A small case of junior high school mathematics teaching
First, teaching material analysis.
Seventh-grade compulsory education curriculum standard experimental textbook Volume II Chapter 7 Section 5.
Second, the teaching objectives.
1, knowledge goal: to understand the internal angles and formulas of polygons.
2. Mathematical thinking: By transforming polygons into triangles, the application of transformation thinking in geometry can be realized, and at the same time, students can experience the method of understanding problems from special to general.
3. Problem solving: By exploring the internal angles and formulas of polygons, trying to find solutions to problems from different angles can effectively solve problems.
4. Emotional attitude goal: through guessing and reasoning activities, I feel that mathematics activities are full of exploration and certainty of mathematical conclusions, and improve students' learning enthusiasm.
Third, teaching is heavy and difficult.
Focus: Explore the sum of the inner angles of polygons.
Difficulties: How to convert polygons into triangles when exploring the sum of internal angles of polygons?
Fourth, teaching methods: guided discovery method and discussion method.
Verb (abbreviation of verb) teaching process;
(1) Create situations, set questions and stimulate thinking.
Teacher: We all know that the sum of the internal angles of a triangle is 180o, so do you know the sum of the internal angles of a quadrilateral?
Activity 1: Explore the sum of internal angles of quadrilateral.
On the basis of independent exploration, students discuss in groups and summarize the methods to solve problems.
Method 1: Measure the degrees of four angles with a protractor, and then add up the four angles, and find that the sum of the internal angles is 360o O o.
Method 2: put two triangular cardboard together to form a quadrilateral, and find the sum of the internal angles of the two triangles as 360o O o.
Next, on the basis of the second method, the teacher guides the students to connect the diagonals of the quadrilateral with the method of auxiliary lines to transform a quadrilateral into two triangles.
Teacher: Do you know the sum of the internal angles of a Pentagon? How about a hexagon? How about a decagon? How did you get it?
Activity 2: Explore the sum of internal angles of pentagon, hexagon and decagon.
Students think about each question independently before group discussion.
Concern: (1) Can students draw a correct conclusion by quadrilateral analogy?
(2) Whether students can adopt different methods.
Students discuss and communicate in groups (sum of internal angles of pentagon)
Methods 1: Divide the Pentagon into three triangles, and the sum of the three 180o is 540o.
Method 2: Starting from a point inside the Pentagon, divide the Pentagon into five triangles, and then subtract a fillet 360o from the sum of five 180o. The result is 540o o o.
Method 3: Divide the Pentagon into four triangles from any point on one side of the Pentagon, and then subtract a right angle of 180o from the sum of four 180o to get 540o.
Method 4: Divide the Pentagon into triangles and quadrilaterals, and then add 360o to 180o to get 540o.
Teacher: How clever you are! I have applied what I have learned.
After the communication, students use the geometric sketchpad to demonstrate and verify the method.
After getting the sum of the internal angles of the pentagon, the students seriously discussed the sum of the internal angles of the hexagon and the decagon. By analogy with the discussion method of quadrilateral and pentagon, it is finally concluded that the sum of internal angles of hexagon is 720o and the sum of internal angles of decagon is1440 o.
(2) Extend thinking and cultivate innovation.
Teacher: From the previous discussion, can you know the sum of the inner angles of polygons?
Activity 3: Explore the internal angles and formulas of arbitrary polygons.
Thinking: (1) What is the relationship between the sum of internal angles of polygons and the sum of internal angles of triangles?
(2) What is the relationship between the number of sides of a polygon and the sum of internal angles?
(3) What is the relationship between the number of diagonal triangles drawn from a vertex of a polygon and the number of sides of the polygon?
Students discuss with thinking questions and exchange the results after discussion.
It is found that the sum of 1: quadrilateral internal angles is the sum of two 180o, pentagonal internal angles is the sum of three 180o, hexagonal internal angles is the sum of four 180o, and decagon internal angles is eight 180o.
Discovery 2: The number of sides of a polygon increases by 1, and the sum of internal angles increases by180o. ..
It is found that there is a (n- 2) relationship between the number of diagonal triangles drawn from the vertices of N-polygons and the number of sides N. ..
It is concluded that the formula of the sum of the interior angles of a polygon is (n-2)? 180。
(3) Practical application and complementary advantages.
1, oral answers: (1) and ()
(2) nonagon's internal angle and ()
(3) The sum of the internal angles of the decagon ()
2. Answer first: (1) The sum of the internal angles of a polygon is equal to 1260o. How many polygons does it have?
(2) If the sum of the internal angles of a polygon is 1440o and the internal angles are equal, then the degree of each internal angle is ().
3. Discuss the answer: The sum of the internal angles of a polygon is 540o more than the sum of the internal angles of a quadrilateral, and all the internal angles of this polygon are equal. How many degrees is each internal angle of this polygon?
(4) General storage.
Students' self-summary:
1, polygon internal angle and formula.
2. Use transformation ideas to solve mathematical problems.
3. Solve problems by combining numbers with shapes.
(5) Homework: Page 93, 1, 2, 3.
Six, teaching reflection:
1, the change of teaching. The role of teachers in the classroom has changed from imparting knowledge to organizing, guiding, cooperating and studying students' learning together. After guiding students to draw, measure and find the conclusion, they can show it intuitively with the geometric sketchpad, so as to stimulate students to consciously explore mathematical problems and experience the fun of discovery.
2. Changes in learning. The role of students has changed from learning to learning. The students in this class don't stop at the level of learning textbooks.
Surface, but from the perspective of researchers into its territory.
3. Changes in classroom atmosphere. The whole class? Smooth, open and cooperative. Hide? A tour guide? As a basic feature, teachers should try their best to let students discuss, think and draw their own conclusions, and the teaching process is relatively smooth.
The whole class and classmates, classmates and teachers? Dialogue? 、? Discuss? Starting from mutual assistance and cooperation and aiming at solving problems, students can choose their own direction of success and judge the value of discovery in a relatively relaxed environment.
Small case of junior high school mathematics teaching II
Learning objectives:
? Knowledge and skills:
? 1. It can be measured and sampled according to actual needs;
? 2. Collate, describe and analyze the collected data according to the extracted samples;
? 3. Make a correct evaluation of the data results and put forward reasonable suggestions.
? Mathematical thinking:
? Through the process of data collection, arrangement, description and analysis, students' statistical ability is cultivated, and some simple practical problems are consciously solved by using statistical ideas.
? Solve the problem:
Be able to accurately describe and analyze statistical data and draw statistical conclusions.
? Emotional attitude:
1. Experience the general process of data processing, know the authenticity of data, and cultivate students' scientific attitude of seeking truth from facts;
2. Through the analysis of statistical results, enhance students' awareness of improving their physique;
3. Develop a learning attitude of active exploration and knowledge, stimulate interest in mathematics, and experience the importance of group cooperation in mathematics activities.
Corresponding curriculum standards: (the following marks, such as 3. 1. 1, refer to article 1 in Part III of the curriculum standards)
Three. Probability and Statistics
In teaching, we should pay attention to the relationship between what we have learned and daily life, nature, society, science and technology, and let students understand the important role of statistics and probability in decision-making. Attention should be paid to let students participate in the whole process of data processing and make reasonable judgments according to the statistical results; Attention should be paid to making students realize the significance of probability in specific situations.
3. 1. 1 is engaged in the activities of collecting, sorting, describing and analyzing data, and can handle more complicated statistical data with a calculator.
3. 1.3 will use a fan-shaped statistical chart to represent data.
3. 1.4 Understand and calculate the weighted average under specific circumstances; According to specific problems, appropriate statistics can be selected to represent the degree of data concentration.
3. 1.5 Discuss how to express the dispersion degree of a group of data, calculate the range and variance, and use them to express the dispersion degree of data.
3. 1.7 Through an example, I realized the idea of estimating the population by using samples, and the mean and variance of the population can be estimated by using the mean and variance of samples.
3. 1.8 Make reasonable judgments and predictions based on statistical results, experience the role of statistics in decision-making, be able to clearly express their views and communicate.
3. 1.9 You can find relevant information according to the problem and obtain data information; Express your views on some data in daily life.
3. 1. 10 Understanding the application of statistics in social life and science can solve some simple practical problems.
Fourth, subject learning.
In this part, students will explore some challenging research topics and cultivate their awareness and ability of applying mathematical knowledge to solve problems; At the same time, we will further deepen our understanding of relevant mathematical knowledge and understand the relationship between mathematical knowledge.
4.3. Get some methods and experience to study problems, develop thinking ability and deepen the understanding of relevant mathematical knowledge.
4.4. Enhance self-confidence in applied mathematics by gaining successful experience and overcoming difficulties.
Process (teaching or learning process)
Description: In this part, clearly describe your teaching steps and the corresponding sequence of activities. Please pay attention to the pertinence of teaching activities and framework issues, and explain the specific resources and environment required for each activity. When using your own document, please indicate the file name and set the corresponding link.
This unit takes about one week (4 class hours).
Pre-class preparation: This project study will be based on study groups, so the teacher will scientifically group the students according to their personality characteristics and academic performance, and elect the group leader (since the new curriculum started, I have been exploring the form of group cooperative learning, so there is a relatively fixed study group in my class). In order to make students use computers better in their study, students should learn WORD, PPT, EXCEL and web page making in combination with information technology classes before class, especially in this learning activity, students should use EXCEL to make statistical calculations and draw statistical charts, which are unfamiliar to students, and they should pay more attention to their study.
Step 1: Students browse? Teacher support station? , clear learning tasks, teachers focus on inspiring students to carry out this activity around the unit framework, and through reading? Student physical health monitoring report? Let the students know the significance of this activity and stimulate their enthusiasm. Discuss the research projects of this group with students as a unit, divide the work into groups, design questionnaires, determine the survey methods, and realize the necessity of sampling survey. Teachers actively encourage each group to extend their activities on the basis of textbook requirements, giving students more independent and creative learning space. [Implementation time: 5. 15 Lesson 2 (1 lesson)]
Step 2: Each study group conducts a data survey, which is completed after class. However, teachers should track the students' investigation process in time, give guidance in time when problems are found, and ensure the correctness and scientificity of the survey data.
Step 3: Each study group uses Word or Excel to sort out and count the collected data. Physical health standards for middle school students? Calculate the total score, describe the data with Word or Excel according to the sorted data, draw a statistical chart, calculate the average, mode, median, range and variance of the data, and draw a conclusion through analysis. When drawing statistical charts and calculations, let each group draw and calculate by computer operation or manual animation. On the one hand, we can consolidate the methods of data analysis and data description we have learned, on the other hand, we can experience the benefits of extensive use of computers. This lesson focuses on solving the content problem in the framework problem. [Implementation time: 5. 16 Lesson 2 (1 lesson)]
Step 4: Each group refers to the student website evaluation scale and the statement evaluation scale, and discusses their own gains in this activity, the enlightenment of this survey, their views on the current situation of middle school students' physical fitness, and the reasonable suggestions for the school to strengthen the physical fitness of middle school students in China.
Refer to the demonstration design card or website structure diagram provided by the teacher to make a student demonstration or student website for the group report. According to the completion of students' tasks, students can be given some extra-curricular time to continue to complete or improve their works. [Implementation time: 5. 16 Lesson 2 (1 lesson)]
Step 5: Each group sends representatives to communicate the process and results of the activities through student demonstrations or web pages. Teachers and students discuss and evaluate the results of the group together. Each group fills in the teacher-student mutual evaluation form after the reports of other groups, and the teacher makes a final evaluation of each group according to the activities of each group and the results of teacher-student mutual evaluation (the evaluation statistical results are completed after class and returned to each group). [Implementation time: 5. 17 Lesson 3 (1 lesson)]
Postscript of teaching:
Personally, I think: Intel Future Education Training is the most successful training implemented in China's education system, which has given us great gains in terms of training form and content. In the process of new curriculum reform, I have been looking for changes in classroom teaching. Intel Future Education? I have pointed out the direction from ideas to teaching forms and students' learning forms. I also changed my classroom teaching mode without hesitation.
Many teachers I have contacted think: Intel Future Education? It is an advanced educational theory and can't be applied to our actual teaching. I think this is a wrong view. There is no denying that at present, we can't fully use it? Intel Future Education? In the form of organizing our teaching, but we can do it selectively, for example, I am in such a place? Project learning? 、? Math activities? Waiting for the application? Intel Future Education? Form the selected content once or twice a semester. Although we can't use it all? Intel Future Education? To organize teaching, but? Intel Future Education? The teaching idea is that the educational idea of our new curriculum is unified. For this reason, I made two major attempts: first, I basically realized that multimedia assisted my own teaching in every class; Secondly, I adopted the way of group cooperative learning in class. In order to improve the efficiency of making or preparing multimedia scaffolding after class, I integrated a set of? Interactive teaching system? (demonstration address), through nearly two years of teaching implementation, the effect is very obvious.
Among the teachers I contacted, many teachers in rural schools think? Intel Future Education? It is difficult to implement in rural schools. Undeniably, at present, our rural schools are worse than the cities in terms of hardware equipment and the quality of teachers and students, but we can create conditions as long as we are determined. Take my school as an example. If the computer is not enough, I will use it as a study group. The computer can't surf the Internet. I will prepare more resources for students to read at the teacher support station first. When a group has to use the Internet, I will let them go to my home to look it up online. In fact, even if these conditions are not met, we can still use them. Intel Future Education? Advanced educational concepts guide our teaching, and I often try to carry out inquiry teaching activities in traditional classrooms without multimedia, so that students can carry out research-based learning, use paper resources instead of network resources, use group activity record cards to pay attention to students' learning process, and use innovative teaching materials to show students' learning experience, which can also cultivate students' various abilities and even stimulate students' advanced thinking.
Junior high school mathematics teaching small case three
First, demand analysis.
Mathematics is relatively heavy and difficult, and the steps in primary school, junior high school and senior high school are regular. Many students begin to encounter difficulties in junior high school, their grades are not high or declining, and even they can't be reversed for a long time, and their interest in learning is lost. However, large-scale, large-class and thousand-school public schools can not meet the individualized, diversified and high-quality educational needs, which leads to the confusion of these students and the distress of their parents.
Junior high school is a key period to improve the ability of understanding mathematical thinking, self-study and mastering correct learning methods, which largely determines whether the study in senior high school can be smooth.
Therefore, focusing on junior high school grades, appropriately extending to the two stages of senior primary school and junior high school, and carrying out personalized, group and diversified high-quality mathematics education can not only significantly improve mathematics grades, but also enable students to master correct learning methods and enhance their comprehensive quality, comprehensive ability and self-study ability, which has broad development space.
Second, the orientation of education.
On the basis of public school education, we will use weekends and winter and summer vacations to carry out quality education to make up for vacancies and needs. Innovative individualized teaching, group counseling, special lectures, outdoor classes and other diverse and effective educational forms and methods will enable students to finish their studies in public schools more smoothly, get development and growth suitable for their special needs, absorb rich mathematical knowledge and literacy, understand a broad mathematical vision, comprehensively improve their comprehensive mathematical ability, and give overall consideration to exam-oriented education and quality education, thus laying a good mathematical foundation for becoming talents from all walks of life who are useful to the country, society and family in the future.
High-end junior high school mathematics education should be: a guide for students to learn mathematics; Open one math window after another for students, so that he or she can breathe more and fresher math air; Let the students who are good at mathematics be cultivated into talents, and let the students who encounter difficulties in mathematics make up for their weaknesses and become stronger; Let every student like both the teacher and the math he teaches. In addition, we should become an educational consultant for parents to monitor or manage their children's mathematics learning, a mathematics teacher that parents understand, trust and admire, effectively promote the connection between family education and school education, and make family education, school education and personalized education form a joint force.
Third, teacher development.
The high level of mathematics and the high level of teaching mathematics are organically combined, and they are high-level mathematics teachers.
Only teachers with high sense of responsibility, high level and high ability can support high-end education. Therefore, achieving high-level development and further study is the primary problem for teachers. With the spirit of grinding a sword for ten years and the mind of all rivers running into the sea, we should strive to develop and further study to become an expert in junior high school mathematics education and a practitioner who organically combines knowledge teaching with interest stimulation, method teaching, ability training and potential development. Can lecture, lecture, and write? Talk and write? Reach considerable height and depth.
Teachers should be professional and honest, think for students all their lives and be responsible for their parents.
Teachers should thoroughly understand the curriculum standards and teaching materials, integrate the curriculum contents of all grades, and devote themselves to the study of educational psychology, learning methods, the application of teaching methods and the rules of the senior high school entrance examination. Master a lot of good examples, exercises and cases, master a lot of mathematical skills and tricks, and know all kinds of mathematical problems, contents, forms, training and examination questions like the back of your hand. Enough understanding: the development of advanced mathematics knowledge in primary school and the wide application of mathematics in other disciplines and production and life practice.
It can quickly discover the problems and difficulties of students in learning mathematics, teach students in accordance with their aptitude, improve the situation and effectively solve these problems and difficulties. It enables students to experience the effective process and method of learning mathematics frequently and profoundly. At the same time, stimulate interest in learning. The teaching method is flexible, instant, unique and effective, which can help students learn to read, think, understand and remember mathematics, avoid mechanical sea tactics, make students understand, be happy, master the tricks, and significantly improve their grades and self-learning ability.
Can have a pleasant and effective conversation with students and communicate with parents happily and effectively. I have enough experience, knowledge and analysis for all kinds of students and parents. Ability to prevent possible twists and turns and misunderstandings in the process of mathematics counseling, resolve measures and improvise.
Strong ability to analyze educational needs, develop educational projects and open up educational markets.
He has extensive experience, broad vision and strong comprehensive ability, which provides strong peripheral support for high-end junior high school mathematics education. For example, he has considerable experience, knowledge and ability in physics, electrical technology, information technology education application, education comparison between ancient and modern China and foreign countries, training and research, management and evaluation, tourism and photography.
Four. Educational goal
1 class goal: students feel that their learning effect is better than usual, and they have a new and good experience in the process of doing problems and listening to lectures. They feel that they have been acupunctured and are willing to continue their studies. Parents think they can look forward to it.
1 term goal: students realize the importance of listening and understanding, and the situation of listening in school is obviously better than before. Recognizing the importance of reading textbook examples carefully, I increased the reading volume of textbook examples. In the process of solving problems, we began to pay attention to every step of thinking and understanding, and bad learning methods and habits changed accordingly, and the previous related knowledge began to be reconsidered, sorted out and consolidated. The interest in learning mathematics is getting stronger and stronger, and the academic performance is rising. Parents trust their teachers.
1 year goal: students gradually find their own learning methods and basically form a good habit of learning mathematics. The effect of listening to lectures and reading textbook examples at school has been further improved. Strong interest in learning, the initiative of learning mathematics and the efficiency of completing school math homework are obviously improved. Every step of the problem-solving process is thought and understood. The writing of problem-solving steps is clearer, smoother and more standardized than before, and some mathematical skills and tricks have been accumulated, such as examining problems, drawing pictures, setting unknowns, setting equations, calculating numerical values, algebraic operations, simplifying consciousness and ability in time, and organizing consciousness and ability in time. The communication between students and parents about math learning is more pleasant and smooth than before. Parents feel that they have found the right teacher and are grateful to the teacher.
Two-year goal: the effect of attending classes in school is good, and I realize the importance of systematic, in-depth and extensive mathematics reading, and I begin to read basic concepts, properties, theorems, formulas (rules) and mathematical thinking methods, and my ability to read textbooks, teaching references and examples is obviously enhanced. The previous mathematical foundation has become more and more solid, and the old and new knowledge have been continuously linked and constructed, which has improved the mathematical literacy, ability and ability of independent exploration, reflection, questioning, discussion and cooperation. I realized the importance of returning to textbooks and basic concepts, mastered many mathematical skills and tricks, experienced the interest and joy brought by mathematical thinking, cultivated mathematical self-confidence and a certain degree of mathematical concentration, and had strong independent thinking ability and self-study ability. The abilities of examining and analyzing questions, modeling, making auxiliary lines, migrating and integrating, using mathematical knowledge flexibly anytime and anywhere, thinking deeply, understanding and exploring basic concepts have been obviously improved. The ability of reading, writing, drawing, speaking and listening in mathematics has been significantly improved. It has had some good influence on the study of other subjects.
Three-year goal: good application of graphic language, symbolic language and natural language in mathematics, further improving mathematical thinking and understanding ability, experiencing the charm of mathematical thinking methods, and having a strong curiosity and thirst for knowledge about mathematics. Have a broad understanding of various mathematical forms, contents and problems, and have a new understanding of the value of mathematics. The ability of writing and discussing mathematics is strong, the ability of guessing, imagining, reflecting and questioning mathematics is further improved, and the willpower to solve mathematical comprehensive problems and overcome complex calculation and operation difficulties is obviously enhanced. Listening to lectures, reading books and doing problems are all highly efficient, effective and well developed in mathematics talent and ability. It has a good influence on the study of other subjects and has a positive effect on the quality of thinking, language ability and living habits.
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