基于“问题解决认知模式”的错题分析及教学改进——以小学一年级数学“看图列式”为例

Error Analysis and Teaching Improvement Based on the Cognitive Mode of Mathematical Problem Solving

分析和解决数学问题是低年级数学学习的重点和难点,通过纠正错题学习数学是提高学生分析和解决问题能力的有效途径。从数学问题解决认知模式的角度分析,可能导致低年级学生解题错误的原因有:忽略符号含义,目标状态不明确;混合概念模型识别困难;工作记忆干扰解题监控;欠缺解题迁移能力。因此,在教学中要明确符号含义,建立符号意识;以身体动作帮助概念识别;用有效交流与反思促进解题迁移;通过动手操作增强解题过程监控并培养良好的做题习惯。

Analyzing and solving mathematical problems is the key and also difficult point in low grade mathematics learning, and learning mathematics by correcting the errors is an effective way to im—prove students, ability of analyzing and solving problems. From the perspective of mathematical problem solving cognitive mode, this article analyz the possible reasons that may lead to errors in low grade stu—dents, mathematics learning： neglecting meanings of mathematical notations and thus being unclear about the target, having difficuly in identifying hybrid concept model, interference of working memory on prob—lem solving monitoring, and lack of transfer ability in problem solving. Therefore, some strategies in teach—ing are suggested as follows： emphasizing meanings and thus help students realizing the importance of mathematical notations, usage of body movements to help identifying of concepts, improvement of stu—dents, transfer ability based on effective communication and reflection, encouraging hands_on exercises to improve monitoring in problem solving, and cultivating good habits in mathematical exercises.