Review of "Understanding Negative Numbers" in Mathematics

After listening to Professor Zhang Qihua's lesson "Understanding Negative Numbers", I was deeply impressed by his unique teaching design and wonderful language. This class didn't use any multimedia-assisted teaching methods, only relying on a piece of chalk and some pictures drawn by the students themselves, we vividly understood the specific meaning of negative numbers and achieved good teaching results. This is a real ecology class. In class, Teacher Zhang directly revealed the topic: "Today we are studying negative numbers. Where have you seen negative numbers? " Students said: thermometer, elevator, height, scores when playing games are all negative; Another student said that there was a overdraft card. Teacher Zhang immediately asked, "If my overdraft card is negative, what does that mean to my wealth?" Let the students understand the meaning of negative numbers. On the basis of understanding the students' learning situation, Teacher Zhang asked the students to write the negative numbers on the blackboard. Students wrote-1, -5℃ and-185 meters. When writing -50 yuan, Teacher Zhang said to the students, "That's enough. This student just wrote to me-5,000 yuan. " The students snickered, and at the same time had a certain perception of the size of negative numbers.

The highlight of this lesson is the stage of learning negative numbers. Teacher Zhang takes four negative numbers written by students as the research object, and asks the group to discuss their specific meanings. On the basis of the discussion, he asked the students to draw the results of the discussion. What is worth learning is teacher Zhang's grasp of details. He instructed one student to draw and two people to discuss, and put forward clear requirements for the division of labor and cooperation of team members, which improved the efficiency of cooperation. When the students explain in front of the blackboard, he also instructs the students to turn it over and don't block the blackboard. Please stand aside after answering and see if there are any questions before communicating. This requirement cultivates students' good habit of answering questions and inspires other students' positive thinking attitude.

According to their own understanding, students demonstrated and drew-1 building, -5℃,-185m and -50 yuan on the blackboard. Around the speeches of these student representatives, the students started active discussions, and they constantly improved their drawings, striving to better express the practical significance of these negative numbers. Teacher Zhang consciously guides the students: mathematically, the ground is called "0", and under the guidance of the students, a dividing line of 0 is drawn between 1 building and-1 building. The teacher asked questions at the right time:-Is the fourth floor higher or lower than the-1 building? In other pictures, Teacher Zhang also pays attention to guiding students to find "0". In the understanding of positive and negative numbers, "0" plays an important role and is the watershed of positive and negative numbers. Teacher Zhang's design has deepened students' understanding of positive and negative numbers: they realize that positive and negative numbers are bounded by 0 and have certain relativity; Positive numbers are greater than 0 and negative numbers are less than 0. Naturally, we understand that 0 is neither positive nor negative. At the same time, with the help of the number axis, students can improve their understanding of logarithm.

There is also a link that is quite cleverly designed. When the students thought they had a certain understanding of negative numbers, Mr. Zhang showed the height data measured by the physical education teacher for his son during physical examination: -2 cm. This suddenly caused the students to discuss: how can it be longer and lower? Don't stand underground? Finally, a lesbian said that the ratio of the standard height of children of the same age was 2 cm. In this way, students have a deeper understanding of the nature of positive numbers and negative numbers.

In a word, reflecting on the success of this class, Mr. Zhang is willing to work hard on how students learn, fully understand the learning situation, fully let students speak, do and comment, respect each student's expression, be good at waiting and listening to students' opinions, and cultivate both knowledge and divergent thinking. This is exactly what I am worth learning.

Understanding negative numbers is the content of the first volume of the sixth grade of primary school. It is the main content of this lesson to have a preliminary understanding of negative numbers in life, to perceive the wide application of negative numbers in life and to understand the meaning of negative numbers. Negative numbers are common in life, but the concept is unfamiliar to beginners. Teacher Chen closely connects with life in teaching and introduces negative numbers in life into the classroom to make students feel familiar and cordial. The teaching of this section, I think the following points are successful:

First, select life materials that students are familiar with, and naturally introduce new lessons.

Weather forecast is something that students are familiar with. Familiar situations are easy to arouse their existing life experiences and let them know negative numbers in specific situations. At the beginning of the new class, teacher Chen played a video of weather forecast. With the change of temperature in different cities, negative numbers gradually appear, which is naturally introduced into the classroom, reducing the difficulty of learning, and students' problems have surfaced: how to record the temperature below zero? According to the students' feedback, Mr. Chen explained it in time. Students have a feeling of being suddenly enlightened, letting them know that +3 and -3 are two different numbers. Use different symbols before "3" because two "3 degrees Celsius" have different meanings.

Second, encourage group cooperation and exchange, and actively guide students to explore and question.

Students are full of personality, and their understanding of teaching content is unique and creative. Some people may have heard of negative numbers for the first time, while others already have some knowledge and experience. In teaching, by creating different situations and using the method of classification, Mr. Chen made students clear the opposite meanings of above-zero temperature and below-zero temperature, and broadened their understanding of logarithm. In the process of teaching, some students think that 0 is a positive number, so Mr. Chen adopted the teaching strategy of guiding students to closely combine situational observation. He guided it like this: "We observed from the thermometer that 0 is the dividing point, the temperature above 0 is represented by a positive number, and the temperature below 0 is represented by a negative number. Also based on sea level, the height above sea level is represented by a positive number, and the height below sea level is represented by a negative number. What did you find out from it? " On the basis of this question, a more definite question is put forward: "Is 0 a positive number? Is 0 a negative number? " At this time, Mr. Yang created an open cooperative research atmosphere for students in the main group, allowing students to discuss and communicate, and then came to the conclusion that 0 is neither positive nor negative, all positive numbers are greater than 0, and all negative numbers are less than 0, so that students can further understand the relationship between 0 and positive and negative numbers. Judging from the feedback information, students have gained a lot and their enthusiasm for inquiry is high.

Third, teaching design is closely related to life, but it is higher than real life.

In this class, Mr. Chen noticed that teaching should be combined with students' real life, such as thermometer, elevator floor, mountain height and recording students' height. He emphasized the essential attribute of knowledge through various examples, that is, negative numbers are quantities representing opposite meanings.

In this way, with the help of life examples, students can have a deeper understanding of the relationship between negative numbers and 0, and at the same time feel the wide application of negative numbers in life, laying the foundation for students to solve problems in life. Teacher Chen's design is widely related to life, but it is higher than life. Let students not only understand that real life is the source of mathematical knowledge, but also realize that mathematical knowledge is a powerful tool to solve practical problems and help students further appreciate the value of mathematical knowledge.

The above is my personal inspiration, please criticize and correct me, thank you.

This time the teacher taught us to understand negative numbers. The whole class didn't use the computer. The teaching AIDS used in class are only a chalk and a blackboard, but the children's performance is always wonderful. Some children even dare to refute the teacher's point of view. The dialogue between students and between teachers and students in the classroom is vividly reflected.

Hearing this, people who have never heard of this course must be curious to know how the teacher's class is taught. Please listen to me one by one: at the beginning of the class, the teacher directly cut into the subject, wrote the word negative on the blackboard and asked, "Students, what are we going to learn in this class?" Then the teacher said, "Do you find negative numbers in your life?" Just listen to the students' colorful answers. Now you must know that the teacher came prepared before coming to class. He asked the students to collect negative numbers in life before class. Just as the students were proud of finding so many negative numbers, the teacher changed the subject: "You all know negative numbers, but I don't believe it just listening to you." Who can write one? " Students easily challenged this level and soon wrote a few negative numbers, but the teacher's problems were not limited to these. Listen, what question did he ask? "It's great that you can not only write negative numbers, but it won't be so easy after I pass." Who can tell me what these four negative numbers mean? Let's talk in groups of four. "

When students cooperate in groups, the teacher pays great attention to patrol. He also caught the students showing their teeth in time to describe the negative meaning, and the camera produced new requirements: "The students' movements are very rich. Please draw a picture in groups of four, and others will make suggestions for revision. It doesn't matter if some pictures can't be drawn, just choose what you can draw. "The teacher selected several students' works and asked them to draw them under the corresponding negative numbers on the blackboard. The students painted them vividly.

The evaluation of the fourth draft of the understanding of negative numbers in mathematics starts from the students' existing knowledge level. For negative numbers, students are not ignorant. In the minds of many children, there is already a preliminary feeling of negative numbers. Teacher Zhang used this sentence, "Where have you seen negative numbers in your life?" As an opening, it evokes the child's initial feeling of negative numbers. Then let the students write negative numbers themselves, and then tell us that there are negative numbers everywhere. Negative numbers are not only preceded by a negative sign, but also less than 0. Then study the meaning of five "-2", so as to know the real negative number. Every class of Mr. Zhang Qihua's is eye-catching.

"Don't repeat others, let alone yourself" is the code of conduct that Teacher Zhang abides by. Poetic teaching language, diverse teaching objectives, profound classroom ideas, exquisite teaching structure, rich classroom process and wonderful reflections from teachers and students constitute the beautiful scenery of his classroom. "After listening to Zhang Qihua's class, it is difficult to predict what he might do in the next link." This huge psychological expectation for the classroom not only attracts teachers, but also plays with every student's curiosity and yearning for mathematics learning. This ingenious design is always beyond your expectation, but it is reasonable. After discussion, the students in this class come to the conclusion that the negative number is less than 0 and the positive number is greater than 0. Express your understanding of -2 with your own ideas, expand an exercise, learn the "height" designed by Teacher Zhang, and experience the "breadth" of Teacher Zhang's training thinking! No wonder I listened to him. Taking classes is a pleasure. No wonder "China fans" follow him enthusiastically.

Evaluation Draft 5 of Mathematics Understanding of Negative Numbers The observation dimension I choose is "consistency of target teaching evaluation". Talk about some simple experiences and feelings in combination with lectures.

There are four teaching links in this class: First, create realistic situations and get a preliminary understanding. Second, intuitive operation deepens understanding. Third, extend in time and enrich the imagination. Fourth, abstract the number axis to improve understanding. Five, layered practice, consolidate and extend.

1. From the perspective of achieving the goal, knowledge is implemented. The preset three-dimensional goal of this course can be effectively achieved. Under the teacher's refined language guidance and ingenious teaching design, students have a solid grasp of knowledge. Judging from students' interest in learning, the classroom is flexible. In this class, students' enthusiasm for learning is very high, and teachers and students cooperate tacitly. Students' reaction in class is as agile as spring water, and teachers' friendly teaching attitude and language give people a very comfortable feeling. Personally, I think there are several points to pay attention to in this class: 1, and the positive and negative examples given by students are still biased towards integers. Most of the data presented by teachers to students may be biased towards integers, and students' thinking mode may also like to give examples of integers. It's best to guide students to give examples from various aspects to make their knowledge more perfect.

2. It seems that how to reflect students' independent inquiry into knowledge is not enough. For example, in terms of temperature, let individual students dial up. If each student can make a mark on the paper thermometer first, discuss how you mark it in the group, and then give feedback, it may better reflect the students' independent inquiry.

3. However, the different opinions of individual students have not been analyzed and dialectical in time, which leads students to think that teachers do not attach importance to their own ideas. In the future, we should pay attention to student-oriented, return the classroom to the students who occupy the main position, and appear in the classroom teaching as a tutor.

4. Questioning in class is ineffective and scattered, which affects the effect of classroom teaching and should be strengthened in the future.

Revision 6 of Mathematics Understanding Negative Numbers is a preliminary understanding of negative numbers on the basis of students' understanding of natural numbers, fractions and decimals, combined with students' familiar life situations. The specific goal is to understand the meaning of negative numbers in familiar life situations and express some problems in daily life with negative numbers. As a transition to further study rational numbers in middle schools, this course only requires students to have a preliminary understanding of negative numbers, understand the significance of negative numbers in specific situations, feel the connection between negative numbers and life, and initially establish the concept of negative numbers. There are no complicated concepts and calculations, and the knowledge level is relatively shallow. According to the content and characteristics of concept teaching in this course, Mr. Xiao adopted the teaching method of "element combination".

First, realize the close relationship between mathematical knowledge and real life.

Mathematics comes from life and is applied to life. This course always relies on the positive and negative figures in some concrete examples such as temperature, pays attention to intuitive understanding and strengthens comparison. First of all, through the appearance of several groups of quantities with opposite meanings in pairs, the practical problems are highlighted in front of students; Secondly, using the life example of urban temperature, the difference between above-zero temperature and below-zero temperature is clear, and then it is realized that 0 is the dividing point between positive and negative numbers; In addition, by guiding students to use thermometers, abstract understanding is implied into intuitive and operational activities. The whole teaching process strives to proceed from the reality of students' life, guide students to extract mathematical problems from realistic and meaningful life situations, deepen their understanding of mathematical knowledge in familiar situations, and finally make students realize the close relationship between mathematical knowledge and real life through extensive examples, thus realizing the value of mathematical learning.

Second, the teaching process reflects the goal consciousness everywhere.

The goal is the starting point and destination of the whole class. As a teacher, we should always have a sense of purpose in order to carry out effective teaching. Teacher Xiao first lets students understand the quantity with opposite meaning in the form of games; Then, through students' dynamic examples, we can understand the negative numbers in life, and focus on the relationship between positive and negative numbers in the thermometer, laying the foundation for understanding the abstract number axis and comparing sizes in the next lesson; Finally, in the form of classification, let students further complete the knowledge network of the numbers they have learned.

Third, understand negative numbers in exploration and communication.

The Standard clearly points out that effective mathematics learning activities can't rely solely on imitation and memory, and hands-on practice, independent exploration and cooperative communication are important ways for students to learn. Teacher Xiao designed it for students to learn negative numbers further in the teaching process. Ask the students to talk about your findings on the basis of observing the thermometer scale. Here, teachers leave enough time and space for students to explore and communicate, so that students can form their own understanding of negative numbers in the process of exploration and gradually improve their thoughts in the process of communication with others.

Fourth, enjoy the study of diversified presentation forms.

The Standard points out that the presentation forms of mathematics content should be diversified to ensure that students actively participate in the whole learning process and make their mathematics learning activities a lively, proactive and personalized process. In the teaching process, Mr. Xiao took the initiative three times, that is, before class, during class and after class, to make the teaching content complete and echo from beginning to end. Multi-dimensional content of grading, three selections gives students the initiative, broadens students' knowledge, makes the teaching process more compact, highlights the teaching focus, and makes the presentation forms of concept teaching more diversified.

This course is a concept teaching course. How to guide students to understand and form concepts, make boring mathematical concepts vivid and concrete, and make them easy for students to accept? From Mr. Xiao's class, I have several experiences:

First of all, introduce the concept intuitively and vividly.

Pupils know a thing and understand a mathematical truth, mainly by virtue of the specific image of things. Try to introduce what students are familiar with in their daily life. In this way, students' interest in learning will be high and their enthusiasm for thinking will be high. For example, the thermometer degree in this class, the information quoted in the passbook, and the vivid and intuitive mathematical information combined with students' life experience make the teaching concept internalized.

Second, the use of old knowledge leads to the emergence of new concepts.

It is easy for students to use their old knowledge to teach new concepts. Suhomlinski said: "Teaching students to acquire knowledge with existing knowledge is the highest teaching skill." In the teaching of this class, Mr. Xiao arranged the figures he learned before class, which laid a solid foundation for the study of this class.

Third, from concrete to abstract, reveal the essence of the concept.

In concept teaching, Mr. Xiao is good at creating conditions for students, guiding students to master concepts through observing, thinking and exploring the meaning of concepts, and along the cognitive process from perceptual knowledge to rational knowledge. This can not only cultivate students' logical thinking ability, but also greatly enhance their initiative in learning mathematics. For example, in the teaching of Example 1 to Example 3, the teacher has a gradient design, in the process of gradual perception and understanding, highlighting the teaching focus, breaking through difficulties and internalizing concepts.

Fourth, encourage students to summarize and form concepts.

In class, Mr. Xiao teaches students a lot of materials, which are analyzed, synthesized and abstractly summarized by students. Abandon the non-essential things of things and phenomena, and grasp the essential characteristics of things and phenomena to form concepts. It is precisely because students have paid mental work that they get it, so they are easy to understand and have a firm memory. After practice and strengthening, the concept of internalization is externalized and promoted.

These are just my simple ideas. Everyone here is my teacher. Please criticize and correct me.