小学数学教学中数学推理的理论和实践

Mathematical Reasoning in Primary Mathematics Instruction:Theories and Practice

数学推理是数学学习的核心,然而对推理的定义和数学推理的形式有许多不同的看法.首先分析了理解数学推理的4种不同视角,涵盖结果视角、过程视角、结构视角、模仿与创造视角.在此基础上,以小学阶段代数、比例和空间3个内容为例,对数学推理能力在其中的具体体现和相关的推理教学进行了分析.教师可通过在教学中设计创造性的推理任务以及鼓励学生解释与表达等方式促进数学推理在课堂教学中的落实.

Mathematical reasoning is the core component of mathematics learning.There are many different views on the definition of reasoning and forms of mathematical reasoning.This article first analyzes four different perspectives for understanding mathematical reasoning,which include product,process,structure,and imitation and creation.Based on this understanding,we examine the specific forms and teaching of mathematical reasoning in three domains of primary mathematics:Algebra,Proportion,and Space.To promote students’mathematical reasoning ability,we suggest that teachers design creative reasoning tasks in mathematics teaching and encourage students to explain and communicate mathematically.