核心素养视域下初高中数形结合教学衔接路径探究——以几何代数化转型为例

Research on Transition Approaches of Number-Shape Combination Teaching across Junior and Senior High Schools Based on Core Competencies—Taking the Algebraic Transformation of Geometry as an Example

摘要: 代数与几何的结合是数学发展的重要一步，而从初中到高中这个阶段数学几何代数化的衔接却让学生在几何学习思维上产生了巨大的断层，初中仅侧重纯几何逻辑推理与辅助线解题，高中解析几何则要求全面代数化建模，学生们往往会出现思维切换困难、数形转化能力薄弱、参数运算不足等问题。本文将从初高中数学课程标准差异出发，剖析几何代数化衔接的核心断层成因，从思维模式、知识体系、解题范式三个维度分析梳理学段割裂问题。结合教学实际，探讨分层衔接教学策略，提出坐标法常态化渗透、一题双解对比训练、动点代数建模专项教学等落地方案。研究旨在依托SOLO分类理论划分学生数形思维层级，结合初三动点最值完整课堂案例验证分层衔接策略的实操性，初步表明分层递进的数形转化训练可在一定程度上缩小初高中几何思维的断层，为初高中一体化几何教学提供可复制课堂范式。

Abstract: The integration of algebra and geometry marks a critical milestone in the evolution of mathematics. Nevertheless, the transition of geometric algebraization between junior and senior high school creates a rift in students’ geometric thinking. Junior high school mathematics focuses solely on pure geometric deductive reasoning and problem-solving with auxiliary lines, while senior high analytic geometry requires comprehensive algebraic modeling. As a result, students frequently struggle with difficulties including inefficient thinking transformation, weak capacity for number-shape conversion, and inadequate proficiency in parametric computation. Based on the disparities between the mathematics curriculum standards for junior and senior high schools, this paper dissects the core causes of disconnection in the geometric algebraization transition, and sorts out the segmentation between the two schooling stages from three dimensions: Thinking modes, knowledge systems and problem-solving paradigms. Combined with real teaching practices, it explores hierarchical bridging teaching strategies and puts forward operable implementation schemes, including regular infiltration of the coordinate method, comparative training with two solutions for one problem, and special teaching on algebraic modeling of moving-point problems. Relying on the SOLO taxonomy to stratify students’ hierarchical thinking of number-shape combination, this study verifies the practicability of hierarchical bridging strategies through a complete classroom case about the maximum and minimum values of moving points for Grade 9 students. This study preliminarily indicates that hierarchical and progressive training on number-shape conversion can, to a certain extent, narrow the gap in geometric thinking between junior and senior high school, and provides replicable classroom paradigms for integrated geometric teaching across secondary school stages.