Research On The Application Of Transformation Thought In Equation Teaching In Junior Middle School

The thought of transformation is one of the most basic mathematical thinking methods,and it is the soul of mathematical thinking methods.The application of transformation thought in teaching has guiding significance for concept learning and method mastery.However,due to the internal recessiveness and fuzziness of ideological methods,the research on the thought of transformation ignores the guiding role of transformation in knowledge learning,is limited to the one-sided cognition of problem-solving application,and there is labeling in practical teaching.In order to improve these problems,around the specific application of transformation in teaching,three research questions are determined: where is transformation reflected in equation knowledge? How is the application status? How to better apply?The research starts with the specific application of transformation thought in equation knowledge,and uses the content analysis method to excavate the idea of transformation between equation and other knowledge and equation knowledge from both vertical and horizontal angles.The embodiment of the thought of transformation in equation knowledge includes:(1)The resolution process of "from new knowledge to old knowledge";(2)The generalization process of equation concept "from concrete to abstract";(3)The essence of dimension reduction and order reduction in equation operation-the transformation process "from unknown to known";(4)The thinking process of "from complexity to simplicity" when solving problems;(5)The experience process of equation thought "from special examples to general models".Excavating the knowledge carrier of the thought of transformation is only the first step of applying transformation to equation teaching.In teaching practice,we also need to understand the actual situation of students' application of the transformation teaching.The results show that students' awareness of the thought is low;The habit of induction,analogy and association is poor;In the process of problem-solving,students are too specific to the problem and not pursue the direction of problem-solving;Lack of reflection on the learning process.According to the attribution analysis of the survey results,the teaching improvement measures of "applying normalization to equation teaching" are put forward,and the design is carried out by taking the univariate first-order equation as an example.From static knowledge mining to dynamic teaching exploration,the research always takes how to use the thought of transformation to promote equation teaching as the research goal,and combines theory with practice.Through the teaching experiment of two classes,the teaching effect of "using the thought of transformation to guide teaching activities and teaching the thought of transformation to students in this teaching process" is verified.According to the process and results of teaching experiment,it is concluded that teachers should pay attention to:(1)Excavate teaching materials and show the connection between knowledge to students;(2)Concept teaching does not simply give a definition,but dialectically treat abstraction and concreteness;(3)Expose the thinking process of problem-solving and clarify the purpose of transformation;(4)Take advantage of favorable conditions and point out the implied transformation of other mathematical thinking methods;(5)Urge students to reflect and monitor their own thinking process;(6)Combine the infiltration of transformation thought with the clarification process.