I. Guiding ideology and theoretical basis

Mathematics is an important subject to cultivate and develop people's thinking. Therefore, in teaching, students should not only "know what it is", but also "know why it is". Therefore, we should fully reveal the thinking process of acquiring knowledge and methods under the principle of taking students as the main body and teachers as the leading factor. Therefore, in this class, I focused on the constructivist teaching method of "creating problem situations-putting forward mathematical problems-trying to solve problems-verifying solutions", which mainly adopts the teaching method of combining observation, inspiration, analogy, guidance and inquiry. In teaching methods, multimedia-assisted teaching is adopted to visualize abstract problems and make teaching objectives more perfect.

Two. Textbook analysis

The inductive formula of trigonometric function is the content of the third section of the first chapter of compulsory mathematics 4 in the standard textbook of high school mathematics experiment (People's Education Edition A), and its main content is formulas (2) to (6) in the inductive formula of trigonometric function. This is the first lesson, and the teaching content is Formulas (2), (3) and (4). The textbook requires students to pass the definition and inductive formula of trigonometric function from any angle they have mastered. Using the idea of symmetry, we can find the symmetrical relationship between any angle and the terminal edge, their relationship with the coordinates of the intersection point of the unit circle, and then find the relationship between their trigonometric functions, that is, we can find, master and apply the inductive formulas of trigonometric functions (2), (3) and (4). At the same time, the teaching materials are permeated with mathematical thinking methods such as conversion and conversion, which puts forward requirements for cultivating students' good study habits. For this reason, this section occupies a very important position in trigonometric functions.

Three. Analysis of academic situation

The teaching object of this class is all the students of Grade One (1) in our school. The students in this class belong to the lower-middle level, but they have a good study habit of being good at hands-on. By using the discovered teaching methods, they should be able to easily complete the teaching content of this class.

Four. Teaching objectives

(1). Basic knowledge goal: Understand the discovery process of inductive formulas and master inductive formulas of sine, cosine and tangent;

(2) Ability training goal: correctly use inductive formula to find sine, cosine and tangent at any angle, and evaluate and simplify simple trigonometric functions;

(3) Innovative quality goal: through the derivation and application of formulas, improve the ability of triangle constant deformation, infiltrate the mathematical thought of regression and the combination of numbers and shapes, and improve students' ability to analyze and solve problems;

(4) Personality quality goal: Through the study and application of inductive formula, we can feel the common law of the relationship between things, reveal the essential attributes of things, and cultivate students' historical materialism by using mathematical thinking methods such as transformation.

Key points and difficulties in teaching verbs (abbreviation of verb)

1. Teaching focus

Understand and master inductive formula.

2. Teaching difficulties

Correct use of inductive formula, finding trigonometric function value and simplifying formulas of trigonometric functions.

Analysis of teaching methods and expected results of intransitive verbs

As teachers, we should not only teach students mathematical knowledge, but more importantly, teach students mathematical thinking methods. How to achieve this goal requires every teacher to study hard and explore seriously. I make the following analysis from three aspects: teaching methods, learning methods and expected results.

1. Teaching methods

Mathematics teaching is the teaching of mathematical thinking activities, not just the result of mathematical activities. The purpose of mathematics learning is not only to acquire mathematical knowledge, but also to train people's thinking ability and improve their thinking quality.

In the teaching process of this class, I take students as the theme, take discovery as the main line, try my best to infiltrate mathematical thinking methods such as analogy, transformation and combination of numbers and shapes, and adopt teaching modes such as questioning, inspiration and guidance, joint exploration and comprehensive application to give students "time" and "space", from easy to difficult, from special to general, and try my best to create a relaxed learning environment so that students can realize the happiness and success of learning.

Study law

"Modern illiterates are not illiterate people, but people who have not mastered learning methods." Many classroom teaching methods are often based on high starting point, large capacity and fast progress to teach students more knowledge points, but ignore that it takes time for students to digest knowledge, thus depriving students of their interest and enthusiasm for learning. How to make students digest knowledge to a certain extent and improve their learning enthusiasm is a problem that teachers must think about.

In the teaching process of this class, I guide students to think, discuss and solve problems, practice and consolidate the process of reappearing exploration, let students participate in the whole process of exploration, and let students cooperate and exchange ideas and explore together after acquiring new knowledge and problem-solving methods, so as to change passive learning into active independent learning.

3. Expected effect

This lesson is expected to enable students to correctly understand the discovery and proof process of inductive formulas, master inductive formulas, and skillfully apply inductive formulas to understand some simple simplification problems.

Seven. Teaching process design

(A) the creation of the scene

1. Review the trigonometric function values of acute angles of 300,450,600;

2. Review the definition of trigonometric function at any angle;

Question: So, can you know the value of sin2 100? As a guide to the new curriculum.

Design intent

The encouragement of self-confidence is to enhance students' self-confidence in learning mathematics, and simple and easy-to-do questions strengthen each student's enthusiasm for learning. The emergence of specific data problems makes students feel confused and confused, to explore their own potential, to find opportunities to prove that I can do it, and to think about solutions.

(2) Exploring new knowledge

1. Ask the students to find out the relationship between the terminal edge of 300 and the terminal edge of 2100.

2. Ask students to find out the relationship between the coordinates of the intersection of the terminal edge of 300 and the terminal edge of 2100 and the unit circle.

3.3 What does it matter? Sin2 100 and sin300?

Design intent

By introducing special questions, students can easily understand and appreciate the boring and excessive teaching process, paving the way for students to explore and discover the relationship between arbitrary angles and trigonometric functions.

(C) the generalization of the problem

Query 1

1. It is found that the terminal edge of any angle is symmetrical with the terminal edge of.

2. It is found that the terminal edge of any angle and the coordinates of the intersection point between the terminal edge of the angle and the unit circle are symmetrical about the origin;

3. Explore the relationship between arbitrary angle and trigonometric function value.

Design intent

Firstly, the unit circle is used to connect the properties of the unit circle with trigonometric function from the point of view of connection, and the number and shape are combined. The relationship between the design questions of the problem from special to general, from line symmetry to point symmetry to trigonometric function value gradually rises, and Formula 2 is summarized in one go. At the same time, it also plays an exemplary role for students to discover and explore formulas 3 and 4 independently. The following exercises aim at familiarizing students with Formula One, making them feel the joy of success and dare to do so.

(4) Practice

Using inductive formula (2), the following trigonometric function values should be answered orally.

( 1).； (2).； (3).。

After the fun, let's set sail again, accept new challenges and introduce new problems.

(5) Problem deformation

Starting from SIN300=, guide students to find the values of SIN (-300) and Sin 1500 with the definition of triangle, and remind students whether to find the values of sin () and sin () if sin = is known.

Students' independent inquiry

1. What is the relationship between arbitrary angle and trigonometric function?

2. Explore the relationship between arbitrary angle and trigonometric function.

Design intent

The law of forgetting is fast first and then slow, and the reproduction of the process is an important way to remember deeply. In the exploration process from thinking-observation and discovery-to general conclusion, from special to general, and the combination of numbers and shapes, students' understanding and mastery of knowledge can go deep into their minds. At this time, students are boldly asked to discuss in groups by asking similar questions, which reproduces the whole process of exploration, deepens the deep memory of knowledge, invisibly stimulates motivation and enhances confidence. The challenge has increased. Independent discussion of new knowledge points also challenges teachers' ability to control the classroom. Mutual trust, mutual trust, a tacit understanding between teachers and students, teachers and students make progress together.

Show the results of students' independent inquiry

Induce formulas (3) and (4)

Give the title of this lesson.

Inductive formula

Design intent

After the topic comes out, students can recall the joy of exploring and discovering success after the whole exploration process, and suddenly look back. Oh, the original knowledge points are easy to master, and it is also a summary of the content of this lesson.

(6) Generalization and sublimation

The trigonometric function value of is equal to the function value of the same name, and the coincidence of the original function value is regarded as an acute angle. (that is, the function name is unchanged, and the symbol is regarded as a quadrant. )

Design intent

Simple memory formula.

(7) practice strengthening

Find the value of the following trigonometric function: (1). sin()； (2).cos(-20400)。

Design intent

The setting of this exercise focuses on multiple solutions to a problem, so that students can not only learn to use the inductive formula of trigonometric function flexibly, but also develop the good habit of dealing with problems flexibly. It should also be pointed out that the "negative angle" in the textbook is changed to "positive angle" for a specific negative angle.

Student exercises

Simplify:

Design intent

Focus on strengthening the comprehensive application of trigonometric function induction formula.

(8) Summary

1. Summarize the steps of simplifying trigonometric function of arbitrary angle into acute angle by inductive formula.

2. Experience the combination of numbers and shapes, and return to symmetry.

3. "Learn" the habit of learning.

(9) Homework

1. Textbook P-27,65438+0,2,3;

2. Extra extracurricular topics.

Design intent

Strengthen students' memory and flexible application of trigonometric function inductive formula, and the setting of additional questions is conducive to students' ability to "by going up one flight of stairs".

(10) blackboard design: (omitted)

Eight. Reflection after class

Before the teaching design of this section, I repeatedly read the curriculum standards and teaching materials, and arranged a series of questions for the content of the teaching materials, so that students can experience the process of knowledge generation and development, actively participate in thinking activities, pay attention to students' thinking development through interaction with students, and guide students to solve problems with the knowledge and methods they have learned, and get the update and expansion of the knowledge system, which has received certain expected results. In particular, the handling of exercises allows students to feel the link of "observation-induction-generalization-application" through individual, group and group attempts to solve problems and questions, develop thinking in the process of knowledge formation and development, gradually cultivate students' ability to find, explore and solve problems and creative thinking, give full play to students' main role, and improve students' sense of cooperation, thus achieving the goal.

But there are still some shortcomings: the content of this section is not difficult, and I think the teacher's intervention (explanation) is still too much.

In the future teaching, for some relatively simple contents, students should be allowed to explore and cooperate more. With the deepening of educational reform, teaching elements such as teaching concept, teaching mode and teaching content are constantly updated. As mathematics teachers, we should renew our teaching concept, design classroom teaching from the perspective of students' all-round development, pay attention to the development of students' personality and potential, and make the teaching process more in line with the requirements of curriculum standards. Arm yourself with brand-new theories to make your class more efficient.