A modelling approach is a popular one in the teaching of mathematics, and we can take this approach for the teaching and learning of Data analytics (and statistics). One of the latest special issues in the journal ZDM Mathematics education publishes papers in modelling approaches in statistics education (https://link.springer.com/journal/11858)
This approach can be used to foster students’ statistical inferences (e.g. Doerr, et al. 2017), because “statistical modeling simultaneously exposes students to statistical and probability concepts and reasoning between real data distributions and simulated data distributions” (Patel and Pfannkuch, in press, p. 2).
A model is “a representation of structure in a given system” (Hestenes, 2010, p. 17), and the curriculum design should consider to provide the following opportunities (p. 33):
- proficiency with conceptual modeling tools
- qualitative reasoning with model presentations
- procedures for quantitative measurement
- comparing models to data
Pfannkuch et al. (2016) proposed a framework for probability/statistics modelling as the following cyclic process ‘Problem situation – What to know – Assumptions – Build the stochastic model – Test the model – Use the model’. This cyclic process promotes students’ seeing structure in given situations and applying structure, bridging mathematical and real world and enriching their thinking and reasoning. English and Watson (2018) also describe a modelling approach with the following four components: “working in shared problem spaces between mathematics and statistics; interpreting and reinterpreting problem contexts and questions; interpreting, organising and operating on data in model construction; and drawing informal inferences.” (p. 103). They consider this approach has potential to foster students’ statistical literacy because in this approach problems are complex, not organised and ill-structured and therefore students have to make sense of problem contexts, organise data so that they can manage and work with, and make decisions and inferences about data and their interpretations. For example, as an example, students can work with a problem:
You are to select Australia’s best 6 swimmers to compete in either the women’s or men’s 100 m freestyle event at the Rio Olympics. Your selection should ensure Australia has the best chance of winning gold. (p. 108).
We are currently trying to design such problems by using weather/climate change data from the Met office in the UK, which hopefully we can start classroom-based research from September 2018!
Doerr, H. M., Delmas, R., & Makar, K. (2017). A modeling approach to the development of students‘ informal inferential reasoning. Statistics Education Research Journal, 16(2).
English, L. D., & Watson, J. (2018). Modelling with authentic data in sixth grade. ZDM, 50(1-2), 103-115.
Hestenes, D. (2010). Modeling theory for math and science education. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies: ICTMA 13 (pp. 13-41). New York: Springer.
Patel, A., & Pfannkuch, M. (in press). Developing a statistical modeling framework to characterize Year 7 students’ reasoning. ZDM, 1-16.
Pfannkuch, M., Budgett, S., Fewster, R., Fitch, M., Pattenwise, S., Wild, C., & Ziedins, I. (2016). Probability modeling and thinking: What can we learn from practice?. Statistics Education Research Journal, 15(2).