以认知理论指导 探究分阶段教学——以数列数学模型为例

Guided by Cognitive Theory to Explore Phased Teaching—A Case Study of Sequence Mathematical Models

摘要: 针对高中生数列建模能力培养中存在的“抽象困难”与“应用脱节”问题，提出分阶段的教学策略。通过具象感知、抽象建构、形式化应用三个阶段的梯度设计，结合数列模型的典型案例(等差数列、等比数列)，阐述如何通过认知策略(如具身操作、问题链引导、元认知反思等)促进学生数学建模能力的螺旋上升，从而使学生的核心素养得到提升。

Abstract: Aiming at the problems of “abstraction difficulty” and “disconnection from application” in cultivating high school students’ sequence modeling ability, this paper proposes a phased teaching strategy. Through the gradient design of three stages: embodied perception, abstract construction and formal application, and combined with typical cases of sequence models (arithmetic sequence and geometric sequence), it expounds how to promote the spiral improvement of students’ mathematical modeling ability through cognitive strategies (such as embodied operation, problem chain guidance and metacognitive reflection), thus enhancing students’ core competencies.