Junior High School Teachers' Understanding Of Geometric Transformations And Teaching And Research

Geometric transformation has been paid more and more attention in the mathematics curriculum reform of international basic education. The field of Space and Figures includes geometric transformation among three stages,since China promulgated the Full-time Obligatory Education Mathematics Curriculum Standards (the following referred to as Curriculum Standards ) in 2001. There are lots of changes between Curriculum Standards and the outline about the requestments of transformation. The main problems of this study are: (1) How do junior middle school mathematics teachers think of transformation? (2) How do they teach transformation and the relevant content?Based on the above issues, this study has analyzed the background of the theme from four perspectives by literature :(1) the mathematics connotation of transformation and its educational value; (2) curriculum standards'requirements of transformation; (3) Status quo of mathematics textbooks on preparing transformation; (4) the status quo of evaluation about transformation in the senior school entrance examination.Through above analysis, the direction of this study has been defined further, aimed to reflect the main problems from the following five perspectives:(1)How do mathematics teachers think of the mathematics connotation of transformation and its educational value?(2) How do they think of curriculum standards'requirements of transformation?(3) How do they think of mathematics textbooks and their feedback on the textbooks?(4) How do they teach transformation and the relevant content?(5) How do they think of and evaluate the items in the senior school entrance examination about transformation.Based on the above analysis,this study has identified interview and case study as main methods. Combined with the study theme and analysis of background information, this study has designed the framework of the interview and also determined the perspectives of case analysis.Through above research, this article has got the following conclusions:(1) Teachers'understanding of transformationAll Teachers know little about the mathematics connotation of transformation among different levels; for the understanding of the educational value , there are relatively many differences between different levels, some excellent teachers has the comprehensive and profound understanding,but the ordinary teachers just consider that as knowledge and tricks; For teachers'concern and understanding of curriculum standards'requirements of transformation, there are also many differences between different levels, the ordinary teachers pay little attention to curriculum standards, they just fell the differences from the evaluation and the textbooks, in fact they do not knew curriculum standards'requirements of transformation exactly.(2) Teachers'teaching about transformationThere are many differences about teachers'consciousness of using transformation to guide students to recognize figures and infiltration conception of transformation among different levels. On the one hand, different in the extent of the attention to teaching sections which reflect the value of transformation when teaching some basic figures,some ordinary teachers trend to be subjected to textbooks, ignore the transformation operation and its benefit to proof. Furthermore, for the infiltration conception of transformation among the normal teaching, most excellent teachers focus on the accumulation and selection of transformation vector, guiding the students to recognize figures from the transformation perspective. But the ordinary teachers seem passive to some extent, if that can be resolved by traditional teaching methods, they will not make use of transformation. In addition, this article has made a corresponding analysis of problems reflected by teachers about Curriculum Standards development, textbooks preparing, and the senior school entrance examination.Finally, with the results of this study, this article has provided relevant recommendations on the professional development of teachers, the curriculum development, textbooks, teaching and evaluation about the geometric transformation. Furthermore, this article has proposed some issues, which need further study, expecting to cause more thinking and discussion about the course of geometric transformation.