Introduction and research question

Pedagogical content knowledge (PCK), as coined by Shulman (1986), pays attention to the way of thinking about teacher knowledge and making a school subject understandable to others. An important concept within the PCK community is the notion of Big Ideas, which involves recognising fundamental principles that underpin the subject. Loughran et al. (2004) emphasised the significance of identifying Big Ideas as a crucial component of articulating one’s PCK. Additionally, Hurst (2019) emphasised that teachers must not only grasp Big Ideas but also understand how these selected concepts interconnect. Furthermore, Chan et al. (2019) highlighted appropriate selection, connection, and coherence of Big Ideas as the first-ordered rubric for measuring the quality of PCK. This paper answers researchers’ calls for further exploration of the fundamental principles underlying the teaching of statistics (Watson et al., 2018). The research aim is to examine how preservice teachers (PTs) select and connect Big Ideas when designing a lesson sequence dedicated to statistics instruction in primary school.

According to Charles (2005), “A Big Idea is a statement of an idea that is central to the learning of mathematics, one that links numerous mathematical understandings into a coherent whole” (p. 10). This definition can be applied to the domain of statistics: A statistical Big Idea represents a statement of an idea central to learning statistics, and connects different statistical concepts and methods into a coherent structure. The findings in this paper are drawn from an ongoing multi-year educational design research aimed at supporting the development of PTs’ PCK in teaching statistical inference (Blomberg, 2022). One research question that has been explored refers to the impact of a reflection and planning tool on the outcome of the PTs’ lesson planning. In the search for potential design principles, I conjectured that predefining Big Ideas in the reflecting and planning tool would enhance the quality of the PTs’ outcomes, particularly regarding their understanding and interconnections of Big Ideas.

Conceptual framework

A recent addition to the PCK research field is the Refined Consensus Model (RCM), developed by Carlson et al. (2019). Unlike previous PCK theories, RCM embraces a more dynamic perspective that acknowledges multiple dimensions of PCK and the exchange of knowledge between these dimensions. Central aspects of teachers’ professional knowledge encompass collective, personal, and enacted PCK, and their interconnections with professional knowledge bases such as content knowledge, curricular knowledge, and pedagogical knowledge. For instance, enacted PCK encompasses activities like instructional planning, teaching, and reflection on teaching practices and student outcomes. To frame the present research and discern the elements under investigation, RCM has served as a background theory.

Within the discipline of statistics education, like the field of mathematics education, there is a noticeable range of perspectives regarding essential elements and ideas for statistical thinking and statistical literacy, and changes in practice are continually influencing them (Zieffler et al., 2018). In this study, I have employed a developed framework as a foreground theory to discern and characterise the outcomes of statistical Big Ideas among PTs. The framework is a combination of data modeling (Lehrer & Schauble, 2004) and informal statistical inference (ISI) (Makar & Rubin, 2009). The components of the statistical inference modeling framework (SI modeling) can be summarised as follows: (a) posing statistical questions within meaningful contexts, emphasising variability through real-world problems; (b) generating, selecting, and measuring attributes that exhibit variation in relation to the posed questions; (c) collecting first-hand data, prompting students to make decisions about investigation design; (d) representing, structuring and interpreting sample and sampling variability; and (e) engaging in informal inferences based on these processes and the interconnectedness of these ideas.

Research inquiries and conjectures in this project are addressed through the implementation of iterative classroom-based investigations, drawing inspiration from the field of educational design research (e.g., Bakker, 2018). Employing a design research methodology enables us to develop better teaching-learning strategies to improve the PTs’ teaching. To capture and document PTs’ significant concepts, we utilise a research-based reflective instrument known as Content Representation (CoRe). The CoRe template, devised by Loughran et al. (2004), serves as a valuable tool for researchers to document research participants’ PCK. At the core of the CoRe template lies its capacity to represent the user’s PCK of the specific subject matter. Initially, the formulation of Big Ideas revolves around a selected theme, followed by addressing PCK-related questions to these chosen Big Ideas. This paper focuses on the PTs selected Big Ideas and their answers to the first question: What do you expect the students to learn about this specific knowledge? The empirical data analysed in this study have been generated in the context of PTs collaborating in groups to plan a hypothetical lesson about statistics. During this planning phase, personal PCK was transformed into enacted PCK as articulable knowledge. Since the completed CoRe is the collective opinion from a group of preservice teachers, it can be assumed to represent a form of collective PCK for that group of PTs. The written outcomes of PTs’ collectively completed CoRe have been analysed with a content analysis approach (Robson & McCartan, 2017). The SI modeling framework has been used as operationalised categories to analyse the outcomes mediated by the CoRes. Four sub-studies have been carried out in the context of PTs education between 2021 and 2022. The research team consisted of one researcher/teacher educator (the same as the author) in collaboration with two to three teacher educators. Each sub-study was carried out with a group of PTs focused on becoming teachers for students aged 6–12 years. These PTs were introduced to the idea of PCK and the framework of CoRe as a valuable PCK tool that offers a way to plan for learning and teaching. In groups of 3-4, they were tasked to plan a hypothetical statistics lesson sequence by taking three Big Ideas as a starting point. For further details, see Blomberg (2022).

The findings from the first two sub-studies draw attention to the challenge of preparing PTs to plan and teach inferential statistics. In short, the first sub-study showed that the PTs’ outcomes clearly emphasised compiling and organising data, interpreting data, and being statistically literate. The PTs’ outcomes regarding inference were almost non-existent, and nearly half of the participating groups highlighted topics from statistical contexts, separate from statistics, as Big Ideas. The second sub-study showed similar findings. Although these PTs were lectured on the measure of distribution and statistical inference, no apparent traces of these big ideas could be found in the results of their completed CoRes. A conclusion from the first two sub-studies points to the need to accommodate the diversity of statistical Big Ideas mediated by CoRes. Otherwise, PTs run the risk of leaving teacher education without any PCK experience of essential statistical Big Ideas (e.g., statistical question, distribution, and statistical inference) and how these Big Ideas are connected. Therefore, an improved teaching-learning strategy was desirable and has been conducted in the sub-studies 3 and 4. A hypothetical design principle tested in study 3 was that reducing the degrees of freedom offered by CoRes can improve the quality of PTs’ findings of Big Ideas and their connections. However, the findings from the last two sub-studies indicate that reducing the degrees of freedom by preparing the CoRe with predefined Big Ideas is an insufficient intervention change. In addition, PTs should be offered specialised knowledge of the relevant learning content and be supported by expert guidance by, for example, providing feedforward on their completed CoRes. Beyond findings in terms of teaching-learning strategies and PCK measurement to support teacher educators, this current work may also contribute methodologically and empirically to the ongoing discussion in collaborative teacher education research.

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