Alison Gibbs. University of Toronto
In Canada, school curricula differ by province, but most Canadian mathematics curricula include glimpses of statistical thinking, typically in the middle grades. In the province of Ontario, tracing the statistics part of the curriculum through the grades reveals a progression in sophistication of tools for summarizing data, with some scattered mentions of the ideas of informal inference. Students are encouraged to make inferences from their observations, but typically without tools to support their generalizability. Teachers are aware that there are important statistical ideas their students need to understand to do this well. For example, they know that a larger sample size is usually better, but they don’t know how to show their students the effects of sample size on the inferences they can make. In addition, teachers often have the challenge of irregular access to technology and uneven expertise and support. In this context, I recently worked with a group of 15 middle school teachers on an activity that uses multiple random samples to better understand the effect of sample size, with only minimal need for technology.
With the random sampler, students can draw random samples of data from the accumulated databases of questionnaire responses from students from participating countries.
Jane Watson, University of Tasmania
I am a statistics educator in the Australian state of Tasmania. Recently I collaborated with a Grade 10 math teacher on a unit on statistics and probability to challenge her advanced mathematics class. The students’ backgrounds were traditional and procedural. There were eight extended lessons of 1½ hours using the TinkerPlots software.
…we gave students a variation on the famous Hospital problem: “Ted and Jed are each tossing a fair coin. Ted tosses his 10 times and Jed tosses his 30 times. Which one of them is more likely to get more than 60% heads or do they have the same chance?” Almost unanimously they said, “the same of course.”
Stephanie Budgett, University of Aukland
At the University of Auckland, our first year statistics course is large. By large we mean about 4500 students per year, with approximately 300 in our summer school semester (lasting 6 weeks, starting early January), 2500 in our first semester (lasting 12 weeks, starting early March) and 1800 in our second semester (starting 12 weeks, starting mid-July). Apart from summer school, we teach in multiple streams with class sizes ranging from 100 students to 400 students per class. Most of our students will not major in statistics and are taking the course because it is a requirement. Over one-half of our students will have taken a statistics course in their last year at school. These students will most likely have taken the Use statistical methods to make a formal inference standard which includes bootstrap confidence intervals. A smaller percentage, say about 20%, may have taken the Conduct an experiment to investigate a situation using experimental design principles standard which includes randomization tests.
From a teaching perspective, we believe that the concept of the tail proportion in the randomization test enhances student understanding of p-values.