The effects of realistic mathematics education and direct instruction on students’ mathematical critical thinking abilities: Considering levels of mathematical resilience
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Abstract
Indonesian elementary school students’ mathematical critical thinking abilities (MCTA) remain suboptimal, highlighting the need for more effective instructional approaches. However, limited evidence has compared the effectiveness of Realistic Mathematics Education (RME) and Direct Instruction (DI) while considering students’ mathematical resilience (MR). This study aimed to examine the effects of RME and DI on students’ MCTA while considering their MR levels. A quantitative quasi-experimental design was employed with 34 fifth-grade students from an elementary school in Padalarang Village, Indonesia. The intervention consisted of three 70-minute instructional sessions. Data were collected using an MCTA test and an MR questionnaire and analyzed using descriptive and inferential statistics. Students in both groups showed significant improvements in MCTA. Although the RME group achieved slightly higher MCTA acquisition than the DI group, the difference was not statistically significant. However, RME produced significantly greater MCTA improvement than DI. Students with different MR levels showed significant differences in both MCTA acquisition and improvement, and MR had a significant positive effect on MCTA. No significant interaction effect was found between the learning approach (RME and DI) and MR. Overall, both RME and DI effectively improved students’ MCTA, with RME yielding greater improvement regardless of students’ MR levels.
INTRODUCTION
Mathematics is one of the fundamental disciplines in elementary education because it equips students with the knowledge, reasoning, and problem-solving skills needed to understand patterns, solve real-world problems, and make informed decisions in everyday life(OECD, 2023). In the twenty-first century, mathematics education is expected to foster higher-order thinking skills that enable students to address increasingly complex and authentic problems(Demircioglu et al., 2023; Lemon & Taylor, 2026). Therefore, mathematics instruction should provide meaningful learning experiences that engage students in developing conceptual understanding instead of simply memorizing formulas and procedures.
Mathematical critical thinking abilities (MCTA) refer to students’ ability to interpret mathematical information, analyze arguments, evaluate evidence, draw logical inferences, explain reasoning, and regulate their thinking when solving mathematical problems(Facione, 1990). These abilities enable students to make reasoned judgments and solve mathematical problems based on logical and reflective thinking. MCTA is essential in the 21st century because it helps students remember and understand mathematical concepts, apply mathematics to problem-solving, develop analytical abilities, and make logical decisions(Demircioglu et al., 2023; Lemon & Taylor, 2026). By thinking critically and mathematically, one can analyze metacognitive problems to arrive at the right solution(Anthonysamy et al., 2024; Kurudirek et al., 2026; Parawansa et al., 2026; Wardana et al., 2024). In contemporary mathematics education, the development of MCTA is increasingly viewed as a multidimensional process involving cognitive, affective, and behavioral components(AlAfnan, 2025; DiNapoli, 2023). Students are expected to interpret problems, evaluate information, justify reasoning, and reflect on their thinking processes(Sutama et al., 2022). These competencies are better developed through instructional practices that emphasize contextual inquiry, collaborative reasoning, and meaningful student participation rather than passive knowledge transmission.
The Programme for International Student Assessment (PISA) mathematics framework indicates that students in Indonesia continue to experience difficulties in mathematical reasoning(OECD, 2023). These processes correspond closely to the dimensions of mathematical critical thinking, indicating that mathematical literacy assessed in PISA is closely associated with students’ MCTA(Facione et al., 2020). Similarly, the 2026 Indonesian National Academic Competency Test reported that Indonesian elementary school students achieved a national average mathematics score of only 43.41(Ministry of Primary and Secondary Education, 2026). Consistent with these national findings,Harianja et al. (2023)reported that 6th-grade students at an elementary school in North Tapanuli Regency, North Sumatra, did not demonstrate optimal MCTA, with an average score of 34.8 on the 2D shapes test. These findings suggest that the current level of students’ MCTA remains below the expected level. In this context, students’ persistence when encountering difficulties becomes one of the factors influencing the development of critical thinking(Muharram et al., 2025). When persistence and confidence are limited, students are more likely to disengage from complex problem-solving tasks, which reduces opportunities to practice higher-order thinking. Furthermore, mathematics learning often involves abstract concepts that require students to construct meaning through connections with prior knowledge and real-life situations(İşözen & Kaçar, 2026). When these connections are not established, students tend to rely on memorization rather than conceptual understanding, thereby weakening their critical thinking(Day et al., 2024). Therefore, instructional strategies should facilitate meaningful learning experiences by encouraging students to actively construct knowledge, test their ideas, and refine their understanding through interaction and reflection(Khan, 2020). Such learning conditions foster deeper engagement and enhance students’ ability to apply mathematical concepts across diverse contexts.
Realistic mathematics education (RME), developed from Freudenthal’s view of mathematics as a human activity, encourages students to construct mathematical knowledge through meaningful real-life contexts, guided reinvention, mathematical discussion, and progressive mathematization(Freudenthal, 1973). Through these learning processes, students actively interpret problems, consider alternative approaches to solving them, provide mathematical justification, and evaluate their own reasoning, thereby supporting the development of MCTA. Moreover, contextual problem solving and guided reinvention encourage students to persist when encountering mathematical challenges, develop confidence through successful learning experiences, and regard mistakes as opportunities for improvement. These mechanisms foster self-efficacy, growth mindset, and persistence, which are fundamental dimensions of MR. Therefore, RME is theoretically expected to support the development of both MCTA and MR. Empirical studies have further demonstrated that RME improves students’ MCTA and overall mathematics learning outcomes. The RME is chosen because it is specifically designed for mathematics education strategies that relate concepts to life situations(Van den Heuvel-Panhuizen & Drijvers, 2020). The RME can improve students’ MCTA and learning outcomes(Hayati et al., 2025; Nursyahidah et al., 2025; Palinussa et al., 2025; Siswantari et al., 2025; Ventistas et al., 2025). Building on this theoretical foundation, it is necessary to compare RME with a more structured instructional approach that remains widely implemented in elementary mathematics classrooms.
The direct instruction (DI) is a well-established instructional approach that emphasizes explicit teaching, systematic content sequencing, guided practice, and immediate feedback to facilitate students’ acquisition of foundational knowledge and procedural skills(de Jong et al., 2023). These characteristics make DI particularly effective for novice learners who require structured instructional support before engaging in more complex problem-solving activities(Momdjian et al., 2025). Despite these advantages, mathematics instruction in many Indonesian elementary classrooms continues to rely predominantly on teacher-centered practices that emphasize procedural learning and teacher explanation(Arega & Hunde, 2025; Maryani et al., 2025; Muhaimin et al., 2026). Consequently, DI serves as an appropriate comparison for evaluating whether RME provides additional benefits in developing students’ MCTA. Although both
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