24 April 2017

Graphs – beauty and truth

Graphs – beauty and truth (with apologies to Keats) A good graph is elegant I really like graphs. I like the way graphs turn numbers into pictures. A good graph is elegant. It uses a few well-placed lines to communicate what would take a paragraph of text. And like a good piece of literature or art, a good graph continues to give, beyond the first reading. I love looking at my YouTube and WordPress graphs. These graphs tell me stories. The WordPress analytics tell me that when I put up a new post, I get more hits, but that everyday […]
14 October 2016

Play and learning mathematics and statistics

The role of play in learning I have been reading further about teaching mathematics and came across this interesting assertion: Play, understood as something frivolous, opposed to work, off-task behaviour, is not welcomed into most mathematics classrooms. But play is exactly what is needed. It is only play that can entice us to the type of repetition that is needed to learn how to inhabit the mathematical landscape and how to create new mathematics. Friesen(2000) – unpublished thesis, cited in Stordy, Children Count, (2015) Play and practice It is an appealing idea that as children play, they have opportunities to […]
6 October 2014

A Statistics-centric curriculum

Calculus is the wrong summit of the pyramid. “The mathematics curriculum that we have is based on a foundation of arithmetic and algebra. And everything we learn after that is building up towards one subject. And at top of that pyramid, it’s calculus. And I’m here to say that I think that that is the wrong summit of the pyramid … that the correct summit — that all of our students, every high school graduate should know — should be statistics: probability and statistics.” Ted talk by Arthur Benjamin in February 2009. Watch it – it’s only 3 minutes long. […]
6 January 2014

Statistics – Singular and Plural, Lies and Truth

Language is an issue in teaching and learning statistics. There are many words that have meanings in statistics, different from their everyday meaning, and even with multiple meanings within the study of statistics. Examples of troublesome words are: error, correlation, regression, significant, model. I wrote about addressing this in Teaching Statistical Language. But the problem starts even with the name of the subject. There are at least three meanings for the term “statistics”. The word is not even consistently singular or plural. I suggest three meanings are: Data (plural), analysis (singular) and information (plural). What we teach focusses on the […]
16 September 2013

How to learn statistics (Part 2)

Some more help (preaching?) for students of statistics Last week I outlined the first five principles to help people to learn and study statistics. They focussed on how you need to practise in order to be good at statistics and you should not wait until you understand it completely before you start applying. I sometimes call this suspending disbelief. Next I talked about the importance of context in a statistical investigation, which is one of the ways that statistics is different from pure mathematics. And finally I stressed the importance of technology as a tool, not only for doing the […]
9 September 2013

How to study statistics (Part 1)

To students of statistics Most of my posts are directed at teachers and how to teach statistics. The blog this week and next is devoted to students. I present principles that will help you to learn statistics. I’m turning them into a poster, which I will make available for you to printing later. I’d love to hear from other teachers as I add to my list of principles. 1. Statistics is learned by doing One of the best predictors of success in any subject is how much time you spent on it. If you want to learn statistics, you need […]
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 […]
26 August 2013

Statistics is not beautiful (sniff)

Statistics is not really elegant or even fun in the way that a mathematics puzzle can be. But statistics is necessary, and enormously rewarding. I like to think that we use statistical methods and principles to extract truth from data. This week many of the high school maths teachers in New Zealand were exhorted to take part in a Stanford MOOC about teaching mathematics. I am not a high school maths teacher, but I do try to provide worthwhile materials for them, so I thought I would take a look. It is also an opportunity to look at how people […]
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 […]
22 July 2013

Conceptualising Probability

The problem with probability is that it doesn’t really exist. Certainly it never exists in the past. Probability is an invention we use to communicate our thoughts about how likely something is to happen. We have collectively agreed that 1 is a certain event and 0 is impossible. 0.5 means that there is just as much chance of something happening as not. We have some shared perception that 0.9 means that something is much more likely to happen than to not happen. Probability is also useful for when we want to do some calculations about something that isn’t certain. Often […]