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.