In many contexts, teacher education programmes are organised around a structural division between mathematics and mathematics education, while institutional arrangements simultaneously require sustained collaboration across these domains. As a result, mathematics teacher educators (MTEs) often work in professional settings where epistemic expectations, evaluative norms, and priorities are not fully aligned. To make sense of such conditions, researchers has increasingly drawn on boundary crossing as an analytic lens for examining professional learning and identity formation across domains (Akkerman & Bakker, 2011; Whitchurch, 2008). Within mathematics teacher education, this perspective has been particularly influential in studies of collaboration between mathematicians and mathematics educators, where boundary practices are commonly framed as productive—supporting integration between mathematics content and pedagogy, mutual learning, and the emergence of hybrid professional positions (Bleiler, 2015; Goos & Bennison, 2018).

These dynamics are especially visible in hybrid departmental structures, where academics with doctoral training in mathematics and mathematics education work within the same departments or programmes and share responsibility for teacher education (Özmantar & Agaç, 2025; Marshman & Goos, 2025). Hybrid departments institutionalise cross-disciplinary proximity and render boundary engagement a persistent feature of everyday professional practice. Research conducted in such contexts has documented both opportunities for collaboration and enduring asymmetries in recognition, authority, and epistemic legitimacy across disciplinary lines (Özmantar & Agaç, 2025).

However, much of the literature on boundary crossing and hybrid work is underpinned by developmental assumptions. Boundary engagement is typically expected to culminate in transformation, epistemic settlement, or productive hybridity. Even when difficulty, tension, or liminality are acknowledged, these experiences are frequently interpreted as transitional phases on a pathway toward integration (Akkerman & Bakker, 2011; Whitchurch, 2008). Recent scholarship has begun to question this teleological orientation. Marshman and Goos (2025), for example, argue that theoretical advancement requires closer attention to trajectories where sustained boundary engagement does not lead to integration or settlement. Large-scale studies of MTEs similarly document heterogeneous identity configurations across hybrid departmental contexts, pointing to the need for more fine-grained and longitudinal analyses of how such configurations are maintained (Özmantar & Agaç, 2025).

Responding to these concerns, this paper foregrounds a boundary-work trajectory that resists dominant developmental narratives. Drawing on boundary-crossing theory (Akkerman & Bakker, 2011), we introduce non-arrival as an analytic lens for examining situations in which sustained boundary engagement does not consolidate into transformation, settlement, or coherent epistemic repositioning. Rather than treating non-arrival as individual failure or temporary disruption, we conceptualise it as a patterned outcome of boundary conditions where prior forms of epistemic authority may lose currency while alternative forms of legitimacy remain difficult to secure.

The analysis is situated in a hybrid mathematics teacher education context where disciplinary boundaries are structurally embedded and continuously negotiated. Adopting a longitudinal qualitative orientation, the paper attends to how boundary engagement reshapes epistemic positioning, professional voice, and claims to competence over time. This focus moves beyond accounts that privilege participation or structural proximity as indicators of integration, and instead examines how boundary practices can function as epistemic barriers, shaping what can be said, by whom, and with what authority in mathematics teacher education work.

The contribution of this paper to mathematics education research is twofold. First, it challenges the assumption that increased cross-disciplinary collaboration or hybrid organisational designs will naturally generate integrative professional learning. Second, it offers conceptual resources for theorising boundary practices that produce durable forms of non-arrival rather than developmental progression. In doing so, the work advances a more differentiated understanding of boundary work—one that accounts for epistemic constraint alongside transformation and hybridity, and that is attentive to the kinds of professional trajectories that existing frameworks tend to overlook.

This study adopts a longitudinal qualitative conceptual self-study design to examine boundary engagement in mathematics teacher education from a close-grained, reflexive perspective. Conceptual self-study in teacher education positions the researcher’s professional experience not as an object of improvement, but as an analytic site for interrogating the limits of existing theoretical frameworks and for generating new conceptual insights (LaBoskey, 2004; Loughran, 2007). Importantly, the study did not begin as a self-study; rather, it emerged through sustained empirical engagement with boundary-work data that exposed limitations in dominant developmental interpretations of boundary practices. The study is situated in a hybrid departmental context in which mathematics teacher education is organised through ongoing collaboration between academics with backgrounds in mathematics and mathematics education. Within this context, the analysis centres on a single, theoretically significant professional trajectory. The decision to focus on one trajectory reflects an analytic commitment to depth, continuity, and process, rather than comparison or representativeness. The case is treated as a theory-challenging instance that enables close examination of boundary engagement that does not align with prevailing assumptions of transformation, hybridity, or epistemic settlement. Data generation unfolded across three analytically connected phases over approximately eight, and the study remains ongoing. In the first phase, in-depth interviews were conducted as part of a broader research programme on boundary practices in mathematics teacher education. During analysis, one trajectory emerged as analytically disruptive due to the persistence of boundary engagement without indications of developmental resolution. The second phase involved follow-up interviews, adopting a longitudinal qualitative orientation that foregrounds continuity and stability in professional experience (Neale, 2019). In the third phase, the study was reconfigured as a conceptual self-study, incorporating reflexive written accounts generated by the researcher to examine how boundary engagement is interpreted, rationalised, and managed within ongoing professional practice. Analysis was iterative and theoretically informed. Rather than coding toward predefined developmental outcomes, analytic attention focused on patterns of continuity, repetition, and non-resolution across time. Particular attention was paid to shifts in epistemic positioning, professional voice, and claims to competence. Reflexivity functioned as a methodological resource throughout the analysis, enabling systematic consideration of how researcher positioning shaped interpretation, consistent with conceptual and relational approaches to self-study (LaBoskey, 2004; Loughran, 2007). This methodological approach does not seek generalisation across cases. Instead, it aims to generate theoretical insight by closely examining a longitudinal trajectory that reveals conditions under which boundary practices consolidate into epistemic barriers rather than developmental progression.

The analyses conducted in this study indicate that boundary engagement in mathematics teacher education does not necessarily culminate in transformation, hybridity, or epistemic settlement, as commonly assumed in boundary crossing frameworks. Instead, the findings highlight a trajectory in which sustained participation at disciplinary boundaries may consolidate into a condition of non-arrival, characterised by the erosion of epistemic authority without the establishment of a viable alternative position. Drawing on longitudinal analysis, the study shows that boundary practices can destabilise previously robust forms of professional competence and confidence. Initial epistemic resources that are valued and recognised within one disciplinary domain may lose currency when boundary engagement becomes a routine feature of professional practice. Crucially, this destabilisation is not followed by the emergence of a new, hybrid, or reconfigured epistemic identity. Rather than indicating transition, the findings point to durability and continuity in this state, suggesting that non-arrival may function as a stable professional condition rather than a temporary phase. Conceptually, the study reframes boundary practices as potentially operating not only as sites of learning and integration but also as epistemic barriers that regulate access to legitimacy, voice, and recognition. This challenges developmental narratives that equate participation, proximity, or collaboration with epistemic advancement. By foregrounding non-arrival as an analytically consequential outcome, the study contributes a language for theorising professional trajectories that remain unresolved despite sustained boundary engagement. The expected contribution of this paper lies in extending boundary crossing theory by identifying limits in its explanatory reach when applied to mathematics teacher education contexts characterised by hybrid departmental structures. Rather than proposing a replacement framework, the study offers a conceptual refinement that invites mathematics education researchers to attend more closely to trajectories marked by epistemic constraint, loss, and non-settlement.

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