从意识到能力:代数推理认知发展的进阶理路

From Consciousness to Ability:Progressive Approach of Cognitive Development of Algebraic Reasoning

《义务教育数学课程标准(2022年版)》新增核心素养部分,并强调核心素养具有整体性、一致性和阶段性的特征,在“数与代数”学习领域增加了代数推理的明确要求。厘清代数推理的认知发展进阶,构建两层五级的代数推理认知进阶发展模型,其中两层指意识层、能力层,五级指具体化算术、结构化算术、符号化概括、形式化建构和一般化推广,有助于更好地把握代数推理的内涵和特征,也为其他学科建构核心素养主要表现的进阶发展提供借鉴。

Compulsory Education Curriculum Standards:Mathematics(2022 Edition)adds core competency section,which emphasizes the integrity,consistency and stage of it,and adds explicit requirements on algebraic reasoning in the field of number and algebra learning.To clarify cognitive development of algebraic reasoning and construct two-layer and five-level cognitive development model of algebraic reasoning(two layers are consciousness and ability layer,five levels refer to concrete arithmetic,structured arithmetic,symbolic generalization,formal construction and generalized extension)is helpful to better grasp the connotation and characteristics of algebraic reasoning,and also provides reference for the construction of core competency in other disciplines.