one
I. teaching material analysis
Status and function
Sequence is one of the important contents of high school mathematics, which not only has a wide range of practical applications, but also has the function of connecting the past with the future. On the one hand, sequence, as a special function, is inseparable from function thought; On the other hand, learning sequence is also a preparation for further learning the limit of sequence. On the other hand, on the basis of students' learning the concept of sequence, arithmetic progression gave two methods of sequence-general formula and recursive formula, which further deepened and broadened his understanding of sequence. At the same time, arithmetic progression also provided a foundation for studying geometric series in the future.
(2) Analysis of learning situation
(1) The students have mastered _ _ _ _ _ _ _ _ _ _ _.
(2) Students have rich knowledge and experience, strong abstract thinking ability and deductive reasoning ability.
(3) Students have lively thinking and high enthusiasm, and initially formed the ability to explore mathematical problems in cooperation.
(4) Students' different reference levels are uneven, and individual differences are obvious.
Second, the target analysis
The new curriculum standard points out that "three-dimensional goal" is a closely related organic whole, which should be a process of acquiring knowledge and skills, and at the same time become a kind of learning and correct values. This requires us to take the cultivation of knowledge and skills as the main line, infiltrate emotional attitudes and values, and fully reflect them in the teaching process. The new curriculum standard points out that the main body of teaching is students, so the formulation and design of objectives must start from the students' point of view, according to the position and role of _ _ _ in the teaching materials, and combined with the analysis of learning situation, the teaching of this class should achieve the following teaching objectives:
(A) Teaching objectives
(1) knowledge and skills
Make students understand the concept of monotonicity of function and master the method of judging monotonicity of function; .
(2) Process and method
Through observation, induction, abstraction and generalization, students are guided to independently construct concepts such as monotone increasing function and monotone decreasing function. Can use the concept of monotonicity of function to solve simple problems; Make students understand the mathematical thinking method of combining numbers and shapes, and cultivate students' ability to find, analyze and solve problems.
(3) Emotional attitudes and values
In the learning process of monotonicity of function, let students experience the scientific value and application value of mathematics, and cultivate students' good habits of observation and exploration and rigorous scientific attitude.
(2) Key points and difficulties
The teaching focus of this lesson is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
Thirdly, the analysis of teaching methods and learning methods
teaching method
According to the content characteristics of this class and the age characteristics of senior two students, and according to the classroom teaching strategy of "354" in Linyi senior high school mathematics, the inquiry-experience teaching method is adopted to complete the teaching. In order to achieve the teaching objectives of this class, I adopted the following teaching methods:
1. Introduce topics through real life problems that students are familiar with, create situations for concept learning, narrow the distance between mathematics and reality, stimulate students' thirst for knowledge and arouse their enthusiasm for participation.
2. In the process of forming the concept, closely follow the key sentences in the concept and form the concept correctly through the participation of students.
3. While encouraging students to participate, the leading role of teachers should not be ignored, and students should be taught clear thinking, rigorous reasoning and successful written expression.
(2) study law
I attach importance to studying law;
1, let students intuitively enlighten their thinking with graphics, and complete the qualitative leap from perceptual knowledge to rational thinking through the construction of positive and negative examples.
2. Let students question, try, induce, summarize and apply from problems, and cultivate students' ability to discover, study, analyze and solve problems.
Fourthly, the analysis of teaching process.
(A) Teaching process design
Teaching is a harmonious whole composed of teachers' "guidance" and students' "learning" and "enlightenment" in the teaching process. Teachers' "guidance" means that teachers inspire, induce, motivate and evaluate students' learning, and transfer learning tasks to students. Students just accept tasks, explore problems and complete tasks. If "teaching and learning" are perfectly combined in the teaching process, that is, taking "problems" as the core, we can organize and promote teaching through deduction, explanation and exploration of the occurrence, development and application of knowledge.
(1) Create a situation and ask questions.
The new curriculum standard points out: "Let students learn mathematics in concrete and vivid situations". In this class, we ask questions from familiar life situations. The design of questions has changed the traditional design method with clear purpose, given students a space to think, and fully reflected the students' dominant position.
(2) Guiding inquiry and constructing concepts.
The formation of mathematical concepts comes from the need to solve practical problems and the development of mathematics itself. However, the high abstraction of concepts brings difficulties to understanding, teaching and learning, which requires students to be exposed to learning activities that are in line with their own reality, and to experience the process of "mathematization" and "re-creation" on the basis of their own experience and existing knowledge.
(3) Self-attempt and preliminary application.
Effective mathematics learning process can not be simply imitated and memorized, especially the understanding and learning process of mathematical thinking. Let students experience and practice in the process of solving problems, teachers and students learn interactively, students cooperate and communicate, and explore.
(4) Consolidation and deepening of in-class training.
Through the participation of students, students can deeply understand the main contents and thinking methods of this lesson, so as to deepen their knowledge again.
(5) Summary, review and reflection.
Summary is not only a simple knowledge review, but also a summary of knowledge, methods and experiences by giving full play to students' dominant position. I designed three questions: (1) What did you learn through this lesson? (2) What have you learned from this lesson? (3) What skills have you mastered through this lesson?
(2) Work design
Homework is divided into compulsory questions and multiple-choice questions. The required questions reflect the knowledge level of students in this course. Multiple-choice questions are an extension of the content of this course, focusing on the extensibility and coherence of knowledge and emphasizing the application of what you have learned. Through homework setting, students at different levels can get the joy of success and see their potential, thus stimulating students' full interest in learning and promoting the formation of a learning atmosphere of independent development and cooperative inquiry.
two
The first volume of senior high school mathematics (1) 1. 1 set (1) teaching case teaching goal: 1, understand the concept and elements of set; 2. Understand the three characteristics of set elements; 3. Representation of commonly used number sets; 4, will judge the relationship between elements and sets,
Teaching case set (1)
. Teaching emphasis: 1, the concept of set; 2. Three characteristics of set elements: 1, three characteristics of set elements; 2. The relationship between several episodes: preparation before class: 1, preparation of teaching AIDS: introduction of multimedia production mathematician Cantor, including head portrait, life and contribution to the development of mathematics; Examples, figures, etc. This class needs. 2. Arrange students to preview the compilation of 1. 1. Instructional design: 1. [Creating a situation] Multimedia display to stimulate interest: a man crazy about science-Cantor (1845-1918), Russia. Cantor was born in St. Petersburg, Russian. His parents are Danish, and his father was born in Copenhagen, the capital of Denmark. He is a wealthy businessman. His mother Mary is an artist. When his parents were young, they moved to St. Petersburg, where Cantor was born. Cantor, the eldest son of his family, moved to Frankfurt in 1856. Because Cantor has changed its nationality many times, many countries think that they have cultivated Cantor's achievements. Cantor was interested in mathematics since he was a child. He received his doctorate at the age of 23 and has been engaged in mathematics teaching and research ever since. The set theory he founded has been recognized as the basis of all mathematics. The concept of infinity put forward by Cantor in 1874 shocked the intelligentsia. With the help of the infinite thought in ancient and medieval philosophical works, Cantor derived a new thinking mode about the nature of numbers, established the basic skills of dealing with infinity in mathematics, and greatly promoted the development of analysis and logic. He studied number theory, expressed functions with trigonometric functions, and found amazing results: he proved that rational numbers are countable, but all real numbers are uncountable. Because the study of infinity often leads to some logical but absurd results (called "paradox"), many great mathematicians are afraid of falling into it and adopt an evasive attitude. During 1874- 1876, Cantor, who was less than 30 years old, declared war on the mysterious infinity. With hard sweat, he successfully proved that points on a straight line can correspond to points on a plane one by one, and can also correspond to points in space one by one. In this way, it seems that there are "as many" points on the 1 cm long line segment as there are points in the Pacific Ocean and the whole earth. In the following years, Cantor published a series of articles about this kind of "infinite set" and drew many amazing conclusions through strict proof. Cantor's creative work has a sharp conflict with the traditional mathematical concept, and some people oppose, attack and even abuse it. Some people say that Cantor's set theory is a kind of "disease", Cantor's concept is "fog in fog", and even Cantor is a "madman". Great mental pressure from mathematics finally destroyed Cantor, making him exhausted, suffering from mental illness and being sent to a mental hospital. Many of his outstanding achievements in set theory were made during his mental illness. At the first international congress of mathematicians held in 1897, his achievements were recognized. Russell, a great philosopher and mathematician, praised Cantor's work as "probably the greatest work that this generation can boast about." But Cantor is still in a trance, unable to get comfort and joy from people's reverence. 1918 65438+1October 6th, Cantor died in a mental hospital. Today, we are going to learn the simple logic of set 1. 1 (1), the first chapter of senior high school mathematics. Let's review the knowledge related to collection in junior high school. Second, [Review old knowledge] Review questions: 1. What sets did we learn in junior high school? Real number set, solution set of binary linear equation, solution set of inequality (group), point set, etc. 2. In junior high school, what did we describe with set? Angle bisector, perpendicular bisector, circle, inside circle, outside circle, etc.
Real rational number irrational number integer fraction positive irrational number negative irrational number positive fraction negative integer natural number positive integer zero 3. Classification of real numbers 3. Classification of real numbers:
Real number positive real number negative real number zero
4. The following is completed by students: (1). Fill in the following numbers in the corresponding circles.
0、、2.5、、、-6、、8%、 19
Integer set, fraction set, irrational number set
(2) Fill in the following numbers in the corresponding braces: 1,-10, -2, 3.6, -0. 1 8, negative rational number set: {}
Integer set: {}
Positive real number set: {}
Irrational number set: {}
3. Solve the inequality group (1) 2x-3 < 5.
4. The integer whose absolute value is less than 3 is ————————————— [Learning Interaction] 1. Observe the following objects (1) 2,4,6,8, 10, 12. (2) All right triangles; (3) Points with equal distance on both sides of the angle; (4) satisfy x-3 >; All real numbers of 2; (5) All boys in this class; (6) four great inventions of ancient china; (7) subjects of the 2007 college entrance examination; (8) Ball events in the 2008 Olympic Games,
In the teaching case of set (1), after the students observed the above objects, the teacher asked: [Concept of set] (1) What is set? When some specified objects are put together, they become a set, which is called a set for short. (2) What are the elements of a set? Each object in a collection is called an element of the collection. (3) How to express a set and its elements? General sets are represented by braces, usually in capital letters; Elements in the collection are represented by lowercase letters. (4) The relationship between the elements in the set and the set A is the element of the set A, which is called A ∈ A; A is not an element of the set A, so A does not belong to A, and is recorded as aA. 2. Discuss whether the following question (1){ 1, 2,2,3} is a set containing 1 1, 2 2, 1 3. (2) Can scientists form a set? (3) Do 3){ a, b, c, d} and {b, c, d, a} represent the same set? Through the discussion between teachers and students, the following conclusions can be drawn: The nature of elements in a set is certain: the elements in a set must be certain. The characteristics of the elements in the set are different from each other: the elements in the set must be different from each other. Disorder: The elements in the set are out of order. The elements that make up a set can be numbers, figures, people, things, etc. [Representation of common number set] (1) natural number set: n means (2) positive integer set: n or N+ means (3) integer set: z means (4) rational number set: q means (5) real number set: r means (positive real number set is represented by R* or R+). The root example 2 of the number (D) equation x2-3x+2=0, which is very close to 2004, is filled with symbols (1) 3.14q (2) π q (3) 0n+(4) 0n.
32(5)(-2)0N*(6)Q
3232(7)Z(8)—R
Verb (abbreviation of verb) [stratified exercise] 1, multiple-choice question (1) The following () A, all triangles B, all questions C and integer D in "Mathematics for Senior One" are greater than π, so irrational number 2, true or false (1) {x2, 3x+.
The common number set belongs to the relationship between the concept elements and the set of a∈AN, N* (or N+), z, q, R.; The nature of the elements in the set is deterministic, anisotropic and disorderly, and does not belong to aA.
The purpose of this lesson design is to stimulate students' interest in learning, prepare before class and cultivate students' autonomous learning ability by creating situations; Multimedia-assisted teaching improves classroom efficiency and enriches teaching presentation. Explore the integration of modern teaching methods and high school mathematics teaching.
three
First, stimulate students' interest and give them the motivation to learn.
Learning high school mathematics well and arousing strong interest are the most effective means. How to stimulate the interest in mathematics learning should be implemented from four aspects. First, pay attention to the teaching of basic mathematics knowledge. Some students think that the content of mathematics is abstract and not easy to understand. In fact, mathematics knowledge is the most basic knowledge, which is closely related to our lives. Mathematics is around us, and our life cannot be separated from mathematics. The second is to strengthen the practical application of mathematics. Many students have misunderstandings about mathematics and think that learning mathematics is of little use. In fact, mathematical knowledge is everywhere in our lives and is inseparable from our lives. It's just that the previous mathematics teaching is seriously out of touch with real life, which leads students to think that mathematics knowledge is of little use. Under the new mathematics curriculum reform, mathematics textbooks have undergone a brand-new reform and development, focusing on the practical application of mathematics, so that students can feel the value and charm of mathematics in mathematics learning, thus loving mathematics. The third is to introduce mathematics experiment teaching. Mathematics is not only the teacher's explanation in class, but also can stimulate students' interest through mathematical experiments, so that students can feel the intuition of mathematics in experimental teaching, participate in the research of mathematical knowledge as explorers, and let students get the joy of success in the process of experiments. Fourth, let students get positive feelings in overcoming difficulties in mathematics. Mathematics knowledge has valuable resource value, and students can gain positive emotions in discovery and creation. The reason why mathematics can attract more people to explore and innovate is because they can get the joy of success and stimulate students' fighting spirit in mathematics learning.
Second, teach students how to learn and let them know how to learn.
We often say, "It is better to teach people to fish than to teach them to fish." This fully shows the importance of methods in teaching. In education and teaching, teachers should not only teach students knowledge, but also teach students learning methods, which is an important magic weapon for students to acquire knowledge. Only when students master the methods can they learn to teach themselves and acquire knowledge. Therefore, under the new curriculum reform, students should not only learn, but also learn. First of all, we should teach students how to read. Some people think that the method of "reading" is not used in senior high school mathematics teaching. In fact, mathematics teaching, like other subjects, is also inseparable from the method of "reading". Only in the process of reading can students understand the content of mathematical problems, discover and summarize the deep meaning contained in mathematical materials, so as to grasp the key points, think about problems and lay a good foundation for students to understand digital knowledge. Secondly, we should guide students to "discuss". The new curriculum reform of mathematics puts forward a cooperative and inquiry learning method, which focuses on cultivating students' ability to analyze and solve problems. Therefore, in mathematics teaching, we should encourage students to speak boldly and explore and discuss, especially for those controversial mathematics problems, and guide students to actively explore and help students improve their ability in exploration and discussion. Third, let students learn to think. Ancient education in China attached great importance to "thinking" and put forward the important conclusion that "learning without thinking is useless". In mathematics teaching, we should also pay attention to cultivating students' "thinking" quality, so that students can develop good thinking habits, learn to distinguish the difficulties of mathematical knowledge and understand the coherence of mathematical knowledge, thus enhancing students' imagination and improving their ability and level of analyzing mathematical knowledge.
Third, cultivate students' ability to question and let them dare to challenge *
Mathematics teaching is inseparable from students' questions, especially under the new curriculum reform. Cultivating students' questioning ability and making them dare to question is an important factor to improve the effect of mathematics teaching. In traditional mathematics teaching, students have no problem consciousness at all. When solving a problem, they always have no self-confidence and can only ask teachers or books for proof, which inhibits the development of students' innovative thinking. At this rate, students will not learn. In the mathematics stage of senior high school, it is of great significance to cultivate students' questioning ability and make them dare to challenge, so as to improve their mathematics ability and quality and cultivate their innovative ability. If you really find out the mistake of "*", it will be a greater spur to students. Therefore, in teaching, teachers should consciously cultivate students' questioning ability, encourage students' new discoveries and new ideas in time, stimulate students' enterprising spirit, let students improve their interest in mathematics learning in questioning, and establish their self-confidence in mathematics learning.
Fourth, teach students learning methods and cultivate their good study habits.
In the new mathematics textbook, there are contents of teaching method guidance and learning method infiltration. For example, each chapter is arranged with relevant knowledge such as "doing", "reading" and "thinking", the main purpose of which is to let students learn to learn, learn to learn and learn to think. Therefore, teachers should pay attention to the guidance of students' learning methods in teaching, so that students can develop good study habits. For example, let students learn how to read questions. Reading questions are not random reading, but let students find valuable content in reading questions, thus laying the foundation for further problem solving. If students find relevant problems in the reading questions, teachers should encourage them in time, establish students' confidence and courage in learning, and let students feel the joy of learning success, thus generating interest and cultivating good habits. At the same time, teachers should learn to create good learning situations in teaching, stimulate students to actively explore mathematics knowledge, make students exercise their abilities and improve their quality in the situations created by teachers, thus laying the foundation for cultivating students' good habits. In a word, high school mathematics teaching is the basis of students' mathematics learning. As a math teacher in senior high school, we must realize the importance of math teaching in senior high school, constantly change our teaching concepts, establish a brand-new concept of math teaching, make math knowledge closely linked with our lives, apply what we have learned, and let students feel the joy of success in math learning, so as to further enhance their initiative in math learning and further improve their abilities in all aspects of math learning.