Teaching Research Of Preliminary Solid Geometry Based On Thinking Visualization

Based on the practical needs of promoting the development of students ’ thinking by subject teaching,Professor Liu Zhuoyuan of East China Normal University puts forward the theory of thinking visualization.Thinking visualization is the process of presenting invisible thinking(thinking methods,thinking paths)by using a series of diagrams or combinations of diagrams in teaching,so that it can be clearly seen.Mathematics is the gymnastics of thinking,and the content of solid geometry unit is an important carrier to develop students ’ mathematical thinking ability.Therefore,the main problems studied in this paper are :(1)What problems do students have in the study of the initial unit of solid geometry ? How do teachers understand thinking visualization ?(2)In order to solve the existing problems,combined with thinking visualization,what teaching strategies can be proposed ?(3)How to apply specific teaching strategies in different types of mathematics classrooms ?In order to study the above problems,firstly,the literature analysis method is used to clarify the connotation of thinking visualization and understand the research status of thinking visualization at home and abroad.Then use the survey method to go deep into the front-line classroom to understand the front-line teachers ’ cognition of thinking visualization and the students ’ learning status in the solid geometry unit.Based on the survey results,combined with thinking visualization,put forward targeted teaching strategies;finally,the case analysis method is used to design the teaching under the guidance of the strategy.The results of investigation and interview show that teachers have the following problems in the cognition of thinking visualization.(1)Teachers are more inclined to knowledge visualization in daily teaching,and do not pay enough attention to thinking visualization.(2)The application of visualization strategies only focuses on classroom teaching,ignoring the application in pre-class preparation and after-class reflection.Students have the following problems in the study of solid geometry units :(1)weak spatial imagination ability,lack of multiple representation of knowledge(2)short thinking chain,lack of ability to build fulcrum independently(3)unclear concept,lack of systematic construction of knowledge.According to the above survey and interview results,combined with thinking visualization,targeted teaching strategies are proposed : 1.Visualization of pre-class preparation thinking to promote teachers ’ teaching thinking.The specific operation can be divided into knowledge structure visualization and teaching goal visualization.The specific operation can be divided into(1)multiple representations,making invisible thinking explicit(2)building fulcrums,making abstract thinking visualized(3)system construction,making scattered thinking structured;(2)visualization of teaching thinking in class,developing students ’ thinking ability,specific operation can be divided into(1)multiple representations,making invisible thinking explicit(2)building fulcrums,making abstract thinking visualized(3)system construction,making scattered thinking structured;the visualization of reflective thinking after class promotes the common progress of teachers and students.The specific operation can be divided into student evaluation visualization and teacher reflection visualization.Based on the above strategies,the teaching design of the two classes of " basic three-dimensional graphics " and " space geometry and ball cutting problem " is carried out.