数学联结力：内涵、价值与培养路径研究

Research on the Connotation, Value and Cultivation Path of Mathematical Connectivity

摘要: 数学联结力作为学生数学核心素养的重要维度，是指学习者在学习与应用过程中，主动识别、建立并灵活运用数学内部以及数学与外部世界各种关系的能力。本文在系统梳理国内外近五年相关研究的基础上，以认知负荷理论为贯穿全文的分析工具，界定了数学联结力的内涵与三层结构，深入阐释其核心价值。文章聚焦当前教学中阻碍联结力形成的关键问题，构建了针对性的培养策略体系，并通过为期一学期的行动研究验证了问题驱动教学模式的有效性。最后，提出包含评价量规在内的实操性实施建议，旨在为我国数学教育从“知识本位”向“素养本位”转型提供理论支撑与实践参考。本文的核心贡献在于系统构建了适合中国本土教学情境的数学联结力培养框架，填补了现有研究中理论与实践脱节的空白。

Abstract: Mathematical connectivity, as an important dimension of students’ core mathematical literacy, refers to the ability of learners to actively identify, establish and flexibly apply various relationships within mathematics and between mathematics and the external world during the learning and application process. Based on a systematic review of relevant research at home and abroad in the past five years, this paper takes cognitive load theory as the analytical tool throughout the text, defines the connotation and three-layer structure of mathematical connectivity, and deeply explains its core value. The article focuses on the key problems that hinder the formation of connectivity in current teaching, constructs a targeted cultivation strategy system, and verifies the effectiveness of the problem-driven teaching model through an action research lasting one semester. Finally, it puts forward practical implementation suggestions including evaluation criteria, aiming to provide theoretical support and practical reference for the transformation of China’s mathematics education from a “knowledge-based” to a “competency-based” approach. The core contribution of this paper lies in systematically constructing a mathematical connectivity cultivation framework suitable for the local teaching context in China, filling the gap between theory and practice in existing research.