Supporting Multilingual Students’ Mathematical Discourse Through Teacher Professional Development Grounded in Design-Based Research: A Conceptual Framework

Abstract

This conceptual paper presents a framework for supporting multilingual students’ mathematical discourse through teacher professional development grounded in design-based research (DBR). Drawing on sociocultural learning theory, the Integrated Language and Mathematics Project (ILMP) was co-developed with elementary educators to promote integrated instruction that simultaneously advances students’ mathematical understanding, language development, and cultural identity. The ILMP framework centers around three instructional pillars: attention to language, attention to mathematical thinking, and cultural responsiveness. Through collaborative inquiry cycles, educators engaged as learners, contributors, and designers of practice, iteratively enacting and reflecting on instructional strategies rooted in students’ linguistic and cultural assets. Teachers implemented discussion-rich mathematical tasks, supported by language scaffolds and culturally relevant contexts, to foster students’ mathematical reasoning and communication. This approach was particularly impactful for multilingual learners, whose language use and problem-solving strategies were both valued and elevated. This paper also discusses the opportunities and challenges of DBR and research–practice partnerships, including flexibility in implementation and navigating district-level priorities. Insights underscore the importance of practitioner agency, asset-based pedagogy, and the co-construction of professional learning. The ILMP framework offers a scalable, equity-oriented model for improving integrated language and mathematics instruction in diverse elementary classrooms and beyond.

1. Introduction

Teachers across various grade levels and contexts hold the responsibility of aiding multilingual (ML) students by concurrently enhancing their language skills and academic knowledge. Currently, our field is in the nascent phases of identifying key teaching practices that can elevate student outcomes in both language and mathematics simultaneously. In this conceptual paper, we explore the conjecture that the effective integration of mathematical and English language development (ELD) requires the robust support of practitioners to implement instructional strategies that align with research-based best practices for teaching mathematics and language in culturally responsive ways. We hypothesize that this integrated approach to teaching content can improve student achievement in mathematical and language proficiency and enhance academic language use and mathematical discourse.

Funded by the National Science Foundation, the Integrated Language and Mathematics Project (ILMP) used a designed-based research (DBR) approach (DBRC, 2003) and collaborative inquiry cycles to develop and investigate a conceptual framework that embodies our conjectures about how best to support teachers’ professional development with integrating mathematical and ELD instructional practice. Within this DBR context, we draw on Sandoval’s (2014) conjecture mapping to specify theoretically salient principles and theories of our learning environment design and how they are predicted to work together to achieve our intended outcomes. This collaboration occurred with 51 elementary teachers in 3rd–5th grade classrooms across ten elementary schools in a large urban district in California. The majority of teachers identified as multilingual teachers of color. The conceptual framework for the ILMP that emerged addresses three instructional pillars that guided continued professional development—attention to language, attention to mathematical thinking, and cultural responsiveness. Below, we describe the research literature supporting our design-based conjectures for how these three pillars can be enacted to improve teaching and learning for multilingual learners. In addition, we discuss the opportunities and challenges that using a design-based research approach afforded us as an interdisciplinary team composed of researchers and practitioners engaged in this work.

2. Literature Review

2.1. Design-Based Research

Design-based research is a flexible method for developing, testing, and revising specific theoretical and practical conjectures about both student and teacher learning processes and how that learning is supported in natural settings (Armstrong et al., 2020). There are several salient features of design research that offer a suitable approach for developing and testing our conjectures for supporting practitioners with simultaneously developing conceptual mathematical understandings and academic language development for ML learners in the classroom. Specifically, design research is theoretically grounded, drawing from different paradigms and methods, and is inclusive of multidisciplinary teams of researchers and practitioners. Moreover, the process of design research occurs in a model of collaborative, systemic, and iterative cycles of development, learning, enactment, and reflection (Bell, 2004; Penuel et al., 2011; Voogt et al., 2015; F. Wang & Hannafin, 2005). Researcher–practitioner collaborations are also central elements of research–practice partnerships where approaches are co-designed and rooted in both research and practice, holding greater potential for addressing persistent and complex problems of practice at the school and classroom level (Coburn & Stein, 2010; Farrell et al., 2021). These collaborations also hold potential for bridging the research–practice gap and increasing the relevance and use of research in practice (Coburn & Penuel, 2016). Design research also strives for greater coherence with existing learning opportunities and instructional policies (Sancar et al., 2021; Timperley et al., 2007) by building upon and enhancing core learning initiatives, such as ELD standards and frameworks, designed to support the achievement of multilingual students. Further, these collaborations position practitioners as co-designers of the learning and solutions to problems, which can lead to greater buy-in, usable knowledge, and the adoption of resulting outputs (Reeves & McKenney, 2012; Penuel et al., 2011; Voogt et al., 2015).

The design research paradigm also has a historied grounding in the learning sciences, supporting the investigation of theoretical models of learning as they occur, and is situated in the context and complexity of educational classroom settings where theories can be further refined in response to multifaceted approaches to influencing different elements of the learning environment (Bakker, 2018; Brown, 1992; Collins, 1992). Design research also has established antecedents for framing inquiry into domain-specific learning processes in mathematics and science education (Aşık & Yılmaz, 2017; Kelly, 2016; Lehrer, 2009) and as methodology for professional development design studies specific to mathematical learning domains (Cobb et al., 2015).

2.2. Teacher Professional Development

Recent changes in California’s instructional frameworks for teaching multilingual learners require teachers to integrate ELD across the curriculum, where content standards and ELD standards are taught in tandem. The language demands for the teaching and learning of mathematics require more productive language use and discourse. Of equal importance is the ongoing professional development of instructional practice that can support the dual development of mathematical understanding and language for multilingual students. Although educators have advocated for language instruction to be integrated systematically across the curriculum, approaches used in teacher preparation programs are fragmented, with many addressing content and English language instruction separately (e.g., Faltis & Valdés, 2016; Lucas & Villegas, 2013; Valdés et al., 2005). Subsequently, there is a continued need to engage in more practice-based research on how to support teachers with flexibly integrating subject matter content learning and language development (Short, 2017; Von Esch & Kavanagh, 2018).

There is, however, a large body of research informing approaches to teacher professional development (Garet et al., 2001; Sancar et al., 2021). An important consideration of our professional learning design was an explicit consideration of the connections between professional development structures for learning, classroom practice, and student learning. Our design considerations draw on several research-based and theory-based approaches supporting the effective teaching of subject matter and language development in a way that features a focus on students’ learning processes (Borko et al., 2010; Huang et al., 2022), engages teachers in iterative, active, and authentic learning processes (L. B. Allen & Crowley, 2017; Webster-Wright, 2009), and is embedded in classroom context and practice (Ball & Cohen, 1999; Darling-Hammond & Richardson, 2009; Korthagen, 2016). Teachers’ content and pedagogical knowledge can be deepened by engaging in researcher–practitioner collaborative learning cycles through content-focused sessions supporting new learning, the iterative enactment of focal practices, and embedded inquiry and reflection (Hill et al., 2008; Sarkar et al., 2024; Shulman, 1987).

Collaborative inquiry is a promising strategy for strengthening teacher learning (Kraft et al., 2018; Lynch et al., 2019) and is a central mode of professional learning aligned with our theory of change. Engaging teachers in collaborative inquiry has the power to impact teacher beliefs about what is possible, leading to meaningful shifts in their instructional practice, and therefore impacting student achievement (Donohoo, 2017; Goddard et al., 2015). Changes in beliefs occur as teachers reconcile discrepancies between initial thinking and new ideas that emerge through the examination of evidence and reflection (Donohoo & Velasco, 2016). By introducing inquiry as a lens through which teachers explore new practices, we hope to establish a culture where they feel comfortable taking risks, trying out new practices, and individually and collectively learning through examining artifacts of student learning.

2.3. Honoring Teachers’ Expertise

We view teacher professional development not only as a strategy to improve professional practice but also as an essential factor enabling or constraining teacher professionalism and agency. We do not explicate a discussion of agency in relation to professional learning here but acknowledge that concepts of identity and agency are central in the education and learning of adults (Dabbagh & Castaneda, 2020; Ecclestone, 2007). The concept of agency also serves as a lens for understanding how teachers negotiate and enact instructional practice within the complexity of educational contexts. Torrance and Forde (2017) argue that the re-professionalization of teaching must promote leadership and inquiry to positively influence teacher agency and evolution of practice, a stance that marks a departure from professional orientations of teaching focused on standards, accountability, and performance management. In a systematic review of the educational research literature on teacher agency, Cong-Lem (2021) asserts that the development of teacher agency is linked to the opportunities teachers have for professional development, research, collaboration, and reflective practice.

Inquiry-based collaboration with researchers and peers affords opportunities for teachers to engage with research and evidence of student learning. Critical reflection can lead to reframed assumptions and new understandings that empower teachers to take risks and engage in new and innovative practices (Jones & Charteris, 2017). Boylan et al. (2023) argue that transformative professional learning is enacted in different ways through three primary, although generic, modes of professional learning: (1) collaborative inquiry and practitioner research; (2) training; or (3) workshops led by experts and peer groups. However, the transformative characteristics of professional development and association with critical forms of professionalism are established through purpose and agency. This can be achieved when, for example, professional development on concepts of social justice and culturally responsive teaching are implicitly or explicitly purposed with a critical ethical orientation toward addressing disadvantage in educational structures and practices. Our framework positions teachers as active participants in their own professional growth and knowledge construction through critical reflection upon the pedagogies and practices they currently enact and must also develop to better support the achievement of multilingual students.

2.4. Integrated English Language Development in Mathematics

Integrated ELD in mathematics sits at the intersection of supporting students in their language and mathematical development through pedagogical practices and specific linguistic and mathematical supports. Furthermore, integrated ELD/mathematics skills include the knowledge and abilities of ML students to communicate their mathematical thinking clearly and coherently to peers, teachers, and others as a crucial part of what it means to know and carry out mathematics (Sammons, 2018). Mathematical language refers to the diverse ways students communicate mathematically across modalities, for example in reading, writing, speaking, and listening (O’Halloran, 2015). The most recent iteration of the Mathematics Framework from the California Department of Education (CDE, 2023) requires students to demonstrate sophisticated academic language functions such as explaining, justifying, negotiating, and revising for engaging in deeper mathematical learning. Thus, language and discourse now, more than ever, are central to what it means to learn and understand mathematics (LMU-CEEL, 2024). S. H. Wang et al. (2021) state that language is part of a larger system of meaning-making, inseparable from all human action. This stance encourages one to consider what students can do and accomplish with language beyond focusing only on the structural elements of language or narrow notions of mathematical language as including only vocabulary or word problems. This requires students and teachers to work towards precision, or exactness, in communicating mathematical meaning and exploring when and how is the right time to focus on language in ways that will enhance, not interrupt, students’ development of mathematical ideas.

Although peer-to-peer interactions in mathematics class have the potential to benefit all learners, including ML students (Banes et al., 2018), it is challenging for teachers to know how to structure these conversations in ways that support and include all types of learners (Bartell et al., 2017). Self-explanations (of one’s own ideas) are effective when scaffolded in ways that draw students’ attention to specific conceptual ideas (Rittle-Johnson, 2024). Zwiers et al. (2017) offer the following design principles for mathematics instruction: (1) support sense-making; (2) optimize output; (3) cultivate conversation; and (4) maximize linguistic and cognitive meta-awareness. Linguistic instructional supports (e.g., sentence starters, scripts, translanguaging) and content scaffolds (e.g., using relevant tasks where mathematics is applied to familiar situations) can be used to support ML students in sharing their mathematical ideas in meaningful ways.

These instructional supports align with the integration of language, mathematics, and culture. For instance, the way that fractions are termed in languages other than English can sometimes be easier for students to comprehend because it can reduce cognitive load. For example, in Turkish and Arabic, the denominator is said before the numerator, making it easier for a learner to think of the size of the parts first, before counting how many there are. Prediger et al. (2019) argue that mathematics concepts are not just in one language or the other; bilingual individuals think in both. The “bilingual connection mode” allows students to connect languages and conceptualizations and move flexibly between thinking about fractions from part to whole (as in German and English) and from whole to part (as in Turkish and Arabic), and they could do this regardless of which language they were speaking at the time (Prediger et al., 2019). Similarly, In Korean, two thirds is literally translated as “of three parts, two”. Thus, unlike the English term “third”, the Korean term for third, sam bun (where sam = three and bun = part(s)), directly supports the concept of the whole divided into three parts. This may extend to an understanding of more complex fractions like 3/5 and 5/8 (Miura et al., 1999; Silver & Libertus, 2022). Thus, incorporating translanguaging during classroom lessons results in students’ ability to simultaneously leverage multiple repertoires when learning new content (García et al., 2017).

Lastly, we call attention to the importance of cultural responsiveness to problem contexts, children’s solution strategies, language use, and instructional activities and norms. Culturally sustaining pedagogy (Coulter & Jiménez-Silva, 2017; Aronson & Laughter, 2016) builds from the idea in which teachers’ build upon students’ cultural, linguistic, and academic assets as they elevate students’ mathematical content knowledge and critical consciousness in relevant ways (Paris, 2012; Paris & Alim, 2017). Culture has a strong effect on teaching and learning, and teachers’ instructional decisions should be guided by the local context (Gay, 2021). For instance, teachers in New Zealand have been promoting more collaboration when students solve mathematics problems so that classroom instruction is aligned with the collectivism values of the Pacific Island students (R. Hunter & Civil, 2021). Teachers also administered mathematically rich story problems that used contexts and terms from various Pacific Islands (J. Hunter & Miller, 2022). In other words, culturally responsive mathematics lessons should be aligned with students’ needs and background knowledge so that teachers build lessons around students’ ideas and prior knowledge.

2.5. Mathematical Identity

Mathematical identity plays a crucial role in determining the academic success of students and their future careers, especially those traditionally marginalized from STEM-related fields. Students’ math identities are specifically important when avoiding stereotypes that reinforce the idea that mathematics success belongs to a small group of people who tend to be Asian or White males (Cvencek et al., 2015). Mathematics identity refers to “the dispositions and deeply held beliefs that individuals develop about their ability to participate and perform effectively in mathematical contexts and to use mathematics to change the conditions of their lives” (Martin, 2012, pp. 57–58). A mathematical identity encompasses a person’s self-understanding and how others see them in the context of performing mathematics. Mathematical identities are complex and change over time (Andersson et al., 2015).

It is critical to explore the mathematical identities of our students and provide opportunities for them to see their funds of knowledge (Civil, 2016; Moll, 2014) represented in texts and authentic mathematical investigations. Elevating students’ mathematical dispositions can be achieved by providing students with opportunities to explain their mathematical solution strategies to a peer(s), valuing their solution pathways, and reinforcing their mathematical and language development (Gresalfi & Cobb, 2006; Herbel-Eisenmann et al., 2015). If students have a strong sense of belonging in the mathematics classroom and have positive math identities, they are more likely to be able to share their arguments with others and critique others’ reasoning (K. Allen & Schnell, 2016).

A mathematical mindset, particularly a growth mindset, is crucial for successful math teaching and learning. Many people tend to think they are either born with “math ability” or without which tends to fall under a fixed mindset (Dweck, 2006; Dweck & Yeager, 2019). People are quick to admit that they are “not math people” (Miller-Cotto & Lewis, 2020). Dweck (2006) emphasizes the importance of teaching students about their mathematics identity. Building on Dwek, more recent research addresses the types of support that teachers can use to grow students’ “math brains” (Alam & Mohanty, 2023; Willis, 2010). Our work is grounded in the assertion that mathematical identity is changeable and negotiated over time.

3. Conceptual Framework

Grounded in sociocultural learning theory (R. Hunter & Civil, 2021; Moll, 2014), our proposed conceptual framework affirms that people learn new content knowledge and simultaneously deepen their language skills through interactions with others (Kibler et al., 2015). Our ILMP framework consists of three integrative instructional pillars: (1) attention to language, (2) attention to mathematical thinking, and (3) cultural responsiveness. These pillars are grounded in productive and asset-based pedagogies. We highlight the key practices and strategies supporting teachers when working with multilingual students during mathematics instruction.

Using a design-based research approach and inquiry cycles, the ILMP framework was designed in collaboration with teachers to improve the teaching of elementary mathematics during the integrated ELD instructional period. Furthermore, we encourage the use of full linguistic repertoires (García et al., 2017) during integrated instruction. Through this framework, our intention is to elevate the linguistic, mathematical, and cultural identities of multilingual learners (see Figure 1).

Similarly to Poehner and Infante (2017), we build from Vygotsky’s (1987) notion that the tools used to mediate learning, guided by teachers’ beliefs, help ML students recognize the relevance of instructional materials that they can use to support their language use during peer-to-peer interactions. Poehner and Infante (2017) refer to this as mediated development and claim that students can produce more knowledge together than when working independently, if the teacher is responsive to students’ individual needs, including language support. Language production in students’ first or second language, which includes self-talk, partner, or group, can act as a resource for planning, deliberating, contemplating, and evaluating (Swain, 2006; Wei, 2018). Not only does language production support content learning but the discussion of mathematical ideas can aid in language learning as well (Baird et al., 2020; Espinas & Fuchs, 2022). Furthermore, enacting pedagogical practices and using curriculum that are culturally responsive support both language development and deepening of mathematical thinking (Abdulrahim & Orosco, 2020).

3.1. Attending to Students’ Full Linguistic Repertoire

We advocate for students to use their full repertoire of language(s) as a resource (García et al., 2017). This means giving students opportunities to talk during instruction, encouraging them to use their full linguistic repertoire, and providing scaffolds for structuring student talk in the context of English language development. This means the teacher needs to provide a discussion-worthy task (Swartz & DeRosa, 2023), let students solve on their own in a way that makes sense to them (Carpenter et al., 1999; Clements & Sarama, 2020), and ask students to share what they know (in pairs, groups, and as a whole class) before, during, and after solving a mathematics problem. Additionally, García et al. (2017) declared that multilingual speakers leverage their entire language repertoire (languages other than English, vernacular, etc.) to make meaning. Therefore, when multilingual learners are making sense of their mathematical ideas, they should be encouraged to use their full linguistic repertoire to demonstrate what they can do with content and language (explain, persuade, argue, compare and contrast, or evaluate). Finally, language scaffolds for English language development can be helpful for children, especially multilingual learners, to have productive conversations about their ideas. Protocols and sentence starters can be used to teach students how to respectfully talk to each other and build conversation skills such as creating, clarifying, fortifying, and negotiating ideas (Zwiers et al., 2014). Language support should make the activity more accessible without diminishing the mathematical rigor of the content.

3.2. Attending to Students’ Mathematical Thinking

The ILMP framework considers and aligns with the latest version of the California Framework for Mathematics (CDE, 2023), which states that mathematics should be rigorous, relevant, and responsive, with an emphasis on meaning-making and problem-solving. Although there are many ways to define rigor, the IMLP framework adopts the California Framework for Mathematics position that students should be given grade-level problems to solve within their zone of proximal development. Problem-based lessons should include opportunities for students to productively struggle (Baker et al., 2020) as they explore, notice, question, solve, justify, explain, represent, and analyze in ways that strengthen their mathematical identities. In addition, when problems are relevant to students’ interests and encourage students to think critically about the world, mathematics is seen as a powerful tool for modeling events rather than a set of rote procedures one is expected to memorize. When students view mathematics as an important role in their lives, it drives students to pursue more STEM-related careers (Daro & Asturias, 2019). Students’ cultural backgrounds, experiences, and languages should be utilized when teaching and learning mathematics (R. Hunter et al., 2019) so that mathematics instruction elevates students’ skills and successes. Variability in students’ backgrounds, perspectives, and learning needs should be viewed as assets and used to inform instructional decisions. Emphasizing grade-level rigor, meaningful contexts, and students’ cultural assets is the best way to ensure that all students deepen their understanding of mathematics and have opportunities to engage in rich mathematics tasks.

To promote the use of grade-level problems and meaningful contexts that foster appropriate productive struggle and utilize students’ cultural assets (CDE, 2023), we advocate for the use of cognitively guided instruction (CGI) in which elementary children are encouraged to solve story problems in a way that makes sense to them, using their prior knowledge, without direct instruction from the teacher (Carpenter et al., 1999; Clements & Sarama, 2020). During CGI lessons, children are expected to share their ideas with each other so they can develop explanations and justifications for their strategies and also be exposed to their peers’ strategies (Carpenter & Franke, 2004; Clements et al., 2023). These strategies can be aligned with learning trajectories that place students’ understanding of mathematics on a developmental continuum (e.g., Empson & Levi, 2011; Jacobs et al., 2024), offering teachers a guide for responding to students’ needs in the moment, such as pairing students with slightly different strategies or sequencing student presentations of their work in order from most accessible to most abstract (Smith & Stein, 2018). Prioritizing student voice ensures that students are the ones forming conjectures and thinking critically, not just the teacher (K. Allen & Schnell, 2016). Whole-class discussions that include a variety of approaches and equitable participation contribute to gains in performance assessments for both ML and English-only (EO) learners (Banes et al., 2018). We maintain that students should be given discussion-worthy (Crespo, 2020; Featherstone et al., 2011) story problems that cultivate the goals of the state framework: exploration, noticing, questioning, solving, justifying, explaining, representing, and analyzing in ways that strengthen their mathematical identities.

3.3. Cultural Responsiveness

In many of our classrooms, teachers’ cultural and linguistic backgrounds are different from students’ backgrounds. Furthermore, teachers often find it challenging to gather sufficient cultural information from students. Cultures are complex; therefore, gaining a deeper understanding requires effort beyond the classroom setting. Understanding students’ individual linguistic, mathematical, and cultural backgrounds is essential for designing instruction around their specific needs. The ILMP framework aims to be both culturally and personally responsive in the focal pedagogical practices, instructional strategies, and mathematical content selected. Kolovou’s (2023) literature review on culturally relevant education in mathematics and science found that teachers in these content areas often lacked confidence in understanding how to learn about and utilize students’ cultural backgrounds during instruction. When there is a cultural and linguistic mismatch between educators and their students, it becomes especially important to engage intentionally in learning about the backgrounds, experiences, and needs of the students we serve. One way for teachers to learn about students’ language backgrounds and to build students’ confidence is to ask learners to create a language identity portrait. A language identity portrait is a visual activity students can engage in to map out their cultural and linguistic identities on a silhouette of themselves (Figure 2). They can use different colors and symbols to represent different languages that are significant to them. This activity encourages children to talk about the different languages that are important to them and how these languages form their identity (Mohamed, 2022). These reflective identity activities can help students gain a greater awareness of their own unique assets and the assets of others by promoting interaction between different knowledge, different ways of knowing, and different knowers (Gutiérrez, 2017).

Culturally sustaining pedagogy means building upon students’ cultural, linguistic, and academic assets as teachers elevate students’ academic knowledge and critical consciousness in relevant ways (Aronson & Laughter, 2016; Coulter & Jiménez-Silva, 2017; Ladson-Billings, 2014). For instance, when teachers familiarize themselves with students’ oral, written, and reading capabilities, they will be able to differentiate and determine the appropriate time and degree of language scaffolds for English language development needed for each student at specific times. Similarly, if teachers are aware of students’ solution strategies on a learning continuum (Empson & Levi, 2011; Jacobs et al., 2024), then they will be able to anticipate how to pair students together or sequence whole-class presentations. Teachers can also structure classroom routines and norms to match the cultural behaviors or values of their students (e.g., collectivism vs. individualism; J. Hunter, 2021). Another approach teachers can take is to modify the problem context to a situation or artifact that they know their students are familiar with (e.g., J. Hunter & Miller, 2022). These are all ways teachers can create culturally responsive classrooms that meet the needs of the individual students in their classrooms.

4. Engaging and Supporting Practitioners’ Enactment of the ILMP Framework

Given the central role that language plays in the mathematical learning of MLs, the design-based approach afforded the opportunity to work collaboratively with elementary school teachers and coaches, drawing on their expertise, to iteratively design and test resources, strategies, and practices that promote integrative teaching and learning. Project researchers and practitioners (teachers and instructional coaches) engaged in monthly co-design and shared learning sessions to deepen pedagogical knowledge of Cognitive-Guided Instruction (CGI) with a focus on fractions, productive and receptive language development, and disciplinary practices supporting mathematical discussions to promote conceptual understandings. Between monthly design sessions, researchers supported practitioners through extended learning activities and cycles of inquiry focused on the implementation of selected tasks and practices during math instruction and collaboratively analyzing artifacts of students’ mathematical solutions based on the trajectory of solution strategies to better understand how to support and extend student thinking.

Artifacts of student learning analyzed for this study were generated from monthly, extended learning activities where practitioners administered selected equal sharing problems designed to elicit student mathematical thinking and explanations of problem-solving strategies. Students were asked to individually solve the problem in more than one way, explain their solution strategy, and justify why their solution is correct. Practitioners used partnering strategies to provide students with opportunities to work with diverse language partners. For example, a Three Reads Protocol was used to engage students in making sense of select math tasks by reading the prompt three different times, each time with a different focus. This protocol supported students with understanding the problem rather than quickly solving it. At the beginning of each year, practitioners were asked to select up to four focal MLs, across proficiency levels, to collect written work and audio, video, and transcribed samples that capture how they think about and communicate mathematical solutions to the selected tasks. Math and language samples were captured from paired focal student (student-to-student) discussions or practitioner-focal student math interviews. A math interview protocol was designed to capture a minimum of four exchanges. Below, we provide a few specific examples of how we engaged and supported practitioners’ enactment of the ILMP framework.

4.1. Triple Track Agenda

Monthly shared learning sessions were facilitated using a triple track agenda, which intentionally engaged practitioners as learners and provided supported and collective opportunities to apply new learning and extend practice (

Table 1. Alignment of three pillars and the triple-track agenda.

3 Pillars	Practitioners as Designers of Their Practice	Teaching Strategies
Attend to Students’ Full Linguistic Repertoires	Practitioners determined when to use more/less language scaffolds for English language development depending on their students’ needs. Practitioners developed different scripts (interview protocol) for different grade levels so they could practice different conversation skills. Practitioners decided when to translate based on students’ language proficiencies. Practitioners chose how to facilitate each phase of the lesson structure based on how well their students knew the norms for each phase.	Scaffolds: Sentence frames. Lesson structure: Three Reads; Partner interview protocol; Math summit.
Attend to Students’ Math Ideas	Practitioners used different numbers in their story problems. These decisions were made by the individual practitioners based on where they thought their students were at developmentally. Practitioners used children’s solution strategies to pair students up during the partner interviews or to sequence student presentations during the whole-class math summit.	Equal-sharing fraction problems; Equal-sharing learning trajectory to anticipate children’s strategies.
Cultural Responsiveness	Practitioners used the practices listed in this section to determine their students’ linguistic needs. Practitioners utilized what they knew about students’ backgrounds to design relevant contexts for the story problems. Math identity activities (in PD and during classroom instruction) fostered a growth mindset among students and practitioners.	Bilingual student profile; Language identity portrait (see Figure 2 above); Math identity activities.

for examples of practices). Pedagogical practices and strategies to support integrated language and math instruction were introduced with the goal of everyone taking on the role of a learner, a contributor, and a designer. As learners, practitioners focus on building their own knowledge before leading the learning of others. As contributors, they exercise agency by setting their own learning intentions and collaboratively engage in co-learning and collective engagement with peers. As designers, practitioners continuously enact and iterate new knowledge and practices in the context of their school and classroom and lead peers in continued growth and professional development. Additionally, we collectively engaged in reflection and discussion about the implementation of practice between sessions and modified subsequent professional development in response to the outcomes of these reflections.

To better illustrate the triple track agenda, let us consider an example. During the initial monthly shared learning sessions, researchers engaged practitioners in learning about and exploring their own math learning journeys and identity using a math identity graph activity (See Figure 3) which could be used with their students in the classroom (Track One). Through this activity, practitioners were able to reflect on the importance of their math identity, the role it plays in their teaching of math, and understand the value of how they might use math identity graphs with students, colleagues, and even with parents to promote positive math identity and growth mindset (Track Two). This simple but deeply reflective activity allowed practitioners to acknowledge their own stance and long-held beliefs about how math identities are formed and re-enforced. As a result, practitioners engaged their students in completing math identity graphs and were able to learn more about their students and how they felt about themselves as mathematicians, which informed their subsequent planning and teaching of math lessons in ways that support the development of positive math identities (Track Three). Learning from professional development sessions was applied to practitioners’ individual learning, learning with colleagues, and in the classroom with their students.

4.2. Multilingual Language Learning Implementations

Multilingual/language learning practices were also applied using the triple track agenda method. These instructional practices supported multilingual learners to productively share and discuss their math ideas. For instance, professional development sessions promoted the use of a lesson structure to introduce constructive conversation skills in math, such as creating, clarifying, fortifying, or negotiating ideas (Zwiers et al., 2014). Building on the lesson structure applied in our work, practitioners learned how to implement the (1) Three Reads protocol, (2) engage their students in a math interview with a partner, and (3) engage their students in a math summit. Sentence frames were also used as a support to guide practitioners with the language needed to express their thinking. Practitioners reflected on these language supports and how they helped them as individual learners. They also reflected on how this would support other adult learners as well as their students. Practitioners used the lesson structure with their students and came back to reflect on the learning that had occurred. Practitioners demonstrated agency going through this process. For example, one group of practitioners created several types of interview protocols to focus on a range of productive conversation skills at different points in the year.

4.3. Mathematical Implementations

Professional development facilitators also used the triple track agenda method to introduce math topics. Equal-sharing fraction problems were identified as a focus given that all practitioners in the project were responsible for attending to this math content to some extent over the course of the academic year. Practitioners learned how to anticipate student responses by solving problems in multiple ways using the equal-sharing learning trajectory put forth by Empson and Levi (2011) and used precise language through modeling. They were able to work together to identify possible solution paths, opportunities to teach precise language, and use this knowledge to implement these strategies with their students. They were then able to collect student work, come back together as a team, and reflect on the strategies students used to solve the problems. Practitioners engaged as designers of their practice by choosing the numbers used in the problems they gave students, based on Empson and Levi’s (2011) recommendations. Practitioners also embraced the opportunity to adapt the problem context to align with their students’ backgrounds.

5. Challenges and Opportunities

5.1. Challenges

Design-based research and research–practice partnerships are not without their challenges (Baker et al., 2020). Working closely with our district partners has helped ensure that our professional learning was grounded in the contexts, cultures, needs, and aspirations of each classroom. However, close partnership has also required flexibility in our study design and implementation, as the district addressed pressing operational concerns over the course of the project (e.g., teacher strikes, shortages, changes in leadership, and school closures in part due to natural disasters). Operational concerns have typically resulted in the rescheduling of professional learning meetings, though in some cases meetings were canceled or consolidated, and communication then took place asynchronously. The most serious challenge, of course, was the COVID-19 pandemic, with its disruption to instruction and general redirection of attention and energy to meeting the day-to-day health and safety needs of educators, students, and their families.

Design-based research and research–practice partnerships, to be implemented successfully, also require adaptability with respect to content and delivery. School districts, especially large-enrollment districts, will often have standardized, established procedures and expectations guiding professional learning and instruction. As researchers, we must be adaptive of local terminology in use (e.g., translanguaging vs. iELD, emergent bilingual vs. English learners) and new methods (scaffolding with sentence frames vs. giving students space to converse in the moment) and compromise where possible while maintaining research integrity.

5.2. Opportunities

While design research collaborations are premised on shared opportunities, frameworks guiding common work, and drawing from diverse perspectives and forms of expertise, they can also give rise to inherent tensions that can emerge from their convergence. As articulated by Lee (2019), the new generation of academic content standards endeavors to make connections across content areas and disciplinary standards, establishing inroads for the alignment between ELD standards and content standards. However, there is often a lack of substantive communication and collaboration between content experts to address underlying issues with convergences and discrepancies within and between ELD and content standards. Yet, integrative instructional practice is expected of classroom teachers. Through the professional development sessions, classroom teachers had opportunities to share their experiences, insights, and questions with school-level instructional coaches, district instructional and administrative personnel, and educational researchers. Collaboratively, we arrived at meaningful change in instructional practices that will benefit all students, but especially multilingual learners.

Our internal research team included content experts in math and English language development pedagogies and in assessment. This gave rise to many opportunities to engage in deep and meaningful conversations across our areas of expertise that continue to inform our own educational practice and research agendas. Our research team engaged with data generated from practice, specifically observations and artifacts, to continually inform the design of professional development sessions and materials which honored teachers’ expertise. The ILMP framework was strengthened by the informed practice and expertise that contributed to its development.

6. Conclusions

This conceptual paper advances a framework for supporting multilingual students’ mathematical discourse through integrative and asset-based instructional approaches. Grounded in design-based research and co-constructed with educators teaching in linguistically and culturally diverse schools, the ILMP framework emphasizes three interconnected pillars—attention to language, attention to mathematical thinking, and cultural responsiveness—as foundational for meaningful and equitable mathematics instruction.

By centering multilingual learners’ linguistic and cultural assets, and by positioning teachers as agents of change through iterative cycles of inquiry and co-design, the ILMP framework holds potential to enrich classroom practice and foster positive mathematical and language identities among students. The integration of productive language use, cognitively demanding mathematics tasks, and culturally relevant pedagogy supports deeper conceptual understanding and more inclusive participation in mathematical discourse. Future research should include empirical evaluations of student academic outcomes to substantiate the feedback provided by teachers regarding the framework’s impact on student learning.

While this framework was developed in the context of upper elementary classrooms, its principles are adaptable across grade levels and subject areas. As educational systems increasingly emphasize both language development and disciplinary learning, the ILMP framework offers a responsive, research-informed model for professional learning and instructional transformation that centers multilingual students’ full potential.