15 February 2017

Educating the heart with maths and statistics

What has love got to do with maths? This morning at the Twitter chat for teachers, (#bfc630nz) the discussion question was, How and what will you teach your students about life this year? As I lurked I was impressed at the ideas and ideals expressed by a mixed bunch of teachers from throughout New Zealand. I tweeted:  “I wonder how often maths teachers think about educating the heart. Yet maths affects how people feel so much.” My teaching philosophy is summed up as “head, heart and hands”. I find the philosophy of constructivism appealing, that people create their own understanding […]
8 March 2016

Papamoa College statistics excursion to Hamilton Zoo

Last week I had a lovely experience. I visited the Hamilton Observatory and Zoo as part of a Statistics excursion with the Year 13 statistics class of Papamoa College. The trip was organised to help students learn about where data comes from. I went along because I really love teachers and students, and it was an opportunity to experience innovation by a team of wonderful teachers.  The students travelled from Papamoa to Hamilton, stopping for pizza in Cambridge. When we got to the Hamilton Observatory, Dave welcomed us and gave an excellent talk about the stars and data. I found […]
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. […]
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 […]
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 […]
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 […]
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, […]
24 June 2013

Difficult concepts in statistics

Recently someone asked: “I don’t suppose you’d like to blog a little on the pedagogical knowledge relevant to statistics teaching, would you? A ‘top five statistics student misconceptions (and what to do about them)’ would be kind of a nice thing to see …” I wish it were that easy. Here goes: Things that I have found students find difficult to understand and what I have done about them. Observations When I taught second year regression we would get students to collect data and fit their own multiple regressions. The interesting thing was that quite often students would collect unrelated […]