American High School Mathematics Textbooks On Orientation Of Big Ideas

Since the 21 st century,the core attainment-oriented education reform has become a new trend in the modernization of global basic education."Mathematics Curriculum Standard for General Senior High School(2017 Edition)" introduces Big Ideas for the first time: "Attach importance to Subject Big Ideas as the core,make the curriculum content structured,theme as the guide,make the curriculum content situational,and promote the implementation of the core quality of the subject." The Standard proposed that curriculum content should focus on Subject Big Ideas and emphasized the important role of Subject Big Ideas in the implementation of the core literacy of mathematics.However,The Standard does not define the basic connotation of the Mathematical Big Ideas,nor does it elaborate the concrete implementation path of Bid Ideas.Therefore,in order to better promote the transformation of attainment-oriented Big Ideas teaching,the research on Big Ideas theory needs to be further improved.As the origin country of Big Ideas,The United States has a certain practical basis on how to integrate Mathematical Big ideas into textbook compilation and classroom teaching,the analysis of the American Big Ideas textbook can provide some enlightenment to the textbook compilation and teaching practice of Big Ideas in China.This research mainly analyzes how Pearson Common Core textbook,edited by Charles and Wiggins,the leading figures of Big Ideas,integrates into Big Ideas in mathematics.Text analysis method,case analysis method and comparative study method are adopted.First of all,this paper summarizes the viewpoints of scholars at home and abroad on behalf of Bid Ideas and Mathematical Big Ideas,and forms the theoretical basis of Big Ideas.Secondly,analysis the Pearson Common Core Textbook,extraction of the implement approach of Big Ideas teaching,contrast analysis of series of equal difference and proportion,derivative and its application in the teaching material Function Big Idea of large vertical infiltration of similarities and differences,in a Linear Function as an example analysis of Function Big Idea in the textbooks lateral seepage,excavate the case of fragment infiltration in teaching materials.Finally,according to UBD of Wiggins,the Big Idea-Unit-Class teaching process is constructed,and an example of Big Idea-Unit-Class teaching design is constructed.The results and conclusions are as follows.1.Construct the basic theory of Big Ideas and define Mathematical Big Ideas.In this paper,five key points of connotation understanding are extracted,including status,structure,application environment,feature and function of Big Ideas.The essential feature of Big Ideas is connection,and transfer is the result.Big Ideas can connect mathematical knowledge as a whole,promote learners' deep understanding of knowledge,and finally realize knowledge transfer.On the basis of Charles' definition,the author adjusted the definition and added another feature of Big Ideas,"life value",to define Mathematical Big Ideas.Mathematical Big Ideas is the core of mathematics learning,which can connect various mathematical understandings into a coherent whole,and can be applied to the statement of important ideas or concepts in various authentic situations,such as inside and outside the discipline.2.Extract the implementation path of Big Ideas in Pearson Common Core textbook.The main implementation paths of Big Ideas in Pearson's textbook are explicit and penetrative,and penetrative can be divided into three paths: horizontal,vertical and fragmentary.By integrating 21 Mathematical Big Ideas from Charles K-8 and 16 Mathematical Big Ideas from Pearson's textbook,a Mathematical Big Ideas system for k-12 grade was formed.3.Implement the teaching of Big Ideas class hour and construct the Unit-Class teaching from the perspective of Big Ideas.Based on UBD theory of Wiggins,the teaching process of Units-Class hour in the perspective of Big Ideas is constructed,and the teaching example of Big Ideas of "Linear Function" is designed according to this process.Taking the class teaching of variables and Functions as an example,this paper uses multiple representations to promote the understanding and construction of the concept of function,which penetrates Philosophical Big Idea,Equivalent Big Idea and Function Big Idea,and concretely explains how to develop the unit-class teaching from the perspective of Big Ideas.4.Put forward suggestions to promote attainment-oriented Big Ideas teaching.Unit teaching from the perspective of Big Ideas should be implemented into class hour teaching,which can be referred to the teaching process of units-class hour from the perspective of Big Ideas.The transformation of Big Ideas teaching materials can help the transformation of big-concept teaching.Teachers should take the initiative to explore the penetration of the Big Ideas in the content of the teaching materials,and transform the recessive links into explicit links to infiltrate students' learning.Teachers should emphasize the connection between Big Ideas and real situation and life value in carrying out Big Ideas teaching.