variation

26 November 2019

Creating and critiquing good mathematical tasks with variation theory

Variation Theory applied to teaching mathematics and statistics Highlights Careful selection of exercises can turn purposeful practice in maths into a task that also develops conceptual understanding. Poor, off-the-cuff or random selection of exercises can create barriers, feed misconceptions and at best miss out on opportunities for better learning. Using a framework of variation theory can help teachers examine and improve their practices and tasks, preferably collaboratively Spurious rules If students can learn a spurious rule for answering questions rather than the desired concept, they will grab it with both hands. In my class a student worked out that if […]
5 June 2019

Achievable challenge in teaching maths

I like a good challenge I always choose the most difficult Sudoku puzzles. I like it best if I get really stumped and have to leave the puzzle and come back later. If I do manage to crack it, I feel a sense of achievement, and completion. From time to time I have tried “The most difficult sudoku” but have never managed to place more than one number. There isn’t a lot of fun in that. Fun exists in what is sometimes called “The Goldilocks zone” – not too easy, not too difficult, but just right. I have also seen […]
18 March 2013

Confidence Intervals: informal, traditional, bootstrap

Confidence Intervals Confidence intervals are needed because there is variation in the world. Nearly all natural, human or technological processes result in outputs which vary to a greater or lesser extent. Examples of this are people’s heights, students’ scores in a well written test and weights of loaves of bread. Sometimes our inability or lack of desire to measure something down to the last microgram will leave us thinking that there is no variation, but it is there. For example we would check the weights of chocolate bars to the nearest gram, and may well find that there is no […]
24 September 2012

Teaching experimental design

Teaching Experimental Design – a cross-curricular opportunity The elements that make up a statistics, operations research or quantitative methods course cover three different dimensions (and more). There are: techniques we wish students to master, concepts we wish students to internalise, and attitudes and emotions we wish the students to adopt. Techniques, concepts and attitudes interact in how a student learns and perceives the subject. Sadly it is possible (and not uncommon) for students to master techniques, while staying oblivious to many of the concepts, and with an attitude of resignation or even antipathy towards the discipline. Techniques Often, and less […]
26 January 2012

Sampling Error Isn't

I hope you committed to a response in the box before reading this post. This is an important topic. Recently I read an amusing blog regarding poor sampling technique. The tweet that led to the link called it “a humorous look at sample error”. I’m hoping the person who tweeted meant bad sampling, because the problem is, the story was not about sampling error. And that is because sampling error isn’t. Isn’t what? It isn’t error. It doesn’t occur by mistake. It is not caused by bad procedures. There is nothing practical you can do when sampling to avoid sampling […]