The Characterization of Metacognitive Regulation in the Resolution of Central Tendency Problems

Abstract: Problem solving is an important topic in mathematics because it allows students to apply what they learn to situations of everyday life. This is why this research aims to characterize how metacognitive regulation favors the processes of solving problems of measures of central tendency. The qualitative approach has a descriptive character, and the methodological design is a case study in which six 8th-grade students are analyzed. The results show how planning, monitoring and evaluation allow students to be more organized, identify and correct errors, know why they perform certain actions, and have control over their own learning. In addition, it is shown how the ontological obstacles demonstrated by learners in the resolution of problems are related to their conceptions, which are influenced by the use of everyday language.摘要：问题求解是数学学科的重要研究议题，其核心价值在于引导学生将所学知识应用于日常生活场景之中。正因如此，本研究旨在阐释元认知调控（metacognitive regulation）如何助力集中趋势量数（measures of central tendency）相关问题的求解过程。本研究采用具备描述性特质的定性研究范式，方法论设计为个案研究，共对6名八年级学生展开分析。研究结果显示，规划、监控与评估环节能够帮助学生提升学习条理性，识别并修正错误，明晰自身行为背后的动因，并实现对自身学习过程的有效掌控。此外，本研究还揭示了学习者在问题求解过程中展现出的本体论障碍（ontological obstacles）与其认知观念之间的关联，而这些认知观念往往受日常语言使用的影响。