As a teaching worker, it is often necessary to write a lecture, which is helpful to improve teachers' language expression ability. So how should the course draft be written properly? The following is my carefully arranged lecture notes (selected 5 articles) of junior high school mathematics Beijing Normal University Edition, hoping to help everyone.
Junior high school mathematics lecture notes 1 1, teaching material analysis
1, the position and function of teaching materials
One-dimensional quadratic equation is one of the main contents of middle school mathematics and occupies an important position in junior middle school mathematics. Through the study of quadratic equation of one variable, we can consolidate our knowledge about real numbers, quadratic equation of one variable, factorization, quadratic roots and so on. At the same time, it is also the basis for learning other high-dimensional equations, unary quadratic inequalities and quadratic functions that can be transformed into unary quadratic equations. In addition, learning the quadratic equation of one variable is also of great significance to other disciplines. This lesson is the concept of quadratic equation of one variable. Let students establish quadratic equation of one variable through abundant examples and summarize the concept of quadratic equation of one variable through observation.
2. Teaching objectives
According to the requirements of the syllabus, the contents of this textbook, students' curiosity, thirst for knowledge and existing knowledge and experience, the three-dimensional objectives of this course are mainly reflected in:
Knowledge and ability goal: Students are required to list a quadratic equation with one variable according to specific problems, understand the model idea of the equation, and cultivate students' inductive and analytical ability.
Process and Method Objectives: Guide students to analyze the quantitative relationship in practical problems, review the concept of linear equation with one variable, organize students to discuss, and let students abstract the concept of quadratic equation with one variable.
Emotion, attitude and values: through the analysis and thinking process of mathematical modeling, stimulate students' interest in learning mathematics, experience the happiness of doing mathematics, and cultivate their consciousness of using mathematics.
3. Teaching emphases and difficulties
To solve practical problems in life by using quadratic equation of one variable, we must first understand the concept of quadratic equation of one variable, and the teaching of the concept should start with a large number of examples. Therefore, the focus of this lesson is to list the concepts of quadratic equation of one variable and quadratic equation of one variable from practical problems. In view of students' lack of social life experience and weak information processing ability, it is difficult to convert practical problems into mathematical equations in this course.
Second, teaching methods and learning methods.
Because the students have learned linear equations and related concepts, I mainly use heuristic and analogy teaching in this class. Try to embody the model of "problem scenario-mathematical model-concept induction" in teaching. However, due to the limited ability of students to transform practical problems into mathematical equations, multimedia-assisted teaching is adopted in this course to guide students to abstract mathematical problems from specific problem scenes and establish mathematical equations through intuitive observation and demonstration, thus breaking through difficulties. At the same time, students experience mathematical modeling in real life situations, and through the learning process of independent exploration and cooperative communication, they have a positive emotional experience, thus creatively solving problems and effectively exerting their thinking ability.
Third, the teaching process design
Create scenarios and introduce new courses.
Because of the origin and life of mathematics, it is easy for students to accept and perceive situations created according to their actual life background. The examples in the textbook are demonstrated and analyzed by microcomputer, which fully shows the vividness and flexibility in microcomputer demonstration, changes the static state of graphics into dynamic state, and enhances the intuition; At the same time, it helps students extract mathematical problems from practical problems, and initially cultivates students' spatial concept and abstract ability. In situation analysis, students naturally think of solving problems with equations, and the listed equations have not been learned before, thus stimulating students' desire for knowledge and smoothly entering the new curriculum.
Junior high school mathematics lecture notes 2 I. teaching material analysis
(1) position and function
Based on students' understanding of straight lines, rays, line segments and angles, this lesson further studies the position and quantity relationship of four angles formed by the intersection of two straight lines on the plane, which lays the foundation for studying geometry in the future and provides a demonstration for proving geometric problems. This class has a very important position and role in further cultivating students' ability to read pictures and stimulating students' interest in learning.
(B) Teaching objectives
According to the students' existing knowledge base and the requirements of the syllabus, the teaching objectives of this course are determined as follows:
1, knowledge and skills
(1) Understanding the concepts of antipodal angle and adjacent complementary angle, we can distinguish antipodal angle and adjacent complementary angle from the diagram.
(2) Master the "property of equal vertex angles".
(3) Understand the reasoning process of equal vertex angles.
2. Process and method
Experiencing mathematical activities such as questioning, guessing and induction can cultivate students' observation ability, transformation ability, reasoning ability and standardized expression ability of mathematical language.
3. Emotional attitudes and values
Through group discussion, cultivate the spirit of cooperation, let students experience the methods and fun of solving problems in the process of exploring problems, and enhance their interest in learning; Feel the existence of mathematics in life in solving problems, and experience mathematics is full of exploration and creation.
(3) Key points and difficulties
According to the students' existing knowledge base and the requirements of the syllabus, the key points and difficulties of this lesson are determined as follows:
Emphasis: the concepts of adjacent complementary angle and antipodal angle and the properties of equal antipodal angle.
Difficulties: write a standard reasoning process and explore the equality of vertex angles.
Second, teaching methods.
In teaching, in order to highlight key points and break through difficulties, I used visual teaching AIDS and multimedia. It increases the intuition of teaching, allows students to observe, compare, induce and summarize, and allows students to experience the cognitive process from concrete to abstract and from perceptual to rational.
Third, study the guidance of law.
Let students learn to observe, compare, analyze and summarize, and learn to abstract general rules from concrete examples. This can improve their generalization ability and language ability, and form good study habits of hands-on, brains and words.
Lecture notes on junior high school mathematics 3. First, talk about the role of teaching materials;
This section introduces the solution method of fractional order equation from the concept of fractional order equation learned before. Related to this part of the content is to use equations to solve application problems later. Learn this lesson well and lay the foundation for the next class.
Second, talk about teaching objectives
1, let students understand the meaning of fractional equation.
2. Master the general solution of the fractional equation that can be transformed into a linear equation with one variable.
3. Understand the reasons for adding roots when solving fractional equations, and master the root test method for solving fractional equations.
4. On the basis of mastering the general solution of fractional order equation and the root test method of fractional order equation, students can further master the solution of fractional order equation which can be transformed into a linear equation with one variable, and master the solution skills of fractional order equation skillfully.
5. By studying the solution of fractional equation, students can understand that the basic idea of solving fractional equation is to transform fractional equation into integral equation and unknown problem into known problem, thus infiltrating the transformation idea of mathematics.
Third, stress the difficulties.
This section focuses on the transformation in solving fractional equations, which can be transformed into one-dimensional linear equations. The basic idea of solving the fractional equation is to remove the denominator of the fractional equation as much as possible and transform the fractional equation into an integral equation, which is the key to solving the fractional equation, so the most important thing in the transformation process is to find the simplest common denominator on both sides of the equation. Difficulty analysis: Students who solve fractional equations are prone to make mistakes, and the key is that they can't understand the causes of root growth in the process of equation deformation, which is difficult for seventh-grade students to understand. We can also let students know that both sides of the equation are multiplied by algebraic expression, which may be zero, which does not conform to the principle of equation transformation. Therefore, the roots must be tested when solving fractional equations.
Fourth, talk about teaching methods:
This section introduces the solution method of fractional order equation from the concept of fractional order equation learned before. Coupled with the characteristics of mathematics, this class adopts heuristic and guided teaching methods. Pay special attention to "intensive speaking and more practice" to truly reflect the students' dominant position. In the process of reviewing knowledge points, we use inspiration and guidance, and at the same time correct some questions in students' answers in time. When doing exercises, we not only let as many students go to the blackboard as possible, but also find out the problems of students in time. Typically, the whole class comments, and individual small problems are solved separately.
Fifth, talk about the teaching process.
(1) review
(1) Review what is fractional equation?
Design intention: Mainly to let students distinguish the difference between integral equation and fractional equation, and let students actively participate in the following links.
(2) Solving fractional equation
① Students recall the basic ideas and general steps of solving fractional equations, and illustrate with examples:
Solution: The original equation can be simplified as:
Multiply the two sides of the equation and remove the denominator, so.
(x+3)—8x=x2—9—x(x+3)
In order to solve this problem, you must
Test: Substitute x=3 into the simplest common denominator (X+3) (X-3) = 0.
∴x=3 is the root of the original equation.
∴ The original equation has no solution.
Design intent; In this link, the teacher encourages students to experience it personally, and stimulates students' enthusiasm for learning. On the basis of consolidating the solution of fractional equation, develop students' inductive ability and publicize their personality. Let teachers really become the promoters of students' learning.
② Discuss communication examples and find two groups of students to try to solve problems on the blackboard.
Design intention: Through students' cooperative research on examples, each student can have a deeper understanding of the solution of fractional equation. In this link, students are encouraged to communicate boldly, express their views and learn to listen. Cultivate students' sense of cooperation. At this time, teachers should make appropriate comments on students' problems and give them encouragement and guidance.
(3) I also designed several small questions to make students think about the solution of fractional equation.
Design intention: let students understand how to find the value of letters in the formula when they know the root of fractional equation.
Teacher's summary:
When the equation is deformed, it may sometimes produce roots that are not suitable for the original equation. This root is called the augmented root of the original equation.
(2) Show your talents.
Design intention: consolidate
Classroom summary of intransitive verbs
1. What did we learn in this class?
Step 2: Ask questions
Junior high school mathematics lecture notes 4 judges:
good morning
The topic of my speech today is that the textbook chosen for this class is the eighth grade textbook of the compulsory education curriculum standard of Beijing Normal University.
I. teaching material analysis
1, the position and function of teaching materials
This textbook is the content of XXXX junior high school mathematics grade textbook and one of the important contents of junior high school mathematics. On the one hand, this is the further deepening and expansion of XXXX on the basis of learning XXXX; On the other hand, it is for learning-XXX, etc.
Knowledge is the basis and tool for further study of XXXX. Therefore, this lesson plays a connecting role in the textbook.
2. Analysis of learning situation
Students have learned XXXX before, and have a preliminary understanding of XXXX, which lays the foundation for successfully completing the teaching tasks of this lesson. However, students may have some difficulties in understanding XXXX (due to its high abstraction), so a simple and clear analysis should be made in teaching.
3. Emphasis and difficulty in teaching
According to the position and function of the above teaching materials, as well as the analysis of the learning situation, combined with the requirements of the new curriculum standard for this class, I will determine the focus of this class as follows:
The difficulty is determined as follows:
Second, the analysis of teaching objectives
According to the teaching concept of the new curriculum standard, in order to cultivate students' mathematical literacy and lifelong learning ability, I have established the following three-dimensional goals:
1. Knowledge and skill objectives:
2. Process and method objectives:
3. Emotional attitude and value goal:
Third, the analysis of teaching methods
In this class, I will adopt heuristic and discussion-based teaching methods, and advocate students to actively participate in teaching practice in the form of independent thinking and mutual communication, and find, analyze and solve problems under the guidance of teachers. In guiding the analysis, I will give students enough time and space to think, associate and explore, and complete the real knowledge self-construction.
In addition, in the teaching process, multimedia-assisted teaching is used to present teaching materials intuitively, so as to better stimulate students' interest in learning, increase teaching capacity and improve teaching efficiency.
Fourthly, the analysis of teaching process.
In order to teach in an orderly and effective way, I mainly arranged the following teaching links in this class:
(1) Review and you will know, and you will learn new things from the old review.
Design intention: Constructivism advocates that teaching should start from students' existing knowledge system, and XXXX is the cognitive basis for this course to study XXXX in depth, so design is conducive to guiding students to enter the learning situation smoothly.
(2) Create situations and ask questions
Design intention: Create situations in the form of a series of questions, which will trigger students' cognitive conflicts, make students doubt old knowledge, and thus stimulate students' interest in learning and desire for knowledge.
By creating situations, students have a strong desire for knowledge and a strong motivation for learning. At this time, I take the students to the next link-
(3) Find problems and explore new knowledge.
Design intention: Modern mathematics teaching theory points out that teaching must be obtained on the basis of students' independent exploration and experience induction, and the process of thinking must be displayed in teaching. Here, through observation and analysis, independent thinking and group communication, students are guided to summarize.
(4) Analysis and thinking to deepen understanding.
Design intention: the theory of mathematics teaching points out the connotation and extension (conditions, conclusions, scope of application, etc. ) mathematical concepts (theorems, etc.). ) it should be clear. By expounding several important aspects of the definition, students' cognitive structure can be optimized, students' knowledge system can be improved, and students' mathematical understanding can break through the difficulties of thinking again.
Through the previous study, students have basically mastered the content of this lesson. At this time, they are eager to find a place to show themselves and experience success, so I lead students into XXXX.
(5) Strengthen training and consolidate double basics.
Design intention: several examples and exercises are from easy to deep, from easy to difficult, each with its own emphasis. Among them, example 1 ... example 2 ... embodies the teaching idea of making different students develop differently in mathematics proposed by the new curriculum standard. The overall design intention of this link is to feedback teaching and internalize knowledge.
(6) Summarize and deepen.
Summary and induction should not only be a simple list of knowledge, but also an effective means to optimize the cognitive structure and improve the knowledge system, so as to give full play to students' dominant position and let students talk about the gains of this class.
(7) Contrast feedback of in-class testing.
(8) Arrange homework to improve sublimation.
Based on the stability and development of homework, I designed mandatory questions and multiple-choice questions. Mandatory questions are feedback to the content of this lesson, and multiple-choice questions are an extension of the knowledge of this lesson. The overall design intention is to feedback teaching, consolidate and improve.
These are my views on this course. Please forgive my shortcomings!
Lecture notes on junior high school mathematics 5 I. teaching material analysis
The position and function of teaching materials;
Rectangular learning is based on students' experience in learning quadrangles and parallelograms. This is one of the key contents of this chapter. It is not only an extension of parallelogram knowledge, but also provides research methods and learning strategies for learning other special parallelograms, which lays a foundation for learning other related knowledge in the future and plays an important role in connecting the preceding with the following.
Second, the teaching objectives
According to the requirements of the syllabus and the characteristics of the content of this class, using the new curriculum concept, combined with the actual situation of students, I set the teaching goal of this class as:
Knowledge and skills:
1. Understand the related concepts of rectangle, and explore and master the related properties of rectangle according to the definition.
2. Understand the application of rectangle in life and solve simple practical problems according to the nature of rectangle.
Mathematical thinking:
1. After exploring the concept and properties of rectangle, cultivate students' reasonable reasoning consciousness and master geometric thinking methods. Develop students' thinking ability and language expression ability through observation, thinking, communication, inquiry and other mathematical activities.
2. According to the nature of rectangle, carry out simple calculation and application, cultivate students' logical reasoning ability, cultivate the habit of transforming geometric intuition into thinking logic, and further understand the thinking method of combining analogy with number and shape.
Solve the problem:
Through students' observation, experiment, analysis and communication, the concept of rectangle is introduced to feel the order of mathematical thinking process and the diversity of problem-solving strategies. By collecting mathematical information in life, we can use what we have learned to solve problems in life, further understand the relationship between mathematics and life, and enhance our awareness of applied mathematics.
Emotional attitude: in the communication and cooperation with others, let students feel that mathematics activities are full of exploration fun, improve students' enthusiasm and enthusiasm for learning, and cultivate students' awareness of cooperative communication, good quality of bold speculation, willingness to explore and ability to find and explore problems. Cultivate students' habit of active exploration and independent thinking.
Teaching emphasis: the nature and application of rectangle.
Teaching difficulties: understanding the particularity of rectangle and exploring its special properties.
Fourth, teaching methods and means:
According to the content of this course, students' characteristics and teaching requirements, the method of teacher guidance-independent inquiry-cooperation and exchange is adopted. The dominant position of teachers and students is fully reflected.
Teaching means: multimedia (PowerPoint, geometric sketchpad) and physical projection are used to assist teaching.
Teaching process of verbs (abbreviation of verb)
The design links of this lesson include: creating situations to introduce new lessons, getting definitions by hands, guiding exploration to get the essence, solving problems by using new knowledge, inducing and consolidating new knowledge, and learning by layers.
In the design of each link of this lesson, we strive to highlight the following aspects:
1, mathematical problems in life
In the design, I follow the curriculum standard that mathematics comes from life and serves life. Pay attention to the creation of problem situations and make math problems come alive. In the 1 activity, I showed my classmates a photo at the campus gate, which made them feel that mathematical information was being transmitted everywhere in their lives. By observing, collecting and analyzing familiar figures, the application of mathematics in life is realized, which leads to activity 2; In the application of nature, calculating the size of TV screen is also a problem closely related to life. Some students don't know the length of the diagonal yet. Through this topic, students can understand the common sense of life, further understand the role of mathematics in life, and cultivate their enthusiasm for learning mathematics through solving problems.
2. Create an independent inquiry situation and give full play to students' initiative.
In order to explore the definition of rectangle, students took out their own parallelogram learning tools and worked in groups. Through students' observation, experiment, analysis and communication, the concept of rectangle is introduced, and the evolution process of parallelogram is transferred to the concept and properties of rectangle, making it clear that rectangle is a special parallelogram. And let students feel the beauty of mathematics and the connection between mathematics and life by looking for examples in their lives. Exploring the nature of rectangle is to let students compare the nature of parallelogram, and through observation, measurement, analysis and proof, (1) let the nature of rectangle "surface" in the activity. In the activity, let students explore by themselves, discover new knowledge in the exploration, sum up new knowledge in the exchange, and give students the initiative to learn. In the evaluation, I praise active groups and individuals, enhance students' creative confidence and experience the happiness of success. The attribute 1 is the proof of the completion of student group communication. Nature 2 requires students to carefully write the process of understanding, verification and proof. On this basis, invite one student to write on the blackboard, and the rest of the students will observe whether the blackboard writing is correct. Cultivate the habit of transforming geometric intuition into logical thinking, cultivate students' divergent thinking ability and develop good problem-solving habits. Let students fully experience the whole process of knowledge formation in the activities. At the same time, I have accumulated good learning experience.
3. Train students' logical thinking and cultivate their rigorous problem-solving habits.
In this lesson, I designed three themes for the application of new knowledge. Exercise 1 is a direct application of the definition of nature. While consolidating new knowledge, guide students to further discover the basic figures contained in rectangles, let students feel the close relationship between rectangles and isosceles triangles and right triangles, let students experience the connection and extension of knowledge, cultivate the habit of transforming geometric intuition into thinking logic, and cultivate students' divergent thinking ability. The design of examples is to let students understand the application of nature, standardize the steps and formats of solving problems, and let students feel the rigor of mathematical thinking. Exercise 2 is a problem in life. Let students experience mathematics in life, combine learning with application, and cultivate their enthusiasm and interest in learning mathematics.
4. Pay attention to reflect that everyone learns valuable mathematics in teaching activities.
First of all, according to the intelligence, ability and foundation of different students, students are arranged into inquiry groups. Pay attention to the help within the group in the inquiry, and use mutual help to promote the improvement of students at different levels. The principle of grouping is: excellent math performance, strong organizational ability, strong hands-on ability, medium performance and poor foundation. Secondly, the design of homework reflects hierarchy. I divide my homework into two types: compulsory and elective. The questions that must be asked are more basic, which can find and make up for the omissions and deficiencies in classroom learning. Multiple choice questions are only available to students with learning ability. In addition, math diary is to help students sum up the gains and shortcomings of this class and cultivate the habit of summing up and reflecting.
5. Make full use of multimedia-assisted teaching.
This course is assisted by multimedia, which enables students to have an intuitive and perceptual understanding and cultivates their ability of observation, expression and induction. So as to successfully complete the teaching objectives.
The above are some of my practices and experiences in designing this course. If you have any questions, please give us more valuable suggestions. Thank you!
;