Mathematics Curriculum Standard advocates that mathematics activities must be based on students' cognitive level and existing knowledge and experience. Students' mathematics learning activities should be a lively, proactive and personalized process. ?
Based on this, what observation points did I determine when watching this lesson? Students study? In dimension? Has the goal been achieved? Perspective? What is the effect of student activities in achieving goals? .
Teacher Zhang Jing's class is divided into five teaching links, with a total of 13 student activities (student activities here mean that teachers are in a relatively static state for a period of time and students are relatively independent). From the content point of view, student activities are rich in content. Judging from the time of students' activities, the total time is 30 minutes, accounting for 67% of the total time of this class. Students' relatively independent activity time can account for such a proportion, which shows that this class embodies the concept of taking students as the main body. From the form of students' activities, various forms of activities are adopted, such as dictation, writing, operation demonstration, exhibition and communication, group cooperation, testing and so on. Among them, dictation and display communication are the main ones. There are 26 collective answers in this class, 1 1 individual answers, 3 individual blackboard newspapers, 4 individual blackboard newspapers, 3 group cooperation and communication, 1 overall test.
The effectiveness of student activities in achieving goals. Teacher Zhang Jing's four learning goals in this class can be roughly divided into two categories. The first three goals focus on knowledge and skills, while the latter focuses on ability and emotion. Process and method goals run through two goals: 3 and 4. The goal of knowledge and skills is mainly achieved through the three student activities independently explored in the second part. Judging from the design of student activities, these activities are conducive to the realization of the goal. Judging from the actual effect of the activities, these activities have promoted the realization of the goals.
Overall evaluation: This is a successful lesson. The teaching objectives are clear, the key points are prominent, and the difficulties are effectively broken through. In the teaching process of this class, students' thinking has been highly active, the classroom atmosphere is active, and student activities have effectively mobilized students' thinking. Invisible? The process and method of students' original thinking are clearly presented through the blackboard presentation of students, so that students can better understand, remember and use knowledge, thus promoting the achievement of goals, which is in line with Vygotsky's? The nearest development zone? Theory, highlighting the beauty of effective activities.
The outstanding advantages of this lesson are:
First, the starting point of mathematical activities is students' original knowledge and experience.
Psychologist Ausubel once said: If I want to reduce all educational psychology to only one principle, then I will say in one sentence that the only important factor affecting learning is what learners already know. In order to find out this, we should teach accordingly. ?
The first part of this lesson:? Review navigation? The design follows the reality of students' existing mathematical knowledge, allows students to explore the judgment of parallelogram through analogy, and triggers students' mathematical thinking. Obviously, the judgment of parallelogram should also be studied from the angle of edge. The starting point of teacher Zhang's mathematical activity design is to transform the learning analogy of new knowledge into existing old knowledge based on students' original knowledge and experience, so that students can experience the process of knowledge generation and easily build new knowledge on the basis of original knowledge and experience in mathematical activities.
Second, the scenes of mathematics activities are familiar and interesting to students.
? Interest is the best teacher? It can stimulate students' interest in learning and arouse their initiative to participate in learning.
The second part of this lesson:? Independent investigation? The design creatively uses the teaching materials, which turns the closed scene of the wooden strips in the teaching materials into a challenging and open problem? After learning parallelogram, Xiao Ming went home and made one with a thin stick. The next day, Xiao Ming showed his classmates a parallelogram made by himself. Xiaohui asked: What makes you sure that this quadrilateral is a parallelogram? Everyone is confused ...? , designed for students to operate with familiar hard paper strips.
According to the students' reality, Mr. Zhang introduces learning themes from the problem situations they are familiar with or interested in, and stimulates students' desire to explore. This purposeful activity of exploring mathematical problems allows students to develop freely in a broader space, allowing new knowledge to emerge naturally, which not only attracts students with the charm of new knowledge, but also stimulates students' interest in learning, brings students into the problem situation and infects the art of teaching.
Thirdly, the mathematization of mathematical activities is the visualization of students' original thinking.
Friedenthal, a Dutch mathematics educator, pointed out that if mathematics is interpreted as an activity, it must be taught and learned through mathematization. He believes that the essential feature of mathematical activities is mathematization, that is, the process in which learners start from their own mathematical reality, draw relevant mathematical conclusions through their own thinking, and establish mathematical models.
The second part of this lesson: in independent inquiry? Three activities? Thinking visualization's platform hands-on demonstration and blackboard performance are designed for seven people, which effectively attaches importance to the development process of students' thinking, enables students to experience the thinking process, understand, feel, discover and solve mathematical problems, continuously improves their thinking level, and shows the effective beauty of mathematical activities.
The highlight of this class is. A set of parallelograms with parallel and equal opposite sides? Hands-on demonstration on the platform, comprehensive analysis of students' classification, explanation of edge positions in parallel and non-parallel ways, and comprehensive consideration of problems. This kind of classroom is a real life-oriented classroom, which allows the whole class to experience the visualization process of original thinking. In the mathematization of mathematical activities, they not only improve their thinking level, improve the level of problem analysis and problem solving methods, but also extract and remember relevant information. How to judge the angle of parallelogram from the side? According to the mathematical conclusion, a mathematical model is established in mathematical activities.
Suggestion:
1. In inquiry teaching, teachers should not only strengthen the goals of knowledge, skills and abilities, but also give full play to various evaluation functions, so as to better realize the goals of emotional attitude and values and stimulate students' interest and enthusiasm in inquiry activities.
2. In inquiry teaching, we should not only sum up knowledge, but also pay attention to the summary of mathematical ideas and analytical methods.
3. In the inquiry-based teaching, there are as many as 26 collective answers in this class, and some students will make up for it, which can be changed into the forms of students with learning difficulties answering questions, individuals rushing to answer questions, and answering each other at the same table.
Harvest:
1. In inquiry teaching, the creative use of teaching materials by using material resources is the key to design problems. The problem should point to the teaching goal, divide the levels, and pay attention to the unity of quality and quantity.
2. Effective use of curriculum resources close to students' life is an important prerequisite in inquiry teaching. Therefore, when selecting materials, we should pay attention to the interesting, typical, targeted, ideological and educational nature of life.
3. In inquiry teaching, students' active participation in classroom teaching activities is an important symbol. The material is close to life, the difficulty of problem design is appropriate, the teacher's guidance is in place in time, and the teaching content is suitable for inquiry, which is conducive to improving students' participation in class.
4. In the usual teaching, we should pay attention to the guidance of students' learning methods and the mathematicization of activities. Invisible? Through student demonstration, blackboard writing demonstration and other forms, the process and method of students' original thinking are clearly presented, which enables students to thinking visualization, thus promoting the achievement of goals and improving students' thinking level.
20 17 Observation Report on Junior High School Mathematics Distance Training 2 Optimizing the effectiveness of classroom teaching is the key and fundamental requirement for deepening curriculum reform at present, and it also conforms to the regulations of the Ministry of Education to reduce students' excessive burden. Effective teaching is reflected in the progress and development of students, which promotes students' effective learning under the condition of changing their learning methods and pays attention to the cultivation of students' emotion, morality and personality, which requires teachers' own professional quality and level to be continuously improved and developed. Through the teaching process, this paper cultivates students' emotion and consciousness, and talks about my personal experience.
First, what is the effectiveness of classroom teaching?
The effectiveness of classroom teaching means that teachers can make students reach the preset learning results and learn to learn through teaching activities, and at the same time make teachers' own quality develop positively. The concrete manifestations are as follows: in cognition, urge students never to understand and never attend meetings; In terms of ability, gradually improve students' thinking ability, innovation ability and problem-solving ability; Emotionally, it urges students to never like mathematics, to like mathematics and then to love mathematics. Through effective classroom learning, students can learn knowledge and skills that are beneficial to their own development and acquire values and learning methods that will affect their future development. For teachers, through effective classroom teaching, they can feel their own teaching charm and value, enjoy many wonderful moments in the classroom, and let teachers pursue endless mathematics teaching.
Second, explore the effectiveness of mathematics classroom teaching methods
1. Pay attention to the process of solving math problems and let students move.
The process of solving mathematical problems is actually a process of applying knowledge, a process of training and consolidating the skills and methods that students have learned in class, and a process of experiencing students' emotions. Teaching practice has proved that paying attention to the problem-solving process requires teachers to carefully design problems in teaching, so that problems are hierarchical and students have them. Jump down and pick grapes? The feeling of; Moreover, we should make the questions challenging, leave space for students to do and think about mathematics, and let students have the opportunity to speak freely in class.
Case: teaching? Real number? In the first class, the teacher assigned a thinking question: Is the sum of two irrational numbers necessarily irrational? The teacher gave the students two minutes to think independently before speaking. Most students cite two opposite figures to illustrate the problem, such as-? Use-? And so on, some students also cited -2, 2- and other opposite numbers to illustrate. When the teacher was ready to finish the problem and continue teaching, he saw another student raise his hand. At that moment, the teacher hesitated. Should students speak again? Time is precious! But in the end, students are allowed to speak: What if a =1.4141414? b= 1.323232323？ , a and b are irrational numbers, but a+b = 2.7737.00000000005 However, it is an infinite cycle decimal and a rational number. The student gave a successful counterexample and skillfully explained the problem from another angle.
In the above cases, it is precisely because the teacher gave the students the space to think and the opportunity to speak that the students had all kinds of solutions to the problems, and each of them was clever, and finally classroom teaching was effectively generated.
2. Pay attention to the formation process of knowledge, and improve students' initiative to participate in mathematics activities.
Bruno, a famous American psychologist, said: Learners should not be passive recipients of information, but active participants in the process of knowledge acquisition. Exploration is the lifeline of mathematics. Without exploration, there will be no development of mathematics. ? Therefore, in teaching, we must return the time to the students to the maximum extent. Let students experience, feel and appreciate mathematics in the process of learning. Only in this way, students can personally experience the joy of their own success, stimulate a strong thirst for knowledge and creativity, and improve their initiative to participate in mathematical activities.
Case: In the fourth quarter of Chapter 24 of People's Education Edition, the author asked students to make a cone model one day in advance, and said in class: In this class, we will learn the lateral area and total area of the cone. How to find the lateral area of a cone? Can you use the knowledge you have learned to explore the lateral area of a cone with your own cone model as a tool? Can lateral area formula of cone be expressed in letters? After about 2 minutes, the author saw that most students found a way to cut the side of the cone into a fan, and some students were at a loss. Ask again:? The side of the cone is a surface. How to find the area of a surface? Transform a surface into a plane by using the transformation idea. ? Most students answered in unison. A small number of students laughed happily and cut the side of the cone. After about 1 minute, a student shouted happily. Teacher, I know: In fact, the lateral area of a cone is the sectional fan-shaped area. S- cone lateral area =S sector area =? ,? Is there any other expression? Teacher, mine is an S-cone. Transverse area =rl? ,? I think it's an S-cone lateral area =? rl？ ,? I think it's an S-cone lateral area =? l？ The students scrambled to answer. After about five minutes, I asked the representatives of various answers to stand up and explain. ? Cut along a generatrix of the cone, the side view of the cone is fan-shaped. According to the calculation formula of sector area, it is concluded that lateral area = of S cone can explain what N and R stand for respectively. N refers to the degree of the central angle of the sector, and r is the base radius of the cone. My method is the same as his, but I get the transverse area of the S cone =lr, where L is the arc length of the sector and R is the radius of the sector. My method is the same, but lateral area of S cone =? Rl, where r is the radius of the bottom surface of the cone and l is the generatrix of the cone. I got the S-cone lateral area =? R, where r is the radius of the bottom surface of the cone and h is the height of the cone. Everyone has a point. Which one should we choose as the formula? Why? The fourth, to find the lateral area of a cone, we should know the correlation of the cone. The third, although we also know the correlation of the cone, is more complicated than the third, so I think we should adopt the third as the formula. ? The author smiled and applauded him. Then, applause thundered in the classroom.
In a word, effective classroom teaching, as an idea, is a kind of value pursuit and teaching practice mode. We need to constantly explore and study in teaching practice, and gradually improve and improve our teaching philosophy and teaching level.
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