"Graph Transformation" Teaching Program Research In GeoGebra Environment

"Graphic transformation" has great educational value for students,but due to students' insufficient spatial imagination and other problems,the teaching cannot achieve the expected effect.According to literature review,The teaching research of "graph transformation" mainly focuses on the teaching research of exercises and theoretical strategy research.The research problem is too broad,not targeted,and less starts from "graph transformation property",which is the most difficult content for students to understand,the reason why students have difficulty in understanding is that they cannot observe the movement of the figure,Just the "procedural implementation" of GeoGebra and other functions can help to break through the "graphics transformation" movement process presented difficulties.Therefore,based on the understanding of the existing teaching problems of GeoGebra and the "properties of graph transformation",this study intends to form the design ideas and procedures of the scheme,and then design and implement the "properties of graph transformation" teaching scheme by using the design program.The main contents of this paper are as follows:Chapter1: questions raised.The research background is expounded;From the three aspects of constructivism teaching theory,humanism teaching theory and the theory of information technology and the integration of curriculum teaching,this paper states the enlightenment of "the nature of graphics transformation" teaching;This paper reviews the research on "graph transformation" and GeoGebra;The project research of GeoGebra integration into "graph transformation" teaching is made clear;Starting from the fact that it is difficult for students to grasp the nature of "graph transformation properties" the research content and framework are proposed(FIG 1.1).Chapter2: An overview of GeoGebra and "properties of graphical transformations".Explains the history of the GeoGebra;The interface characteristics of GeoGebra are described;The four functions of GeoGebra are analyzed: resource sharing,number-form combination,process realization and convenient operation;The seven advantages of GeoGebra are obtained through the comparison with the function of geometric sketchpad.From the overall perspective of transformation,the essential meaning of "graph transformation property" and three learning requirements are obtained;Based on the analysis of course standards and textbooks,the textbook knowledge structure of "graph transformation properties" is obtained(FIG.2.11);Based on the requirement of learning,the logic of discovering the knowledge of teaching materials cannot make students grasp the essence of knowledge,Thus,the knowledge logic lines of "translation property","axisymmetric property" and "rotation property" are sorted out from the Angle of motion change;Combined with the functional characteristics of GeoGebra and the content characteristics of "graph transformation properties",the suitability of the combination of the two is analyzed,and the combination of the two is necessary and feasible.Chapter3: analysis of the existing teaching problems and the causes of the problems.Using case analysis,this paper analyzes 22 typical instructional designs on zhiwang or baidu from three parts,namely "translation property","axisymmetric property" and "rotation property",thre teaching problems and their causes are found;The comparison reveals three common problems in these three parts: the failure of the inquiry process to reflect the internal connection of knowledge,the exploration of "nominal",the measurement of deviation from knowledge itself,and the common reasons(FIG 3.4).Chapter 4: GeoGebra incorporates the "properties of graph transformations" teaching program.On the basis of elaborating the design basis,design ideas(figure 4.2)and design procedures(figure 4.3),the teaching of "translation property","axisymmetric property" and "rotation property" are designed respectively,the teaching scheme of "translation property"(FIG.4.8),the teaching scheme of "axisymmetric property"(FIG.4.13)and the teaching scheme of "rotation property"(FIG.4.18)were obtained;Through the summary of the scheme,five principles to be followed for GeoGebra's integration into mathematics teaching are obtained.Chapter 5: GeoGebra is integrated into the implementation of the "properties of graph transformations" teaching scheme.In order to test whether the improvement of teaching is effective,the students in a regular class of grade two in a certain school are selected,and the math teachers in that class are communicated and implemented the teaching programs of "translation property","axisymmetric property" and "rotation property";Classroom observation is used to analyze the teaching segments of "translation property","axisymmetric property" and "rotation property",it is found that GeoGebra's solution of incorporating the "properties of graph transformations" into teaching can promote students' understanding in four aspects,two shortcomings of the teaching program have been improved,four teaching inspirations of GeoGebra incorporating "properties of graph transformation" are obtained.Chapter 6: summary and prospect.The understanding and analysis of GeoGebra,"graphic transformation properties" and their suitability provide references for the selection of information technology and the combing of knowledge in teaching at the theoretical level;The analysis of the teaching problem,the design of the teaching scheme and the implementation of the scheme of the "properties of graph transformation" bring to promote students' understanding of "properties of graph transformation" in practice.In combination with this study,the author prospected the collection of feedback information from students' perspective and the promotion of design ideas and procedures.