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The Role of Metacognitive Scaffolding in Mathematical Communication on Mathematics Students Damar Rais; Yue Wen Yan; Muhammad Kashif
Journal of Multidisciplinary Science: MIKAILALSYS Vol 4 No 2 (2026): Journal of Multidisciplinary Science: MIKAILALSYS
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mikailalsys.v4i2.10375

Abstract

Although written mathematical communication is central to students’ ability to express reasoning coherently, the role of metacognitive scaffolding in connecting internal thinking with external mathematical discourse remains insufficiently examined. This study investigates whether metacognitive scaffolding functions as a bridge between internal thought and external discourse in students’ written mathematical communication and whether initial metacognitive awareness moderates this effect. A quasi-experimental pretest–posttest control group design was employed with 72 mathematics education students. The experimental group received six sessions of metacognitive scaffolding through guided prompts, such as “What is your first step and why?” and “How does this step connect to the next?”, whereas the control group received conventional instruction without such prompts. Written mathematical communication was assessed using a validated test measuring structural coherence, including logical flow, mathematical language use, and step-linking. Metacognitive awareness was measured using an adapted Metacognitive Awareness Inventory questionnaire. The ANCOVA results revealed a significant and large effect of metacognitive scaffolding on structural coherence, ηp² = 0.292, p < .001, with the strongest effects observed in logical flow and step-linking. Metacognitive awareness also significantly moderated the intervention effect, B = -3.41, p = .009, indicating that students with lower initial metacognitive awareness benefited most from the intervention. Qualitative think-aloud protocols further showed that scaffolding activated internal discourse, promoted the use of logical connectors, and strengthened self-monitoring during written mathematical explanation. These findings contribute to commognitive theory by demonstrating that improving external mathematical communication can support internal cognitive processes. Practically, the study suggests that mathematics educators can integrate metacognitive prompts into worksheets to help students produce more coherent written explanations, particularly those with underdeveloped metacognitive skills.
Reducing Extraneous Cognitive Load to Improve Analytic Geometry Problem Solving among Undergraduate Mathematics Students Damar Rais; Yue Wen Yan; Silvie Rama Yuliane; Deswandhana AS
Journal of Multidisciplinary Science: MIKAILALSYS Vol 4 No 2 (2026): Journal of Multidisciplinary Science: MIKAILALSYS
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mikailalsys.v4i2.10376

Abstract

Mathematical problem solving in higher education requires students to coordinate symbolic, graphical, and conceptual information within limited cognitive resources. This study examines the effect of extraneous cognitive load on undergraduate mathematics students’ problem-solving performance in an Analytic Geometry course and determines whether cognitively optimized task presentation can improve performance by reducing unnecessary mental effort during mathematical reasoning. A within-subject explanatory mixed-methods design was employed with 25 mathematics department students. Participants completed equivalent Analytic Geometry problem-solving tasks under two presentation conditions: a conventional format and a cognitively optimized format. Data were collected through problem-solving tests, perceived extraneous cognitive load ratings, time-on-task records, written solution analysis, and semi-structured interviews. The results showed that students achieved higher problem-solving scores in the cognitively optimized condition than in the conventional condition. They also reported lower extraneous cognitive load and completed the tasks in less time. Correlation and regression analyses indicated that higher extraneous cognitive load was associated with lower problem-solving performance, suggesting that unnecessary processing demands constrained students’ mathematical reasoning. Qualitative findings supported these results by showing that students benefited from integrated diagrams, clearer symbolic representations, and reduced information search. The study concludes that extraneous cognitive load is a critical factor in undergraduate mathematical problem solving and that optimizing instructional presentation can improve cognitive efficiency without reducing mathematical rigor. These findings contribute to research on cognitive load, mathematical thinking, and educational technology, while offering practical implications for designing Analytic Geometry learning materials that support efficient and meaningful mathematical reasoning.