1. Example of Senior One Mathematics Presentation
Teachers: Hello, everyone! My name is XX, and I come from Hunan University of Science and Technology. I said that the topic of the class is "The Concept of Algorithm", and the content is selected from the first section of the first chapter of the new curriculum "Compulsory 3 of People's Education Edition A". The class hours are arranged in two classes, and the content of this class is the first class hour. Next, I will elaborate my analysis and design of this course from five aspects: teaching material analysis, teaching goal analysis, teaching method analysis, learning situation analysis and teaching process analysis:
I. teaching material analysis
1. The position and function of teaching materials
Modern society is a society with rapid development of information technology. The introduction of algorithms in high school mathematics reflects the needs of the times. It is an indispensable basic knowledge in today's society. Learning algorithm is a necessary step before using computer to solve problems, which can let students know how to use modern technology to solve problems. Because the algorithm can be combined with information technology in concrete implementation. Therefore, the study of algorithm is very beneficial to improve students' logical thinking ability and cultivate their rational spirit and practical ability.
2. Emphasis and difficulty of teaching
Key points: Understand the definition and idea of algorithm, and be able to describe the difficulty of algorithm in natural language: transform natural language into algorithm language.
Second, the analysis of teaching objectives
1. Knowledge objective: to understand the meaning and idea of the algorithm; Able to describe the algorithm for solving specific problems in natural language; Understand the requirements that the correct algorithm should meet.
2. Ability goal: let students feel the general law of people's understanding of things: from concrete to abstract, and then from abstract to concrete, and cultivate students' observation ability, expression ability and logical thinking ability.
3. Emotional goal: Have a basic understanding of the algorithmic language of computers, make clear the requirements of algorithms, realize that computers are a powerful tool for human beings to conquer nature, and further improve their ability to explore and understand the world.
Third, the analysis of teaching methods
Using the teaching method of "problem inquiry" and multimedia as auxiliary means, students can actively find, analyze and solve problems, and cultivate their inquiry ability, argumentation ability and logical thinking ability.
Fourthly, the analysis of learning situation.
This part of the algorithm is very practical and closely related to daily life. Although it is a newly introduced chapter, it is easy to stimulate students' interest in learning. Under the guidance of teachers, students can easily master the content of this lesson through multimedia-assisted teaching.
2. Example of Senior One Mathematics Lecture Notes
I. teaching material analysis
1, the position and function of teaching materials
Parity is the third section of the concept of set and function in the first chapter of version A, and the second section of the basic properties of function.
Parity is an important property of functions. The textbook systematically introduces the parity of functions from the aspects of students' familiarity, from special to general, from concrete to abstract, and focuses on the application of information technology. From the perspective of knowledge structure, it is not only the expansion and deepening of the concept of function, but also the basis for further study of exponential function, logarithmic function, power function and trigonometric function. Therefore, this lesson plays an important role in connecting the preceding with the following.
2. Analysis of learning situation
Judging from the students' cognitive basis, students have already learned axisymmetric graphics and central symmetric graphics in junior high school, and they have a certain number of simple functions. At the same time, I have just learned the monotonicity of functions and accumulated the basic methods and preliminary experience of learning functions.
Judging from the development of students' thinking, the thinking ability of senior one students is changing from image experience type to abstract theory type, and they can think and solve problems with assumptions and reasoning.
3. Teaching objectives
Based on the above analysis of teaching materials and students, as well as the concept of new curriculum standards, I designed such a teaching goal:
Knowledge and skills
1, you can judge the parity of some simple functions.
2. We can use algebraic features and geometry of function parity to solve some simple problems.
Process and method
Experience the formation process of parity concept and improve the ability of observation abstraction and induction from special to general.
Emotions, attitudes and values
Through independent exploration, we can experience the idea of combining numbers with shapes and feel the symmetrical beauty of mathematics.
Judging from the classroom reaction, the expected effect has been basically achieved.
4. Teaching emphases and difficulties
Emphasis: the concept and geometric significance of functional parity.
Several years' teaching practice has proved that although the knowledge point of function parity is not difficult to understand, students with incomplete knowledge points are prone to make the following mistakes. They are often superficial and can only be tested according to the definition of parity, ignoring the problem of function domain. Therefore, when introducing the definition of parity function, we must reveal the implicit conditions of the definition from both positive and negative aspects, and clarify the connotation and extension of the definition. Therefore, I design the concept of function parity as the focus of this lesson. In addition to paying attention to the explanation of concepts, I also specially arranged an example to strengthen the explanation of key issues in this lesson.
Difficulties: Mathematical refining process of parity concept.
Because students' view of problems is still static and one-sided, and their ability of abstract generalization is relatively weak, this has caused certain difficulties in the construction of parity concept. Therefore, I design the mathematical refining process of parity concept as the difficulty of this lesson.
Second, the analysis of teaching methods and learning methods
1, teaching methods
According to the content and arrangement characteristics of the teaching materials in this section, in order to highlight the key points and break through the difficulties more effectively, according to the students' cognitive rules, following the guiding ideology of teacher-oriented, students-oriented and training-oriented, the method of guiding discovery is adopted, supplemented by intuitive demonstration and analogy. In teaching, we should carefully design one inspiring and thinking question after another, create problem scenarios, and induce students to think, so that students are always in a positive state of actively exploring problems, thus cultivating students' thinking ability. Judging from the classroom reaction, the expected effect has been basically achieved.
Step 2 study law
Let students participate in the occurrence, development and formation of knowledge independently in the learning process of observation, induction, inspection and application, so that students can master knowledge.
Third, the teaching process
The specific teaching process is the process of teacher-student interaction, which is divided into six links: setting questions and introducing pictures to stimulate interest; Guide observation and form concepts; Students explore and understand the definition; Application, consolidation and improvement of knowledge; Summarize the feedback; Work in layers and apply what you have learned. Let me explain these six links.
(A) the introduction of questions, watching pictures to stimulate interest.
Because the content of this section is relatively independent and thematic, I adopt a direct introduction method to directly point out what I want to learn, so that students can quickly orient their thinking and achieve the effect of defining goals and highlighting key points from the beginning.
Show a group of pictures with multimedia, so that students can feel the symmetrical beauty in life. Then let the students observe several special function images. By allowing students to observe pictures and introduce them into new lessons, they not only stimulate students' strong interest in learning, but also pave the way for learning new knowledge.
(2) Guiding observation and forming concepts
In this link, * * * designed two inquiry activities.
In exploring 1 and 2 mathematics, there are also many forms of symmetry. In this lesson, we will take the functions sum =︱x︱ and sum as examples to discuss. This kind of inquiry is mainly realized by students' independent inquiry. Because of the bedding of the picture, most students quickly said that the function image is symmetrical about the Y axis (origin). Then students fill in the form and study this feature of the image from the digital point of view. What is the law between independent variables and function values? Guide students to be concrete first, and then express them with mathematical symbols. With the help of courseware demonstration, students can find that the symmetry of two functions reflects the characteristics of function values, and then give a strict proof through analytical expressions, further explaining that this characteristic is true for any one in the definition domain. Finally, the definition of even function (odd function) is given (blackboard writing).
In this process, students transform their perceptual knowledge of graphic laws into quantitative laws, and then rise to rational knowledge, and actually experience a process from special to general.
(C) students explore and understand the definition
Question 3: Are the following function images even?
Design intention: to deepen the understanding of parity concept. Key point: the premise of function parity is that the domain is symmetrical about the origin. (Break through the difficulty of this lesson)
Application, consolidation and improvement of knowledge
I designed four questions in this link.
Example 1 Judge the parity of the following functions
Choose (1) and (3) crossword books of example 1 to demonstrate the steps of solving problems, and ask students to complete the other crossword puzzles below.
The design intention of the example 1 is to summarize the steps of judging parity:
(1) Find the domain first to see if it is symmetrical about the origin;
(2) Then judge whether f(-x)=-f(x) or f(-x)=f(x).
Example 2 Judge the parity of the following functions:
Example 3 Judge the parity of the following functions:
Examples 2 and 3 aim to explore possible types of functional parity.
Example 4( 1) judges the parity of a function.
(2) As shown in the figure, some function images are given. Can you draw the image on the left side of the y axis according to the parity of the function?
Example 4 is designed to strengthen the application of geometric meaning of function parity.
In this process, I focused on the expression of students' reasoning process. By solving these problems, students' knowledge, understanding and application of function parity can be improved to a great height, and the effect of digestion and absorption can be achieved in class.
(5) Summarize the feedback.
In the above-mentioned classroom records, the interactive mode of teaching method and learning method is fully demonstrated, and questions run through the whole process of inquiry, which truly embodies the characteristics of heuristic and problem-based teaching method.
At the end of this class, briefly review the knowledge points and guide students to sum up the experience of solving problems that should be accumulated in this class. Knowledge lies in accumulation, and learning mathematics lies in the accumulation of application experience of knowledge. Therefore, it is a very important strategy to improve the application ability of knowledge and the ability to predict errors.
(6) Work at different levels and apply what you have learned.
Required question: Exercise 1-2 on page 36 of the textbook.
Multiple-choice questions: Exercise 6 in Group 3A on page 39 of the textbook 1.
Thinking: exercise 1, group 3B, question 3 on page 39 of the textbook.
Design intention: Facing all students, paying attention to individual differences, strengthening the pertinence of homework, and grading homework for students can not only enable students to master basic knowledge, but also improve students who have the spare capacity to study, and further realize the different development of different people in mathematics.
3. Example of Senior One Mathematics Lecture Notes
Briefly analyze the structure and content of the textbook 1 the position of this section in the whole book and chapters;
"Vector" appears in section 1 in Chapter 5 of the first volume of senior high school mathematics (Volume II). The content of this section is the basic part of plane analytic geometry in the traditional sense, so it occupies an extremely important position in mathematics.
2 Analysis of mathematical thinking methods:
(1) From the transformation between "number" and "shape" reflected by "vector can be represented by directed line segments", we can see the quantification and materialization of mathematics itself.
(2) From the perspective of structural means, we can see the idea of "combination of numbers and shapes" in the materials provided by the textbooks.
Second, the teaching objectives
According to the analysis of the structure and content of the above textbooks, and taking into account the psychological characteristics of students' existing cognitive structure, the following teaching objectives are formulated:
1 Basic knowledge Objective: To master the concept and representation of "vector" and use them to solve related problems.
2 Ability training goal: gradually cultivate students' ability of observation, analysis, synthesis and analogy, accurately expound their own views and opinions, and focus on cultivating students' cognitive and metacognitive abilities.
3. Innovative quality goal: guide students to dig mathematics content from daily life, and cultivate students' awareness of discovery and integration ability; Vector teaching aims at cultivating students' awareness of "knowledge reorganization" and their ability of "combination of numbers and shapes".
Personality quality goal: cultivate students' innovative quality of being brave in exploration, good at discovery, independent consciousness and constantly surpassing themselves.
Three. Teaching emphases, difficulties and keys
Key point: Introduce the concept of vector.
Difficulties: the perfect combination of "number" and "shape".
Emphasis: This course focuses on cultivating and developing students' cognitive and flexible abilities through the combination of numbers and shapes.
Fourth, the teaching material processing.
Constructivist learning theory holds that construction is the formation of cognitive structure, and its process is generally to string knowledge points into knowledge lines according to logical clues and internal relations, and then form a knowledge surface from several knowledge lines, and finally form a comprehensive knowledge body from the knowledge surface according to its content, nature, function, causality and other relations. Why does this course propose the combination of numbers and shapes? It should be said that this treatment method is based on the embodiment of this theory. Secondly, the course of this lesson tries to solve the following questions: How did knowledge come into being? How to develop? How to abstract practical problems into mathematical problems, and give abstract mathematical symbols and expressions, and how to reflect the simple and harmonious relationship between objective things in life.
Verb (abbreviation of verb) teaching mode
Teaching process is a very complex dynamic whole of teachers' activities and students' activities, and it is a collective cognitive process in which teachers and all students actively participate. Teaching is dominant, learning is the subject, and the two are objects of each other. Advocate students' autonomous learning, inspire and guide students to practice mathematical thinking process, satisfy themselves, seek laws and since the enlightenment principles, and actively develop thinking and ability.
Sixth, learning methods.
1, so that students can focus on the metacognitive process in the cognitive process.
2. Let students combine independent thinking with multi-directional communication.
4. Example of Senior One Mathematics Lecture Notes
I. teaching material analysis: 1. The position and function of teaching materials;
The function of this section in the whole book and chapters is: "1.3. 1 surface area of cylinder, cone and platform" is the content of the first chapter of Space Geometry and the third section of Mathematics II in senior high school mathematics textbooks. Before this, students have learned the structure, three views and intuitive diagrams of space geometry, which has paved the way for the transition to this section. The content of this section occupies an important position in space geometry. And lay a foundation for other disciplines and future study.
2. Education and teaching objectives:
According to the above teaching material analysis, considering the psychological characteristics of students' existing cognitive structure, the following teaching objectives are formulated:
Knowledge and ability:
(1) Understand the surface areas of cylinders, cones and platforms.
(2) The surface areas of cylinders, cones and platforms can be calculated by formulas.
(3) Cultivate students' spatial imagination and thinking ability.
Process and method:
Let students experience the actual solution of geometric surface area, perceive the shape of geometric body, and cultivate their ability to transform mathematical problems.
Emotions, attitudes and values;
Through learning, students can feel the solution process of geometric surface area, stimulate their awareness of exploration and innovation, and enhance their enthusiasm for learning.
3. Key points, difficulties and determination basis:
Based on the new curriculum standards and thorough understanding of teaching materials, I have established the following teaching priorities and difficulties.
Teaching emphasis: derivation of surface area formulas of cylinder, cone and platform
Teaching difficulties: the transformation between the expansion diagram of column, cone and platform and space geometry
Second, the analysis of teaching methods
1. Teaching methods:
How to highlight key points and break through difficulties, so as to achieve teaching objectives. In the teaching process, the following operations are planned: teaching methods. According to the characteristics of this course, we should pay attention to the teaching methods of cooperative inquiry and group discussion.
2. Teaching methods and theoretical basis: adhere to the principle of "taking students as the main body and teachers as the leading factor", and adopt the inquiry discussion method with high participation of students according to the law of students' psychological development. Students themselves give the calculation methods of the surface area of various geometric figures, pay special attention to different problem-solving methods, ask questions to students at different levels, and face the whole, so that students with poor foundation can also have the opportunity to express themselves, cultivate their self-confidence and stimulate their enthusiasm for learning. Effectively develop the potential intelligence of students at all levels, and strive to make students develop on the original basis. Inspire students to return to social practice from book knowledge. Provide students with mathematical knowledge closely related to life and the surrounding world, learn basic knowledge and skills, actively cultivate students' learning interest and motivation in teaching, and make clear the learning purpose. Teachers should fully mobilize students' learning enthusiasm and stimulate students' most powerful motivation in class.
Thirdly, the analysis of learning situation.
We often say: "Modern illiterates are not illiterate people, but people who have not mastered learning methods", so we should pay special attention to the guidance of learning methods in teaching.
(1) Analysis of students' characteristics: Psychological research of middle school students points out that in high school, grasping students' characteristics, actively adopting vivid and diverse teaching methods and learning methods with students' extensive and active participation will certainly stimulate students' interest, effectively cultivate students' ability and promote students' personality development. Physiologically, teenagers are active and easily distracted.
(2) Motivation and interest: Teachers should have a clear learning purpose, fully mobilize students' learning enthusiasm in the classroom, and inspire the most powerful motivation from students.
Finally, let me talk about the teaching process of this course in detail:
Fourthly, the analysis of teaching process.
(1) is introduced by an animated video: rich and vivid to attract students' attention and arouse their enthusiasm for learning.
(2) The introduction leads to a new problem to be discussed in this lesson-the calculation of geometric surface area.
(3) explore the problem. Teach students the initiative completely, let them explore actively, get ideas to solve problems, and exercise their hands-on ability and practical problem-solving ability.
(4) Summing up conclusions and strengthening understanding. The summary of knowledge content can transform the knowledge taught in classroom teaching into the summary of students' quality and mathematical thinking method as soon as possible, which can make students understand the position and application of mathematical thinking method in solving problems more deeply and gradually cultivate students' good personality quality goals.
(5) See the study plan for examples and exercises.
(6) assign homework.
According to the difference of students' quality, hierarchical training can not only help students master basic knowledge, but also improve students who have spare capacity for learning.
(7) summary. Ask the students to sum up the gains of this lesson. The teacher summed it up in time.
5. Example of Senior One Mathematics Lecture Notes
1. Textbook 1. The main content of this lesson is the meaning of linear programming and the concepts of linear constraints, linear objective function, feasible region, feasible solution and solution, and the linear objective function is established according to the constraints. The graphic method of linear programming is applied to solve some practical problems.
2. Function: Linear programming is a branch of mathematical programming with complete theory, mature methods and wide application, which can solve many practical problems such as scientific research, engineering design and economic management. Simple linear programming is a simple application of linear equation on the basis of learning linear equation. Through this part of the study, students can further understand the application of mathematics in solving practical problems, so as to cultivate their interest in learning mathematics, their awareness of applying mathematics and their ability to solve practical problems.
3. Teaching objectives
(1) Knowledge and skills: Understand the meaning of linear programming and the concepts of linear constraints, linear objective functions, feasible regions, feasible solutions and solutions, and be able to establish linear objective functions according to constraints.
Understand and apply the graphic method of linear programming to solve some practical problems.
(2) Process and method: Improve students' ability to put forward, analyze and solve problems with mathematics, develop students' awareness of mathematical application, and try to think and judge some mathematical models contained in the real world.
(3) Emotion, attitude and values: Experience mathematical ideas such as the combination of numbers and shapes and equivalent transformation, gradually understand the application value of mathematics, improve the interest in learning mathematics, and establish self-confidence in learning mathematics well.
4. Key points and difficulties
Key points: Understand and use the graphic method well.
Difficulties: How to find the solution of linear programming by graphic method.
Second, talk about teaching methods.
The teaching process is a process in which teachers and students participate together, which inspires students to learn independently and fully mobilizes their enthusiasm and initiative. Effectively infiltrate mathematical thinking methods and improve students' quality. According to this principle and the teaching objectives to be achieved, and to stimulate students' interest in learning, I adopted the following teaching methods:
(1) Enlighten and guide students to think, analyze, experiment, explore and summarize. This can fully mobilize the initiative and enthusiasm of students.
(2) adopt the methods of "from special to general", "from abstract to concrete" and "from static to dynamic". This is helpful for students to actively construct knowledge; Conducive to highlighting key points and solving difficulties; It is also conducive to giving full play to students' creativity.
(3) Reflect the thinking method of "equivalent transformation" and "combination of numbers and shapes". This can give full play to students' subjective initiative and help improve students' various abilities.
Three. Guidance of speaking and learning
Teaching students methods is more important than teaching students knowledge. This class focuses on mobilizing students to actively think and explore, and increasing the time and space for students to participate in teaching activities as much as possible. I have been instructed in the following learning methods: observation and analysis, association transformation, hands-on experiment and practice consolidation.
(1) observation and analysis: through examples, let students observe, turn old knowledge into new knowledge, and cause cognitive conflicts among students.
(2) Association transformation: Students analyze and explore, and come up with solutions to problems.
(3) Hands-on experiment: Through drawing and experiment, the general problem-solving steps are obtained.
(4) Practice consolidation: let students know that mathematics is focused on application, so as to test the application of knowledge and find out what they have not mastered and the gaps.