(d) Students' mistakes in the eighth grade math paper
The error rate of collected samples is 49%. Collectors collect samples in Ma Jianping.
School Shaoxing county hua she Shufu primary school
Source of Wrong Questions Unit 5 Questions
Type the basic time
computer class
New teaching
Subject Source Clearing Test Comprehensive Unit Practice Course √
The characteristics of the related knowledge triangle create specific problem situations, so that students can find that "the sum of any two sides of the triangle is greater than the third side" in the active exploration activities (Example 3) to expand the general review class.
Knowledge attribute declarative knowledge (√) procedural knowledge () strategic knowledge ()
After the students have learned the knowledge about triangles, a brief introduction to the teaching of problems in a study test is given.
◆ Typical wrong questions
Isosceles triangle, one side is10cm, the second side is 5cm, and the third side is () cm.
Wrong answer: 5 cm.
◆ Cause analysis
1. When a student is restricted by double or multiple conditions, his attention (especially some underachievers) can only take care of one, and the problem of thinking and analysis lacks comprehensiveness. When it comes to isosceles triangle, students often only pay attention to isosceles, that is, the two sides of a triangle should be equal, while ignoring the "triangle", that is, the necessary condition for forming a triangle: the sum of any two sides should be greater than the third side. This is also because the cognitive development of primary school students lacks rigorous thinking.
2. But it is puzzling that since the condition of isosceles is emphasized, why don't these students choose 10 cm? After the interview, I learned that in fact, the necessary condition for students to form a triangle is implicit condition, because there is no clear hint in the topic, and they didn't notice it at all. 10 cm and 5 cm are only optional.
◆ Teaching suggestions
1. Strengthen the comprehensive training of students' critical thinking ability and problem analysis under multiple conditions.
2. Teachers should design conditional open questions such as insufficient conditions, redundant conditions and implicit conditions to cultivate students' thinking quality.
3. In the new teaching, students should be given more hands-on operation and experience to form a good sense of numbers.
◆ Resource link
A rope with a length of 17 cm can be cut into three sections and made into a triangle. How many verses can you write? (The length of each side is a whole centimeter)
(d) Students' mistakes in the eighth grade math paper
The error rate of sample 32 was 75%, which was collected by Han Honggang.
School Shangyu Huawei Wen Lan Primary School
Source of Wrong Questions Unit 5 Triangle Questions
Type the basic time
computer class
New teaching
Topic Source Network Operation Comprehensive Unit Exercise Courseware
Classification and expansion of related knowledge triangle √ General review class.
Knowledge attribute declarative knowledge (√) procedural knowledge () strategic knowledge ()
This is a problem in Unit 5 "Triangle" network homework. Students have mastered the knowledge of triangle, classification by angle, classification by edge, sum of internal angles of triangle and so on, and have been able to measure "angle" with protractor.
◆ Typical wrong questions
Topic: Judgment: In the same triangle, the longest side has the largest angle. ( )
Students' wrong solution: ×
◆ Cause analysis
The author interviewed several students who made the above mistakes. Most of them are negatively transferred by "the size of the angle has nothing to do with the length of both sides of the angle", which interferes with the judgment of this problem. They mistakenly think that "the length of the edge" has nothing to do with "the size of the angle corresponding to the edge", so they naturally think that this question is "wrong". The reasons for the above mistakes are as follows: first, when teachers teach the classification of triangles, they lack the understanding of the relationship between "the length of the side" and "the size of the diagonal", which leads to the vague understanding of this relationship among most students; The second is the lack of students' good habit of solving problems. When students are uncertain about this question, they lack the habit of using "painting" to help them understand. Thirdly, teachers lack the comparison and speculation between this topic and "the size of the angle has nothing to do with the length of both sides of the angle".
◆ Teaching suggestions
1. Enhance contrast perception. In the teaching of triangle classification, teachers should pay attention to the comparative understanding of the relationship between "edge" and "diagonal". Through students' observation and comparison, I realized the law that "in the same triangle, the angle of the long side is relatively large, the angle of the short side is relatively small, and the angles of the same side are equal".
2. Cultivate the habit of drawing. Teachers instruct students (especially students with learning difficulties) to develop the habit of drawing before judging when they have difficulty in understanding such problems.
3. Pay attention to speculation. Teachers can put "the size of the angle has nothing to do with the length of both sides" and "in the same triangle, the angle opposite to the longest side is the largest" together, so that children can compare and speculate and let students understand this problem deeply.
◆ Resource link
1. It is observed that in each of the following triangles, which side has the largest angle? Which side faces the smallest corner? What did you find?
2. In the same triangle, the angles on the same side are the same. Right? (Please draw a picture to explain)
(d) Students' mistakes in the eighth grade math paper
Sampling sample 3 1 error rate 19% collector
Han Honggang Collection
School Shangyu Huawei Wen Lan Primary School
Source of Wrong Questions Unit 5 Triangle
(People's Education Edition)
Type the basic time
Machine category √ Category
New teaching
Topic Source People's Education Edition Teaching and Learning 43 pages Comprehensive Unit Practice Course √
The Internal Angle of the Triangle of Related Knowledge and the Extension of the General Review Course
Knowledge attribute declarative knowledge (√) procedural knowledge () strategic knowledge ()
Introduction to Teaching This content is a comprehensive exercise for students after learning the knowledge of triangle internal angles. Before this question, students have learned that the sum of the internal angles of a triangle is 180, and two triangles are put together to practice finding the degrees of the internal angles and converting them.
◆ Typical wrong questions
Title: Known: ∠ 1 = 37, ∠ 2 = 55, ∠ 3 = 58.
Q: ∠4= (), ∠5= ()
Students' misunderstanding: ∠ 4 = 67, ∠ 5 = 76.
◆ Cause analysis
Students understand that the sum of the angles in a triangle is 180. They will also do the problem of knowing the degrees of two angles and finding the third angle. However, due to the complexity of this problem, many children don't know the required degrees of angle 4 and angle 5, so they must first find an intermediate quantity-the obtuse angle next to angle 4, which leads to obstacles in solving the problem. The reasons are as follows: first, teachers usually lack the training to find the intermediate quantity for children; Second, there is a lack of similar topics in the textbooks.
◆ Teaching suggestions
1. Find a solution to the problem. In the error correction teaching of this topic, students should first understand the thinking of solving problems. To know the degree of ∠4, first ask the size of the unknown angle in the left triangle, that is, 180-55-58 = 67, and then calculate ∠4 = 67 according to the angle of 180.
2. First, strengthen the training of seeking moderate quantity. You can show a similar topic, and then ask the students to say according to the topic, "What information does the topic tell you? What else can you think of? " Through such training, children's ability to solve unknown information according to existing information is cultivated, and their ability to seek "intermediate quantity" is also cultivated.
◆ Resource link
/article/show.asp？ Id=782 Clever use of mistakes, brilliant achievements.
(d) Students' mistakes in the eighth grade math paper
Zhu Ying collected 44 samples with an error rate of 26.7%.
School Dongpu town ludong complete primary school
Source of Wrong Questions Unit 6 Decimal Addition and Subtraction Questions
Type the basic √ time.
Machine category √ Category
New teaching
Title source
Comprehensive unit practice class √
Related knowledge: vertically calculate decimal addition and subtraction, understand the arithmetic of decimal point alignment, and expand the general review class.
Knowledge attribute declarative knowledge () procedural knowledge (√) strategic knowledge ()
On the basis of students' initial mastery of decimal addition and subtraction methods, through practice, students can further consolidate decimal addition and subtraction rules and use them to perform accurate operations.
◆ Typical wrong question: 9.8+6.28 = 7.26 0.704-0.25 = 0.679.
◆ Cause analysis
Teacher: Students can understand and summarize that decimal point alignment is necessary when calculating decimal addition and subtraction in the first class. The decimal point alignment and ending alignment in the exercise design of the first class are basically the same, with few mistakes. The teacher mistakenly thought that the students had really understood the similarities and differences between decimal point alignment and ending alignment.
Student:
1. Influenced by the mindset, students always align at the end when calculating addition and subtraction from school to now, so students habitually align at the end when calculating, and do not consider the difference of decimal places when adding and subtracting decimal places, but the end alignment is not the addition and subtraction of numbers on the same digit.
2. Poor study habits, first of all, the lack of good habit of examining questions, getting exercises, not analyzing them carefully, just doing them and doing things hastily. Secondly, there is a lack of inspection awareness of evaluation.
Textbook: this topic is to consolidate and improve students' computing ability. It is boring and unattractive for primary school students, which leads students to do it in a hurry in order to finish it.
◆ Teaching suggestions
1. In the first class, strengthen the special training of mathematical understanding of "decimal point alignment", for example, rewrite the horizontal style with the same and different decimal points into vertical style, and comment on why some exercises are finally aligned and some are not.
2. Develop the habit of carefully examining questions before writing.
3. Strengthen the teaching of estimation, and get into the habit of using estimation to preliminarily check the calculation results.
◆ Resource link
(d) Students' mistakes in the eighth grade math paper
Zhu Ying collected 44 samples with an error rate of 72.7%.
School dongpu rd dong complete primary school
Source of Wrong Questions Unit 6 Decimal Addition and Subtraction Questions
Type the basic time
Machine category √ Category
New teaching √.
Topic Source Exercise Book P42 Every 2 questions are integrated √ Unit Exercise Class
Name-number conversion of related knowledge units and calculation and expansion of decimal addition and subtraction
Knowledge attribute declarative knowledge () procedural knowledge (√) strategic knowledge ()
The solution of this exercise is widely used in life. It is practiced on the basis that students master the vertical calculation of decimal addition and subtraction in Unit 4 and the conversion of composite numbers into singular numbers. Exercises are designed to fill in the blanks, which is helpful to master the strategies and steps of solving such problems. Pave the way for the next exercise lesson, Exercise 6 of textbook 16.
◆ Typical wrong questions
2 tons 35 kg +600 kg =(2.35) tons +(0.6) tons =(2.95) tons.
36km-8km 564m = (36) km -(8.564) km =(28.564) km.
◆ Cause analysis (it can be analyzed from three dimensions: teachers, students and textbooks)
Teacher:
Usually, students in class have short independent homework time and less interaction time between peers and teachers, which forms a bad habit of students rushing to do homework. The conversion of the unit name in the previous unit has not been realized, so that every student can convert it correctly. Don't give instructions before homework.
Student:
Poor working habits, poor analysis and thinking on exercises, such as the conversion between kilograms and tons, the advance rate of the first half of the same topic is 100, and the second half is 1000. When correcting, most students can quickly find the cause of the error and calculate carelessly. There is no requirement for vertical calculation, and few students are doing vertical calculation. Lack of conscious inspection consciousness, some students still can't find the direction when they send it down for review, and think they are right. Students will only respond when they are reminded of vertical inspection and calculation.
Teaching materials:
The conversion of unit names and numbers was learned in Unit 4. For most students, this knowledge is difficult. It is really difficult to consider not only the speed of progress, but also the position, moving direction and number of decimal points, or from complex number to singular number. Moreover, it has been a while, and today is the first lesson of decimal addition and subtraction.
◆ Teaching suggestions
1. Leave as much homework time as possible for students and develop good homework habits.
2. Give some guidance before operation, especially the unit conversion rate.
3. As the first class, students can be required to calculate vertically.
◆ Resource link
(d) Students' mistakes in the eighth grade math paper
The error rate of sampling 44 is 43. 1%.
School Dongpu town ludong complete primary school
Source of Wrong Questions Unit 6 Decimal Addition and Subtraction Questions
Type the basic √ time.
Machine category √ Category
New teaching √.
Title source
Comprehensive unit practice class
Simple operation and expansion of the decimal total review course of related knowledge
Knowledge attribute declarative knowledge () procedural knowledge (√) strategic knowledge ()
Teaching introduction takes solving problems as an opportunity to guide students to exchange experience and evaluate. Through a number of limited simple calculation examples, it helps students to reasonably deduce and understand the law of addition operation, which is also applicable to decimal operation. Then choose a textbook to do basic exercises, and then cultivate students' sense of numbers and ability of oral calculation through the special exercises of complement in workbook 1. Finally, let the students finish Workbook 3 independently according to the data characteristics.
◆ Typical wrong questions
15.49-5.49+4.5 1
= 15.49-(5.49+4.5 1)
= 15.49- 10
=5.49
◆ Cause analysis
1. Influenced by fixed thinking, students think it can be simplified when they see how simple it is, and the operation order of simplified calculation will definitely change. The sum of 5.49 and 4.5 1 can be added to 10.
2. Students don't really understand the operation rules thoroughly, and take rounding as the main goal. In any case, they can achieve the purpose of simple calculation by rounding.
3. The examination is not comprehensive, and rounding of addition is more sensitive than subtraction.
◆ Teaching suggestions
1. Strengthen the cultivation of examination consciousness, and guide students to comprehensively analyze the data characteristics and operation symbols of exercises before writing. through
Let the students look at the questions and say how to calculate it is more convenient. Through the collision between individuals and within individuals, students' sense of numbers and symbols is cultivated.
2. Hierarchical teaching, so that students can judge which questions are easy to use the algorithm and which questions are reasonably calculated according to the original operation order before calculation.
◆ Resource link
(d) Students' mistakes in the eighth grade math paper
The error rate of 37 collected samples is 54.05%, which was collected by Liu Yunjuan.
School Shaoxing Chang 'an Experimental School
Source of Wrong Questions Unit 8 Mathematics Wide-angle Questions
Type the basic √ time.
Machine category √ Category
New teaching √.
Topic source book comprehensive unit exercise class
Related knowledge: the problem of not planting trees at both ends expands the general review class
Knowledge attribute declarative knowledge () procedural knowledge () strategic knowledge (√)
Teaching Introduction Unit 8 Mathematics Wide Angle is about three situations of planting trees. This topic is example 2 in the textbook, which is about planting trees at both ends in an unclosed graph. In the previous study, students planted trees at both ends in an unclosed figure, and they also had a certain understanding of the relationship between the interval and the number of trees. This topic is a mistake made by asking students to try and practice before adopting the new class teaching.
◆ Typical wrong questions:
The elephant hall and the orangutan hall are 60 meters apart. Students should plant trees on both sides of the road between two museums, and the distance between two adjacent trees is 3 meters. How many trees will be planted?
Wrong solution ① 60 ÷ 3+ 1 = 2 1 (tree), 2 1× 2 = 42 (tree).
Wrong solution ② 60 ÷ 3- 1 = 19 (tree)
◆ Cause analysis
1. From the students' point of view:
(1) There are still some problems in students' examination, such as understanding that trees cannot be planted at both ends between two banks, and not considering the difference from the problem of planting trees at both ends in the closed graph that they have learned before; At the same time, it is overlooked that planting trees on both sides of the path requires that the number of trees on one side be multiplied by 2.
(2) The problem of planting trees should be analyzed according to the actual situation. Some children can't start by trying independently, can't think, and can't use some helpful methods, such as drawing.
2. From the perspective of teachers:
Trying to practice independently is one of the reasons for the high error rate of students, and it also shows that a large number of students will not solve problems independently with their own thinking. Teachers should strengthen inspiration in students' thinking and lack guidance in solving problems.
◆ Teaching suggestions
1. Teachers can list all kinds of mistakes made by students on the blackboard, let students talk about their own ideas, and then let students discuss and analyze themselves to judge their answers.
2. Using the mapping method, we can understand and study the situation of planting trees at both ends according to real life, and judge the relationship between the interval and the number of trees. It is found that if both ends are not planted, the number of trees planted on the straight road is less than that in the interval 1. So as to master the solutions and ideas of this kind of tree planting problem.
3. Through some targeted exercises, master and establish the "mathematical model" of tree planting.
◆ Resource link
Exercise:
The distance between the two buildings is 56 meters. How many cedars can be planted every 4 meters?
(2) Arbor Day is coming. Young Pioneers will plant 8 poplars between two buildings 72 meters apart. If both ends are not planted, how many meters should the average distance between every two trees be?
(3) Party A and Party B plant trees on both sides of a 300-meter-long highway, plant a willow tree every 20 meters, and plant two buttonwood trees between every two adjacent willows. It is known that Party A has more trees than Party B 12. How many trees are there in each category?
Attached 1
Summary of the results of a large sample survey of typical errors in the second volume of grade four
I don't know how to ask questions, I hope to adopt them. Your adoption is my motivation to answer questions.