当前很多国家的文件都指出中小学教育不仅需要重视知识与技能，更重要是促进学生思维与能力的发展。如中国的《国家中长期教育改革和发展规划纲要（2010-2020）》，美国2010年颁布的《美国州共同核心数学标准》，日本2008年颁布的中小学《学习指导要领》（小学部分于 2011年4月1日起全面实施）都提到学生的能力培养。迁移能力是一种重要的能力。由于学校不可能教会学生所有的知识、技能与问题，教育者都希望学生能够“举一反三”。但是，新课标中对迁移能力培养只是一个抽象的要求，不易在实际的数学教学中落到实处。教师通常基本按照知识点课本排序和凭借直觉经验（主要是材料的表面相似性）设计学习材料进行教学来促进迁移。概念与概念之间的迁移关系并没有得到清晰解析，同时也容易忽视课程真正需要迁移的内容仅做了表面的迁移设计。而教师最终也只能凭借学生是否解题正确来判断学生是否发生了迁移，对教学设计在何时落到实处依旧只能凭直觉和经验判断，缺少分析和判断的标准。本研究以心理学和小学数学教育理论为基础，研究小学数学问题解决迁移。在心理学和教育学领域中，影响迁移的因素有很多，各因素联合起来对迁移起作用。但本文仅关注学习材料对迁移的影响。研究内容主要包括以下四部分：（1）学习材料的表征方式对小学数学问题解决迁移影响。本研究从抽象和具体类比源角度总结了促进迁移的源材料的表征方式，并设计了实验比较对表面特征与内在结构与源材料相似的三种靶问题的迁移效果。总结了小学数学领域学习材料（源材料）设计中影响迁移的关键因素。（2）概念间具有层级关系的问题解决迁移研究。小学数学的知识是一个体系，前一个概念是后一个概念的基础。本研究从纵向上分析概念间具有层级关系的问题的迁移路径，并使用基于认知心理学的知识分类方法和产生式系统描绘这个路径，并用认知模拟工具编程模拟该问题解决的过程，从而帮助教师更好理解迁移设计。同时也能帮助教师通过对迁移路径的追溯为诊断学生在问题解决迁移中的出现的问题。（3）基于认知的小学数学问题解决迁移模型的建构与验证。本研究以小学生的心理特点为基础，分析了小学数学问题解决迁移的内在机制，并在已有的基于认知的问题解决模型的基础上构建了问题解决迁移的模型。研究选择对同一问题解决表现出不同迁移特征的个案（5个）做口语报告，利用口语报告的分析结果对认知模型进行验证和修正。（4）设计学习材料促进迁移。本研究设计了促进学生思维发展和迁移的学习材料，并应用于教学实践。将使用了不同学习材料的两堂课程做了话语转录（部分），对比分析具体的迁移过程与效果。从而提出何种学习材料的设计更能促进学生迁移。本研究的创新之处在于从认知角度分析了小学数学问题解决迁移的内在机制，建立了模型并验证和修正了它。设计了旨在促进迁移的学习材料并应用与课堂实践中，通过对课堂问题的分析提出了促进迁移的学习材料的设计方法。此外，还为教师提供了一种基于知识和产生式的分析方式帮助教师理解概念之间的迁移，以及如何为问题解决过程中出现障碍的学生做认知诊断。

Contemporary, many countries have current documents indicate primary and secondary education requires not only on the learning of knowledge and skills, but more focus on how to promote the development of students' thinking and ability. Such as"Long-term Education Reform and Development Plan (2010-2020)"in China, "US State Common Core Math Standards"(2010), “Japan primary and secondary schools Learning Instruction"(2008) (primary section fully implemented from April 1, 2011). Transfer is an important capability. Because schools can not instruct students all the knowledge, skills and problems. Educators hope students can "learn by analogy." However, cultivate transfer ability is an abstract require in The new curriculum standards, teachers teaching in accordance with generally basic knowledge to explain the sequence, it is hard to imply in the actual teaching of mathematics. Teachers usually follow a basic knowledge ordering in textbook and intuitively experience (mainly surface material similarity) design learning materials to promote transfer. Although each version of the textbook is well-designed, for teacher, especially novice teacher, transfering relationship between concepts is stll difficult to clear resolution. Their instructional design is also easy to overlook the real-needed transfer content, but focus on the surface transfer. Lacking objective standards to analyze and judge whether instructional design is really act.Based on psychology and elementary mathematics education theory, this paper aimed to study elementary school mathematics problem solving transfer mechanisms. Although there are many factors that influence the transfer, this study is only focus on learning material. The main study content includes the following four parts:(1) The inflluece of Representation of learning materials occurs in elementary school mathematics problem solving migration. Based on cognitive psychology theory, the study summarizes three main source material representation, and the design corresponding mathematical material to do transfer experiment. Compareingt the effects of transfer.(2) Study on problem solving transfer which precursor source concept has hierarchical relationship system. Elementary mathematics Knowledge is a hierarchical ystem. Most concepts has its precursor concepts and successor concepts. In this study, a longitudinal analysis has done on transfer path between the hierarchical concepts which has been vertified by cognitive simulation, is aimed to help teacher find the best way to promote transfer. Teachers can also to do the cognitive diagnosis for students by traced his or her transfer path. (3) Based on recognize theory and psychological characteristics of elementary students, this study construct a mathematical problem solving transfer model. Selecting 5 cases to make oral reports, using the results of the oral report to verificate and corrent the model.(4) Designing learning materials to promote problem solving transfer. This study has designed learning material to promote the development of student thinking and transfer. Choosing two course transcription (part) which using different learning materials, comparative analysis their specific migration process and results. Finally, proposing the learning material designing susgestions to promote student transfer.The innovation of this study is analyze of elementary school mathematics problem solving internal transfer mechanism from a cognitive point of view. Then build a model, verified and correct it. Moreover, designed learning material and put it into practice.Through analysis of course, this study proposed learning material designing method. In addition, provided a analysis method which based on recognized theory and production system for teacher to help them understand the transfer between concepts, and how to do recognized diagnosis for student who obstacled in problem solving.