Investigation And Study On The Current Situation Of Rural Junior Middle School Students’ Application Of The Idea Of Combining Numbers With Shapes

The idea of combining numbers and shapes is one of the most important and widely used mathematical ideas in junior high school mathematics,and is also an indispensable tool for students to understand and master knowledge,analysis and problem solving.However,after three years of educational internship,I found that rural junior secondary school students’ understanding and application of the idea of combining numbers and shapes was weak,and there were many problems in teachers’ teaching of the idea of combining numbers and shapes to students.Therefore,it is necessary to study the current situation of the use of number and shape combining ideas by rural junior high school students.This study focuses on the question: "What is the current situation of the use of number and shape combining ideas by rural junior high school students? What are the factors that affect the use of number and shape combining ideas by rural junior high school students? What are the strategies to improve rural junior high school students’ ability to use number and shape combining ideas?" The three questions were developed.In this study,306 students from two rural general complete secondary schools in a township in P city were taken as the research subjects.Through literature analysis,questionnaires,tests and interviews,the current situation of rural junior high school students’ use of the idea of combining number and shape was studied and the following conclusions were drawn:1.Rural junior secondary school students generally believe that the idea of combining numbers and shapes is helpful to mathematics learning and mathematics problem solving,but most students have misunderstandings about the idea of combining numbers and shapes,are not clear about the real meaning of the idea of combining numbers and shapes,and only regard the idea of combining numbers and shapes as a kind of problem solving method,which is only associated with mathematics problem solving,and the test papers show that students’ ability to use the idea of combining numbers and shapes needs to be improved,which indicates that the two secondary schools’ This indicates that the mathematics teachers in the two secondary schools did not adequately teach the connotation and application of the idea of combining numbers and shapes in their teaching.2.This important mathematical idea of combining numbers and shapes has received a lot of attention from teachers,and teachers have been consciously trying to infiltrate the idea of combining numbers and shapes in their classroom teaching.This shows that teachers do not know enough about the teaching materials related to the idea of combining numbers and shapes in the teaching materials,and do not teach the connotation of the idea of combining numbers and shapes sufficiently and effectively.3.Compared with "using number to help shape" and "combining number and shape",rural junior high school students are slightly more capable of using "using shape to help number".At an overall level,rural junior high school students did not perform well in all three types of number-shape transformations.The main problems that the students showed in the test paper were: they were not careful in examining the questions and did not understand the meaning of the questions;they could not accurately identify the key information and construct the figures based on the information in the questions,and their ability to recognize and construct figures was weak;they could not accurately construct the correspondence between numbers and shapes;some students did not have a firm understanding of the basic knowledge of mathematics,lacked problem-solving skills,and did not develop the habit of summarizing;a very small number of students lacked self-confidence and did not work hard on the questions.A very small number of students lack self-confidence,do not pay attention,make frequent mistakes in arithmetic,and are withdrawn and bored.4.The overall level of the rural junior high school students’ ability to use the idea of combining numbers and shapes is average,and the average student is at the level 2stage,with much room for improvement.In terms of overall level,the test results show that 7.6% of students are at level 0,27.7% at level 1,42.2% at level 2 and 19.4% at level 3.In terms of individual level,the test results show that 85.1% of students meet the requirements of level 1,52.4% meet the requirements of level 2 and only 26.7%meet the requirements of level 3.5.There was no significant difference in the ability of rural junior high school students to use the idea of combining numbers and shapes in the two rural general secondary schools in general,nor was there a significant difference between the sexes of male and female students.The factors affecting rural junior high school students’ ability to use the idea of combining numbers and shapes are divided into two aspects: students’ factors:(1)biased understanding of the idea of combining numbers and shapes;(2)poor learning methods for the idea of combining numbers and shapes;(3)weak ability to transform numbers and shapes;(4)weak grasp of basic knowledge;(5)weak ability to recognize and construct diagrams.Teachers’ factors:(1)insufficient awareness of the cultivation of the idea of combining numbers and shapes;(2)lack of depth in digging into the standards and teaching materials;(3)inadequate teaching methods for the idea of combining numbers and shapes;(4)lack of proficiency in the use of multimedia technology.Based on the analysis of the current situation of rural junior high school students’ use of the idea of combining numbers and shapes and the influencing factors,and combined with personal practical experience,strategies to improve rural junior high school students’ ability to use the idea of combining numbers and shapes are proposed from both student and teacher aspects.Students’ learning:(1)overcoming fear and increasing self-confidence in learning;(2)improving learning methods and enhancing learning efficiency.Teachers’ teaching:(1)change their teaching philosophy and enhance their awareness of the infiltration of mathematical ideas;(2)focus on teaching basic knowledge and consolidate the foundation of students’ mathematical knowledge;(3)study the standards and teaching materials in depth and explore the teaching materials of the combination of numbers and shapes in the teaching materials;(4)use cooperative learning and error files as entry points to improve teaching and learning;(5)seek diversified teaching methods to cultivate students’ ability to transform numbers and shapes;(6)make scientific use of information technology to enhance students’ ability to recognize and combine numbers and shapes;(6)scientific use of information technology to enhance students’ ability to read and compose diagrams.