For different topics I teach, I try to pull out what the three key aspects are that will be connected and tested to uncover student understanding. This approach is not the same as trying to define what happens at each stage of PPDAC. Trust me, I have developed detailed rubrics for every statistics standard and while teachers/students alike really like having these I struggle with how specific and mechanistic these can become. As teachers, we have a strong desire to take a complex topic and break it down into smaller chunks so that students can understand each part, and often we do this by creating tick lists or elaborate diagrams. The problem is that this can become really structured, really specific, and really boring (and perhaps even limit creativity). By breaking stuff down into parts we can lose sight of the whole. Ideally, what we want is a message like “Stop, drop and roll” – something that has minimal structure (just three key things to remember what to do), optimal transfer (these actions work well for different situations involving fire) and where instead we focus on getting students to experience applying these things as many times as possible across a wide variety of situations and contexts. So what could our awesome messages be? Maybe something like (1) It matters how much data you have and how you got that data (2) It matters what you are measuring and how you are measuring it (this applies not just to variables but also statistical measures or models) and (3) It matters that you are uncertain and there is variation.
Like I said earlier, we teachers like to provide diagrams and “how to guides” for our students, and I am no different. While my messages for students throughout their learning about confidence intervals and sample-to-population inference were based on the “big ideas”, I still provided additional structure. This diagram was an attempt to provide a framework for thinking about the investigation (the stuff in rectangles in the middle) but also a way to emphasise the kinds of questions we ask ourselves as we work through the process of trying to make a sample-to-population inference (the stuff in the ellipses). This was constructed towards the end of the learning as a summary of our investigative process, not given to students at the beginning of the learning phase as the blueprint to follow – I think the time of when we use scaffolds is important. It was also an attempt to provide an exemplar of how to think during an investigation without providing a finished written up investigation which the students have a tendency to copy and paste from.
This post is based on a plenary I did for the Christchurch Mathematical Association (CMA) Statistics Day in November 2015 where I presented 10 ways to embrace the awesomeness that is our statistics curriculum. You can find all the posts related to this plenary in one place here as they are written.