Developing learning and formative assessment tasks for evaluating statistically-based reports
This post provides the notes and resources for a workshop I ran for the Auckland Mathematical Association (AMA) on developing learning and formative assessment tasks for evaluating statistically-based reports (specifically AS91584).
Notes for workshop
The starter task for this workshop was based around a marketing leaflet I received in my letterbox for a local school back in 2014. I was instantly skeptical about the claims being made by the school and went straight to sources of public data to check the claims. As was often the case, this personal experience turned into an activity I used with my Scholarship Statistics students to help them develop their critical evaluation skills. The task, public data I used, and my attempt at answers (from my past self in 2014) are provided at the bottom of this post. My overall conclusion was that most of the claims check out until around 2011, but not so much for 2012 – 2013, leading my to speculate that the school had not updated their marketing leaflet. The starter task is all about claims and data, and not so much about statistical processes, study design, or inferential reasoning – all of which are required for students to engage with the evaluation of statistically-based reports. However, I used this task to set the focus of the workshop, which was to focus on the claims that are being made, and whether they can be supported or not, and why.
The questions used for the external assessment tasks for AS91584 (available here) are designed to help scaffold students to critique the report in terms of the claims, statements or conclusions made within the report. Students need to draw on what has been described in the report and relevant contextual and statistical knowledge to write concise and clear discussion points that show statistical insight and answer the questions posed. This is hard for students. Students find it easy to write very creative, verbose and vague responses, but harder to write responses that are not based only on speculation or that are not rote learned. We see this difficulty with internally assessed tasks as well, so it’s not that surprising that students struggle to write concise, clear, and statistically insightful discussion points under exam pressure.
Teachers who I have spoken to who have taught this standard (which includes me) really enjoy teaching statistical reports to students. In reflections and conversations with teachers on how we could further improve the awesome teaching of statistical reports, a few ideas or suggestions emerged:
- Perhaps we focus our teaching too much on content, keeping aspects such as margin of errors and confidence intervals, observational studies vs experiments, and non-sampling errors too separate?
- Perhaps we focus too much on “good answers” to questions about statistical reports, rather than “good questions” to ask of statistical reports?
Great ideas for teaching statistical report can be sourced from Census at School NZ or from conversations with “statistical friends” (see the slides for more details). These include ideas such as: experiencing the study design first and then critiquing a statistical report that used a similar design, using matching cards to build confidence with different ideas, keeping a focus on the statistical inquiry cycle, teaching statistical reports through the whole year rather than in one block, and teaching statistical reports alongside other topics such as time series, bivariate analysis, and bootstrapping confidence intervals. I quite like the idea of the “seven deadly sins” of statistical reports, but didn’t quite have enough time to develop what these could be before the workshop – feel free to let me know if you come up with a good set! [Update: Maybe these work or could be modified?]
When I taught statistical reports in 2013 (the first year of the new achievement standard/exam), I was gutted when I got my students’ results back at the start of 2014. I reflected on my teaching and preparation of students for the exam and realised I had been too casual about teaching students how to respond to questions. In particular, I had expected my “good” students would gain excellence (the highest grade – showing statistical insight) because they had gained excellences for the internally-assessed students or were strong contenders to get a Scholarship in Statistics. So, a bit later in 2014, when the assessment schedules came out, I looked carefully at what had been written as expected responses. To me, it seemed that a good discussion point had to address three questions: What? Why? How? Depending on the question being asked, the whats, whys and hows were a bit different, but at the time (only having one exam and schedule to go with!) it seemed to make sense. At least, in my teaching that year with students, I felt that using this simple structure allowed me to teach and mark discussion points more confidently. You can see more details for this “discussion point” structure in the slides.
The last part of the workshop involved providing teachers with one of three statistical reports (all around the theme of coffee of course!) and asking them, in groups, to develop a formative assessment task. After identifying one or two key claims made in the report, they had to select three or four questions from previous year’s exams that would be relevant for questioning the report in front of them (relevant to the conclusions made in the report). We didn’t quite get this finished in the workshop – the goal was to create three formative assessment tasks that could be shared! However, perhaps some of the teachers who attended the workshop will go on to develop formative assessment tasks and email these to me to share at a later date. I do feel strongly that all teachers of statistics should feel confident to write their own formative or practice assessment tasks for whatever they are teaching – if you’re not sure about what understanding you are trying to assess and what questions to ask to assess that understanding, how do you feel confident with what to teach? I’m hoping to launch a project next term to help support statistics teachers to feel more confident with writing formative assessment tasks, so watch this space 🙂
Resources for workshop (via Google Drive)