The Teaching Idea Of ??the New Curriculum Change Geometry Transformation Under Freudenthal Theory

Under the background of the New Curriculum Reform, the methods of students' mathematics learning should be varied, practical and developmental. Currently the New Curriculum Reform is still in exploring stage, and it exists a general phenomenon that people take more attention on theory research than implementation research. How to improve teaching effect with the concept of the New Curriculum Reform is a problem troubling the majority of teachers.Hans Freudenthal, a mathematics educator borned in Dutch, has put foward some mathematics education theories like‘realistic mathematics', ‘mathematilization',‘re-creation', which get general recognization and extensive research from educators at home and abroad. It also reflects some of the mathematics study philosophy advocated by the New Curriculum Reform,showing us a teaching mode for useful reference.Therefore,we can learn about Freudental's mathematical teaching theory and try to combine it with the teaching practice in our country, aiming to improve the effectiveness of the New Curriculum Reform implemention.eometric transformation has got more and more attention in the national mathematics curriculum reform of different countries in recent years. Meanwhile the geometry is a mathematical element closely related with real life, and is also used as effective material to explore the mathematical teaching theory of Freudental. So this paper selects content of geometric transformation teaching in the compulsory education stage as the object of analysis, in order to finish the writing purpose of improving the implementation of the New Curriculum Reform by refering to Freudental's mathematical teaching theory in the specific teaching content.Owing to the phenomenon that people pay more attention on the theoretical research of the New Curriculum Reform rather than its implementation, this paper will analyse some aspects of elementary geometry transform teaching, combining with Freudental's mathematical teaching theory, design lesson plans aimed at the specific teaching content‘axial symmetry transform', which aims to reflect the new ideas of the New Curriculum Reform. selects the specific teaching content ‘axial symmetry transform' in the compulsory education stage as the object of anlysis, by analysing the textbook teaching material and excellent teaching cases, this paper designs lesson plans combining Freudental's mathematical teaching theory, in order to wispily promote the implementation of the New Curriculum Reform in the form of providing the concrete teaching case reference. At the same time,influenced by the teaching progress, we will select the lesson of ‘drawing method of axis symmetry graphics in graph paper' to do a contrast teaching experiment,in order to detect the effect of the teaching plan.In the first period of teaching,combining with Freudental's mathematical teaching theory, the lesson plan has made improvements as follows:(1)Induct the teaching by the theory of ‘realistic mathematics' to arouse students' learned power.(2)Guide students to carry out ‘re-creation' in the concept teaching,making the students deepen the understanding of concepts and the knowledge system.(3)Cultivate the students' ‘vertical mathematics' although in the elementary school,to improve their mathematical thinking and ability.In the second period of teaching,the lesson plan has made improvements as follows:(1)Utilizing ‘realistic mathematics' to turn ‘programmed learning' to ‘tool's assistant learning',let the students experience the producing pogress of new knowleledge,understand its rationality and realistic adaptation.(2)Revealing the textbooks' logic of knowledge production and application,make the students learn to solve the problems by the understanding of roots and improve the understanding and application ability of new knowledge.In the third period of teaching,the lesson plan has made improvements as follows:(1)Utilizing ‘realistic mathematics' to turn ‘life reality' to ‘students' reality',make the imagination instead of real operation in order to save times in class.(2)Utilize‘horizontal mathematics' to import the new concept and utilize ‘vertical mathematics' to understand the new concept.(3)Problem-driven to clarify the new concepts and deepen understanding.Influenced by the actual teaching progress,this artical just choose the second period of teaching to do contrast teaching experiment and detect its teaching effection.After the experiment, we found that the teaching combined with Freudental's mathematical teaching theory arouse students' creativity in a greater degree,but also had some shortageslike low class-controllability,insufficient time distribution,poor students' memory of systemic knowledge and so on,which needs us to do furder analysis to improve it.It requires further illustration that the improvement of the efficiency of the New Curriculum Reform is not in a day,which needs us to move our visual angle from the high level of theory to the teaching implement on specific content. Due to the limited length,this article just talks specifically on the lesson of ‘axial symmetry transform', and the other relevant contents still need further improvement in the future.