Study On The Infiltration Of Transformational And Inductive Thinking In The Teaching Of Graphics And Geometry In Primary School Mathematics

The Compulsory Education Mathematics Curriculum Standards(2011 Edition)takes the "Four Bases" as a teaching goal and emphasizes the importance of mathematical thinking.The idea of Transformational and Inductive thinking is one of the most basic and core mathematical ideas in mathematics thinking,and is the basis of other mathematical ideas,for example,the combination of numbers and shapes is the Transformation between numbers and forms.The knowledge of "graphics and geometry" in elementary school mathematics is relatively abstract and difficult to understand for primary school students.It is teachers' job to make difficult knowledge easy,abstract knowledge specific in math teaching so that the students can easily understand and master it.Therefore,Transformational and Inductive thinking is very necessary in the teaching of "graphics and geometry".However,there also exist some problems,such as inadequate infiltration due to the teachers' lack of knowledge in Transformational and Inductive thinking,and obscure enlightenment stage of this thinking.This paper constructs the methods and strategies of permeating transformational and inductive thinking on how to effectively permeate the ideas in "graphics and geometry" of primary school mathematics to enhance students' innovative consciousness and promote the development of students' mathematical literacy.The main contents are as follows:Questionnaires and interviews were conducted among the teachers of the author's school and surrounding schools to find out the problems on transformational and inductive thinking in “ graphics and geometry ” teaching of primary school.According to the problems,the author first systematically sorted out the contents which include transformational and inductive thinking in the "Graphics and Geometry" of the primary school grades 1-5 and analyzed them in details.Then,from the aspects of the transformation of numbers and shapes,special and generalization,this paper puts forward the four infiltration principles and methods of transformational andinductive thinking: mathematization,familiarization,simplification and visualization,and strategies on how to infiltrate the ideological before,in and after class.The specific method is : from the shallow to the deep,from the concrete to the general;the strategy is: excavate the implications of transformational and inductive thinking in the preparation of lessons,and integrate them into the teaching objectives;gradually permeate the thoughts in introduction,new contents,and classroom summary,and guide students to perceive the thoughts in this process;and based on the teaching methods such as after-school reflection to improve the professional quality of teachers to lay the foundation for cultivating students' sense of transformational and inductive thinking.Based on the above teaching strategies,the teaching content of “Awareness of Line” and “Area of Trapezoid” was designed and implemented.The practical results show that the teaching with effective transformational and inductive thinking can help students to improve their innovative thinking and mathematical literacy,and lay a good foundation for independent learning of graphics and geometric knowledge in junior school and high school.