Vol.:(0123456789) 1 3 ZDM (2018) 50:1139–1150 https://doi.org/10.1007/s11858-018-0956-y ORIGINAL ARTICLE Statistical modelling and repeatable structures: purpose, process and prediction Katie Makar 1  · Sue Allmond 1 Accepted: 5 June 2018 / Published online: 12 June 2018 © FIZ Karlsruhe 2018 Abstract Children have limited exposure to statistical concepts and processes, yet researchers have highlighted multiple benefts of experiences in which they design and/or engage informally with statistical modelling. A study was conducted with a class- room in which students developed and utilised data-based models to respond to the inquiry question, Which origami animal jumps the furthest? The students used hat plots and box plots in Tinkerplots to make sense of variability in comparing distri- butions of their data and to support them to write justifed conclusions of their fndings. The study relied on classroom video and student artefacts to analyse aspects of the students’ modelling experiences which exposed them to powerful statistical ideas, such as key repeatable structures and dispositions in statistics. Three principles—purpose, process and prediction—are highlighted as ways in which the problem context, statistical structures and inquiry dispositions and cycle extended students’ opportunities to reason in sophisticated ways appropriate for their age. The research question under investigation was, How can an emphasis on purpose, process and prediction be implemented to support children’s statistical modelling? The prin- ciples illustrated in the study may provide a simple framework for teachers and researchers to develop statistical modelling practices and norms at the school level. Keywords Statistics education · Informal statistical inference · Statistical modelling · Repeatable structures 1 Introduction Statistical modelling has been suggested as a way to provide students with a more authentic experience in learning sta- tistics. The perspective taken in this paper is that a model consists of a representation of a system with its relations and incorporates the method, meaning-making and cul- tural activities that surround it (Font et al. 2007; Hestenes 2010). In the past few years, statistical modelling has had a resurgence and broadened its audience to include novice users of statistics, including young children (e.g. English 2012). There is wide agreement in this revival that models and modelling need to be better situated within problems that include statistical investigations (Biehler et al. 2017). However, there is still little guidance for those wanting to teach statistical modelling to those who are less experi- enced, such as primary children. This article considers the critical importance of attending to three principles as cen- tral to teaching children statistical modelling—repeatable structures that attend to purpose, process and prediction. Repeatable structures consist of tools, concepts, represen- tations, processes and their relationships that can be used across multiple contexts and connect as big ideas in statis- tics. Therefore, repeatable structures add coherence to the learning of statistics by holistically integrating statistical content, reasoning and processes (Bakker and Derry 2011). The aim of the research was to gain insight into how each of these principles—purpose, process and prediction—are foundational to the practice of statistical modelling with school children. The research question under investiga- tion was, How can an emphasis on purpose, process and prediction be implemented to support children’s statistical modelling? The research question is addressed with excerpts that illustrate these three principles in practice using a study with primary school children in an inquiry-based classroom as they investigated which of two origami animals jumped further. To respond to the research question, in Sect. 2 we provide background on the perspective of statistical mod- els and modelling taken in this paper through a review of * Katie Makar k.makar@uq.edu.au 1 School of Education, Social Sciences Bldg, The University of Queensland, Brisbane 4072, Australia