An Analysis Of The Idea Of Combination Of Number And Shape In Example Exercises ——Taking The 7th Grade Mathematics Textbook Of The Jiangsu Education Edition As An Example

With the development of the new curriculum reshape,the idea of combination of number and shape have attracted more attention of scholars and teachers."number" and"shape",as two major research objects,have a very important position in the basic education of our country.These two objects are closely related,which helps their combination.As one of the most important mathematical ideas,the combination of "number" and "shape" is also a vital tool for students to solve problems.Therefore,paying attention to the application of the combination of number and shape in educational practice is not only very important,but also helps teachers improve the quality of teaching in the so-called double reduction policy.Taken the seventh grade textbook of compulsory education in the Jiangsu Education Edition as an example,and based on the writer’s own teaching experience,this paper deeply explores the importance of infiltrating the combination of numbers and shapes when teaching example exercises in the seventh grade textbook.What’s more,this paper proposes some strategies which helps improve students’ ability to apply the combination of number and shape in the example exercises.The thesis consists of six chapters in total.Chapter 1 explains the background and meaning of combinations of numbers and shapes,and defines the combination of number and shape as well as example exercises.Chapter 2 introduces numbers and shapes,as well as domestic and international studies.Chapter 3 categorizes the number and shape combination ideas contained in the practical examples from the Jiangsu Education 7th Grade Mathematics Textbook.Chapter 4 describes the current situation of students’ application of the combination of numbers and shapes when solving problems by analyzing the questionnaire data and reading related literature.Chapter 5 summarizes and analyzes the factors that affect students when solving problems with combinations of numbers and shapes.Chapter 6 reviews the work done in this study,finds deficiencies and proposes directions for future research.By compiling two test papers with the same content but different shapes,they are completed for students with different learning levels,and then the test papers and statistical results are analyzed.This test shapeat is the biggest innovation of this paper.Through investigation and comparison,this research finds several factors that affect students’ use of the combination of number and shape as follows:（1）Students’ ability to convert algebraic and graphical representations is insufficient.（2）Students lack in-depth analysis of graphic representations.（3）Students with different learning levels have great obstacles in understanding mathematical language.Then,the writer conducts a case analysis of the shapeation of the above-mentioned influencing factors and finds that the main reasons are as follows:firstly,the students’ geometric foundation is weak and the drawings are not standardized;secondly,students cannot use the intuitive thinking to analyze the graphical representation;thirdly,students cannot understand the mathematical language by the way of mathematical thinking.Based on the above results of the study,we make the following recommendations:（1）teachers should change the teaching concepts to improve students’awareness of using the combination of number and shape;（2）teachers should focus on textbooks and study the typical cases of the combination of number and shape;（3）teachers should cultivate students’ comprehension ability and help them master the transshapeation of three mathematical languages;（4）teachers should help students enhance their drawing ability by using technology.This research sorts out he idea of combination of number and shape contained in the example exercises of the seventh grade.The selected questions try to originate from the textbooks.The conclusions obtained from the investigation are not only conducive to improving the professional quality of teachers and students’ mathematical literacy,but also promote the in-depth understanding of mathematics ideology and theory in junior high school.It is also convenient for scholars and teachers to conduct in-depth research in this field in the future.