The review followed the PRISMA 2020 guidelines, the international standard for reporting systematic reviews, and was conducted using a carefully constructed search of the Scopus database supplemented by Google Scholar. The researchers formulated their central research question using the PICO protocol, which structures questions around population, intervention, comparison, and outcome. Their search equation combined keywords such as argumentation, mathematical argumentation, argumentation skills, teaching strategies, didactic strategies, instructional strategies, teaching methods, and pedagogical approaches using Boolean operators. The initial Scopus search on August 30, 2025 yielded 134 documents, comprising 96 journal articles, 15 book chapters, 14 conference papers, 8 reviews, and 1 book. After applying language filters that restricted inclusion to Spanish, Portuguese, and English publications, reducing the records to 130, and screening 138 total records against inclusion and exclusion criteria, 12 studies met the requirements and were selected for detailed analysis.

The inclusion criteria were demanding. Studies had to address the teaching of argumentation at primary, secondary, or tertiary education levels and report measurable outcomes related to argumentative skills. Studies were excluded if they addressed argumentation only peripherally without focusing on didactic strategies, if they pertained to disciplines other than mathematics education, or if they were review articles themselves. The temporal delimitation starting in 2019 reflects the authors’ interest in capturing the most recent trends in a field that has witnessed accelerated growth in publications, driven in part by the consolidation of key theoretical frameworks and the expansion of empirical research contexts. The methodological quality of the included studies was assessed using the Mixed Methods Appraisal Tool, though in accordance with the tool’s recommendations, no numerical score was assigned to any study since summing or averaging scores across criteria is explicitly discouraged.

Four main categories of instructional strategies emerged inductively from the collaborative analysis carried out by both authors. The first category comprises technology-mediated approaches, including the use of GeoGebra, Scratch, WhatsApp, Argunet, and educational video games. The second encompasses dialogic and debate-oriented models such as DAIM, ACODESA, and peer feedback. The third integrates historical and contextual approaches that weave the history of mathematics into the teaching of proof. The fourth involves gamification and STEAM-based strategies designed to enhance motivation and mathematical communication. These categories did not come from a predetermined classification scheme but rather surfaced from the analysis of the included studies themselves, giving the review an empirical grounding that many syntheses lack.

The co-citation analysis conducted on the reference lists of the 12 included studies using VOSviewer version 1.6 revealed the theoretical pillars that sustain current research on the teaching of mathematical argumentation. Four clusters were identified, each reflecting a distinct theoretical orientation. Among the most prominently cited authors are Conner, Yackel, Pedemonte, Krummheuer, Cobb, Knipping, Osborne, Boero, and Singletary. Toulmin’s model constituted the predominant analytical framework across the reviewed studies, appearing in at least seven of them. Sociocultural perspectives and socio-mathematical norms were also extensively drawn upon to account for the dialogical dimension and co-construction processes. The pragma-dialectical framework and other dialectical models emerge as alternative approaches that emphasize negotiation and critique in argumentation. More recently, approaches related to STEAM, gamification, and motivational theories such as Keller’s ARCS model have been incorporated to enhance engagement, motivation, and creativity in teaching and learning processes.

The theoretical backbone of the review draws on some of the most influential contributions to the debate on argumentation and proof. Duval’s work establishes a clear distinction between arguing and proving: an argument is not necessarily defined by the validity of the reasoning that supports it but rather by its semantic coherence, whereas a proof is constructed through a chain of deductive reasoning governed by the laws of formal logic. Duval emphasizes that no matter how elaborate an argument may be, it does not constitute a proof, thereby highlighting the cognitive gap between these two processes. Boero and colleagues examined the connections between argumentation and proof through the construct of cognitive unity, understood as the cognitive continuity between conjecture formulation and proof construction. This construct posits that the elements, intuitions, and arguments produced during conjecturing can be retrieved and reorganized within a formal proof, though the authors emphasize that this transition is not automatic and requires teacher mediation to guide the reorganization of students’ reasoning.

The findings of the reviewed studies indicate a progressive transition among students from empirically based arguments to more deductive forms of reasoning, fostered by various instructional interventions. In this process, the use of counterexamples, refutations, and critical debate has become consolidated as a set of key elements for enhancing the quality, coherence, and validity of arguments. Similarly, the integration of digital technologies fostered collaborative environments and provided visual resources that supported mathematical argumentation, though their effectiveness was contingent upon teacher mediation. Strategies such as guided discussion, deliberate questioning, and the use of contingencies reported by Solar and colleagues and by Zhuang and Conner align with Boero’s claim that the transition from conjecture to proof is not automatic and requires teacher intervention to reorganize students’ reasoning. Meadows and Caniglia explicitly draw on cognitive unity to link geometric constructions with formal demonstration, representing the most direct application of this construct among the reviewed studies.

Regarding the educational level and population of the included studies, the majority focused on teacher education contexts, either with pre-service teachers or with in-service teachers, accounting for seven of the twelve studies. Three studies were conducted with university students in non-teacher education programs, and two studies focused on secondary school students. No study in the reviewed sample addressed mathematical argumentation at the primary education level, a striking gap given that argumentation is increasingly recognized as a fundamental competency across all educational stages. The countries with the highest representation are the United States and Spain, each contributing three publications, followed by Colombia, Peru, and Turkey, each with two publications. For collaborative studies involving researchers from more than one country, all authors’ affiliations were considered in this analysis.

Several notable trends in instructional strategies for teaching mathematical argumentation were identified across the reviewed literature. One such trend is the strategic use of errors and unanticipated student responses as catalytic resources for initiating argumentative discussion and supporting the collective construction of arguments. Another notable trend is the use of open-ended tasks and non-routine problems, which act as catalysts for discussion and the development of justifications. Technological mediation and digital learning environments have gained importance, with tools such as GeoGebra, WhatsApp, Argunet, and Scratch or educational video games being employed. Gamification and game-based learning approaches have been designed to enhance students’ motivation and mathematical communication. The centrality of scientific debate and the co-construction of meaning also stand out as key axes of argumentative practice. Finally, some studies integrate the history and epistemology of mathematics to enrich the teaching of proof and to connect cognitive and cultural dimensions.

The review emphasizes the need for longitudinal and cross-cultural research and offers insights for teacher education and curriculum design. Several limitations must be acknowledged: the inclusion of studies published only in English, Spanish, and Portuguese introduces a language bias that may have excluded relevant research produced in other academic traditions. The reliance on Scopus as the primary database, supplemented by Google Scholar, may have introduced a publication bias, as indexed databases tend to overrepresent studies with statistically significant or otherwise favorable results. Gray literature such as doctoral dissertations, institutional research reports, and non-indexed policy documents was not included, which may limit the comprehensiveness of the synthesis. The coding and data extraction process was conducted collaboratively rather than independently, and no formal inter-rater reliability coefficient was calculated, which may affect the replicability of the categorization of instructional strategies. The temporal restriction to studies published between 2019 and 2025 excludes foundational research on mathematical argumentation that predates this period. Despite these constraints, the synthesis makes clear that teaching students to argue mathematically requires the integration of cognitive, social, and technological dimensions, and that innovative instructional approaches foster engagement and reasoning even as most studies report limitations related to small sample sizes and short intervention periods. Future research should prioritize large-scale, longitudinal, and cross-cultural studies to strengthen the evidence on sustainable impact, and the limited focus on primary education stands out as an area warranting systematic investigation.

Subject of Research: Mathematics Education

Article Title: Teaching strategies to foster mathematical argumentation: a systematic review (2019–2025)

Article References: Ríos-Cuesta, W., & Ospina-Marulanda, L. P. (2026). Teaching strategies to foster mathematical argumentation: a systematic review (2019–2025). Discover Education, 5(1), Article 850. https://doi.org/10.1007/s44217-026-02056-x

Image Credits: AI Generated

DOI: 10.1007/s44217-026-02056-x

Keywords: mathematical argumentation, systematic review, mathematics education, teaching strategies, Toulmin model, cognitive unity, GeoGebra, gamification, Teaching, strategies, foster, mathematical