Understanding large numbers beyond 1,000 represents a persistent challenge in primary mathematics education. While enactive place-value materials such as base-ten blocks are widely acknowledged as powerful tools for developing early bundling concepts and place-value understanding (Padberg & Benz, 2021; Käpnick, 2014), their pedagogical function becomes increasingly problematic in extended number ranges. Physical representations of ten-thousands, hundred-thousands, or millions are neither proportional nor practically manageable and may even foster misconceptions (Gaidoschik, 2025; Schipper et al., 2018). As a consequence, learners are expected to shift from concrete manipulation to fully mental bundling processes—often without explicit instructional support for this transition.

Although research consistently emphasizes the importance of withdrawing concrete representations and fostering relational and structural interpretations of numbers (Bruner et al., 1988; Schulz & Wartha, 2021), little is known about how teachers design and scaffold this transition in classroom practice. In particular, there is a lack of empirically grounded insights into how instructional materials can support learners’ mental bundling processes without creating new dependencies on visual representations.

Against this background, the present project develops and evaluates an iconically supported instructional format that functions as a deliberately limited bridge between enactive experience and mental place-value reasoning. Rather than representing large quantities themselves, the iconic materials visualize bundling structures and hierarchical relations of the decimal system, thereby supporting learners in mentally simulating bundling and unbundling processes (Ruwisch, 2015; Schulz & Wartha, 2021). From a cognitive perspective, this design builds on evidence that large numbers are primarily processed through relational and structural representations rather than through analog magnitude comparisons (Dehaene, 1992; Schneider et al., 2016).

The study follows a formative evaluation approach (Döring, 2014) and is embedded in a professional development programme for primary school teachers. Its analytical focus lies on the teachers’ perspective, as teachers play a key role in shaping instructional transitions between representation levels and in deciding how learning materials are integrated into classroom practice.

The study addresses the following research questions:

Q1a: Which didactic steps and instructional strategies do teachers describe as particularly supportive for fostering a robust understanding of place value and bundling in the extended number range beyond 1,000?

Q1b: How do teachers integrate the iconically supported place-value material into their existing instructional practices, particularly in relation to textbooks and established routines (e.g., as an addition, substitution, or restructuring of tasks)?

Q1c: Which challenges and difficulties do teachers identify when using the iconic material and when supporting learners’ transition from enactive bundling to fully mental bundling processes?

Q2: How do teachers assess the practicality and instructional usefulness of the iconically supported material across different instructional phases (e.g., introduction, consolidation, practice, and reflection)?

Empirical data are collected across two school years using a qualitative multi-method design combining open questionnaires and short group discussions (Kuckartz & Rädiker, 2024; Vogl, 2014). This design allows for the reconstruction of individual didactic reasoning as well as shared interpretative patterns among teachers.

Preliminary findings from the first evaluation cycle suggest that teachers perceive the iconic material as a meaningful scaffold for structuring instructional transitions between representation levels. At the same time, the data point to differentiated challenges regarding timing, fading strategies, and alignment with heterogeneous student prerequisites.

By systematically linking teachers’ experiential knowledge with theoretically grounded design principles, the project contributes to current debates on how educational research can connect knowing and acting. In line with the ECER 2026 theme, it illustrates how insights from mathematics education and cognitive psychology can be translated into instructional action through iterative design and reflective teacher engagement.

The study adopts a qualitative formative evaluation design aimed at generating practice-relevant insights while supporting the iterative development of an instructional innovation (Döring, 2014). Rather than testing effectiveness in a summative sense, the project focuses on identifying conditions under which iconically supported materials can meaningfully facilitate the transition from enactive to mental bundling in the extended number range. Context and Participants The research is embedded in a year-long professional development programme (“Didaktische Pakete”) at a university college for teacher education. Across two cohorts, approximately 50 in-service primary school teachers participate. All teachers work in grade four, where the curricular transition to extended number ranges is formally addressed. Teaching experience varies considerably, allowing for differentiated perspectives on instructional routines and innovation. Data Collection Three complementary qualitative instruments are employed: Open paper-pencil questionnaire (baseline): This instrument captures demographic information, prior experiences with place-value instruction, and existing strategies for addressing large numbers. It serves to contextualize subsequent analyses. Open online questionnaire: Administered after initial classroom implementation, this questionnaire focuses on instructional integration, perceived usability, and observed student difficulties related to bundling and place-value reasoning. Open-ended formats allow for differentiated accounts of instructional decision-making. Short group discussions (15–20 minutes): Conducted within professional development sessions, group discussions focus on collective interpretations, shared challenges, and negotiated understandings of the material’s role in different instructional phases (Vogl, 2014). Data Analysis All qualitative data are analysed using qualitative content analysis following Kuckartz and Rädiker (2024). A combined deductive–inductive coding framework is developed, drawing on central theoretical constructs such as bundling, representational transitions, and instructional structuring. Descriptive summaries complement the analysis to highlight recurring patterns across participants.

The project demonstrates how research-based material development can function as a productive interface between educational theory and instructional practice. By foregrounding teachers’ perspectives, it highlights the role of professional judgement in mediating between abstract didactic principles and concrete classroom action (Seidel, 2014; Helmke, 2022). From a mathematics education perspective, the findings underscore the importance of transitional representations that support learners’ cognitive processes without replacing mental activity. Iconic materials appear to function as effective scaffolds when they are explicitly framed as temporary supports and embedded within reflective instructional practices (Bruner et al., 1988; Käpnick, 2014). This aligns with cognitive research emphasizing the centrality of relational and structural representations for understanding large numbers (Dehaene, 1992; Schneider et al., 2016). In relation to the ECER 2026 theme “Knowing and Acting”, the project illustrates how theoretical knowledge from mathematics education and cognitive psychology can be translated into instructional action through iterative design and formative evaluation. Rather than prescribing universal solutions, the study positions teachers as co-interpreters and co-developers of instructional innovations. Future analyses will further explore how teachers negotiate the balance between support and withdrawal, and how different instructional contexts shape the perceived usefulness of iconic representations. The project thus contributes to broader discussions on the changing potentials of educational research in connecting theory, design, and classroom practice.

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