Statistical Modelling: An enquiry into novice students’ co-creation of reasoning and practice

Abstract

Inferring from data to make decisions, draw conclusions or understand phenomena is not only an educational goal for students learning in classrooms but also for their everyday lives. Technology has changed the statistics education landscape by providing model building environments and simulations that support unified chance and data notions for inference. There is a need to investigate statistical modelling as an educational approach that approximates professional practice, and to discover how students acquire and develop concepts and practices that underpin statistical inference. A review of the statistics education research literature could not locate theoretical frameworks for statistical modelling that provided detailed accounts of student conceptual development during learning and of the processes involved. Therefore, these two distinct but related areas were investigated to determine how students encounter and navigate concepts and processes during statistical modelling. Using design research, a learning sequence of 12 statistical modelling lessons was developed for novice students. The sequence revolved around three model eliciting activities (MEAs), where students could construct chance-based models of real-world data-based problem situations using TinkerPlots. The students’ MEA models and associated reasoning informed the follow-up tasks (FUTs), which concentrated on the concepts and processes that required development as well as seeding new ideas. The participants were six student volunteers from a mid-decile multicultural intermediate school. The lessons took place over two years when the students were 11- and 12-years old. The data collected and analysed included movies of the students interacting with TinkerPlots as they reasoned about building, testing and using their models and communicating their findings. The study showed that the students were able to use data from the real world to build mechanistic models, which enabled a characterisation of how the students co-created their statistical reasoning and statistical practice or processes when immersed in a modelling environment mediated by technology, tasks and the teacher. Two frameworks co-emerged from the data: (1) the Statistical Reasoning and Action framework, based on the learning theory of inferentialism, explicated how students encountered, navigated and deepened their understanding of statistical concepts; and (2) the Statistical Modelling Processes Framework, which classified and defined the types of practice and reasoning that students need to acquire in a statistical modelling environment. The frameworks refined and explained the relationship between conceptual growth and practice.