—— An investigation on the teaching quality at the end of the first semester of the 06-07 school year in Anqing; Analysis of seventh grade mathematics examination questions.

Anqing No.4 Middle School Li Peng Ling Yu Ting

The survey and test of teaching quality at the end of the first semester of the 2006-2007 school year in Anqing showed that there were 6668 students in 20 schools in the city. After the unified marking in the whole city, we selected 354 survey papers by random sampling, registered them for the record, and further classified and analyzed them. The conclusions are as follows:

First, the overall evaluation of the test paper

(A) the characteristics of the test paper

This mathematics research paper involves algebra, geometry, probability and statistics in the seventh grade mathematics textbook of Shanghai Science Edition last semester. The proposition adopts the model and structure of the examination paper for senior high school entrance examination in our province. There are 7 big questions and 24 small questions in the test paper, and the test time is two hours, with a full score of 150. The scores and proportions of the knowledge points examined and the knowledge of each part, as well as the difficulty (see the table below).

List of knowledge points (table 1)

Question number examines knowledge points

Significance and simple calculation of a rational number 1

The meaning of the 2nd generation value

Basic properties of equation 3

4 the concept of similar term and the solution of linear equation with one variable

The Significance and Calculation of Algebraic Formula 5

6 Understanding of Spatial Geometry

7 the meaning of the line segment

Significance of 8-angle addition and subtraction

Comparison of the sizes of 9 angles

Read the data in 10 line chart.

1 1 two scientific counting methods

Representation and writing of 12 algebraic expression

The significance of the midpoint of 13 line segment

Significance of 14 bisector

/kloc-data reading of 0/5 bar chart

Mixed operation of three rational numbers 16

Solution of 17 One-dimensional Linear Equation

Comparison of the Drawing Method of Number Axis 18 and Rational Numbers

Addition and subtraction of 19 algebraic expression

The distance between two points is the shortest line segment.

Sum-difference relation of 2 1 angle

6-22 Drawing of Sector Statistical Chart

23 Using the idea of equation to solve practical problems

7.24 The meaning of absolute value

Score and proportion of knowledge in each part of the test paper (Table 2)

Probability and Statistical Algebra Part Geometry Part

The titles are 1, 2,3,4,5, 1 1 2, 16, 17, 18,18.

Score 74 58 18

The proportion is 49% 39% 12%

Comparison table of knowledge scores and difficulty of each part (Table 3)

Title score difficulty average difficulty title score difficulty average difficulty

Algebra part 1 4 0.87 0.75 geometry part 6 4 0.93 0.62

2 4 0.79 7 4 0.79

3 4 0.90 8 4 0.72

4 4 0.89 9 4 0.48

5 4 0.69 13 4 0.66

1 1 4 0.53 14 4 0.6 1

12 4 0.79 20 10 0.57

16 8 0.7 1 2 1 10 0.44

17 8 0.77 24 14 0.4 1

18 10 0.79 probability statistics part 10 4 0.90 0.86

19 10 0.53 15 4 0.88

23 10 0.7 1 22 10 0.8

Based on the formation of students' mathematical literacy, the examination paper focuses on examining basic knowledge and improving thinking ability. Basic knowledge is the first key for students to open the door of mathematics and the first basic theory for students to form basic mathematics literacy and further study. The whole volume pays full attention to the core content of mathematics this semester, from basic mathematical concepts to common problem-solving methods and mathematical ideas. The topic setting and copying methods are diverse, and the questions are novel, closely following the pulse of the senior high school entrance examination, emphasizing the examination of the operation process and thinking ability, and there is basically no complicated calculation.

In algebra, the understanding and flexible application of concepts and algorithms learned this semester is the main object of examination. In geometry, the reasonable application of basic geometric concepts, geometric facts and geometric knowledge is the object of examination. In statistics and probability, students' understanding ability of three kinds of statistical charts is comprehensively investigated, including the making of fan charts. The examination paper not only highlights the basic knowledge, but also embodies the training of thinking ability, as shown in the following table:

Comparison of scores between basic questions and ability questions (Table 4)

Basic problem, ability problem

Question score question score

Multiple choice questions 6 24 4 16

Fill in the blanks 5 20

Solution 5 46 4 34

Total 16 90 8 50

Score percentage 66.67% 60% 33.33% 40%

(2) Analysis of candidates' scores

The statistical data of sampling test paper scores are as follows:

Statistical Table of Basic Situation of Examination Paper (Table 5)

The highest score, the lowest score, the average score, the passing rate, the excellent rate, the standard deviation and the degree of difficulty discrimination.

150 0 94 60. 18% 1 1.59% 36.79 0.62 0.64

(Note: above 90 marks are qualified, and above 135 marks are excellent)

Statistical Analysis Table of Candidates' Achievements (Table 7)

Question Quantity Score Average Test Difficulty Standard Deviation Discrimination

1 43.462 0.87 1.359 0.30

2 4 3. 138 0.79 1.645 0.38

3 4 3.6 14 0.90 1. 180 0.46

4 4 3.572 0.89 1.240 0.42

5 4 2.786 0.69 1.844 0.83

6 4 3.7 13 0.93 1.045 0.68

7 4 3. 175 0.79 1.629 0.7 1

8 4 2.896 0.72 1.798 0.8 1

9 4 1.952 0.48 2.002 0.9 1

10 4 3.6 1 1 0.90 1.2 1 1 0.64

Two1142.1610.531.998 0.84

12 4 3. 166 0.79 1.645 0.73

13 4 2.685 0.66 1.892 0.60

14 4 2.473 0.6 1 1.954 0.5 1

15 4 3.546 0.88 1.309 0.84

Iii168 5.685 0.713.560 0.77

17 8 6. 189 0.77 3.249 0.73

4 18 10 7.938 0.79 2.995 0.69

19 10 5.304 0.53 4.573 0.56

V 20 10 5.738 0.57 3.527 0.72

2 1 10 4.425 0.44 4. 152 0.59

6 22 10 8.006 0.80 3.690 0.68

23 10 7.096 0.7 1 4.396 0.87

Seven 2414 4.687 0.413.759 0.44

Through the above data, it can be reflected that the algebra part of the test questions is moderately difficult, the difficulty coefficient of two questions is below 0.6, the difficulty of 1 question is 0.9, and the difficulty of the other nine questions is between 0.6 and 0.9, which can reflect the problems existing in teaching and learning from all levels; The geometry part is slightly more difficult, 4 out of 9 questions have difficulty coefficients below 0.6, and 3 questions are concentrated in the solution. The difficulty of the 0.9 question is only 1, and the other questions are between 0.6 and 0.8, so the students' answers are not optimistic. The number of questions in probability statistics is moderate, and there are one multiple-choice question, one fill-in-the-blank question and one answer question, which is not difficult, basically meets the requirements of the new curriculum standard and can well examine students' basic knowledge and ability.

Second, the analysis of test questions and answers

(1) Analysis of Candidates' Answers to Multiple-choice Questions and Fill-in-the-Blank Questions

1 question, taking the temperature change in Anqing city as the background, examines students' understanding of the meaning of rational numbers and their basic operations. The score rate is relatively high, and only a few students have some obstacles in understanding the concept of temperature difference, which leads to wrong answers.

The second question, finding the algebraic value when appropriate, focuses on students' understanding of the meaning of "algebraic value". The score rate of this question is slightly lower than that of the previous question, mainly because some students can't pay attention to the appropriate algebraic value, which leads to the wrong choice of answers and the loss of points.

Question 3: It is required to name the equation and examine students' understanding and application of the basic properties of the equation. When naming an equation by its basic properties, it should be noted that each term on both sides of the equation needs to be multiplied by the least common multiple of the denominator. It is precisely because a few students ignored this point that they made wrong judgments and choices.

The fourth question requires students to find the value of the letter sum according to the condition that "sum is similar" This topic comprehensively examines two knowledge points: "the concept of similar term" and "the solution of linear equation with one variable", which requires students to use the basic properties of the equation flexibly to solve the equation and make the right choice on the basis of mastering what similar term is. The concept of similar terms is easily confused by students, and a few students just lack this concept.

Question 5: Ask students to find out the shadow area according to the figures and the data marked on the figures. Because the data are all expressed by monomial, this question is actually to test students' ability to read pictures and calculate algebraic expressions with numbers as the carrier. The difficulty of this question is moderate, but some students lose points because of poor calculation.

Question 6: With the help of the expansion diagram of the cube, examine the students' spatial imagination ability.

Question 7: Ask the students to correctly count the number of line segments in the picture (as shown on the right).

This kind of investigation on the concept of line segment can only grasp the essence of the meaning of line segment.

Don't miss the solution when solving this problem. It is precisely for this reason that there is no

Few students lose points on this issue.

Question 8: Ask the students to answer which of the angles 15, 65, 75, 135, 145 can be drawn by triangles. When using the angle of triangular printing, we must be very clear about the degree of each inner angle of a triangular plate, and then we can use a triangular plate for proper combination, and draw some angles with a certain degree according to the relationship between the sum and difference of angles. Therefore, whether the degree of the inner angle of the triangle is not remembered or the combination method of the triangle is incorrect, it is the reason for losing points in this question.

Question 9: Turn a right triangle around its right vertex, and let the students judge which of the four conclusions provided by the selected answer is correct. This is a difficult problem. According to the graph, the wrong answer is A, that is, >. I didn't notice that graphics can be changed, and naturally I didn't find that it equals possibility. Among the wrong students, most choose A, and a few choose other answers.

Questions 10 and 15 test the ability to read and understand statistical charts. The only difference is that the question 10 requires students to estimate the patient's temperature at noon 12 according to the nurse's temperature change chart, and check the line chart. Question 15 requires students to follow the histogram of the number of boys and girls.

Question 1 1, under the background of cherishing and saving water resources, students are required to calculate how much water Xiao Ming put in without screwing the tap after washing his hands according to the actual background, which is a common problem in the national senior high school entrance examination. It is difficult to test students' mastery and understanding of scientific counting methods, and the score rate is not high. When students answer questions, there are not many mistakes in scientific counting method, and more students can't calculate correctly, including some students who can't convert units correctly. This problem is closely related to social reality and the background of the times. It is not only an inspection of students' knowledge and skills, but also a profound education.

Question 12, using a familiar nursery rhyme to test students' ability of induction and summary is novel, interesting and moderately difficult, and most students can answer the questions smoothly. However, some students still can't understand the meaning of the question correctly, or they are careless when reading the question and take it for granted to fill in the answers. This reflects that our students don't pay enough attention to some problems with very familiar scenes as the background. At the same time, it also reflects that some students have problems in their learning attitude and problem-solving attitude, and some students also have sub-health in their examination psychology.

The questions 13 and 14 focus on the meaning of the midpoint and the bisector of a line segment respectively, and require students to skillfully use the common problem-solving ideas they have learned to solve problems on the basis of accurately grasping the essence of these two knowledge points. But nearly half of the students answered these two questions incorrectly. There are two fundamental reasons: on the one hand, they can't grasp the basic concepts, operating methods and laws of the textbook. On the other hand, senior one students have just started to learn geometry, and there are still some problems in their understanding of graphics, especially 13, which requires students to draw their own pictures according to the meaning of the questions, which also brings difficulties to students in solving problems to some extent.

(2) Candidates' analysis of the answers and solutions to the calculation questions.

16 and 17 examine students' elementary arithmetic of rational numbers, so as to examine students' ability to solve linear equations with one variable. Students are required to correctly and flexibly use the law of mixed operation of rational numbers and the basic properties of equations so that they can successfully answer these two questions. In the process of marking papers, it is still found that some students get partial marks or fail to get full marks due to calculation errors or mistakes, which are mainly manifested as: (2) operational errors caused by weak primary school foundation; (3) lose the negative sign when applying multiplication and division; ④ The basic properties of algebraic expressions are not firmly grasped; ⑤ There are a few reasons such as not fully understanding the rules of removing brackets, and there are clerical errors in students' answers. The answers to these two questions fully reflect that students' computing ability needs to be further strengthened.

18 requires students to mark six rational numbers on the number axis and arrange them in order from small to large. This question examines the meanings of the three concepts of students' reciprocal, reciprocal and absolute value, and also examines the application of students' number axis. Although the score rate of this question is not low, it can also be seen that some students can't grasp the basic concepts correctly and comprehensively, and some students draw irregular axes. For example, some students have no positive direction on the number axis, some students have drawn a ray on the number axis, and some students have not marked the number of points required by the topic on the number axis, resulting in only partial scores.

Problem 19, there is such a problem: calculate the value, in which. A student mistakenly copied ""as "",but his calculation result is also correct. Try to explain the reason and find out the result. To answer this question correctly, we must first understand the meaning of the question. When marking the paper, I found that a few students could not understand the meaning of the question and did not know the requirements of the question, so they could not start. In addition, quite a few students can't simplify algebra correctly, which shows that students still have the problem of how to merge similar items in more complicated algebra, and the mistakes in this respect are mainly symbol errors; After simplification, some students did not give necessary explanations and explanations to the phenomena in the topic, resulting in unnecessary loss of points. This is a wonderful topic, which requires students not only to master the basic calculation methods and skills, but also to understand the significance of algebraic values, change the simple investigation and calculation in the past, and sublimate the investigation of knowledge points to a higher level, which meets the requirements of the new curriculum standard and is worth popularizing.

Question 20 is a question about the application of geometry knowledge in real life, with novel ideas and unique style. Based on the investigation of "the distance between two points is the shortest line segment", the topic gives two well-known scenes in life:

Situation 1: From the classroom to the school library, there are always several students crossing the lawn instead of taking the sidewalk. Why? Apply what you have learned.

Mathematical knowledge to illustrate this problem.

Scene 2: A and B are two villages on both sides of the river. Now it is necessary to build a pumping station by the river to supply water to these two villages. Require pump station maintenance.

Where do you need the shortest pipeline? It is required to mark the location of the pumping station on the drawing and explain the reasons.

The problem itself is not difficult to solve. Most students can accurately answer the reason that "the distance between two points is the shortest line segment", but a large number of students have problems in drawing. There are two typical examples: one is to describe the location of the pumping station in language without drawing, or just connect point A and point B without marking the location of the pumping station; The other is that we don't understand that "the distance between two points is the shortest line segment", and mistakenly think that connecting two points, A and B, takes the midpoint of line segment AB as the location of the pumping station. At the same time, this problem also reflects a considerable number of students' weak moral consciousness from one side, because there is a question at the end of the topic: "Which of the above practices do you agree with?" What do you think should be paid attention to when applying mathematical knowledge? " Nearly 20% of the students agreed with the scene 1 on the grounds that they used their own mathematical knowledge reasonably. Some even replied that walking is so short that there is no need to take a detour on the sidewalk. They don't realize that crossing the lawn is an immoral and uncivilized behavior.

Question 2 1, give a geometric calculation problem and give the solution process. Suppose the students are teachers, and ask them to answer whether they can get full marks in the process of solving the questions provided, and if so, give reasons; If not, it is necessary to point out the mistakes and give the correct solutions. The original problem is: if, on the same plane, we find the degree. The answer should be two cases: the first case is inside the ray; The second case is that the ray is outside, and the solution process of the test only gives the first case. This test mainly examines whether students can correctly and comprehensively analyze and understand the meaning of the question. The problem-solving process provided by the test can be said to be a hint to students. However, from the process of marking papers, we can find that some students have solid basic knowledge and correct ideas. We can think that the problem-solving process provided by the test questions lacks the second situation, but they did not draw the correct answers themselves. There are also some students who agree with the solutions provided by the test questions, but they did not expect to discuss them in different situations; There are also some students.

It is considered that the format and process of solving problems are not standardized.

Question 22, this is a question about making pie charts. The question is, "Will you offer your parents a glass of water when they come home?" On the basis of investigation, this paper records the relevant data of active pouring, occasional pouring and no pouring. First calculate the degree of the central angle of the fan chart, and then make the fan chart. Although the students' answer to this question is good, the real test paper that loses points is mainly that the degree of the central angle is not accurately drawn when making a fan chart, and some students miscalculate the degree of the central angle.

Question 23: In the form of a table, tell the math scores in the mid-term exam of grade one in a school in Anqing, and let the students count the number of people who passed and failed. This question examines students' ability to solve problems by using equations, and requires students to find out the equivalence relationship according to the table in order to achieve the purpose of solving problems. Judging from the overall effect of marking, students' understanding and application of the linear equation of one yuan is better.

Question 24 is the finale of this paper, which is a reading comprehension question centered on the distance between two points on the number axis. In recent years, reading comprehension is becoming more and more popular among the senior high school entrance examination questions, which is a very effective question to examine students' comprehensive quality. The perfect score rate of this question is very low, less than 0.3%, but there are not many students with zero scores, which is regarded as a question with less zero scores in the whole article. Most students can get 3 to 8 points, and there are not a few students who get more than 10. The main problem is that when students answer the third question, they can't classify it correctly, which leads to losing points, or they can't link the question with the reading materials of the test questions, and they can't find a solution to the problem. At the same time, this classification is a bit complicated. Students' geometric language has not been effectively trained for a long time, and the expression of questions is ambiguous.

In this set of test papers, there are questions 1, 2, 3, 4, 6, 7, 1 1, 12, 13, 14, which take basic knowledge points as the object of investigation. Question 5, 16, 17, 19, 2 1, 23 were investigated. There are 10, 15, 22 and 23 questions with chart information as the propositional medium; There are problems in the investigation of classified thoughts 22 1 and 24. In addition, the moral education function of mathematics discipline is embodied by applying mathematical knowledge in the test paper and inspecting mathematical quality. For example, the question 1 1, educating students about national conditions with scientific counting methods and building an economical society, is a buzzword. Question 20: Make use of the reasonable application of geometry knowledge in real life to educate students on civilization and morality in building a harmonious society; There is also the 22 nd question, using the survey drawn by the sector diagram to educate students on traditional filial piety.

Looking at the whole set of papers, the difficulty is moderate, the questions are novel and rich, the knowledge is comprehensive, and it has distinct characteristics of the times. At the same time, it is closely related to the new curriculum standard, and its style is similar to that of the senior high school entrance examination paper in our province. It should be said that this is a relatively successful final teaching quality survey paper.