6 but meaning something else, maybe a goal scored or something and I started to wonder what our Year 7s make of it all. At the same time I’d started working with David Spiegelhalter and was really impressed with his approach using whole numbers as far as possible.

Skip to 2 minutes and 16 seconds A colleague is South Africa gave me the idea of spinners and a new way forward opened up. I worked on the classroom resources both with South African teachers and with classes and teachers in the UK. Eventually David and I felt we had enough material to write a book, which proved very timely as the new GCSE curriculum in the UK for instance uses the idea of natural frequencies, and whole numbers, so the book and the course are very much of the moment. This week we will start by trying to pin down what we mean when we talk about probability and give you a chance to reflect on the importance of this topic.

Skip to 2 minutes and 52 seconds We will then fairly quickly get down to some practical ideas for teaching probability, getting you to do experiments, collect the results and represent the outcomes in a range of ways.

# Week 1 Introduction

Watch this video, in which Professor Sir David Spiegelhalter introduces the course.

• After watching, please use the comments to introduce yourself, and tell us what you hope to gain from the course.

Derek Huby says: “I’m an experienced mathematics teacher, adviser and writer. I’m interested in how learners make sense of mathematics and probability in particular, both inside and outside the classroom.” Derek will be your Course Mentor for Teaching Probability, and will be looking in frequently to check on your progress and help with any questions you may have.

David Spiegelhalter says: “I got interested in teaching probability through my work on risk communication, where research had convincingly shown that the idea of ‘expected frequencies’ was helpful in improving understanding of probability, both for professionals and school students. I started working with school groups, and then developed teaching materials with Jenny as part of the Cambridge Millennium Mathematics Project’s NRICH site. The idea for a book was born.”

Jenny Gage says: “As a maths teacher, I found teaching probability uninspiring at best, and often difficult. My students either could do it, or they couldn’t, and it was hard to help them understand - because when it came down to it, I too was simply operating techniques without much real understanding. We teachers were urged to do more experiments, because that would help. Well, it was more fun, certainly, but the interpretation of the experiments was often quite limited, with big jumps in understanding ignored. When I started working with teachers in South Africa, for whom probability was new, I tried everything I knew - and found it lacking. David Spiegelhalter’s approach, based on whole numbers, opened my eyes! As I worked with him, and with other teachers, both in the UK and in South Africa, I became increasingly excited that there was a way to teach probability which wasn’t dry and boring, or just doing experiments that didn’t really teach anything much. As we worked on the set of probability resources for NRICH, the thought of a book became more and more a possibility, and ultimately a reality. The online course is one way to ensure that what we have discovered about teaching probability, and the structured approach we have devised, get as wide dissemination as possible.”