| Analogical reasoning is defined as the process of identification and transfer of a relational structure from a known system (the source) to a less known system (the target). Analogy is considered a central component of human cognition. It has been argued that all intellectual actions involve analogical thinking. People learn new knowledge and new skills by analogy. In addition, analogy is also a kind of strategy people use to make inventions and communication. In psychology the research on analogical reasoning mainly focuses on two aspects: one is classic analogical reasoning, the other is problem analogical reasoning. The early research mainly focused on the former. But after 1970s', with the development of cognition psychology and the deeper research on problem solving, the latter is paid more and more attention to and has gradually become one of the focuses in problem solving and Artificial Intelligence.Problem analogical reasoning is also named analogical problem solving or analogical transfer. It is defined as the strategy that individuals often use the solution to a problem they have already known when seeking to solve a new problem. Currently many theories have been put forward to try to explain the cognition process of analogical transfer. Among all these theories, Genter's structure mapping theory and Holyoak's multi-constraint theory are accepted more extensively. Based on these explanations, many computational models are formed. Except for these, researchers also make much exploration on the division of sub-processes, the identification of the kinds of analogical transfer, the identification of influential factors and the strategies improving analogical transfer, etc.In the field of mathematics education, analogy, as one of the most important thinking methods, has always been attached much importance to. In how to solve it and mathematics and imagination, Polyya illuminated the nature, kinds and the uses of analogy thinking. Basing their research on Polyya's, many other researchers made much explosive work. However, both their research and Polyya's haven't exposed the micro-process of analogy and the difference between individuals. Therefore their research hasn't improved school teaching effectively. In summary, both psychologists and mathematics educationalists have made much achievement and their researches stand up for each other. However, they study analogy from different angles so that their researches show difference in some aspects. For example, psychologists often use the model of "source problems with solution + target problems to be solved" to explore how subjects finish analogical transfer in psychology laboratory, whereas mathematics educationalists explore how mathematicians found out past experience to accomplish analogy in natural situation. Therefore, psychologists and mathematics educationalists study two levels of analogy in two different situations. In fact, students' mastering analogy shows not only in using worked problems' solution to solve some isomorphic problems, but also in establishing the relation between problems flexibly in natural situations. Therefore, it is very important to strengthen students' consciousness of using analogy. To achieve the goal, this paper puts forward the hypothesis that the sequence of presenting examples is a key factor and the sequence of first difficult then easy will probably improve students' consciousness of using analogy. In addition, this paper also emphasizes that student should make analogies with some theories' guidance.Thirdly, in the research on analogical transfer, source problems and their solutions are always presented simultaneously. Thus subjects are in two different situations when they learn and solve problems so that they might encode problems in different formats and their achievements will be influenced. So this paper proposes to spare time for students to think over the source problems before presenting the solution to them. This paper demonstrates all the above hypothesis. In addition, some teac...
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