The Integration Of DGS And Geometry Teaching In Middle School

As a mathematical information technology, DGS, which is based on Euclid Geometry and implicate axiomazation, has come into being right to its place. The previous research has proved that students' inferential capability and creativity can be improved when integrating DGS into geometry teaching in middle school. At present, the integration is becoming an important trend in the curriculum reform in 21-centrury. But in the classroom, the validity of DGS has not been made full use of. For one thing, teachers understand little about this integration; For another, the related research is very scarce. Therefore it is of great importance and urgency to do research, both theoretically and practically, on the integration of DGS and geometry teaching in middle school.The article probe into the integration theory on information technology and the integration process of mathematical instruction. Then based on this theory, we construct the framework of the integration process according to the traits of geometry teaching in middle school. Besides, we put this framework into the teaching practice, and its rationality and validity is testified initially. At last, based on the class analysis and the discussion about the DGS-based integrative teaching strategies, the features of the integration process and some related problems are summarized.The major conclusions and its traits:(1) Theoretical understanding on the integration process of information technology and mathematics teachingAccording to the instrumental theory , the main purpose of integration is to transform the general technology into instruction instrument, it can be realized through the socialization of the technology, the technologization of the subject and development of the teaching content. Secondly, to be more specific, in the field of classroom activities, integration means to facilitate the link and interaction between the subject's physical and the mental operation, the Conceptualization of activity and the activation of concept are supposed to realize strongly this process of transformation: the former refers to the internalization of technology and it's a major means in promoting comprehensible leaning; the latter means the externalization of the inner mental activity to technology, it is a problem-solving process and a more advanced mental activity. The two processes interact with each other and drive the development of students' operating and mental skills, which, as a result, can promote a benign recycle of the entire integration system.(2) The construction of integration process framework about DGS and geometry teachingAccording to the theory of TTT, the integration process include three apects : As task is the primer, the acquisition of the technology technique is the key, for based on this, students can obtain the correspondent geometry theory together with the development of intelligence. In this process, tehnology is the medium linking the technology and paper-pencil environment, and promoting the realization from task to geometry understanding.Based on the theory of TTT and the learning traits of plane geometry, this dissertation analyzes the DGS technology, the Conceptualization of activity and the activation of concept in the integration process of geometry teaching, the framework of the integration process is also constructed. In practice, the Conceptualization of activity includes four modes: geometry figure, concrete attribute, geometry invariance and geometry theory. The geometry figure is the conveyer of students' activities; the concrete attribute comes from the drag of technology and checking , accurate but less general; the geometry invariance is the abstraction of the concrete attribute, and the gain of theory must experience the proving and interpreting, then put it into the intrinsic cognitive structure, thus, the students can gain understandable learning. The activation of concept includes four modes: geometry theory, physical drawing, geometry figure and geometry sketch. In these processes, the geometry theory is the basic condition, physical drawing is rooted in the understanding of geometry theory, formed in the construction activity in technology, but the rationality should be testified by the drag of technology. In these sequential processes of construction and drag, the testing is ubiquitous, it guides the completion of geometry figure, enhances the links between concepts and sets up the geometry model of itself.(3) Probes into the strategies of integration teaching about DGS and geometry teachingBased on the practical analysis of integration teaching from the experiment, integration strategies on DGS and geometry teaching are advanced as follows: strategies of accuracy-based figure-to-data transformation; strategies of abundance-based generalization; strategies of dynamic-based test-driving; strategies of scene-based pre-generation; strategies of dynamic variability-based extending.In accordance with the framework of integration process and the experimental teaching design, conclusions are drawn as the following:â‘ The existence of the process sketch are proved, and the development of conceptualization may follow a zigzag way;â‘¡The validity the process sketch are proved;â‘¢The adaptation of the process sketch is proved , because we discovered that the technology value is mostly unleashed through the anlysis of the technology activity.â‘£Differences are found between the main school and the common school concerning students' activity, therefore, different activity patterns and strategies are to be selected.The innovation of this research lies in two aspects: for one thing, the theoretical construction of the integration process between DGS and geometry teaching in middle school is established, which reflects the feature of the integration and its process, the traits of DGS and geometry. For another, based on experiment, strategies on the integration of DGS technology into geometry teaching in middle school are summarized, which in turn provides both maneuverability and pertinency for the DGS technology and geometry teaching .the dificienc of the research lies in two aspects: one is that the process sketch is lacking of psychological theory; the other is that the sample is a little small and induce the anlysis about integration practice be not enough.