Study On Penetration Of Functional Thinking In The Primary Mathematics Textbook

Function as a mathematical model that reflects the law of change and correspondence from the quantitative point of view,always been the core of mathematics teaching in the world.Since the beginning of this century,F·Klein has been the world in the modern movement of mathematics education " Teaching the Teaching of Primary and Middle Schools with the Idea of Function " The core of the function is that function thought and function thought are regarded as one of the important contents of basic mathematics thought,which is of great concern in the course of compulsory mathematics curriculum standard(2011 edition)(hereinafter referred to as "mathematics curriculum standard").Attaching importance to the infiltration of function thought in elementary school mathematics textbook has become one of the main trends of primary school mathematics in our country.However,most of the research in China has focused on fragmented practice,and the research of textbook editors on the idea of function is also in experience.Therefore,the study of the function of thinking in the primary school mathematics textbook penetration,found that the functional existence of the problem and put forward the improvement strategy is imminent.This research is divided into six chapters,the first three chapters of background,problems,design,methods described;The fourth chapter in text analysis,new edition and North Division amounted to 24 volumes of 1-6 grade students ' book from the penetration number,content distribution,specific performance,rendering,render vector text analysis and presentation of six dimensions and quantitative statistical data;The fifth chapter interviews about teacher identities of infiltration to function;Sixth chapter two editions of textbooks by comparative method comparative analysis of the infiltration of the thoughts of the function,summed up the ideological penetration of two versions of textbooks functions basic features,writing features and problems,based on function improvement strategies for effective penetration.Specific conclusions are as follows:1.The Law of Thought Penetration of Two Edition Textbook Functions(1)The idea of function can be infiltrated in the textbooks of primary school mathematics.Function of the "two variables between the interdependent changes in the relationship between" can be infiltrated in primary school mathematics textbooks.The three expressions of the function can also be used.Function ideas can be used as a main line to guide the content of other courses.(2)The infiltration of functional thought is both continuous and helical.The idea of function in the two versions have appeared 159 times,according to the spiral of the five steps in continuous distribution in the first grade of each textbook.(3)Exercises play an important role in the penetration of functions.The number of exercises of the two versions of is much higher than the number of the carrier of the example,136(86.6%)for the human education and 119(75.3%)for the Bei Shi.(4)Example as the most able to reflect the function of thinking the effect of the carrier,the function of the idea of the basic success.The average level of infiltration is 2.1(the highest score is 4 points),and the distribution ratio of primary and secondary is 71.4%.The mean level of penetration of the textbook is 2.0(the highest score is 4 points),and the distribution ratio of primary and secondary is 66.3%.2.The Characteristics of the Thought of the Two Editions of TextbookIn the textbook of human education,the synthesis and practice and the "wide angle of mathematics" are the "base" of the function thought infiltration,and the whole set of 20 textbooks in the comprehensive and practical activities embodies the idea of function.Teachers use books on the textbook 33.3% of the function of a clear description of the idea that the guidance of teachers with a relatively clear book.Bei Shi version of the textbook concerned about the example of illustrations can show the important value of the idea of thinking,the example of the number of carriers is about 2 times the teaching version.At the same time pay attention to digging graphics and geometry in the function of thinking,in this part of the number of people is 3 times the teaching version,accounting for 13.2% of the total."Math fun" as a "secret garden" of infiltration functional thought,a total of 2 times.3.Function thought of two edition textbook seepage problemsThe proportion of the four forms of teaching in the textbook is 60.4%,19.5%,3.9% and 16.2% respectively,and the significant difference is that the form is relatively single.The number of examples is only 13.4% of the total,indicating less penetration through the example of the idea of function.Bei Shi version of the textbook in the synthesis and practice part(0 times)did not show the function of thinking.Teachers use only about 20% of the textbook function to explain the idea that the lack of functional thinking requirements.The penetration of the textbooks into the function of the two versions shows the common characteristics of the unbalanced distribution in the various knowledge fields,The number of people in the number and algebra show 145 times,the remaining three parts only show 14 times,The number of the division and the algebra is 128 times,and the other three parts are presented 21 times.In addition,teachers' lack of understanding of functional thinking is systematic.4.Suggestions for improvementThe textbook of human education should pay more attention to the form of balance function,appropriate increase in the proportion of tables and image presentation functions and forms of alternating or "team" appears,the penetration of the idea of thinking better.Appropriate adjustment of the proportion of examples of infiltration function,the example should focus on the connection between students and daily life,give full play to the example of penetration in the function of thinking and exemplary role.Bei Shi version of the textbook should pay attention to the application of the value of the idea of thinking,combined with the idea of integration and practice of infiltration function for students will be thinking about the idea of thinking into a function to solve the problem to provide an opportunity.Teachers' book should do a clear idea of specific arrangements for teachers to grasp the function of thinking and infiltration in teaching to provide a reference.Aiming at the common problems of the two versions of the textbooks,it is appropriate to map the geometric,statistical and probabilistic and comprehensive and practical aspects of the existing functions.To improve the teachers of the functional thinking of the systematic understanding,the specific methods include teachers to comprehensively learn and master the functional thinking entire set of textbook,the idea of the infiltration of thinking really implemented.The requirements of the function of the mathematical curriculum can be more clear,for example,the primary school mathematics should reflect the relationship between the two variables,the primary stage should be the function of the expression,the primary stage should be the relationship between the function and the equation.