13 November 2018

Conceptual knowledge and procedural fluency when teaching maths and stats

Conceptual vs procedural when teaching maths and stats April 2008, Salt Lake City. It was my first NCTM conference and I was awed by the number of dedicated teachers of mathematics in one place. I had soaked in a pre-conference series about teaching statistics and my head was full of revolutionary ideas. I can’t remember the workshop I was attending but I declared that I saw no point in teaching students to calculate standard deviations by hand – and that I never did. The response was awesome! There was just about a stand-up battle between teachers who agreed with me […]
14 July 2016

Enriching mathematics with statistics

Statistics enriches everything! In many school systems in the world, subjects are taught separately. In primary school, children  learn reading and writing, maths and social studies at different times of the day. But more than that, many topics within subjects are also taught separately. In mathematics we often teach computational skills, geometry, measurement and statistics in separate topics throughout the school year. Textbooks tend to encourage this segmentation of the curriculum. This causes problems as students compartmentalise their learning.  They think that something learned in mathematics can’t possibly be used in Physics. They complain in mathematics if they are asked […]
9 March 2015

Divide and destroy in statistics teaching

A reductionist approach to teaching statistics destroys its very essence I’ve been thinking a bit about systems thinking and reductionist thinking, especially with regard to statistics teaching and mathematics teaching. I used to teach a course on systems thinking, with regard to operations research. Systems thinking is concerned with the whole. The parts of the system interact and cannot be isolated without losing the essence of the system. Modern health providers and social workers realise that a child is a part of a family, which may be a part of a larger community, all of which have to be treated […]
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 […]
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 […]
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 […]
1 April 2013

Context – if it isn't fun…

The role of context in statistical analysis The wonderful advantage of teaching statistics is the real-life context within which any applicaton must exist. This can also be one of the difficulties. Statistics without context is merely the mathematics of statistics, and is sterile and theoretical.  The teaching of statistics requires real data. And real data often comes with a fairly solid back-story. One of the interesting aspects for practicing statisticians, is that they can find out about a wide range of applications, by working in partnership with specialists. In my statistical and operations research advising I have learned about a […]
25 February 2013

Interpreting Scatterplots

Patterns, vocab and practice, practice, practice An important part of statistical analysis is being able to look at graphical representation of data, extract  meaning and make comments about it, particularly related to the context. Graph interpretation is a difficult skill to teach as there is no clear algorithm, such as mathematics teachers are used to teaching, and the answers are far from clear-cut. This post is about the challenges of teaching scatterplot interpretation, with some suggestions. When undertaking an investigation of bivariate measurement data, a scatterplot is the graph to use. On a scatterplot we can see what shape the […]
21 January 2013

Statistics or Calculus? Do both!

This post is prompted by two 17 year old boys, Cam and Thomas, who are about to enter year 13, the final year of High school in New Zealand. They are both academically capable, with highly educated parents. And both boys are struggling with a dilemma – should they  take Calculus or Statistics at school this year. I suspect their maths teachers are pushing for calculus, whereas their parents appreciate the value of statistics. Let’s take a look at the alternatives and see if we can help. (This makes no pretense of being a balanced view – that’s what comments […]
15 October 2012

Optimal instruction in Statistics and Operations Research

Optimise everything! I had a colleague who believed that everything could and should be optimised. He had a diet Linear Program which he used to plan his meals to provide optimal nutrition. Unfortunately the Linear Program didn’t seem to have a constraint to ensure the food was palatable, and he would eat combinations like sardines, broccoli and sunflower seeds for lunch. My colleague also believed that there must be an optimal way to teach, that would maximise the learning outcome. I am doubtful that there is such a thing, bearing in mind the diversity of human experience. However I like […]