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 […]
29 July 2013

Let’s hear it for the Triangular Distribution!

Telly monster is my favourite character on Sesame Street, and a few years ago I was lucky enough to actually meet him. This morning I was delighted to find out from my resident Sesame Street expert that Telly monster is a triangle lover. I too am becoming a triangle lover. I have learned recently about the triangular distribution. For some reason it is in the New Zealand curriculum and I wondered why, never having used it or seen it in any statistics textbook. I still don’t know the official motivation for including it, but it is a really good idea. […]
22 July 2013

Conceptualising Probability

The problem with probability is that it doesn’t really exist. Certainly it never exists in the past [once we know the outcome]. (Looking for the Experimental Design post linked from our Newsletter? Use this link.) 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. […]
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 […]
5 November 2012

Probability, Perception and False Positives

An understanding of probability empowers people to make informed choices in matters of great importance, including health screening, insurance, major weather events and terrorist threat. Unfortunately it has been shown that this understanding of probability eludes even some of our most educated professionals and decision-makers Perceptions of Probability and Risk There is a considerable body of work studying people’s perceptions of probability and risk, particularly by Amos Tversky and the Nobel prize-winning Daniel Kahnemann. This has uncovered many systematic errors humans make in judging the relative probabilities of uncertain events. The brain’s tendency to find patterns results in heuristics or […]
3 September 2012

What Mathematics teachers need to know about statistics

My post suggesting that statistics is more vital for efficient citizens than algebra has led to some interesting discussions on Twitter and elsewhere. Currently I am beginning an exciting venture to provide support materials for teachers and students of statistics, starting with New Zealand. These two circumstances have led me to ponder about why maths teachers think that statistics is a subset of mathematics, and what knowledge and attitudes will help them make the transition to teaching statistics as a subject. An earlier post called for mathematics to leave statistics alone. This post builds on that by providing some ways […]
10 July 2012

Statistics and chocolate

Some time ago I promised to blog about how to teach statistics with chocolate. Anyone who has watched my youtube videos may have noticed a recurring theme. Helen sells Choconutties. These are a fictitious chocolate bar, originally devised to require a table of prices, which would require the use of absolute and relatives references. As the series developed Helen had all sorts of issues with her sales, which required statistical analysis, often using spreadsheets. For the “choosing the test” video I managed to come up with seven different chocolate-based scenarios. I’ve had complaints from my students that using my materials […]
26 June 2012

All models are wrong

In my title I quote George Box, who wrote,  “Essentially, all models are wrong, but some are useful“. I wish economists would remember this more often. Statistics and Operations Research (and many other sciences) are based on the concept of a mathematical model. Aspects of a “real world” problem are quantified, analysed, explored, experimented with, sometimes even optimised, and the results are linked back to the original problem. This idea of a model is one we have tried to teach our students. It is a surprisingly difficult idea, and one that needs frequent revisiting. The following diagram is more complex […]
7 May 2012

Uncertainty, luck and control

Is probability mathematics or statistics? Probability is often taught alongside statistics, and it is a rather uneasy alliance. Mathematics teachers like probability. It behaves as a good mathematical topic should, and gives nice exact answers. But it also provides the theoretical underpinnings to the rather murkier subjects of statistics, modeling and operations research. An understanding of probability is needed for simulation, queueing theory, inference, decision analysis, project management and inventory control. Mathematics teachers should love probability as it is a subject that lends itself to hands-on activities and real-life applications. Problem is, the whole uncertain nature of probability means that […]