Conference Agenda

1. Research Objectives / Questions

The Content-and-Language-Sensitive Approach to Multilingualism in School (CaLSAM) project (funded by Erasmus+/ EU and Movetia/ Switzerland) aims to foster European teachers’ competence to actively use multilingual resources in mathematics education in Primary School (Kuzu et al., 2025). This paper presents design-based research (DBR) insights from the development and pilot phase of CaLSAM’s vignette-based Teacher Professional Development (TPD) modules. These modules are grounded in four design principles that connect theory and practice through translanguaging pedagogy, linguistic relativity, and dialogic learning. The objectives of this paper are: (1) to present the theoretical and methodological rationale behind the CaLSAM design principles; (2) to illustrate how vignette-based TPD activities support teachers’ noticing, reflection, and competence-oriented perspectives on multilingualism; and (3) to provide first qualitative insights into the perceived impact of the vignettes and design principles on teachers’ professional vision regarding multilingual mathematics classrooms. The overarching research questions are: How can design principles derived from translanguaging theory and critical mathematics education be operationalized in teacher professional development? In what ways do vignette-based learning processes support teachers’ noticing and reflection on multilingual meaning-making in mathematics education?

2. Framework

CaLSAM conceptualizes multilingualism as a content-and-language-sensitive phenomenon, where linguistic diversity is treated as a cognitive and pedagogical resource rather than a challenge. The framework builds on 1) Translanguaging pedagogy (García & Wei, 2014), emphasizing dynamic and creative meaning-making across languages, 2) Linguistic relativity (Kuzu, 2023; Prediger et al., 2019), focusing on how languages shape mathematical conceptualization, 3) Critical mathematics education (Skovsmose, 2011; 2018 & Freire, 1970), highlighting the role of language in equitable access to mathematical meaning, and 4) Teacher noticing theory (Jacobs et al., 2011; Güler et al., 2020), framing teachers’ professional vision as attending to, interpreting, and responding to multilingual students’ mathematical thinking (Kuzu et al., 2025). The vignette-based structure of the CaLSAM TPD connects these perspectives through dialogic learning sequences (ME–YOU–WE phases; Wegerif, 2007), encouraging teachers to move from individual awareness to collaborative meaning-making. Vignettes act as “capsulated” practice situations - short transcripts, videos, or student artifacts - used to discuss multilingual interactions, scaffolding, and translanguaging in mathematics classrooms.

This contribution describes an Erasmus+ project, Access Maths in STEM (AMiS), and its main outputs. The main objectives of the project have been to improve the teaching of maths to enhance student outcomes in terms of proficiency and enjoyment. This has been achieved through collaboration with teachers from five schools across Austria, the Czech Republic, Sweden and Ireland. Participating teachers formed a Community of Practice (CoP) centred on educating and providing access to mathematics for all students. Theories of Lave (1991) and Wenger (1998; 2000) underpinned the development of the CoP. In addition, the model of Mathematical Proficiency, proposed by Kilpatrick et al. (2001) has been foregrounded to ensure that core mathematical competencies and skills remain at the heart of teaching. This model is comprised of five “strands” (procedural fluency, conceptual understanding, strategic competence, adaptive reasoning and productive disposition) that are understood as core to effective mathematical development for students.

For participating schools, not only was there diversity of student population, but the participating countries do not share curricula, and their pedagogical approaches have different epistemological roots. Given this variety, CoP was fruitful as a research approach. Drawing on Wenger (2000), this meant cultivating a shared purpose centred on developing teaching and learning approaches that promote access to mathematics. Through collaborative work teachers formed relationships and established norms around their shared mission. A core focus of the CoP was teachers’ co-design of suites of innovative, inclusive, and student-centred maths lessons. Hence, a shared repertoire was established, in which communal resources (language, routines, artefacts, tools, etc.,) were developed (Wenger, 2000). To achieve this, six week-long, in-person learning exchanges facilitated the collaboration within and between schools, with access to a shared, online space (via MS Teams) supporting the generation of the shared repertoire. On-site meetings were hosted at participating institutions in each country. During these meetings, participants collaborated on joint tasks, visited each other’s schools, took part in teaching demonstration and met staff and students at host institutions.

One key focus of the CoP was the development of a common understanding of what it means to be mathematically proficient, and how its development can be supported in the classroom. According to the definition of Kilpatrick et al., (2001), the concept of Mathematical Proficiency, includes “five components, or strands:

• conceptual understanding—comprehension of mathematical concepts, operations, and relations
• procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
• strategic competence—ability to formulate, represent, and solve mathematical problems
• adaptive reasoning—capacity for logical thought, reflection, explanation, and justification
• productive disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.” (p. 116)

While it is generally accepted that these concepts are important, it is challenging to come to a common agreement on what they are comprised of, what educators can do to support their development, and how we might recognise that they have been achieved.

The CoP established by the project supported structured, sustainable, and longitudinal development of what can be understood as an adaptive feedback loop. In this way, teachers were well positioned to overcome the limits of what Skovmose (2006) termed “the prototype mathematics classroom,” through the creation and exploration of cross-cultural contexts, and opportunities for critical reflection. This is of particular importance given that teacher factors, such as their beliefs and perceived barriers feed into their own reflection and metacognition, and subsequently into their actions, ultimately affecting students and their opportunities to develop mathematical proficiency. Thus, within this project and the CoP, we were able to identify and develop collective competence and experience.

Language is central to mathematics education because it shapes how mathematical ideas are communicated, conceptualised, and learned. What can be meaningfully expressed is constrained by language; mathematics classrooms foreground how concepts are constituted through linguistic, symbolic, and representational systems. Teaching and learning are, therefore, language-mediated processes in which meaning is negotiated through talk, symbols, gestures, and inscriptions (Schleppegrell, 2007). Mathematical discourse is also highly specialised, characterised by technical vocabulary, dense symbolism, and precise syntactic relations. It supports rigour but can disadvantage learners still developing proficiency in the language of instruction or academic registers (Planas et al., 2018). Importantly, mathematics-specific language predicts achievement beyond general language skills (Peng & Lin, 2019). Classroom discourse is largely shaped by teachers, whose talk introduces and regulates mathematical meanings (Himmelsbach et al., 2023).

Within this landscape, teachers act as linguistic mediators, bridging students’ everyday language and informal representations with the mathematics register (Pöhler & Prediger, 2015). Language-responsive teaching emphasises intermediate linguistic forms that foreground mathematical structure without oversimplification, and such practices are closely tied to teachers’ professional knowledge, such as Mathematical Knowledge for Teaching (MKT) (Ball et al., 2008), including subject matter knowledge and pedagogical content knowledge (Shulman, 1986). Empirical studies suggest that stronger MKT is associated with more precise and conceptually aligned mathematical language, higher instructional quality, and improved student learning.

In parallel, teacher noticing has become a key lens on professional competence in mathematics teaching, typically defined as teachers’ capacity to attend to mathematically relevant features of instructional situations, interpret students’ thinking, and respond in ways that advance learning (Sherin et al., 2011). Noticing is often theorised as a mechanism linking teacher knowledge to instructional action and student learning (Krauss et al., 2020). Yet, evidence indicates it is related to, but not reducible to, teachers’ mathematical knowledge, marking it as a distinct component of teaching expertise (Copur-Gencturk & Rodrigues, 2022).

Despite this conceptual proximity, language use and noticing have largely been studied separately. Noticing research, especially in cognitive–psychological traditions, often analyses teachers’ interpretations of students’ strategies while bracketing the linguistic and semiotic resources through which thinking is expressed and teachers’ interpretations are articulated (König et al., 2022). Conversely, language research has frequently examined registers and discourse patterns without explicitly theorising how noticing processes shape teachers’ language in instructional moments. Only limited work has begun to connect language use and noticing, leaving open questions about how teachers notice language-related aspects of students’ mathematical activity and how this is reflected in explanations, evaluations of solutions, and references to mathematically critical ideas/quantities (Planas & Pimm, 2023). Recent syntheses therefore call for integrated approaches that treat language, teacher knowledge, and noticing as mutually constitutive aspects of professional competence, especially in tasks with multiple valid solutions that require teachers to recognise key ideas and quantities and communicate distinctions with mathematical precision and pedagogical productivity.

Division tasks with correct answers expressible as a mixed number (e.g., 4 1/3) or as quotient–remainder form (e.g., 4R1) illustrate this complexity. Both may be mathematically correct, but they foreground different interpretations of quantities and ideas. Supporting students’ understanding requires teachers to move beyond merely naming relevant quantities at a surface level and to use language that makes underlying structures visible and meaningful. Against this background, the present study investigates the interrelations among teachers’ mathematical knowledge, language use, references to ideas and quantities, and content-specific noticing when responding to a division problem analysis task with two correct solutions. The research question is: How are teachers’ mathematical knowledge, evoked mathematical ideas and quantities, language use, and content-specific noticing skills associated when responding to a division problem analysis task?