5 February 2018

The Central Limit Theorem – with Dragons

To quote Willy Wonka, “A little magic now and then is relished by the best of men [and women].” Any frequent reader of this blog will know that I am of a pragmatic nature when it comes to using statistics. For most people the Central Limit Theorem can remain in the realms of magic. I have never taught it, though at times I have waved my hands past it. Students who want that sort of thing can read about it in their textbooks or look it up online. The New Zealand school curriculum does not include it, as I explained […]
9 January 2018

Videos for teaching and learning statistics

It delights me that several of my statistics videos have been viewed over half a million times each. As well there is a stream of lovely comments (with the odd weird one) from happy viewers, who have found in the videos an answer to their problems. In this post I will outline the main videos available on the Statistics Learning Centre YouTube Channel. They already belong to 24,000 playlists and lists of recommended resources in textbooks the world over. We are happy for teachers and learners to continue to link to them. Having them all in one place should make […]
20 July 2017

Dragon Trainer rich mathematical task

I love rich mathematical tasks. Here is one for all levels of schooling. What do you think? Background to rich tasks A rich task is an open-ended task that students can engage with at multiple levels. I use the following information from the nrich website when I am talking to teachers about rich tasks. Background to Dragonistics data cards In this task we use our Dragonistics data cards, which are shown here. For a less colourful exercise you could use 24 pieces of card with numbers 1 to 8 on them. Each dragon has a strength rating of between 1 […]
18 January 2016

The normal distribution – three tricky bits

There are several tricky things about teaching and understanding the normal distribution, and in this post I’m going to talk about three of them. They are the idea of a model, the limitations of the normal distribution, and the idea of the probability being the area under the graph. It’s a model! When people hear the term distribution, they tend to think of the normal distribution. It is an appealing idea, and remarkably versatile. The normal distribution is an appropriate model for the outcome of many natural, manufacturing and human endeavours. However, it is only a model, not a rule. […]
23 May 2014

Introducing Probability

I have a guilty secret. I really love probability problems. I am so happy to be making videos about probability just now, and conditional probability and distributions and all that fun stuff. I am a little disappointed that we won’t be doing decision trees with Bayesian review, calculating EVPI. That is such fun, but I gave up teaching that some years ago. The reason probability is fun is because it is really mathematics, and puzzles and logic. I love permutations and combinations too – there is something cool about working out how many ways something can happen. So why should I […]
16 December 2013

Deterministic and Probabilistic models and thinking

The way we understand and make sense of variation in the world affects decisions we make. Part of understanding variation is understanding the difference between deterministic and probabilistic (stochastic) models. The NZ curriculum specifies the following learning outcome: “Selects and uses appropriate methods to investigate probability situations including experiments, simulations, and theoretical probability, distinguishing between deterministic and probabilistic models.” This is at level 8 of the curriculum, the highest level of secondary schooling. Deterministic and probabilistic models are not familiar to all teachers of mathematics and statistics, so I’m writing about it today. Model The term, model, is itself challenging. […]
23 September 2013

On-line learning and teaching resources

Twenty-first century Junior Woodchuck Guidebook I grew up reading Donald Duck comics. I love the Junior Woodchucks, and their Junior Woodchuck Guidebook. The Guidebook is a small paperback book, containing information on every conceivable subject, including geography, mythology, history, literature and the Rubaiyat of Omar Khayyam.  In our family, when we want to know something or check some piece of information, we talk about consulting the Junior Woodchuck Guidebook. (Imagine my joy when I discovered that a woodchuck is another name for a groundhog, the star of my favourite movie!) What we are referring to is the internet, the source […]
2 September 2013

Open Letter to Khan Academy about Basic Probability

Khan academy probability videos and exercises aren’t good either Dear Mr Khan You have created an amazing resource that thousands of people all over the world get a lot of help from. Well done. Some of your materials are not very good, though, so I am writing this open letter in the hope that it might make some difference. Like many others, I believe that something as popular as Khan Academy will benefit from constructive criticism. I fear that the reason that so many people like your mathematics videos so much is not because the videos are good, but because […]
19 August 2013

The importance of being wrong

We don’t like to think we are wrong One of the key ideas in statistics is that sometimes we will be wrong. When we report a 95% confidence interval, we will be wrong 5% of the time. Or in other words, about 1 in 20 of 95% confidence intervals will not contain the population parameter we are attempting to estimate. That is how they are defined. The thing is, we always think we are part of the 95% rather than the 5%. Mostly we will be correct, but if we do enough statistical analysis, we will almost definitely be wrong […]
5 August 2013

Parts and whole

The whole may be greater than the sum of the parts, but the whole still needs those parts. A reflective teacher will think carefully about when to concentrate on the whole, and when on the parts. Golf If you were teaching someone golf, you wouldn’t spend days on a driving range, never going out on a course. Your student would not get the idea of what the game is, or why they need to be able to drive straight and to a desired length. Nor would it be much fun! Similarly if the person only played games of golf it […]