2020 Senior High School Mathematics Teaching Plan 1
plane vector
Teacher: Hello, everyone!
I am very happy to attend this lecture. It is also a rare opportunity for me to study and exercise. Thank you for your guidance in your busy schedule. I hope that the judges and teachers will give me valuable opinions on my teaching content.
The content of the class I am talking about is; The textbook used in this course is the first volume of the full-time textbook for ordinary senior high schools (trial revision-compulsory) published by People's Education Publishing House, and the teaching content is pages 96 to 98 in the first section of Chapter 5. Our school is a first-class key middle school in Zhejiang Province, with good students. I also fully considered this point when designing teaching.
Next, I will report my teaching ideas for this class from four aspects: teaching material analysis, the determination of teaching objectives, the choice of teaching methods and the design of teaching process.
Teaching material analysis.
(1) status and function
Vector is one of the important basic concepts in modern mathematics, which has a profound geometric background and is a powerful tool to solve geometric problems. After the introduction of the concept of vector, congruence parallelism (translation), similarity, verticality, Pythagorean theorem and so on can be transformed into vector addition (subtraction), number multiplication vector and product operation (operation rate), thus transforming the basic properties of graphics into vector operation system. Vectors are alternating algebra, geometry and pythagorean.
The basic concept of plane vector is that students learn vector further on the basis of understanding vector concepts such as force and displacement in physics, and lay the foundation of knowledge and methods for learning vector knowledge system.
(2) Adjust the teaching structure
The teaching of this part of the textbook is a class hour. Firstly, the concept of vector is abstracted from the distance and direction of the ship, and the difference between vector and quantity is emphasized. Then the basic concepts such as geometric representation of vector, length of vector, zero vector, unit vector, parallel vector, * * line vector and equivector are introduced. In order to make students better grasp these basic concepts and deepen their cognitive process and inquiry process, in teaching, examples and exercises are mainly analyzed by students themselves according to the concepts and completed independently.
(3) Key points, difficulties and key points
Because this lesson is the first lesson in this chapter, it is the basis for students to learn this chapter. In order to learn the knowledge behind this chapter, we must first master the concept of vector and the essence of vector: size and direction. So the concept of vector, the equality of vector and the geometric representation of vector are the key points of this lesson. This class is designed for the students in the first half of the senior high school, although the students at this time already have certain learning methods and habits. However, according to the previous teaching experience, most students' understanding of vectors is relatively simple, only considering its size and ignoring its direction, which requires students' understanding ability, so I think the concept of vectors is also the difficulty of this lesson. The key to solve this difficulty is to use the isotropic line segments in complex geometric figures to let students identify and deepen their understanding of vectors.
Second, the determination of teaching objectives
According to the characteristics of the textbook, the teaching requirements of the new syllabus and the reasonable needs of students' physical and mental development, I have determined the following teaching objectives from three aspects:
(1) Basic knowledge goal: Understand the concepts of vector, zero vector, unit vector, * * line vector, parallel vector and equal vector, express vectors with letters, read and write vectors in known graphs, and judge whether vectors are parallel, * * line and equal according to graphs.
(2) Ability training goal: to train students to observe, summarize, analogy, association and other general methods to discover laws, and to train students' ability to observe, analyze and solve problems.
(3) Emotional goal: Let students feel the fun of learning in democratic and harmonious activities.
Third, the choice of teaching methods.
First, teaching methods
In this class, I adopted the "heuristic inquiry" teaching method. According to the characteristics of teaching materials and the actual situation of students, I emphasized the following two points in my teaching:
(1) According to the characteristics of teaching materials, analogical thinking is established as the main line of teaching.
From the content of the textbook, the concept of plane vector is similar to the concepts of directed line segment and vector in physics. Therefore, analogy is the main line of thinking in teaching, so that students can fully understand the relationship between mathematics knowledge and other disciplines and the process of its occurrence and development.
(2) According to the students' characteristics, establish the learning method of independent inquiry.
Usually, students are boring and uninterested in concept classes, so we should consider students' emotional needs and find some subjects that students are interested in to stimulate students' interest in learning. In addition, students have the desire to express themselves and hope to be recognized by teachers and other students. We should praise them more, and we must inspire their enthusiasm for learning. Considering that our students have a good foundation and active thinking, they also have a certain understanding of autonomous inquiry learning methods. Therefore, in teaching, by creating problem situations, I inspire and guide students to use scientific thinking methods for independent inquiry, and put students' independent thinking, independent inquiry, exchange and discussion throughout the whole process of classroom teaching, highlighting students' main role.
Second, teaching methods
In this class, in addition to the conventional teaching methods, I also use multimedia projectors and computers to assist teaching. Multimedia projection provides a platform for teachers and students to communicate and discuss. The drawing process of computer demonstration is helpful to penetrate the idea of combining numbers with shapes, and it is easier to understand concepts and break through difficulties.
Fourthly, the design of teaching process.
First, the stage of knowledge introduction-put forward learning topics and define learning objectives.
(1) Creating Situation-Introducing Concept
Mathematics study should be combined with students' life. Starting from students' life experience and existing knowledge background, let them discover mathematics, explore mathematics, understand and master mathematics in their lives.
This paper introduces the specific examples of vectors in life: the route of ships in the sea, and the moves of "horse" and "elephant" in China chess. These are in line with the characteristics of high school students' active thinking and rich imagination, and are conducive to stimulating students' interest in learning.
(2) observation and induction-forming concepts
The concept of directed line segment is derived from examples, and the three elements of directed line segment are: starting point, direction and length. Once the starting point, direction and length of a directed line segment are clearly known, its end point can be determined. Then carry out purposeful design to guide students to summarize the new knowledge points of this lesson: the concept of vector and its geometric representation.
(3) Discussion and research-deepening the concept
After getting the concept, summarize and deepen it, and then ask the students the following three questions:
① What are the elements of a vector?
② Can the vector sizes be compared?
③ What is the difference between vector and quantity?
At the same time, it is pointed out that this is the theme we will study and study in this class.
The second stage of knowledge exploration-exploring the concepts of parallel vector and equal vector of plane vector.
(1) Summary and reflection-raising awareness
Non-zero vectors with the same or opposite directions are called parallel vectors, that is, * * line vectors, which stipulate that 0 is parallel to any vector. Vectors with the same length and direction are called equal vectors, and the zero vector is equal to the zero vector. Parallel vectors are not necessarily equal, but equal vectors must be parallel vectors, that is, vector parallelism is a necessary condition for vector equality.
(2) Instant training-consolidating new knowledge
In order to deepen students' understanding of knowledge, so as to achieve the effect of consolidation and improvement, I specially designed a set of real-time training questions to consolidate new knowledge through students' observation, discussion and research, as well as the guidance of teachers.
[Exercise 1] Judge whether the following propositions are correct. If not, please briefly explain the reasons.
2020 Senior High School Mathematics Teaching Plan II
Law of Sines
Hello, everyone. Today I'm going to tell you that the theme of my class is sine theorem. Below I will introduce my teaching design for this course from the following aspects.
Teaching material analysis.
This section of knowledge is the first section of the first chapter of compulsory five, solving triangles, which is closely related to the basic relationship between the sides and angles of triangles and the judgment of triangle congruence learned in junior high school. In daily life and industrial production, we often encounter the problem of solving triangles, and the relationship between triangles and trigonometric functions is often tested in the college entrance examination. So the knowledge of sine theorem and cosine theorem is very important.
According to the analysis of the contents of the above textbooks, taking into account the psychological characteristics of students' existing cognitive structure and their original knowledge level, the following teaching objectives are formulated:
Cognitive goal: in the created problem situation, guide students to discover the content of sine theorem, deduce sine theorem and simply use sine theorem and triangle inner angle to understand two kinds of problems of oblique triangle.
Ability goal: guide students to summarize sine theorem from special to general through observation, deduction and comparison, cultivate students' innovative consciousness and observation and logical thinking ability, and realize that geometric problems can be transformed into algebraic problems by using vectors as tools and combining numbers and shapes.
Emotional goal: create an equal teaching atmosphere for all students, mobilize students' initiative and enthusiasm through exchanges, cooperation and evaluation between students, teachers and students, give students a successful experience and stimulate students' interest in learning.
Teaching emphasis: the content of sine theorem, the proof of sine theorem and its basic application.
Teaching difficulties: the exploration and proof of sine theorem, judging the number of solutions when the diagonal solutions of two sides and one of them are known.
The second teaching method
According to the characteristics of the content and arrangement of teaching materials, in order to highlight the key points and break through the difficulties more effectively, based on the development of academic students, following the students' cognitive rules, following the guiding ideology of taking teachers as the leading factor, taking students as the main body and taking training as the main line, the inquiry-based classroom teaching mode is adopted, that is, in the teaching process, under the inspiration and guidance of teachers, students' autonomy and cooperation are the premise, and "the discovery of sine theorem" is the basic exploration content. The means to break through the key points: seize the excitement of students' emotions, stimulate their interest, encourage students to make bold guesses, actively explore, and encourage them to be brave and enterprising in time. In addition, starting from the students' original cognitive level and required knowledge characteristics, teachers should give appropriate hints and guidance under the students' main body. The way to break through the difficulties: grasp the students' ability line, link the methods and skills to make it easier for students to prove the sine theorem, and break through the difficulties through examples and exercises.
Three learning methods:
Instruct students to master the thinking method of "observation-conjecture-proof-application", adopt various attempts of individuals, groups and groups to solve problems and doubts, and apply what they have learned to the exploration of the nature of arbitrary triangles. Let students study, observe, analogize, think, explore, summarize and try in the problem scenario, which embodies the students' dominant position, enhances their mathematical thinking ability from special to general, forms a scientific attitude of seeking truth from facts and enhances their perseverance in learning.
Fourth, the teaching process
First: it takes about 2 minutes to create the scene.
Second, it takes about 25 minutes to explore and form a concept.
Third, it takes about 13 minutes to apply concepts and expand reflection.
(A) the creation of situations, cloth suspected exciting interest
"Interested teachers", a good beginning of a class means half the battle. This lesson is introduced by a practical problem, "A triangular model of a worker's master is broken, leaving only the part shown on the right, ∠ A = 47, ∠ B = 53, and the length of AB is1m.. If you want to repair this part, stimulate students' enthusiasm for helping others and interest in learning, so as to enter today's learning topic.
(2) Explore special circumstances and put forward conjectures.
1. Stimulate students' thinking, and start with a familiar special case (right triangle) to find the sine theorem.
2. Does this conclusion apply to any triangle? Instruct students to divide into groups, and use tools such as scale, protractor and calculator to verify the approximate triangle.
3. Ask students to summarize the experimental results and make a guess:
In a triangle, the angle satisfies the relationship with the opposite side.
This builds confidence for the next proof, and makes students' understanding of the conclusion gradually rise from perceptual to rational.
(C) logical reasoning, proving conjecture
1. It is emphasized that the transformation of conjecture into theorem requires strict theoretical proof.
2. Encourage students to prove the height by converting it into a familiar right triangle.
3. Encourage students to think about what knowledge can link length with trigonometric function, and then think about the level of vector analysis, and take the product of quantity as a tool to prove theorem, which embodies the mathematical idea of combining numbers with shapes.
4. Think about whether there are other ways to prove the sine theorem, arrange after-class exercises, prompt, make the circumscribed circle of the triangle to construct a right triangle, or prove it by coordinate method.
(D) Summary, simple application
1. Let students describe the sine theorem in words, guide students to find that the theorem has the beauty of symmetry and harmony, and enhance the enjoyment of mathematical beauty.
2. The content of sine theorem, discuss what kind of problems about triangles can be solved.
3. Use sine theorem to solve the side length problem of triangular parts introduced in this lesson. Participating in solving practical problems can stimulate students' knowledge and apply it to practical value.
(5) Illustrate and consolidate the theorem.
1. Example 1. In △ABC, it is known that A = 32, B = 8 1.8, and A = 42.9 cm. Solve triangles.
Example 1 is very simple, and the result is a solution. If the sides between two angles of a triangle and the opposite sides of two angles and one of them are known, the triangle can be solved by sine theorem.
2. Example 2. In △ABC, it is known that A = 20 cm, B = 28 cm and A = 40, and the triangle is solved.
It is difficult for students to make it clear that there are two possibilities for finding angles by sine theorem. Students are required to be familiar with all kinds of triangle solutions when they know the diagonal of two sides and one of them. Then give the time to the students.
(6) Classroom exercises to improve and consolidate.
1.△ABC, the following conditions are known to solve triangles.
( 1)A=45，C=30，c= 10cm
(2)A=60, B=45 and c = 20 cm.
2. In △ ABC, the following conditions are known to solve triangles.
( 1)a=20cm，b= 1 1cm，B=30
(2) C = 54cm, b = 39cm, C= 1 15.
Students perform on the blackboard, teachers patrol, find problems and answer them in time.
(7) Summing up reflections and raising awareness.
Through the above research process, what knowledge and methods have the students mainly learned? What do you think of this?
1. sine theorem is proved by vector, which embodies the mathematical idea of combining numbers with shapes.
2. It expresses the relationship between the sides of the triangle and the sine value of the diagonal.
3. Theorem proof starts from right angle, acute angle and obtuse angle respectively, using the idea of classified discussion.
Starting from practical problems, the sine theorem is finally derived through thinking methods such as conjecture, experiment and induction. The outstanding feature of our research is from special to general. In the whole process of exploration, we not only obtained conclusions, but also mastered the general methods of studying problems. Emphasis is placed on research-based learning methods, students' dominant position, and students' enthusiasm is mobilized to make mathematics teaching become the teaching of mathematics activities. )
(eight) task extension, independent inquiry.
If two sides of a triangle and their included angles are known, what about a third side? If sine theorem is not applicable, then naturally transition to the next section, cosine theorem. Assign homework and preview the next section.
2020 Senior High School Mathematics Teaching Plan III
Curves and equations
I. teaching material analysis
1. Textbook background
As the beginning of curve learning, the section "Curve and Equation" is very thoughtful and takes about three class hours. The first class introduces the concepts of curves and equations. In the second class, I will talk about the solution of curve equation; The third lesson focuses on the test of equations.
This class is the second class.
The main contents are: analytic geometry and coordinate method; The method (literal translation method), steps and examples of solving curve equations are discussed.
2. The position and function of this course
Connecting the past and the future, combining numbers and shapes.
Curves and equations are not only natural extensions of straight lines and equations, but also necessary for learning conic curves, the theoretical basis for learning plane curves, and the key chapters connecting the preceding with the following.
"Curve" and "equation" are two forms of the locus of a point. "Curve" is the geometric form of trajectory, and "equation" is the algebraic form of trajectory. Solving curve equation is the forerunner of studying curve with equation, and it is the first problem of two kinds of problems to be solved in analytic geometry. It embodies the essence of coordinate method-algebraic treatment of geometric problems and is a model of combination of numbers and shapes.
Inheritance and query
Finding the curve equation is essentially finding the equivalent relationship between the abscissa and the ordinate of any point (x, y) on the curve, but it is often impossible to predict the type of curve trajectory in advance. The characteristics of motion changes can be vividly displayed through multimedia demonstrations, but how to get the curve equation? By creating situations, stimulating students' interest and giving full play to their dominant position, the learning process is very exploratory.
At the same time, the content of this lesson provides a method preparation for the later trajectory exploration, and will continue to improve the solution method of trajectory equation in the future.
Mathematical modeling and demonstration function
Curve equation is the core of analytic geometry. The process of solving curve equation is similar to the process of mathematical modeling, which runs through the whole process of analytic geometry. Through the examples and variants of this lesson, we can summarize the laws and master the methods, which will provide a demonstration for the trajectory exploration of conic curves in the future.
The Cultural Value of Mathematics
The invention of analytic geometry is the first milestone of variable mathematics and one of the two symbols of the rise of modern mathematics. It is a relatively complete and typical historical example of major mathematical innovation. The deeds and spirit of the founders of analytic geometry, especially Descartes, the pursuit of scientific truth and methods, and the questioning scientific spirit are all inspiring and inspiring textbooks. According to the actual situation of students, when conditions permit, students can be guided to collect relevant information after class and write research reports through analysis and collation.
3. Analysis of learning situation
The students in our class have a good mathematical foundation and active thinking. After learning "Equation of Curve and Curve of Equation", students have a preliminary understanding of this concept, which must be both pure and complete, and have a preliminary understanding of the scientificity, accuracy and superiority of studying geometric problems with algebraic methods, and have a natural desire to learn whether and how specific (plane) figures correspond to equations.
Second, the target analysis
1. Teaching objectives
Knowledge and skill objectives
Understand the function and significance of coordinate method.
Master the general methods and steps to solve the curve equation, and choose the appropriate coordinate system to solve the curve equation according to the given conditions.
Program objective
Through the active participation of students, we can experience the process of obtaining curve equations, experience the advantages of coordinate method in dealing with geometric problems, and infiltrate the mathematical thought of combining numbers with shapes.
Through independent exploration and cooperative communication, students have gone through the cognitive model of "special-general-special" and perfected the cognitive structure.
Through in-depth, cultivate students' divergent thinking ability and deepen their understanding of the essence of curve equation.
Emotion, attitude and values goals
Through cooperative learning, students, teachers and students communicate with each other, feel the joy of exploration and success, understand the rationality and rigor of mathematics, and gradually develop the scientific spirit of questioning.
Show the spirit of humanistic mathematics, reflect the cultural value of mathematics and its important role in social progress and the development of human civilization.
2. Teaching emphases and difficulties
Key points: methods and steps to solve the curve equation.
Difficulties: Algebraization of Geometric Conditions
Basis: Finding curve equation is one of the two kinds of problems studied, which is both important and difficult, and it is the source of material for solving college entrance examination questions. It mainly includes two kinds of equations for finding curves: one is the undetermined coefficient method when the curve shape is known; The second is to explore the trajectory equation of moving point. The focus of this lesson is to explore the curve equation of moving point.
Curves and equations are knowledge that runs through the plane and are the core of analytic geometry. Solving curve equation is the premise of algebraic learning of geometric problems, and the process of solving curve equation is similar to mathematical modeling, which is a difficult point that must be broken through in class.
Third, teaching methods and teaching materials processing
1. Teaching method: inquiry and discovery teaching method.
Follow the modern educational principle of taking students as the main body, teachers as the leading factor and development as the main theme, and always set questions in the "nearest development area" of students' knowledge. Through students' active exploration, active participation, exchanges and cooperation, with the guidance and cooperation of teachers, students can "jump" to pick fruits and realize the construction and development of knowledge in analyzing and solving problems.
2. Guidance on learning methods
Students learn the law: discuss and explore with each other.
Because students often encounter some difficulties in the process of trying to solve problems, such as the connection between old and new knowledge, the choice of strategies, the use of thinking methods, etc., which need the guidance of teachers. As the organizer, guide and participant of student activities, teachers should help students review old knowledge related to problem solving, give students time to think and opportunities to express themselves, and * * * reflect on the process of problem solving, thus inspiring students in the interaction between teachers and students.
In this way, the established teaching methods can help students better acquire a complete cognitive structure and make students' thinking and ability develop harmoniously.
3. Design concept:
Solving the curve equation is to transform the geometric representation of points on the curve into algebraic representation. In this transformation process, students make their learning process a re-creation under the guidance of teachers through active participation and bold exploration, which is also the essential requirement of constructivism theory; Follow students' cognitive rules, respect students' individual differences, base on teaching materials, recreate examples, and embody the teaching principles of integrating theory with practice, step by step, and teaching students in accordance with their aptitude, so that students at different levels can develop to varying degrees; By stimulating interest, emphasizing independent exploration and cooperative communication, students can gradually move from learning to learning, from passivity to initiative, from classroom to society, laying a good foundation for students' lifelong learning and lifelong development, which is also the basic concept pursued by the current new curriculum.
Fourth, the teaching process (teaching design)
According to the characteristics of the externalization of the geometric features of the teaching content of this course, grasp the geometric conditions of the moving points that constitute the trajectory, and use the means of coordinates and the thinking method of equivalent transformation and combination of numbers and shapes to break through the difficulties and highlight the key points. The teaching design concept of this course is:
Creating situations-from understanding perceptual tracks (graphics) to solving real life examples, arousing students' desire for knowledge, grasping students' eager cognitive psychology, naturally introducing the significance of coordinate method and solving curve equations.
Example Inquiry-Example 1 reflects the connection between the past and the future of knowledge. Through the presentation of example 1, students can explore and obtain the solution of the problem independently with the help of existing knowledge and experience, and under the guidance of teachers, students can feel the significance and steps of solving the curve equation; Example 2 and variant solve the difficulty of building a department, and the openness of building a department is both a challenge and a creation for students; The two examples are from the shallow to the deep, step by step, which embodies the teaching of students in accordance with their aptitude. At this point, students can initially understand the general methods and steps to solve the curve equation.
Inductive Steps-Students experience the process of finding the curve equation personally, so that students can induce (in their own language) and express the steps of solving it, embody the cognitive law of "special-general" and gradually realize the teaching goal.
Variant exercise-through the variant of an example, let students solve and answer the meaning of variant, deepen their understanding of cognitive structure, initially understand the rationality and rigor of mathematics, and gradually develop the habit of questioning and reflecting.
Feedback exercise-using students' cognitive level to solve practical problems in scenario creation, on the one hand, it can examine students' consciousness and ability to solve practical problems by using their mathematical knowledge; On the other hand, it is the natural adaptation and release of students' thinking, which is a "general-special" process and the teaching goal is fully achieved.
Three articles related to high school mathematics teaching plans in 2020;
★ Teaching plan of basic inequality in senior high school mathematics in 2020
★ 2020 High School Mathematics Equal Ratio Series Teaching Plan Design Complete Book
★ Five Work Plans for Senior High School Mathematics Teachers in 2020
★ Mathematics Teaching Plan for Senior High School in 2020
★ 2020 Senior High School Mathematics Power Function Teaching Plan
★ There are 5 teaching work plans of senior high school mathematics teaching and research group in 2020.
★ Five Work Plans of Senior High School Mathematics Teaching and Research Group in 2020
★ Random sampling teaching plan for senior high school mathematics in 2020
★ Teaching Work Plan for Senior High School Mathematics Teachers in 2020
★ Five Summaries of Senior High School Mathematics Teachers' Work Experience in 2020