Reasoning In High School Mathematics, Applied Research, Inquiry Learning

With China's deep reform of the mathematics education in primary school and middle junior school, such opening and creative educational conventions as research learning and reasonable illation have been attached increasing importance in recent years. Those new educational conventions incarnate the direction of mathematics education with its prime token as the cultivation of mathematics creativity. The process of creating mathematics is like other sciences, which is the result of a set of scientific methods consisting of observation, experiment, induction, analogy, generalization, restriction, supposition and association. In 2003, The Mathematics Curriculum Criteria in General Senior High School issued by China's Department of Education has clearly listed research learning as an important way, and the subject of "Illation and Testify" has also been listed in "Criteria", in which the reasonable illation has been introduced in the compiling of teaching materials for the first time. Statistics shows that the research on the theory of the research learning and reasonable illation of Mathematics has been complete, while the research on the transformation into practice has a long way to go, and this process is much more difficult than expected.In fact, researches indicate that, in the practical teaching, research learning and reasonable illation involve in many difficult questions. For example, there exist the following defects in the process of practical mathematics teaching: (1) Mathematicization. That is to say, the learning of mathematics should not be inclined to the practical operation, and only with the internalization, the mathematics thinking can be developed. (2) Re-creation. Research learning is an uncertain re-creative process, in which learning knowledge is just an inevitable way in human beings' growing process, and the real aim is to create. (3) Learn how to learn. For one thing, research learning allows students to know the dynamic process of knowledge, and for another thing, it can teach students how to learn. These vital ways of thinking in the researching process, however, have been neglected, which exerts a great influence on the effectiveness of mathematics research learning. The phenomenon of the narrowalization of the reasonable illation in the practical teaching, that is, teachers just teach the students with the knowledge in the textbooks as a kind of concept. On the contrary, reasonable illation has been greatly neglected as a kind of broad application of mathematics illation and method, which leads to the fact that students cannot make full use of the way of reasonable illation in their learning. Professor Zheng Yu-xin classifies the reform of mathematics into three steps: enthusiasm, confusion and putting it into practice. So, it's the time for us to figure the confusion out with enthusiasm as the conviction and putting it into practice as the attitude.Based on the above research questions, this thesis attempts to make a tentative research on the significance of the combination of reasonable illation and mathematics research learning from the perspective of a new curriculum reform to make a breakthrough and creation on the basis of the previous studies. And it aims to cultivate students' ability of reasonable illation with the study of the application of reasonable illation in mathematics research learning as the content and reasonable illation as a means of promoting students' mathematics research learning. Finally, this thesis provides a methodological support for the improvement of mathematics research learning's effectiveness.The present study has made some findings both theoretically and practically which include the following aspects:(1) The ineffective incarnation of the reasonable illation in mathematics research learning in Senior High School.(2) The theoretical framework of the application of the reasonable illation in mathematics research learning in Senior High School.(3) The practical plan of the reasonable illation in mathematics research learning in Senior High School.