| Chinese Summary In recent years, China's advocacy of quality education and innovation in education, some new mathematics teaching patterns generated. (Zhang Dian-chou, 2003). Teaching is teaching the theory of specific, but also for direct guidance and teaching practice, with operable, it is teaching theory and practice of teaching as a bridge between. (Wiki network, "the new teaching model"). We believe that the implementation of new curriculum standards marks a major change in education mode, sending hope to achieve from the elite education to the popularization of the transformation of education (new teaching model Study Series - mathematics, 2006). China's new high school math curriculum standards the first time as an elective sensible reasoning, this is conform to the needs of the times, but also a new high school curriculum to bring about a series of teaching should be in-depth study of issues, including: sensible What are the educational functions of reasoning ? Sensible reasoning of the teaching mode ? What are the relevant overseas experience ? Students of the difficulties encountered ? In specific classroom and how to carry out the implementation and evaluation ?This article in two parts, first part of a literature review and analysis based, more systematic exposition of the main teaching model at home and abroad as well as China's new high school math courses sensible reasoning for the request.Among the second part of the case studies, of which the case originated from the Organization Department of Haimen, a new high school mathematics courses of study, focusing on teaching of sensible reasoning in the four focal points: (1) the content of sensible reasoning What are the requirements for teaching ? (2) select examples of what kind of sensible reasoning will be more conducive to teaching ? (3) classroom teachers how to guide the students to explore and understand the idea of sensible reasoning ? (4) of modern information technology in the teaching of sensible reasoning should play what role ? The case problems, although this has been a preliminary analysis, but more hope and send the majority of teachers reflect on the practice.Throughout the course of the study, the author of two Grade 11 classes to 118 people into reasoning, analogical reasoning in the performance of a test survey of five teachers and 10 students in the collective sub-group interviews. Draw the following conclusions: 1. Conjecture students into the mathematical ability is its own basic knowledge and basic skills of a master degree is related to 2. Characterization information with the knowledge of the ways to increase and consolidate the slow increase by 3. Secondary school students into math reasoning Capacity development is very slow, just a spontaneous development. The reasons are: teaching in 2005 to add a chapter sensible reasoning; Kaogang not appropriate to the status of sensible reasoning, in teaching guess almost forgotten in the status of the students guess the sense of being neglected. 4. Sensible reasoning to strengthen the teaching contribute to the development of sensible reasoning abilities. Finally, starting from the results of the study, the author of the textbook part of the way and set up the classroom teachers teachingmethods and made some suggestions to be to continue to explore the issue.The innovation lies in this study: To compare the systematic study on the mode of teaching at home and abroad and quality education and innovation in education under the new teaching model, the mode of teaching theory to guide the new curriculum in the new "reasonable inference" of the teaching modules . Teaching and the corresponding recommendations. Its theoretical significance lies in deepening the understanding of the teaching model, the practical value lies in facilitating the development of reasonable teaching objectives, the implementation of effective teaching and learning.
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