错误是学生问题解决过程中正常而普遍的现象，学生的错误有其存在的合理性。利用学生错误的合理因素能够促进学生真实的、真正的发展。不少教师虽然在思想层面已明确学生错误的重要性，但是如何将这种行为意识转化为课堂教学实践中具体的教学行为确是很多老师困惑的问题，而已有的关于学生错误的研究中对此也缺少专门的研究。本文以学生的合理错误作为研究对象，以小学高年级数学问题解决教学为研究背景，从历史、现实和理论三个维度进行了分析和思考。论文首先对中外历史上关于错误及合理错误的研究进行了回顾，梳理了其发展脉络，并总结了哲学、心理学和教育学上有关错误及合理错误研究的成果。其次，通过问卷调查、课堂观察和个案分析，探讨了小学高年级数学问题解决过程中学生合理错误的现状与不足。研究发现小学高年级学生对错误的认识有待进一步深化，课堂教学中教师对待学生合理错误的行为呈现出忽略合理错误、简化合理错误、合理错误资源化三种类型，教师对待学生的错误越来越表现出宽容与理解，学生从合理错误中获得发展的程度差异明显。基于历史和现实的研究结果，论文指出合理错误有四种表现形态，即知识缺陷型、经验替代型、思维限制型、技能缺乏型，并进而探讨了小学高年级数学问题解决过程中学生合理错误的内涵和价值功能。论文认为小学高年级数学问题解决过程中合理错误促进学生发展的过程包括正误对比、觉察“盲点”、认知共鸣三个阶段，其中学生的自主反思是实现合理错误促进学生发展的核心要素，教师对待合理错误的态度是合理错误促进学生发展的制约条件，班级文化氛围是实现合理错误促进学生发展的外在环境。最后，论文基于小学高年级数学问题解决过程中学生合理错误的现状，在理论分析的基础上对小学高年级数学问题解决教学提出了几点教学建议：一是确立正确的错误观，二是创造从错误中学习的机会，三是培养学生的自主反思能力，四是营造反思型的班级文化氛围。

Students usually make errors during problem-solving process, which is a very common phenomenon; however, these errors exist reasonably. If teachers pay more attention on the good affect of students' errors, they can make contribution to students' real development. In fact, some teachers have recognized the importance of students' errors in their opinions, but they don't know how to do in teaching practice. At the same time, we can't find there are many study about students' errors when we review literature. So in my paper I try to study students' reasonable errors which come out during math problem-solving of high-grade primary school from the perspective of history, practice and theory.Firstly, the study on error and reasonable error is reviewed both home and abroad to explore its historical development, and the philosophic, psychological and educational study on error and reasonable error is summed up.Secondly, the thesis investigates the status and problems on reasonable error of math problem-solving process in high-grade primary school through questionnaire、classroom observation and individual interview. The thesis finds out that students’ understanding need to be strengthened. Teachers treat students’ reasonable errors in three ways: neglecting reasonable error; simplify reasonable error and transform the error into teaching resources. Teachers become more and more tolerance and understanding to students’ errors. The differentiation of students’ development from reasonable errors is obvious.Based on the analysis of history and reality, the thesis pointed out four types of reasonable errors: knowledge deficient; experience alternative; thinking limited and lack of skills. Next, the thesis analyzes the intention and valuation of students’ reasonable errors of math problem-solving process in high-grade primary school. The thesis put forward that there are three stages for the reasonable errors to promote students’ development: contrast; aware of “blind spots” and cognitive resonance. To promoting students’ development from reasonable errors, students’ self-reflection is the element; teachers’ attitude is the key factor and classroom cultural atmosphere is the external environment.Finally, based on the status quo and theory analysis, the thesis puts forward several pieces of advice for math problem-solving instruction in high-grade primary school: first, to cultivate the right understanding of errors; second, to set up opportunity for students’ to learn from errors; third, to cultivate students’ ability of self-reflection; and fourth, to build reconsidering classroom cultural atmosphere.