<![CDATA[his empirical study examines the critical relationship between metacognitive skills and mathematical problem-solving performance through a focused case study on series summation problems. Conducted with 50 seventh-grade students, the research involved a structured online lecture covering rational number series and algebraic transformations, followed by two problem-solving tasks and a detailed metacognitive questionnaire aligned with Polya’s four-phase framework. Results demonstrated a significant disparity: while all students (100%) successfully solved the initial summation problem , only 29 students (58%) correctly solved the more complex squared summation problem . Analysis of the metacognitive questionnaire revealed pronounced differences in strategy use. Students solving both problems successfully reported significantly higher engagement in metacognitive behaviors: reading problems multiple times (72.4% vs. overall 42%), schematic representation (100% vs. 78%), strategic planning (100% vs. 78%), solution monitoring (86%), and calculation verification (100% vs. 90%). Statistical analysis confirmed strong positive correlations between these specific metacognitive strategies and successful problem-solving outcomes. The study robustly concludes that explicit metacognitive strategy deployment, particularly in problem representation, planning, and evaluation, is a decisive factor in successful mathematical problem-solving, especially for non-routine tasks. These findings underscore the imperative for systematic integration of metacognitive skill development within secondary mathematics curricula to enhance students' conceptual understanding and transfer abilities.]]>
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