Conference Agenda

In educational research, imitation has been conceptualized as the intentional use of another’s observed action as a source of information for achieving one’s own goal (Verba & Winnykamen, 1992). Imitative play is considered as a fundamental mechanism for the transmission of cultural practices and knowledge (Heyes, 2023). The effects of worked examples have been widely documented in the literature (Sweller & Cooper, 1985). Empirical studies show that worked examples are processed more efficiently by students, requiring less time to study. However, a single worked example within a teaching domain is unlikely to be sufficient to produce a durable learning effect (Sweller, 2006). From a didactic perspective, the learning potential of a worked example depends on the way it is followed up in classroom activity. After studying a worked example, students need to engage with a related problem in order to assess what they have understood. The follow-up phase should foster active cognitive processing of the example : at first students could be invited to imitate the worked example and then to lead an own inquiry (Dewey, 2018). Based on these research, we have written a sequence for posing and solving arithmetic problems for young students, who are 7 to 9 years old (Athias et al. , 2024, Vicente et al., 2022) .The sequence is grounded in the principle of worked examples (Van Gog et al., 2019). Problem solving is described as an essential criterion for the appropriation of mathematical skills (Schoenfeld, 1985).Problem posing has been recognized as a great activity in mathematics education (Silver, 1994). However, researchers (e.g.Cai, 2022) have shown that it is complex to teach mathematics through problem posing. The worked example could be described as follow : the teacher is solving an example on the board in front of the whole class, thereby making explicit the targeted procedures and forms of reasoning, thanks to a specific joint action (Sensvy, 2014 ; Athias & Sensevy, 2023). In this paper, we thus investigate this research question: how does the joint action of the teacher and students lead students to engage in their own inquiry about mathematic problems based on worked examples?

This communication addresses the role of representations in problem-posing within mathematics education, a research field that has been active for over thirty years (e.g. Silver, 1994) and continuing in contemporary studies (Cai & Leikin, 2025). Problem-posing is defined as teaching students to formulate mathematical problems rather than merely solving predefined ones. Its educational value is justified by two complementary arguments. From a logical standpoint, learning mathematics involves engaging in practices similar to those of professional mathematicians, who routinely pose problems. From a normative perspective, posing problems is cognitively more demanding than solving them and therefore fosters deeper conceptual understanding.

Building on this rationale, Cai (2022) proposes an instructional model for problem-posing-based learning that includes four stages: presenting a problem situation, introducing a problem-posing prompt, having students generate problems, and collectively addressing those problems. In this model, the problem is both the activity of posing and the resulting mathematical product. This dual nature has been identified as a central research issue by Baumanns & Rott (2022). Further refinement is offered in a four-stage process model—problem orientation, connection of problem elements, problem generation, and reflection—developed by Cai & Rott (2024). While early stages may occur internally, the authors argue that external representations become indispensable during the generation of problems.

External representations are representations that are publicly accessible and available for observation and manipulation, following Goldin (2020). From a pragmatic perspective inspired by Östman & Wickman (2014), we also apprehend these representations as tools that support the individual’s own thinking. Drawing on Dewey (1938), we argue that ideas must be materialized through symbols in order to be examined, developed, and reflected upon. Consequently, representations are seen as prerequisites for effective problem generation, supporting both orientation and the connection of elements in the problem-posing process.

We adopt a broad conception of representation, inspired by Hacking (1983), who considers both simple sketches and sophisticated theories to be external, public representations. This perspective emphasizes the importance of semiotic registers and highlights the difficulty of moving between them, a challenge well documented in mathematics education research by Duval (2017). In addition, Radford (2014) argues that representations should not be treated merely as objects but as integral components of knowledge-producing activity. This leads to the central research question: how are representations used at different stages of problem-posing, which semiotic registers are mobilized, and what is their educational potential?

We conduct our research within the framework of the Joint Action Theory in Didactics (JATD; Sensevy, 2011, 2019). JATD is based on three key assumptions: the primacy of action grammar, the fundamentally joint nature of didactic action, and the immanence of knowledge in cultural practices. Knowledge is not viewed as an independent entity but as something that “lives” through the joint action of teachers and students (Tiberghien, 2016). Students’ access to disciplinary knowledge is mediated by the didactic milieu (Sensevy, 2015), which provides both constraints and feedback, and by the didactic contract (Brousseau et al., 2014), i.e. the implicit system of expectations governing teacher-student interactions.

Within JATD, the teaching-learning process is understood as a dialectical process between the didactic contract and the didactic environment, as well as between didactic reticence (what the teacher withholds) and didactic expression (what the teacher makes explicit). Reframed in JATD, our research question asks how representations contribute to establishing productive balances within these two dialectics. Specifically, we scrutinize how different semiotic registers support action, feedback, and learning in the didactic environment during problem-posing activities, thereby enabling effective joint didactic action.

This paper arose from professional research discussions and review of data relating to young (pre-school/kindergarten) children’s mathematical experiences in outdoor play and learning. Common interests in outdoor learning, Science, Technology, Engineering and Math (STEM ) and pedagogies for teaching in a fast-changing world informed our cross-Atlantic discussions leading to new insights of signficance to a range of educators. A dialogic review of primary data on outdoor play and learning in the US and UK prompted consideration of aspects of developmentally appropriate pedagogy to support young children’s situated interactions and critical awareness in the fast changing 21^st Century.

We situate ourselves as always already posthuman (Braidotti, 2021), calling into question dominant assumptions of Western humancentric thinking by giving greater consideration to the role of material objects, animals and the environment. This has been called the age of the Anthropocene (Crutzen and Stoermer, 2000) in acknowledgement that human activity has become a major environmental force of change. Many global issues and social and technological changes are also influenced by an economically driven computational culture (de Freitas, 2025). Artificial Intelligence (AI) and mass algorithms are impacting on prior accepted understandings of culture, ethics and truth. The future increasingly appears ever more technologically informed, fluid and unknown. Navigation of these innovations and understandings will require 'higher order thinking' (OECD 2018) and a conscious critical ability when engaging with the technological and environmental milieu. Machine learning has also played a role in shaping many contemporary understandings of learning, explanation, pedagogy and even cognition (de Freitas, 2026). The promotion of computational thinking in young children (Bers. Strawhacker and Sullivan 2022),) aligns with this trend (OECD 2018) .

The very mention of computational thinking might prompt a perspective which is ‘programmable’ and deterministic (de Freitas, 2025). However, on the other hand yet with so many changes and innovations in technology and society, and an information or data overload, there is a greater need for children to have skills to critically interpret and assess what is newly encountered including responses to the material flows and networks, in the milieu of potential engagements with which they might be entangled. We engage with the philosophical work of de Freitas (2025) who values computational thinking but notes that it suggests that a system is programmable in deterministic frame, and so calls for an 'artisan approach' We propose ‘creative artisans’ move beyond the technical templated approaches with predicted ends, to work with the flows, the grain of the wood, the texture of the paint, the wind and movement of the sand. We identify that as artisan researchers children do engage with the milieu’s many directions, making new understandings.

Our questions were: what can we observe in relation to how children intra-act with, think about and engage with STEM in their free play activity; what thinking processes occur, and how might we support a pedagogic approach which recognises young (post)humans as responding to material flow, both radically extended and influenced by the milieu of experiences and things within which they find themselves, but also with supported skills to abstract and make patterns of meaning from those experiences? We queried, ‘what might it mean for pedagogic practice to acknowledge that young children are always already posthuman, capable of acting as creative artisans, but able to apply computational thinking skills too? Is it possible to bring together the linearity of computational thinking, with its systems of decomposition and abstraction, and the new material pedagogies of divergence and multiple potentiality that are often stated as responsive and affective rather than analytical?

Modern physics topics are among the most challenging areas for students and pre-service teachers to learn, as they involve highly abstract concepts. In particular, the topic of atomic spectra in modern physics is one of the core areas in which this difficulty becomes especially evident, since it requires a simultaneous understanding of the relationships among energy levels, electron transitions, photon energy, and wavelength (Xue et al., 2022). The literature indicates that students’ and pre-service teachers’ explanations of atomic spectra often remain at a descriptive level; individuals experience difficulties in establishing causal relationships among concepts and, in particular, are unable to adequately justify fundamental distinctions such as absorption and emission spectra (Di Uccio et al., 2020). These findings suggest that instructional approaches in modern physics that focus solely on the teaching of concepts are insufficient for supporting conceptual learning (Ivanjek et al., 2020).

Contemporary research in science education emphasizes that conceptual learning is not limited to arriving at correct answers; rather, it requires establishing relationships among concepts, justifying these relationships with scientific principles, and examining the quality of the explanations produced (Kersting et al., 2024). In this context, scientific argumentation emerges as a fundamental approach that enables learners to construct their claims using evidence and scientific reasoning. The Claim-Evidence-Reasoning (CER) framework, which is frequently employed in the analysis of scientific argumentation, is regarded as a powerful analytical tool that allows for the systematic examination of the structural components of scientific explanations. The CER framework reveals not only what learners say, but also the observations and scientific principles on which they base their explanations (McNeill & Krajcik, 2008). Recent studies argue that argumentation is not used solely as an instructional strategy; rather, it provides researchers with an analytical framework that reveals the underlying reasons for the explanations developed by learners during their natural learning processes (Altun & Özsevgeç, 2025). Accordingly, it is emphasized that argumentation-oriented instructional and analytical approaches are employed not only as classroom activities but also as tools for uncovering pre-service teachers’ conceptual explanation and justification structures within their natural learning processes (Mi et al., 2024).

In line with this perspective, the present study seeks to answer the question: ‘How do pre-service physics teachers structure their understanding of atomic spectra in terms of CER components?’ Through this research question, the study examines pre-service physics teachers’ conceptual understanding of atomic spectra and their ways of justifying this understanding from a qualitative perspective. In the study, conceptual understanding will be determined through epistemic patterns emerging in the explanations produced by pre-service teachers, with a focus on their ways of making claims, using evidence, and constructing reasoning (Mazibe & Rollnick, 2024). This study aligns with the goals emphasized in European science education policies regarding the development of scientific reasoning, argumentation, and epistemic practices, and it aims to offer comparable and transferable didactic implications for teacher education by focusing on the analysis of pre-service teachers’ conceptual understandings developed within the context of modern physics.