Implementing and analysing statistical inquiry approaches in primary and lower secondary school statistics

Statistics plays a unique role in how school mathematics contributes to citizenship. Students
meet statistical claims and analyses in both school and in society at large, so one aim of school
mathematics is to prepare students to relate critically to such claims and even engage themselves
in statistical work. This thesis examines a variety of statistical inquiry approaches, realised in
primary and lower secondary schools. One of these inquiry approaches is the relatively new
approach from the anthropological theory of the didactic, called the paradigm of questioning
the world. In this approach, learning begins with questions that are in themselves important (to
students, to citizens). The main purpose of the study is to develop answers to such questions
and also, more generically, to develop an inquiry stance among students.
The thesis draws on several closely related research projects: two large-scale Danish research
and developmental projects, a study of paradidactic infrastructure and sustainable lesson study
in Denmark, a comparative study of how statistical inquiry was implemented in two lessons
taught in Denmark and Japan, and a design research project about how study and research paths
(SRP) can contribute to primary school students’ development of statistical knowledge. In our
research, we present and expand the theoretical idea of paradidactic infrastructure. Paradidactic
infrastructure affects the implementation of a statistical inquiry in several ways and, taking
these influences explicitly into consideration, is essential when trying to implement new
practices for teachers’ professional development.
Due to the variety of the research projects, we applied different methodologies, such as case
studies and different formats of design research, which involve more or less extensive
involvement of teachers’ experiences and observations in efforts to improve the SRP design.
The data gathered in the projects were qualitative in nature and consisted of classroom
observations, field notes, teacher interviews, contextual information about participating
teachers, institutions and paradidactic elements (such as curricula, textbooks and teachers’
opportunities to participate in professional development activities).
Regarding theoretical frameworks, we mainly drew on two major theoretical paradigms of
rather different provenance: the anthropological theory of the didactics from mathematics
education research, and cultural-historical activity theory which originates in cognitive
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psychology and its adaptations to educational studies. We modelled students’ participation in
statistical inquiry in question-and-answer diagrams and as statistical praxeologies. We analysed
the conditions and constraints that affect statistical inquiry classrooms and the paradidactic
infrastructure that supports teachers’ professional development. We further modelled teachers’
participation in research and developmental projects as interacting activity systems and as a
process of expansive learning.
The overall research results indicate how statistical inquiry approaches can support students’
development of statistical knowledge. Most notably, the dialectic of students’ study and
research of statistical knowledge in a digital milieu enables sustained, recursive sequences of
statistical inquiry to be developed with primary school students. In our studies, we saw how
statistical inquiry within such a dynamic allowed the students to autonomously develop
statistical knowledge, and in the SRP approach, we observed that students were encouraged to
use and develop theoretical ideas related to statistical practices. The SRP contrasted with
common forms of statistics teaching in which statistical techniques are demonstrated and
practiced but not further elaborated or questioned.
The ecology of statistical inquiry consists of several conditions and constraints. Among the
favourable conditions one can count a mathematical curriculum that endorses and supports
statistical inquiry approaches, and also resources, such as textbooks and digital tools, that
scaffold implementation of inquiry in the classroom. Unsurprisingly, the role of the teacher is
also crucial, for example, in establishing a new didactic contract. However, teachers’ autonomy
(e.g. to choose textbooks and decide how to organise classroom teaching) can also act as a
constraint, for instance when a detailed didactic design for inquiry is to be implemented.
We observed a variety of assumptions about the nature of statistical inquiry that are held by
teachers and researchers, as well as the difficulty of achieving truly shared views. We question
specific views of interaction between researchers and teachers and investigate the hypothesis
that research could work as an integrated part of paradidactic infrastructure, such as in the
format of lesson study and other forms of teacher–researcher collaborations. It would be
interesting to further investigate how such paradidactically integrated research can lead to new
sustainable statistical inquiry practices, and to what extent external support is needed after the
research intervention stops.