Investigation And Research On The Errors In Solving Problems Of Rational Numbers Among The Students Of Grade 7

After more than ten years of mathematics teaching in junior high school,the author finds that the teaching of rational numbers is a difficult point,and many students find it difficult at the beginning of contact with rational numbers.On the basis of the existing research,the author explores the concept of rational number,the related concept of rational number and the operation of rational number.After collecting and analyzing the data by testing tools,the author makes a research on the concept of rational number,the related concept of rational number and the operation of rational number.(1)what are the major mistakes of seventh grade students?(2)Are there any differences between the two schools in the seventh grade?(3)are there differences among students of different sexes in the same grade?(4)VII,VIII,Are there any differences between ninth graders?In this study,a random sampling method was used to select the seventh,eighth and ninth grade students from two junior middle schools in A County of Xingtai City,with a total of509 students.The author mainly used the observation method,the literature method,the test questionnaire method and the case interview,in the analysis middle school mathematics curriculum standard,the teaching goal,the teaching material content,the teaching request and the student’s mental development level,Referring to the test questions about rational number concept and calculation compiled by experts at home and abroad,according to the purpose of this study,the rational number Test Paper is carefully selected and adapted,respectively,from the concept of rational number,The related concepts of rational numbers and the operation of rational numbers are carried out in three aspects.Field research,mainly using qualitative and quantitative analysis of the information and data obtained,to draw the following conclusions:1.The lowest score rates of seventh grade students are related concepts of rational numbers and rational number operation.The main errors are as follows:(1)nearly 1/2 students do not have a thorough understanding of rational numbers and their classification criteria are not clear,and one-sided view is that "negative numbers" are rational numbers.The concept of the number learned is confused.(2)it is difficult to use the number axis to represent the geometric intuition of the rational number.39% of the students consider the distance from the number axis to a certain point from a single aspect.It is difficult to understand that any rational number can be represented by points on the axis of the number.When comparing rational numbers,students can correctly distinguish positivenumbers,zero numbers and negative numbers,but in the case of negative numbers,nearly20% of students have applied the rule of positive numbers to compare sizes,and can not flexibly grasp the ordering of rational numbers.(3)they cannot understand the absolute ordering of rational numbers.when comparing negative numbers,nearly 20% of students have applied the rule of positive numbers to compare sizes.The geometric meaning of the value is out of line with the number of axes,and only the absolute value is positive.In the calculation of the absolute value,when the absolute value of a certain number is known,one-half of the students only know to write a positive number,and ignore the negative number.(4)30% student has a symbol problem,especially a "+",whether the "-" is an operational symbol or a property symbol cannot be mastered.The sign of sum and the absolute value of sum when two numbers are added.The symbolic problem of multiplying the time product of two negative numbers.The sign problem of the fractional part in the negative part of the score.If there are several numbers in parentheses,and the parentheses are preceded by negative signs,you cannot change the symbol of each number in parentheses when you remove them.In the mixed operation of rational numbers,it is affected by the law of combination because of the more content involved,how to calculate simply and how to calculate,the students mix with the law of operation,and the order of operation is reversed.There are also many students self-created "division allocation rate," for the distinction(5)69% of students are unable to correct the connection between rational numbers and real life situations.Make sure that the real meaning of the life context of the topic.When it comes to the practical problem of multiplicative meaning,students can not abstract the concept and operation of multiplier.2.There is no difference in problem solving between the two schools in the same grade.3.There is no significant difference in problem solving among students of different sexes in the same grade.4.By using EXCEL software,using one-way variance analysis in the concept of rational number,the concept of rational number and rational number calculation,it is found that there are significant differences among grades,with the increase of grade,the problem-solving situation of rational number concept,rational number related concept and rational number operation are found to be significant,with the increase of grade.For the rational number of problem-solving overall upward trend,the eighth,ninth grade is significantly higher than the seventh grade.Finally,according to this study,some suggestions are given for the teaching of rational numbers:(1)strengthening the relationship between the axis of numbers and rational numbers;(2)emphasizing the consideration of rational numbers in terms of symbol and absolute value;(3)using various methods to strengthen the understanding of arithmetic,(4)paying attention to the understanding of quantitative relations in application problems.According to this suggestion,the author has also carried on the teaching design of "the comparison of rational numbers by means of the axis of numbers",and has probed into the method of making students master the ordering of rational numbers better,hoping that it will be helpful to the first-line teachers.