6 September 2016

The nature of mathematics and statistics and what it means to learn and teach them

I’ve been thinking lately…. Sometimes it pays to stop and think. I have been reading a recent textbook for mathematics teachers, Dianne Siemon et al, Teaching mathematics: foundations to middle years (2011). On page 47 the authors asked me to “Take a few minutes to write down your own views about the nature of mathematics, mathematics learning and mathematics teaching.” And bearing in mind I see statistics as related to, but not enclosed by mathematics, I decided to do the same for statistics as well. So here are my thoughts: The nature of mathematics Mathematics is a way of modelling and […]
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 […]
10 February 2014

Why I am going to ICOTS9 in Flagstaff, Arizona

I was a university academic for twenty years. One of the great perks of academia is the international conference. Thanks to the tax-payers of New Zealand I have visited Vancouver, Edinburgh, Melbourne (twice), San Diego, Fort Lauderdale, Salt Lake City and my favourite, Ljubljana. This is a very modest list compared with many of my colleagues, as I didn’t get full funding until the later years of my employ. Academic conferences enable university researchers and teachers from all over the world to gather together and exchange ideas and contacts. They range from fun and interesting to mind-bogglingly boring. My first […]
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 […]
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 […]
1 July 2013

Why learning objectives are so important

Update in 2017 This is one of the most popular posts on this blog. You may also be interested in a case study of what happens when students do not get learning objectives: Why people hate statistics. Original post: The most useful thing I learned in my teacher training at Auckland College of Education in 1985 was to write learning objectives. Not many years, and two babies later, I began lecturing at the University of Canterbury in Management Science/Operations Research. I was the only academic staff member to have formal teacher-training. My first task, when put in charge of MSCI210, […]
17 June 2013

Why engineers and poets need to know about statistics

I’m kidding about poets. But lots of people need to understand the three basic areas of statistics, Chance, Data and Evidence. Recently Tony Greenfield, an esteemed applied statistician, (with his roots in Operations Research) posted the following request on a statistics email list: “I went this week to the exhibition and conference in the NEC run by The Engineer magazine. There were CEOs of engineering companies of all sizes, from small to massive. I asked a loaded question:  “Why should every engineer be a competent applied statistician?” Only one, from more than 100 engineers, answered: “We need to analyse any […]
27 May 2013

Probability and Deity

Our perception of chance affects our worldview There are many reasons that I am glad that I majored in Operations Research rather than mathematics or statistics. My view of the world has been affected by the OR way of thinking, which combines hard and soft aspects. Hard aspects are the mathematics and the models, the stuff of the abstract world. Soft aspects relate to people and the reality of the concrete world.  It is interesting that concrete is soft! Operations Research uses a combination of approaches to aid in decision making. My mentor was Hans Daellenbach, who was born and […]
8 April 2013

Which comes first – problem or solution?

In teaching it can be difficult to know whether to start with a problem or a solution method. It seems more obvious to start with the problem, but sometimes it is better to introduce the possibility of the solution before posing the problem. Mathematics teaching A common teaching method in mathematics is to teach the theory, followed by applications. Or not followed by applications. I seem to remember learning a lot of mathematics with absolutely no application – which was fine by me, because it was fun. My husband once came home from survey school, and excitedly told me that […]