In the face of 21st-century challenges such as digital transformation, labor market uncertainty, and increasing social complexity, secondary education is confronted with the pressing need to redefine the competencies students must develop. In this context, competence development must move beyond mere knowledge acquisition and focus instead on the ability to mobilize cognitive, emotional, and social resources to act critically, autonomously, and contextually ( Zhu et al., 2021). Among these, mathematical competence and critical thinking stand out as essential capacities that strengthen academic performance, civic preparedness, and the ability to solve real-world problems ( Pramasdyahsari et al., 2023; Pratiwi et al., 2025; Pereira-González et al., 2024).

According to the PISA framework, mathematical competence involves the formulation, use, and interpretation of mathematics across a variety of contexts, highlighting its functional and social dimensions ( Beccuti, 2024). This competence goes beyond numerical operations; it encompasses complex cognitive skills such as logical reasoning, modeling, data interpretation, and evidence-based argumentation. Numerous studies have directly linked mathematical competence to academic achievement, problem-solving ability, and readiness to face novel situations ( Alegre et al., 2019; Wahono et al., 2020).

Critical thinking, on the other hand, is defined as the ability to analyze, evaluate, and construct arguments in a reasoned, reflective, and context-sensitive manner ( Rahmatika et al., 2024). Within the educational sphere, it enables students to question assumptions, make informed decisions, and transfer knowledge across diverse contexts. Although multiple theoretical approaches exist regarding its development, authors such as Pereira-González et al. (2024) agree on its transversal and situated nature, meaning it is closely tied to specific domains of knowledge such as mathematics.

However, the intersection between mathematical competence and critical thinking remains insufficiently explored from an integrative perspective. Despite their natural complementarity, both requiring logical reasoning, interpretation, and contextual analysis, they are often addressed separately in many curricula. This theoretical and practical disconnection is reflected in classrooms, where students struggle to apply mathematical concepts in real-life situations requiring critical judgment ( Er, 2024; Li & Oon, 2024).

Recent literature highlights persistent barriers to the integration of these competencies in secondary education: rigid curricula, lack of teacher training in active methodologies, weak student research culture, and limited use of interactive technologies ( Chacón-Cueva et al., 2023; Cruz et al., 2022; McLure et al., 2022). These limitations hinder pedagogical innovation and compromise the quality of learning during a crucial stage in adolescent cognitive development.

In response to this context, several educational paradigms, such as constructivism ( Vygotsky, 1978), critical pedagogy ( Freire, 1970), and competency-based learning, converge in emphasizing the need to provide meaningful, collaborative, and contextually relevant experiences. Models such as Problem-Based Learning (PBL), Project-Based Learning (PjBL), and STEM education have proven effective in simultaneously fostering critical thinking and mathematical competence ( Mayorga-Aguirre et al., 2024; Setyawati et al., 2022).

Nevertheless, despite increasing interest in this field, there remains fragmentation in the available empirical evidence. Few studies jointly examine both competencies, and even fewer systematically analyze the methodologies employed, their outcomes, and limitations. Therefore, this systematic review aims to critically examine the recent scientific literature on the integration of mathematical competence and critical thinking in secondary education, considering the impact of pedagogical strategies, identified barriers, and emerging trends.

The research questions guiding this review are:

RQ1: How are mathematical competencies and critical thinking integrated in secondary education?

RQ2: What is the impact of integrating mathematical competencies and critical thinking on academic performance and the development of cognitive skills in secondary school students?

RQ3: What are the main barriers and challenges to the integration of critical thinking in mathematics instruction at the secondary level?

This systematic review was conducted in accordance with the PRISMA 2020 protocol guidelines ( Page et al., 2021) with the aim of identifying, evaluating, and synthesizing empirical evidence on the integration of mathematical competencies and critical thinking in secondary education.

As detailed in Table 3 ( Section 2, Methods), the 24 studies included in this systematic review exhibit significant diversity in their methodological designs, geographic contexts, and target populations. This heterogeneity provides the empirical foundation for the thematic analysis presented below, which is structured around the three research questions (RQ1, RQ2, and RQ3).

To enhance readability and ensure consistency in the interpretation of the results, all percentages reported in this section were rounded to the nearest whole number, following the guidelines of the Publication Manual of the American Psychological Association (7th ed.; American Psychological Association, 2020, §6.36), which recommends expressing percentage values with a level of precision appropriate to the size and nature of the dataset.

Interest in integrating mathematical competencies and critical thinking in secondary education has shown steady growth between 2019 and 2025. Over the past three years (2022–2024), scientific output increased by 67%, with 2023 emerging as the most prolific year, accounting for six studies, 25% of the total. These data reflect a sustained upward trend in the field, responding to the educational imperative of fostering higher-order thinking skills in diverse school contexts.

In terms of geographic distribution, 50% of the studies were conducted in Latin America, particularly in Ecuador and Peru (five studies each) and Colombia (two studies). Europe accounts for 29% of the total, with research conducted in Spain (four studies), Portugal (one), Germany (one), and Finland (one). Asia contributes 13%, represented by two studies from Indonesia and one from Taiwan, while Oceania is represented by a single study (4%) conducted in Australia. The absence of studies from Africa and North America highlights a limitation in the global generalizability of the findings and reveals a geographic gap that future research could address.

From a methodological perspective (see Table 3), the analyzed studies display a wide range of approaches. Quantitative designs predominate, comprising nine studies (38%), mostly quasi-experimental or descriptive in nature, aimed at evaluating the effects of active learning methodologies or digital tools on mathematics learning ( Chacón-Cueva et al., 2023; Castro-Valle et al., 2023; Hilario, 2021; Curto et al., 2019; Del Cerro & Morales, 2021; Maskur et al., 2022; Saldarriaga-Cantos et al., 2024; Viro & Joutsenlahti, 2020; Hillmayr et al., 2020).

Three studies (13%) applied a mixed-methods approach, combining quantitative and qualitative analyses to gain a comprehensive understanding of the pedagogical impact of the implemented strategies ( Del Cerro & Morales, 2021; Mayorga-Aguirre et al., 2024; Saldarriaga-Cantos et al., 2024).

Four studies (17%) employed qualitative methodologies, ethnographic, field-based, or participatory action research, focused on classroom experiences, teachers’ perspectives, and collaborative learning processes ( Sutama et al., 2022; Jiménez-Cortés & Vesga-Bravo, 2022; Alvis-Puentes et al., 2019; Ordóñez-Barberán & Sánchez-Godoy, 2024).

Finally, eight studies (33%) correspond to systematic, theoretical, or exploratory reviews, including meta-analyses, scoping reviews, and documentary analyses that provide a broad overview of the state of the art and conceptual trends in the integration of mathematical competencies and critical thinking ( Pinos-Vargas et al., 2024; Farfán-Pimentel et al., 2022; Moreira et al., 2024; Urdanivia et al., 2023; Alegre et al., 2019; McLure et al., 2022; Wahono et al., 2020; Val Fernández, 2023).

The most relevant results of this study are presented below, based on each of the research questions posed (RQ1, RQ2, and RQ3).

This systematic review critically examined the integration of mathematical competence and critical thinking in secondary education, highlighting both the impact of pedagogical strategies and the contextual barriers affecting their implementation. The findings confirm that this integration is currently in a stage of consolidation, characterized by an increasing use of active methodologies mediated by technology. However, beyond validating the effectiveness of approaches such as Problem-Based Learning (PBL), Project-Based Learning (PjBL), STEM/STEAM, or gamification, this discussion seeks to understand why these strategies work, under what conditions they generate impact, and what their structural and contextual limitations are.

From a theoretical perspective, the findings reveal three common pedagogical mechanisms that explain the effectiveness of these strategies: the contextualization of knowledge through real problem-solving, technological and symbolic mediation, and guided and reflective collaboration. These principles, derived from constructivism ( Piaget, 1972), critical pedagogy ( Freire, 1970), and sociocultural learning theory ( Vygotsky, 1978), conceive learning as an active, situated, and transformative process. In line with this, studies such as those by Chacón-Cueva et al. (2023), Hilario (2021), and Sutama et al. (2022) demonstrate that PBL and PjBL foster logical reasoning, argumentation, and metacognition when implemented in flexible environments with reflective guidance. Comparable findings were reported by Soia et al. (2024), who showed that project-based learning fosters both critical thinking and teamwork skills among future mathematics and computer-science teachers, supporting the collaborative and reflective principles identified in this review. Similarly, Li and Oon (2024) and Khalil et al. (2023) show that critical thinking emerges when learning encourages dialogue, autonomy, and the co-construction of knowledge.

Some studies, however, warn of significant limitations. Trisnani et al. (2024) and Moreira et al. (2024) report that in contexts characterized by rigid curricula or limited teacher training, PBL implementation can devolve into a sequence of activities lacking reflective depth. This finding aligns with Le (2024), who notes that active methodologies may fail if not supported by coherent institutional structures. Furthermore, the lack of explicit theoretical alignment between empirical designs and epistemological frameworks remains a cross-cutting weakness. This disconnect, also identified by Sánchez-García and Reyes-de-Cózar (2025) and Van der Zanden et al. (2020), limits the replicability and transferability of findings and underscores the need for more robust methodological models that integrate instructional design, psychometric evaluation, and longitudinal analysis.

The STEM/STEAM approach has emerged as an integrative strategy that combines logical reasoning, creativity, and problem-solving in interdisciplinary contexts ( Mayorga-Aguirre et al., 2024; Maskur et al., 2022; Pratiwi et al., 2025). Recent quasi-experimental evidence also shows that STEM-based learning produces significantly higher gains in mathematical critical thinking compared to conventional instruction, reinforcing its value as an integrative pedagogical model ( Pratiwi et al., 2025). This result is consistent with the findings of Margot and Kettler (2019), who argue that STEM facilitates the transfer of mathematical knowledge to real-world contexts. Brandsæter and Berge (2025) further extend this perspective by demonstrating that programming-based activities effectively strengthen mathematical competence through computational reasoning, highlighting the potential of digital environments to promote mathematical fluency and problem-solving. However, the review reveals significant contrasts across regions and institutional levels. While Yohannes et al. (2024) and Er (2024) report sustained improvements in cognitive transfer and motivation, Suherman et al. (2022) and Kalinin and Toropova (2024) warn that gender gaps, limited curricular interdisciplinarity, and unequal teacher preparation condition the outcomes. These differences confirm that the effectiveness of STEM is context-dependent: its benefits do not derive solely from the pedagogical model itself but also from the institutional conditions that support it, as observed by Hillmayr et al. (2020) and Duma et al. (2024).

Findings related to technological mediation represent another central axis in the integration of competencies. Digital tools such as Kahoot, Quizizz, GeoGebra, and augmented reality function as symbolic mediators that promote immediate feedback, active participation, and self-regulated learning ( Curto et al., 2019; Del Cerro & Morales, 2021). Nevertheless, several studies caution that the instrumental use of these technologies does not necessarily guarantee deep learning. Nurdin et al. (2023) found that PBL environments supported by Google Sites significantly enhanced students’ mathematical critical thinking, confirming that digital scaffolding amplifies the reflective and metacognitive components of active learning. Nashrullah et al. (2023) and Saldarriaga-Cantos et al. (2024) similarly noted that teachers’ digital competence and structured pedagogical design are essential to transforming technology from a motivational tool into a medium for higher-order reasoning. This divergence aligns with McLure et al. (2022), who recommend a reflective and situated use of technological tools that integrates authentic assessment and collaborative learning criteria.

The reviewed studies identify a recurring set of structural barriers: rigid curricula, insufficient teacher training, weak student research culture, and the absence of instruments for assessing higher-order skills ( Castro-Valle et al., 2023; Cruz et al., 2022; Kintoko et al., 2024). These limitations do not operate independently but interact, creating a “funnel effect” ( Nicholus et al., 2023) in which methodological innovations are diluted by inflexible institutional structures or memorization-based assessments. Accordingly, PBL and PjBL tend to fail in environments with rigid timetables and limited curricular autonomy, while the lack of authentic assessment obscures progress in critical and logical reasoning.

Another critical finding is the prevalence of publication bias: most of the reviewed studies report positive effects, while mixed or null results are rare ( Moreira et al., 2024; Le, 2024). This pattern, also highlighted by Hillmayr et al. (2020) and McLure et al. (2022), underscores the need to promote more transparent research practices, including sensitivity analyses, open data, and cross-context replication. Encouraging longitudinal and multicultural studies would help prevent the overestimation of effectiveness and yield a more nuanced understanding of the mediating factors that influence success.

Based on the evidence analyzed, three key practical implications can be identified. The first concerns strengthening initial and continuing teacher training focused on critical reflection, formative assessment, and the pedagogical use of interactive technologies ( Hillmayr et al., 2020; Duma et al., 2024). The second highlights the need to design flexible, interdisciplinary curricula that integrate mathematics with other domains to foster cognitive transfer, creativity, methodological experimentation, and authentic assessment ( Er, 2024). The third relates to implementing institutional policies for educational innovation that ensure technological infrastructure, pedagogical support, and context-sensitive evaluation systems to apply these strategies equitably and sustainably ( Peralta et al., 2025; Melo-López et al., 2025; Jaramillo-Mediavilla et al., 2024). These recommendations, consistent with the proposals of United Nations Educational, Scientific and Cultural Organization ( UNESCO, 2023) and the Organisation for Economic Co-operation and Development ( OECD, 2022), aim to transcend the academic sphere and inform public policy and teacher development initiatives.

Finally, it is important to acknowledge the limitations of this review. The geographic concentration of studies in Latin America and Southern Europe introduces a contextual bias that restricts the generalizability of the findings. Further research is needed in underrepresented regions, such as Africa, Central Asia, and the Middle East, to compare outcomes and advance toward a global understanding of the phenomenon. Future studies should prioritize intercultural and collaborative approaches supported by validated psychometric models to strengthen comparability and sustainability.

Overall, this review provides a critical synthesis that integrates pedagogical, technological, and structural evidence concerning critical mathematical education, contributing to the construction of an educational action framework grounded in recent empirical evidence. Its impact will depend on the ability of educational systems to generate structural, policy, and training conditions that ensure its sustainable and equitable implementation.

This systematic review demonstrates that the integration of mathematical competencies and critical thinking in secondary education is still in a stage of conceptual consolidation rather than full pedagogical maturity. The analysis of 24 studies (2019–2025) reveals that while active methodologies, such as PBL, PjBL, STEM/STEAM, and gamification, consistently produce positive cognitive and motivational outcomes, their success depends strongly on contextual variables such as institutional support, teacher expertise, and curriculum flexibility.

The main contribution of this review lies not in reaffirming the effectiveness of these strategies, but in identifying the underlying mechanisms and systemic conditions that enable their impact: authentic problem-solving and contextualization of learning; guided collaboration that cultivates metacognitive reflection; and technological mediation that promotes autonomy and formative assessment. These principles form the basis of an emerging integrative pedagogical framework linking critical reasoning, creativity, and digital fluency in mathematics education.

At the same time, this synthesis exposes persistent structural inequities: most successful interventions occur in well-resourced schools with high teacher autonomy. Thus, replicability in less favorable contexts remains uncertain. For policymakers and practitioners, this review highlights the need to move beyond isolated innovations and toward systemic reform, strengthening teacher professional learning communities, investing in digital infrastructure, and embedding authentic assessment of reasoning and argumentation in curricula.

Ultimately, the integration of mathematical and critical thinking competencies should be viewed not as a set of discrete strategies, but as a transformative capacity of educational systems to generate equitable and evidence-informed environments where students learn to think mathematically and critically about real-world challenges.