From traditional teaching to argumentation-based instruction: A student-centered approach in mathematics education

2.1 Toulmin's model of argumentation

Toulmin (1958) reconceptualized argumentation beyond formal logic, emphasizing its social and context-dependent nature. His model includes five components: claim, data (evidence), warrant, backing, and rebuttal (Katzavitz, 2012; Kaya, 2013; Simon, 2008). This framework provides a useful analytical lens for examining classroom discourse and reasoning in science and mathematics education.

The components are defined as follows (see Figure 1): a claim is a statement open to debate; data provide evidence supporting the claim; a warrant explains the logical connection between data and claim; backing strengthens the warrant through theoretical or empirical justification; and rebuttal introduces counter-arguments or exceptions.

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Figure 1.

Argument components – the Toulmin model.

In educational research, Toulmin's model is widely used to analyze the structure and quality of reasoning in classroom discourse, allowing examination of students’ and teachers’ use of evidence, justification, and responsiveness to alternative viewpoints (Katzavitz, 2012; Simon, 2008).

For example, in a free-fall context, the claim that heavy and light objects fall at the same rate can be supported by observational data, warranted by physical principles, backed by Newtonian mechanics, and challenged by considerations of air resistance. This illustrates how argumentation connects empirical observation with theoretical reasoning in science and mathematics learning.

To operationalize Toulmin's model in empirical research, several studies (e.g., Katzavitz, 2012; Simon, 2008) have developed hierarchical frameworks that classify arguments based on the presence and combination of structural components. This enables a systematic assessment of reasoning quality and cognitive engagement in classroom discourse.

The framework consists of five levels of argumentation, ranging from simple claims to complex structures integrating evidence, warrants, backing, and rebuttals (see Table 1).

Level 1 includes claims only (C).

Level 2 includes a claim with either data or a warrant (CD/CW).

Level 3 includes combinations of claim, data, warrant, or rebuttal (CDW/CDR/CWR).

Level 4 includes claim, data, warrant, and backing (CDWB).

Level 5 includes rebuttal-based extended arguments integrating claim, data, and warrant (CDWR).

This gradation captures increasing complexity in argumentation, from basic assertions to fully elaborated reasoning involving justification and counter-argumentation, and provides an operational measure of critical thinking in classroom discourse.

For example, in a 10th-grade mathematics discussion on functions, a student's claim that “Vertex A has the same values as vertex B due to symmetry” reflects a Level 2 (CW) argument. When another student challenges this by introducing reasoning related to negative values, the argument advances to Level 3 (CWR), indicating deeper engagement with justification and critique.

In this study, the framework is applied to both teacher- and student-generated discourse to analyze the distribution and levels of argumentation, and to link interactional patterns to broader pedagogical orientations toward argumentation-based learning.

In the context of this study, ABI is defined as a pedagogical approach that engages students in constructing, justifying, evaluating, and revising claims through evidence-based reasoning and dialogic interaction. ABI positions learners as active participants in knowledge construction who articulate ideas, respond to peers, and engage with alternative viewpoints.

A substantial body of research identifies ABI as an effective approach for developing students’ reasoning, critical thinking, and conceptual understanding in mathematics and science education. It is grounded in constructivist and sociocultural perspectives, which conceptualize learning as occurring through dialogue, justification, and reflection.

Structurally, ABI is informed by Toulmin's (1958) model of argumentation, which conceptualizes arguments as consisting of claims, data, warrants, backing, and rebuttals. This framework has been widely used to analyze the quality and complexity of reasoning in classroom discourse (Katzavitz, 2012; Kaya, 2013; Simon, 2008) and serves as an analytical lens in the present study. Importantly, a distinction is made between argument as a product and argumentation as a process of constructing and negotiating meaning through discourse (Staples & Conner, 2022).

Empirical studies demonstrate the effectiveness of ABI across educational contexts. Kaya (2013) found that ABI improved pre-service teachers’ conceptual understanding of chemical equilibrium and enhanced the quality of their arguments. Ozdem et al. (2013) reported diverse reasoning patterns in pre-service teachers’ mathematical arguments, including causal, observational, and example-based reasoning.

From a sociocultural and dialogic perspective, argumentation is understood as a collective practice in which students build on, critique, and refine each other's ideas to develop shared understanding (Asterhan & Schwarz, 2016; McNeill & Pimentel, 2010; Yackel, 2002). Research consistently shows that such practices require explicit instructional support, as argumentation does not develop spontaneously (Makar et al., 2015; Pi-Jen, 2018). Teachers play a central role in scaffolding discourse, shaping norms of justification, and supporting students’ progression from descriptive talk to evidence-based reasoning.

Empirical evidence further demonstrates ABI's effectiveness across age groups. Rumsey and Langrall (2016) showed that fourth-grade students engaged in ABI developed stronger abilities to hypothesize, justify, and reason collaboratively in mathematics. Reuter (2023) similarly demonstrated that even early childhood learners can engage in exploratory mathematical argumentation that supports claims and justifications.

Collectively, these studies suggest that ABI fosters learner agency and transforms classrooms into communities of inquiry. In mathematics education, argumentation is conceptualized not only as formal justification or proof but also as a socially situated practice in which mathematical meanings are constructed and refined (Mariotti et al., 2018; Stylianides et al., 2016).

Research further emphasizes that the quality of mathematical argumentation depends on sustained dialogic interaction, in which students build on and challenge each other's reasoning (Staples & Conner, 2022; Zhuang & Conner, 2022). However, such interaction requires deliberate instructional design and teacher orchestration (Cramer & Kempen, 2022; Durand-Guerrier et al., 2012; Knipping & Reid, 2019), highlighting the central role of pedagogy in shaping argumentative practices.

Building on these theoretical and empirical foundations, recent studies have further examined how argumentation is developed, supported, and enacted across diverse educational contexts.

2.4 Recent studies on argumentation in mathematics and science education

Recent studies (2023–2025) have advanced understanding of argumentation in mathematics and science education, highlighting three main trends: (1) the role of teacher noticing and professional development, (2) variations in the enactment of argumentation across contexts, and (3) the impact of structured instructional designs combining inquiry and dialogue.

Nama and Ayalon (2025) found that a targeted university course improved secondary-school mathematics teachers’ ability to notice both structural (claims, evidence, warrants) and dialogic features of classroom argumentation, including turn-taking and uptake. This demonstrates that professional development focused on noticing can enhance teachers’ instructional sensitivity to argumentation.

Similarly, Altun and Ozsevgec (2025) reported that a short instructional module for pre-service science teachers improved both oral and written argumentation, with participants demonstrating more sophisticated reasoning schemes and increased use of scaffolding strategies. These findings suggest that even relatively brief interventions can strengthen argumentation competencies in teacher education.

From a curriculum perspective, Lehmann and Friend (2025) identify a persistent gap between the recognized importance of argumentation in mathematics and its limited presence in classroom tasks and assessment practices, which continue to prioritize procedural fluency. They call for integrating argumentative writing into both curriculum design and assessment frameworks.

In addition, intervention studies such as Debate-Based Inquiry Learning (DBOIL) show that combining inquiry with structured debate improves students’ ability to construct and evaluate claims compared to inquiry alone (Hendratmoko et al., 2024). Likewise, Ayalon et al. (2024) demonstrate that authentic, context-based tasks enhance the quality and engagement of students’ mathematical argumentation.

Collectively, these studies reinforce the importance of scaffolding, instructional design, and teacher support in developing argumentation competencies across age groups (Makar et al., 2015; Pi-Jen, 2018; Reuter, 2023; Rumsey & Langrall, 2016). They also converge on the view that argumentation is a teachable practice that requires explicit curricular and pedagogical structuring rather than spontaneous classroom emergence.

Despite these advances, three key gaps remain. First, research in non-Western and minority contexts, including Bedouin education, is still limited. Second, most studies focus on short-term interventions rather than sustained classroom enactment. Third, few studies integrate teachers’ stated beliefs with fine-grained analyses of their actual classroom discourse within the same empirical setting (e.g., Mariotti et al., 2018; Staples & Conner, 2022; Stylianides et al., 2016).

The present study addresses these gaps through a context-sensitive case study in Bedouin Arab secondary schools, integrating teacher interviews with repeated classroom observations. It examines the relationship between teachers’ perceptions of ABI and classroom discourse.

Accordingly, the study addresses the following research questions:

How do secondary-school mathematics teachers perceive ABI?

3.1 Research approach

The present study employs a qualitative case study design. Case study research is considered a methodological strategy that enables an in-depth examination of a phenomenon within a bounded context, drawing on multiple sources of evidence and perspectives (Creswell, 2013). A qualitative case study is particularly appropriate when the aim is to explore a complex, context-specific process such as teachers’ enactment of ABI, which cannot be fully captured through quantitative measures.

The choice of a single case—one Arab Bedouin high school in southern Israel—allows for a deep exploration of how argumentation manifests within a culturally and socio-educationally unique environment. Rather than seeking broad generalization, this design aims for analytical generalization, generating theoretical and pedagogical insights that may inform similar contexts (Josephine, 2016).

This approach is grounded in the assumption that analyzing a specific case can shed light on broader behavioral patterns and deepen our understanding of complex educational processes. By examining both teachers’ reported attitudes and their enacted practices, the study bridges the gap between espoused theory and practice in mathematics instruction.

3.2 Research population and sample

Although a substantial portion of the literature on ABI has focused on pre-service teachers, particularly in the context of teacher education programs, fewer studies have examined how argumentation is enacted by in-service teachers within everyday classroom practice. Research on pre-service teachers has provided important insights into the development of argumentative competencies and pedagogical beliefs (e.g., Kaya, 2013; Ozdem et al., 2013). However, the transition from theoretical understanding to sustained classroom enactment remains underexplored among practicing teachers who operate under curricular, institutional, and cultural constraints.

By focusing on in-service mathematics teachers with several years of teaching experience, the present study builds on this body of research and extends it by examining how ABI is perceived and enacted in authentic school contexts. In doing so, it contributes empirical evidence on the challenges and possibilities of implementing argumentation-based pedagogy beyond initial teacher training.

The study was conducted among mathematics teachers in an Arab Bedouin secondary school in southern Israel. The sample included five mathematics teachers (three men and two women) teaching grades 7–12. All participants held at least a bachelor's degree in mathematics education, and their teaching experience ranged from three to ten years (see Table 2).

The school was selected purposefully as it represents a typical secondary-school setting within the Arab-Bedouin community in southern Israel. Importantly, Arab schools in the southern region of Israel predominantly serve Arab-Bedouin community, whereas most non-Bedouin Arab schools are geographically concentrated in the northern region of the country, particularly in the Galilee, and in the central Triangle area. As a result, the educational, cultural, and socio-economic context of Arab schools in the south is largely shaped by the specific characteristics of Arab-Bedouin society.

This context is characterized by distinct cultural and social norms, relatively limited access to educational resources, and heightened pressure related to academic achievement and national examinations. Instructional practices in many Bedouin schools therefore tend to be predominantly teacher-centered and exam-oriented, which may constrain opportunities for dialogic and student-centered pedagogies.

At the same time, recent educational reforms have gradually introduced student-centered approaches into Bedouin secondary schools, creating an ongoing tension between traditional instructional norms and pedagogical innovation. This intersection of cultural tradition and emerging reform-oriented practices makes the selected school a particularly relevant context for examining the enactment of ABI in everyday classroom practice.

While the findings of this study are grounded in a specific Bedouin context, the use of purposeful sampling (Creswell, 2013) allows for analytical generalization. Accordingly, the insights generated may be relevant to other Arab schools in Israel and to minority educational settings that face similar cultural, institutional, and systemic constraints.

In addition, five classroom observations were carried out in mathematics lessons taught by Teacher Qasem, who also served as the homeroom teacher of the observed class (Grade 10-1). The class consisted of 32 students (27 girls and 5 boys), majoring in biology. Observing a single class across multiple lessons allowed the researcher to track the evolution of argumentative discourse over time and to identify consistent patterns rather than isolated events.

Teacher Qasem was selected for classroom observation through purposeful sampling, as he taught a class that was accessible for repeated observations and expressed willingness to participate in the study. His selection was not based on prior expertise in ABI or formal training in argumentation pedagogy. Rather, the aim was to observe the enactment of argumentation within routine classroom practice of an experienced in-service teacher.

This choice aligns with the study's goal of examining how argumentation emerges under ordinary instructional conditions, rather than in exemplary or intervention-based settings. None of the participating teachers reported having received formal training in ABI during their academic studies or professional development, allowing the study to capture naturally occurring practices and perceptions.

3.4 Data analysis

Participation in the study was voluntary and based on informed consent. Teachers were informed of their right to withdraw at any time and assured of confidentiality. All data were anonymized using pseudonyms, and identifying details were removed from transcripts. Written informed consent was obtained from all participants prior to their participation, in accordance with ethical guidelines (Shperling, 2021).

4.1 Observation findings

The following findings are based on repeated observations of a single focal classroom and are intended to provide an in-depth illustration of argumentation practices rather than generalizable patterns.

The findings presented in this section draw on the analysis of classroom observations conducted across five mathematics lessons and are organized around recurrent patterns identified in the data. Argumentative events were defined as episodes of classroom discourse in which a mathematical claim was explicitly articulated and accompanied by at least one additional argumentative component—such as evidence, justification, or rebuttal—in accordance with the analytic framework described in Section 3.4.

Overall, classroom instruction was predominantly structured around teacher-led questioning followed by brief student responses. Instances of argumentation were typically embedded within problem-solving activities and did not develop into extended, whole-class explorations of competing claims. Rather than being systematically planned as an instructional strategy, argumentation tended to emerge incidentally during task engagement.

Across the five observed lessons, 16 argumentative events were identified. These events are presented as illustrative of the dominant patterns observed in the focal classroom. Selection criteria included (a) the presence of an explicit mathematical claim, (b) observable attempts to justify, explain, or challenge the claim, and (c) interactional engagement involving teacher–student or student–student exchanges. The selected episodes are therefore analytic exemplars rather than an exhaustive representation of all classroom discourse.

Of the 16 identified episodes, 10 were initiated by students and 6 by the teacher. In terms of structural quality, the majority of arguments (13 episodes) were classified as Level 2, consisting of a claim supported by data or a warrant. Only three arguments reached Level 3, incorporating a claim, data, and a warrant. No arguments were identified at Levels 4 or 5, which would involve theoretical backing or sustained rebuttal.

Table 4 presents representative examples of argumentative exchanges and illustrates how argument levels were classified according to the coding framework.

Table 4 illustrates that although elements of higher-level argumentation occasionally emerged (e.g., counter-arguments), such exchanges were typically brief and often resolved through teacher intervention. As a result, opportunities for sustained dialogic development were limited, and most argumentative episodes remained at relatively low levels of structural complexity.

More specifically, most argumentative exchanges involved claims supported by evidence or explanations but did not evolve into extended dialogic sequences characterized by critique, comparison of alternative explanations, or theoretical justification. Even when students challenged one another's claims, these interactions tended to conclude shortly after teacher clarification, limiting the development of multi-turn argumentative discourse.

For example, during a lesson on quadratic functions, a student claimed that two parabolas were identical based on their visual symmetry. When prompted to justify the claim, the student referred to graphical features. A second student questioned this reasoning and introduced an algebraic perspective. Although this exchange included elements of justification and critique, it did not develop into a sustained comparison of alternative explanations and therefore remained structurally limited. This example illustrates how argumentation was present but interactionally bounded.

These patterns can be understood in relation to the predominance of initiation–response–evaluation (IRE) interactional structures in the observed lessons. Most exchanges followed a sequence in which the teacher initiated a question, a student provided a brief response, and the teacher evaluated the response without inviting further elaboration or peer engagement. Such patterns have been widely associated with teacher-centered instruction and limited opportunities for dialogic interaction (Duschl & Osborne, 2002; Mehan, 1979).

Within this study, a distinction is made between arguments as individual units of reasoning and argumentation as an interactional process through which these units are taken up, elaborated, and negotiated. While structural analysis focused on the quality of individual arguments, the broader analysis of argumentation examined how ideas developed across turns of talk.

In this respect, dialogic argumentation was identified when classroom interactions extended beyond IRE sequences to include student-generated claims, requests for justification, challenges, or elaborations unfolding across multiple turns. Although such instances were observed, they remained limited in scope and duration. The findings therefore suggest that while the potential for dialogic argumentation was present, it was only partially realized within the observed classroom context.

These observations provide an important empirical basis for interpreting teachers’ perceptions of ABI presented in the following section.

The analysis of interview data revealed several recurring categories related to teachers’ perceptions of ABI, including conceptual understanding, student capability, motivation, teacher efficacy, and contextual constraints.

To enhance analytic transparency, the categories presented in this section were derived through a systematic coding procedure involving iterative comparison across interview data. As illustrated in Table 3, interview excerpts were progressively coded, compared, and organized into sub-categories and broader conceptual categories.

The analysis was theoretically grounded in research on teacher beliefs and teacher cognition, which conceptualize teachers’ perceptions as interconnected belief systems shaping instructional decisions and pedagogical practices (Borg, 2003; Fives & Buehl, 2012; Thompson, 1992). From this perspective, teachers’ views on ABI were examined as reflecting beliefs about teaching and learning, students’ capabilities, teachers’ professional competence, and contextual conditions.

Using a grounded theory-informed approach, the interview data were analyzed through iterative coding and constant comparison. This process resulted in five analytically derived yet interrelated categories, representing central dimensions of teachers’ perceptions of ABI. Each category is presented below with illustrative examples demonstrating how it was expressed in teachers’ discourse.

Overall, teachers associated ABI with the promotion of conceptual understanding, particularly through connecting ideas, supporting explanations, and identifying students’ prior knowledge. At the same time, teachers expressed ambivalent views regarding students’ ability to engage in argumentation, often emphasizing the need for guidance and scaffolding.

Additional categories reflected teachers’ perceptions of motivation, professional confidence, and contextual constraints, including time pressure, curriculum demands, and differences in student ability. Taken together, these findings highlight how teachers’ orientations toward ABI are shaped by a complex interplay of pedagogical beliefs, perceived student readiness, and contextual conditions.

4.3 Bridging observations and interviews

The purpose of this subsection is to integrate findings from classroom observations and teacher interviews in order to develop a more comprehensive and context-sensitive understanding of how ABI is perceived and enacted in practice. While classroom observations provide insight into enacted instructional practices within a specific classroom context, the interviews illuminate how teachers interpret, justify, and make sense of these practices across participants. Examining these two data sources together enables a richer and more nuanced interpretation of the findings.

It is important to note that this integration does not constitute full triangulation across participants, as classroom observations were conducted in only one focal classroom. Accordingly, the relationship between observed practices and teachers’ reported perceptions should be interpreted as explanatory and context-sensitive rather than confirmatory.

The integration of the data revealed both alignment and misalignment between teachers’ expressed beliefs and observed classroom practices. In the observed classroom, argumentation was typically limited in structural complexity and often embedded within traditional initiation–response–evaluation (IRE) interactional patterns (see Section 4.1). In contrast, interview data indicated that teachers consistently expressed strong support for the conceptual and motivational value of ABI (see Sections 4.2.1 and 4.2.5). This contrast suggests a gap between teachers’ pedagogical intentions and their classroom enactment.

Further analysis indicates that argumentative exchanges in the observed classroom were rarely extended to include counter-arguments, theoretical justification, or sustained student–student dialogue. Interview findings across participants help contextualize these patterns by highlighting perceived constraints, including exam-oriented curricula, time limitations, and concerns regarding students’ ability to engage in complex reasoning (Sections 4.2.2 and 4.2.3). These insights do not directly explain the observed classroom case, but rather provide a broader interpretive framework for understanding such instructional patterns.

At the same time, classroom observations revealed moments in which students initiated claims and attempted to justify their reasoning, indicating a latent potential for more dialogic and argumentation-rich instruction. Teachers’ interview responses similarly reflected an awareness of this potential, alongside a perceived need for greater professional confidence and pedagogical support in facilitating argumentation-based discourse (Section 4.2.4).

Taken together, the complementary use of observational and interview data points to a recurring pattern within the present study: although teachers express strong pedagogical support for ABI, its enactment in classroom practice remains partial, situational, and context-dependent. Importantly, the integration of data sources is analytically bounded. The observational findings are derived from a single focal classroom, whereas the interview data reflect broader perspectives across participants. This distinction clarizes the analytic logic of the study and supports a nuanced interpretation of the relationship between teachers’ beliefs and classroom practice, without implying generalization or confirmatory triangulation.

4.4 Summary of key empirical insights

(Based on observational and interview data from the present study)

The findings indicate a discrepancy between teachers’ positive orientations toward ABI and its classroom enactment. Implementation was shaped by curriculum demands, time constraints, and challenges associated with facilitating dialogic discourse. The following discussion situates these findings within the broader literature and examines their implications for teaching and teacher education (see Table 5).

The integrated findings presented in this section and summarized in Table 5 are grounded in the empirical data of the present study and are interpreted in relation to existing research. While some patterns resonate with findings reported in the literature, their significance here lies in how they manifest within the specific instructional and cultural context examined.

5.1 ABI: between procedural and exploratory practices

Classroom observations of the focal classroom revealed a pattern of partial enactment of ABI. Most argumentative episodes were structurally limited and were typically classified as Level 2 arguments, consisting of claims supported by data or warrants. Argumentation was generally embedded within problem-solving activities and rarely developed into sustained, whole-class explorations of competing ideas. This pattern reflects what Stylianides et al. (2016) describe as local or procedural forms of justification, which remain limited to immediate problem-solving contexts and do not develop into collective mathematical reasoning. Similarly, Mariotti et al. (2018) emphasize that higher-quality argumentation involves the negotiation of meaning and the comparison of alternative explanations, features that were only partially observed in the present study.

For example, in a lesson on quadratic functions, students justified a claim regarding the similarity of two parabolas based on visual symmetry in their graphical representations. Although a second student referred to the algebraic form of the functions, the exchange did not develop into a discussion of underlying mathematical structures, counter-claims, or theoretical justification. This episode illustrates procedural forms of argumentation, characterized by localized justification that remains interactionally bounded. While such exchanges indicate students’ engagement in justification, they do not extend into exploratory argumentation involving sustained critique, comparison of alternative explanations, or engagement with underlying mathematical structures. Importantly, the distinction between procedural and exploratory argumentation is reflected not only in the structural features of individual arguments but also in the extent to which these arguments are taken up, elaborated, and negotiated within classroom interaction.

This example demonstrates how argumentation was present yet remained limited to localized justification, without developing into a dialogic exploration of competing mathematical ideas.

This distinction aligns with research in mathematics education that differentiates between arguments focused on surface-level justification and those that engage with collective reasoning, structural analysis, and the evaluation of alternatives (Knipping & Reid, 2019; Mariotti et al., 2018; Stylianides et al., 2016). It also resonates with frameworks that conceptualize argumentation as a collective and dialogic process, in which reasoning is co-constructed through interaction rather than produced by individuals in isolation (Cramer & Kempen, 2022; Mueller et al., 2012). Moreover, prior research indicates that without deliberate instructional design and sustained scaffolding, classroom argumentation tends to remain fragmented and procedural (Duschl & Osborne, 2002; Simon, 2008).

Recent studies further emphasize the central role of the teacher in supporting transitions from procedural to dialogic argumentation, particularly through instructional moves that sustain collective reasoning and encourage engagement with alternative ideas (Bayindir et al., 2025; Knipping, 2008).

From a methodological perspective, it is important to emphasize that these findings are based on an in-depth analysis of a single focal classroom. Accordingly, the observed patterns should be interpreted as illustrative rather than representative of mathematics classrooms more broadly. The contribution of this analysis lies in its fine-grained account of how argumentation unfolds in a specific instructional context, interpreted in relation to the broader range of teachers’ perceptions elicited through interviews.

5.2 Teachers’ perceptions of conceptual understanding and the role of argumentation

Interview findings indicated that teachers consistently viewed ABI as a powerful means of promoting conceptual understanding. However, closer analysis suggests that teachers primarily associated conceptual understanding with students’ ability to explain procedures, connect representations, and justify answers, rather than with engaging in extended inquiry, critique, or collective knowledge construction.

Teachers frequently emphasized helping students “see connections between ideas” or “understand why a rule works,” reflecting a relational view of understanding that goes beyond rote application but does not necessarily entail sustained argumentative dialogue. This interpretation corresponds with distinctions in the literature between conceptual understanding and procedural fluency (Hiebert & Grouws, 2007; Thompson, 1992).

At the same time, these findings suggest that teachers’ interpretations of conceptual understanding may not fully align with perspectives in the argumentation literature that emphasize the role of critique, refutation, and the comparison of competing explanations as central to mathematical reasoning (Alcock & Attridge, 2023; Pedemonte & Balacheff, 2016).

While teachers clearly recognized the epistemic value of justification, their classroom enactment of argumentation—as reflected in the structure and quality of classroom arguments—rarely aligned with the dialogic and collective practices emphasized in recent research on mathematical argumentation. In particular, although students were often prompted to justify their claims, these justifications typically remained limited in scope and did not develop into extended argumentative exchanges involving critique, comparison of alternative explanations, or collective reasoning. This gap between teachers’ expressed beliefs and observed classroom practices underscores the importance of examining not only teachers’ stated orientations toward ABI, but also how these orientations are enacted within the constraints of classroom interaction.

This interpretation suggests that teachers’ views of conceptual understanding may align more closely with explanation-based reasoning rather than with dialogic argumentation, which, according to Pedemonte and Balacheff (2016), requires engagement with critique, refutation, and the evaluation of competing arguments.

5.3 Teacher efficacy, professional confidence, and instructional support

Teachers’ sense of professional efficacy emerged as a central factor shaping the implementation of ABI. Interview data indicated that teachers’ uncertainty was not general but practice-oriented and topic-specific. In particular, teachers reported difficulties in facilitating open-ended discussions, responding to unexpected student arguments, and managing multiple solution paths within limited instructional time.

These findings align with research on teacher self-efficacy, which emphasizes the role of professional confidence in managing instructional uncertainty and responding to students’ ideas when adopting dialogic and inquiry-oriented practices (Bandura, 1997; Borg, 2003; Fives & Buehl, 2012). More specifically, prior studies suggest that positive beliefs about argumentation are not sufficient for its effective classroom enactment without concrete pedagogical support and experience in orchestrating classroom discourse (Asterhan & Schwarz, 2016; Simon, 2008).

In addition, research on classroom argumentation highlights that the development of dialogic practices requires access to pedagogical repertoires that enable teachers to manage uncertainty and sustain multi-voiced discourse (Zhuang & Conner, 2022). From this perspective, teachers’ reported challenges may reflect not only individual confidence but also limited opportunities to develop and enact such repertoires in practice.

Consistent with this interpretation, teachers in the present study expressed a clear need for professional development focused on the practical orchestration of argumentation, including facilitating classroom dialogue, supporting justification, and productively addressing student errors, rather than on theoretical principles alone.

This interpretation is further supported by recent research on collective argumentation, which highlights the critical role of teacher facilitation in sustaining dialogic engagement and advancing argumentative discourse in classroom settings (Bayindir et al., 2025).

Overall, these findings suggest that the enactment of ABI is closely tied to teachers’ perceived efficacy and access to contextually relevant pedagogical support.

5.4 Tensions around student capability and equity

A notable tension emerged between teachers’ positive orientations toward ABI and their concerns regarding students’ ability to participate meaningfully in argumentative discourse, particularly among lower-achieving students. While teachers valued argumentation in principle, they often expressed uncertainty about students’ readiness to justify claims, engage in sustained discussion, or respond to alternative perspectives.

This tension can be understood as reflecting teachers’ situated interpretations of students’ capabilities, shaped by prior classroom experiences, instructional expectations, and contextual constraints, rather than as indicating inherent limitations in students’ abilities. Similar patterns have been documented in the literature, which suggests that students’ participation in argumentation can be significantly enhanced through appropriate scaffolding, structured support, and opportunities for guided engagement (Boaler, 2016; Staples, 2014; Zhuang & Conner, 2022).

From this perspective, teachers’ concerns may influence the extent to which argumentative opportunities are made available in the classroom. When expectations regarding students’ capabilities are relatively cautious, opportunities for extended reasoning and dialogue may be limited, potentially reinforcing existing participation patterns. At the same time, these interpretations should be understood as context-dependent and grounded in teachers’ professional experiences rather than as fixed or universal assumptions.

Overall, these findings highlight the importance of supporting teachers in developing pedagogical strategies that enable diverse learners to engage in argumentation, thereby expanding opportunities for equitable participation in classroom discourse.

5.5 Contextual constraints and the Bedouin educational setting

Teachers frequently referred to systemic and contextual constraints, including exam-oriented curricula, time pressure, and parental expectations. These factors appeared to shape instructional priorities and to limit opportunities for sustained engagement in argumentation. For example, one teacher noted that “parents expect us to focus on what appears in the exam,” grounding these constraints in participants’ reported experiences.

In addition, interview data pointed to perceived challenges in the development of mathematical discourse, particularly regarding students’ participation in classroom discussions and their ability to articulate reasoned arguments. Teachers described situations in which students were reluctant to express their views or experienced difficulty explaining their reasoning to peers. These accounts reflect participants’ perspectives and should not be interpreted as direct evidence of student behavior.

While the present findings are derived from interview data and observations of a single classroom, they can be considered in relation to prior research on education in Bedouin society in the Negev. Abu-Saad (2016) and Al-Krenawi (1999) highlight the role of broader sociocultural and structural conditions, including patterns of authority, social organization, and community expectations, in shaping educational experiences in Bedouin communities. In the context of mathematics education, Abu Qouder and Amit (2018) further suggest that learning practices may be influenced by norms that emphasize authority, transmission of knowledge, and respect for established procedures.

Taken together, these perspectives provide a lens for understanding the interactional patterns observed in this study, including the predominance of procedural forms of argumentation. At the same time, these connections are theoretically informed and should not be interpreted as direct causal explanations of the observed classroom practices.

More broadly, sociocultural research indicates that high-stakes assessment regimes and community expectations can influence the extent to which dialogic pedagogies are enacted, particularly in minority and marginalized educational contexts (Gutstein, 2006; Nasir et al., 2008). In addition, studies of classroom discourse emphasize that practices of argumentation and participation are not culturally neutral but are shaped by social and cultural norms (Cazden, 2001; Gutiérrez, 2008). From this perspective, the patterns identified in the present study may be understood as situated within broader institutional and sociocultural conditions.

Importantly, the present study does not directly examine sociocultural structures but interprets teachers’ accounts in relation to existing literature. Accordingly, the analysis offers a context-sensitive interpretation of the findings rather than a generalizable account of the Bedouin educational context.

5.6 Integrating observations and interviews: implications for research and practice

The complementary integration of classroom observations and interviews highlights a central insight of this study: although teachers in this study express strong pedagogical support for ABI, its enactment in classroom practice remains partial, situational, and highly dependent on contextual conditions and professional confidence. Importantly, this interpretation is derived from the analytical integration of distinct data sources rather than from generalization beyond the observed case.

The integration of data sources in this study is explanatory rather than confirmatory, providing analytic depth into the relationship between teachers’ beliefs and classroom practice without implying generalization across all participants. Each data source contributes a distinct perspective: classroom observations provide fine-grained insight into enacted instructional practices, while interviews illuminate teachers’ interpretations, perceived constraints, and professional considerations.

This integrated perspective responds to calls in the literature to connect teachers’ beliefs with detailed analyses of classroom discourse. By demonstrating how beliefs, contextual constraints, and instructional practices interact within a specific setting, the study extends existing frameworks and offers a context-sensitive account of ABI in practice (Creswell & Plano Clark, 2018; Denzin, 1978).

Taken together, the findings highlight the complex and often fragile relationship between teachers’ pedagogical beliefs and their enacted practices. While teachers expressed strong conceptual support for ABI and recognized its potential for fostering conceptual understanding and student engagement, classroom discourse revealed only limited and uneven enactment of argumentative practices. These patterns appear to be shaped by an interplay of systemic constraints, curricular pressures, teachers’ perceived instructional efficacy, and the broader sociocultural context in which teaching and learning take place.

Rather than presenting ABI as a fully realized pedagogical shift, this study offers a context-sensitive account of how teachers’ beliefs, institutional conditions, and classroom discourse interact to shape the partial and uneven enactment of argumentation in everyday practice. In doing so, it contributes to a more nuanced understanding of the challenges involved in translating pedagogical ideals into classroom reality and underscores the need for contextually grounded professional support.

6.1 Implications for teaching and teacher education

The findings suggest that promoting ABI requires more than raising awareness of its benefits. Professional development should focus on practical strategies for orchestrating dialogue, scaffolding justification, and managing multiple solution paths, alongside productive engagement with student errors.

Second, addressing teachers’ concerns about student ability is essential. Instructional designs should support participation across diverse learners through scaffolding, modeling of argumentative practices, and classroom norms that value reasoning and critique.

Finally, teacher education and policy initiatives should be sensitive to contextual constraints in minority and marginalized settings. Implementing dialogic pedagogies such as ABI requires alignment with local norms, assessment systems, and community expectations.

6.2 Limitations

This study has several limitations. First, findings are based on a single focal classroom and should be interpreted as illustrative rather than generalizable. Second, only one teacher's classroom practice was observed, limiting the scope of belief–practice comparisons. Third, while argumentation levels provide a structured analytic tool, they do not fully capture the dynamic and collective nature of classroom discourse. Finally, self-reported data may reflect contextual and professional influences and should be interpreted alongside observational evidence.

6.3 Directions for future research

Future research should examine ABI across multiple classrooms and contexts, including longitudinal studies that trace changes in teacher practice over time. Further studies may also explore how sustained professional development influences the development of dialogic argumentation in diverse educational settings.