First, the analysis of teaching content
The definition of conic curve reflects the essential attribute of conic curve, which is highly abstract after countless practices. When XX is properly used to solve problems, simplicity can control complexity in many cases. Therefore, after learning the definitions, standard equations and geometric properties of ellipse, hyperbola and parabola, we should emphasize the definition again and learn to skillfully use the definition of conic curve to solve problems. "
Second, the analysis of students' learning situation
Students in our class are very active and active in classroom teaching activities, but their computing ability is poor, their reasoning ability is weak, and their mathematical language expression ability is also slightly insufficient.
Third, the design ideas
Because this part of knowledge is abstract, if we leave perceptual knowledge, it is easy for students to get into trouble and reduce their enthusiasm for learning. In teaching, with the help of multimedia animation, students are guided to find and solve problems actively, actively participate in teaching, find and acquire new knowledge in a relaxed and pleasant environment, and improve teaching efficiency.
Fourth, teaching objectives.
1. Deeply understand and master the definition of conic curve, and can flexibly apply XX to solve problems; Master the concepts and solutions of focus coordinates, vertex coordinates, focal length, eccentricity, directrix equation, asymptote and focal radius. Can combine the basic knowledge of plane geometry to solve conic equation.
2. Through practice, strengthen the understanding of the definition of conic curve and improve the ability of analyzing and solving problems; Through the continuous extension of questions and careful questioning, guide students to learn the general methods of solving problems.
3. With the help of multimedia-assisted teaching, stimulate the interest in learning mathematics.
Five, the teaching focus and difficulty:
Teaching focus
1. Understand the definition of conic.
2. Using the definition of conic curve to find the "maximum"
3. "Definition method" to find the trajectory equation
Teaching difficulties:
Clever use of quadratic curve XX to solve problems
2. Examples of teaching plans in the first volume of senior three mathematics.
First, the teaching objectives
Knowledge and skills
Master the monotonicity and range of trigonometric functions.
Process and method
Experience the monotonicity exploration process of trigonometric function and improve the logical reasoning ability.
Emotional attitude values
In the process of guessing, improve the interest in learning mathematics.
Second, the difficulties in teaching
Teaching focus
Monotonicity and range of trigonometric functions.
Teaching difficulties
The process of exploring monotonicity and range of trigonometric functions.
Third, the teaching process
(A) the introduction of new courses
Ask a question: How to study the monotonicity of trigonometric functions?
(2) Summarize the homework
Question: What did you learn today?
Guide students to review: basic inequalities and the process of derivation and proof.
Homework after class:
Think about how to compare the values of trigonometric functions with monotonicity.
3. Examples of teaching plans in the first volume of senior three mathematics.
I. Objectives
Knowledge and skills: understand the relationship between monotonicity of differentiable functions and their derivatives; We can use derivatives to study monotonicity of functions and find monotonic intervals of functions.
Process and method: let students give more examples of propositions and cultivate their discriminating ability; Cultivate their ability to analyze and solve problems;
Emotion, attitude and values: stimulate students' interest in learning mathematics through participation.
Second, the key points and difficulties
Teaching emphasis: Using derivative to study monotonicity of function, we can find the monotonic interval of polynomial function with no more than 4 degrees.
Difficulties in teaching: When we study the monotonicity of a function with derivatives, we will find that the monotone interval of a polynomial function does not exceed 4 times.
Third, the teaching process:
It is very important for us to study the properties of the function, such as the rate of gift reduction, increase and decrease, and the value or minimum value of the function. By studying these properties of functions, we can have a basic understanding of the law of quantity change. We use derivative as a tool, which is very convenient for us to study the increase and decrease, extreme value and maximum value of functions.
Fourthly, the analysis of learning situation.
Our students belong to parallel classes and there is no experimental class, so there is a gap between the existing knowledge and the experimental level. It needs teachers' guidance and intuitive understanding with the help of animation.
Teaching methods of verbs (abbreviation of verb)
Discovery types and heuristic methods
The basic links of the new teaching are: preview inspection, summing up doubts → situation introduction, showing goals → cooperative inquiry, intensive lecture → reflection summary, in-class inspection → issuing guidance plans and arranging preview.
Sixth, preparation before class
1. Students' learning preparation:
2. Teachers' teaching preparation: making multimedia courseware, previewing learning plans before class, exploring learning plans in class and expanding learning plans after class.
Seven, schedule:
1 class hour
Eight, the teaching process
(A) preview the inspection, summing up the doubts
Check and implement students' preview, understand students' doubts, and make teaching targeted.
Ask a question
1. What are the methods to judge the monotonicity of a function?
Guide students to answer "definition method" and "image method" )
2. For example, to judge the monotonicity of y=x2, such as
How to proceed? (Guide students to review with definition method and image method respectively. )
3. Is there any other way? If a function is encountered:
Y=x3-3x to judge monotonicity? Let the students spend a short time.
Once in a while, I tried to finish it and found a "definition method".
The symbol trouble of judging the difference after making the difference; With the "image method", it is difficult to draw an image. )
4. Is there a shortcut? (Students don't understand, which leads to the topic) This is going to use the derivative method we are going to learn today.
Review old knowledge in the form of questions, and at the same time lead to new questions: monotonicity, definition and image of cubic function judgment are inconvenient, is there a shortcut? By creating problem situations, students can have a strong sense of problems and actively participate in learning.
(2) Scene introduction and display objectives.
Design intention: lead in step by step, attract students' attention, and define learning objectives.
Q: What is the relationship between monotonicity and derivative of a function?
Teachers still take y=x2 as an example, with the help of the geometric sketchpad dynamic demonstration, let students record the results in the second line of the table distributed before class:
Function and positive and negative derivatives of monotonicity tangent slope k of image
Q: What did you find? (Student answers)
Q: Is this result average?
(3) Cooperative inquiry and intensive teaching.
Let's examine two general examples:
(The teacher instructs the students to do the experiment: put the prepared toothpick on the image of curve y=f(x) in the table as the tangent of the curve, move the tangent, and record the results in the third and fourth rows of the table above. )
Q: Can you draw any rules?
Let the students sum up. The teacher can simply write on the blackboard:
In a certain interval (a, b),
if f '(x)>； 0, then f(x) is the increasing function on (a, b);
If f' (x) < 0, it is a decreasing function on f(x)(a, b).
Teacher's notes:
To correctly understand the meaning of "an interval", it must be an interval within the definition domain.
1. This part is the theoretical basis for finding the monotone interval of a function with derivatives, and its importance is self-evident. But students only learn the meaning of derivative and some basic operations, so it is unrealistic to get a strict proof. Therefore, students are only required to draw conclusions intuitively with the help of geometry, which is consistent with the requirements in the new curriculum standard.
2. Teachers demonstrate concrete examples dynamically, and students verify the general situation through experiments. From observation and conjecture to induction and summary, let students experience the process of knowledge discovery and occurrence, and turn knowledge into students' active acquisition of knowledge, thus making it the main body of classroom teaching activities.
3. After drawing the conclusion, the teacher stressed that correctly understanding the meaning of "a certain interval" must be a certain interval within the definition domain. This will be reflected in variant 3 of example 1.
4. Considering the large capacity of this class, it is not mentioned that monotonicity is not affected by the zero derivative of the function at individual points (for example, y=x3 when x=0), and this question will be supplemented for students in subsequent courses.
Finding monotone interval of function by derivative
Example 1. Find the monotone interval of function y=x2-3x.
(Guide students to get the idea of solving problems: seeking guidance →
If the order f'(x)>0, the monotonic increasing interval of the function is obtained, thus f' (x)
Variant 1: Find the monotone interval of function y=3x3-3x2.
(Competition: Divide the class into two groups and specify the definition of monotonicity and the solution of derivative respectively. Each group recommends a student's answer for projection. )
Finding monotone interval is an important application of derivative and the focus of this section. Therefore, an example of 1 and three variants are designed:
The design example 1 can guide students to get the steps of solving monotone interval by derivative method.
Design variant 1 and competition activities can stimulate students' enthusiasm for learning, let them learn to compare and deeply understand the advantages of derivative method.
Consolidate and improve
Variant 2: Find the monotone interval of function y=3ex-3x.
(Students answer on the blackboard)
Variant 3: Find the monotone interval of the function.
Design Variant 2, which allows students to answer questions on the blackboard, can standardize the problem-solving format, and at the same time make students understand that the monotonous interval of more complex functions can be found by derivative method.
Design variant 3 can make students realize the necessity of considering the domain.
Example 1 and its three variants involve quadratic function, cubic function, exponential function and inverse proportional function in turn. This problem is changeable and gradually deepened, so that students can understand how to apply it and what kind of monotonicity problem to solve with "derivative method".
Explore the multimedia display of thinking problems.
Teachers patrol to observe and guide students in the process of grouping experiments. (class record),
(4) Reflection and summary, classroom test.
Teachers organize students to reflect and summarize the main contents of this lesson and conduct classroom tests.
Design intention: Guide students to build a knowledge network, and simply feedback and correct what they have learned. (Class record)
(5) Make a counseling plan and arrange preview.
Design intention: arrange the preview homework for the next class to consolidate and improve this class. After class, the teacher will review the expansion training in this section in time.
Nine, blackboard writing design
Example 1. Find the monotone interval of function y=3x2-3x.
Variant 1: Find the monotone interval of function y=3x3-3x2.
Variant 2: Find the monotone interval of function y=3ex-3x.
Variant 3: Find the monotone interval of the function.
Ten, teaching reflection
The design of this class adopts the preview study plan issued before class. Students preview the content of this class and find out their own confusion. In the classroom, teachers and students mainly solve the key points, difficulties, doubts, test sites, exploration points, forgettable and confusing points in the students' learning process. Finally, they conduct in-class tests and expand after class to improve classroom efficiency.
4. Examples of teaching plans in the first volume of senior three mathematics.
I. teaching material analysis
1, the position of this section in the whole book and chapters: monotonicity of function is a compulsory course, which is 1 the third section of the first chapter. It is one of the key examination contents of college entrance examination and an important property of function. It is widely used in comparing the sizes of several numbers, finding the range of functions, qualitative analysis of functions and synthesis with other knowledge. Through the study of this lesson, students can deepen their understanding of the nature of functions. It also makes full preparations for studying the properties of specific functions in the future, and plays a connecting role.
2. Teaching objectives: Based on the analysis of the structure and content of the above textbooks, and taking into account the existing cognitive level of students, I have formulated the following teaching objectives:
Basic knowledge goal: to understand the concepts of increasing function, subtraction function, monotonicity and monotone interval that can be correctly expressed in written language and symbolic language; Clearly grasp the methods and steps to prove the monotonicity of function by using the definition of monotonicity of function; And the monotonicity of some simple functions can be proved by definition;
Ability training goal: to cultivate students' rigorous logical thinking ability, and to analyze and deal with problems by means of action change, combination of numbers and shapes, and classified discussion.
Emotional goal: let students feel the fun of learning in democratic and harmonious activities.
Emphasis: Form the formal definition of the increase (decrease) function.
Difficulties. In the process of forming the concept of increase and decrease function, how to transition from the intuitive understanding of image rise and fall to the mathematical symbol language expression of function increase and decrease; Prove monotonicity of function by definition.
In order to clarify the key points and difficulties, so that students can achieve the teaching objectives set in this section, I will talk about teaching methods and learning methods again:
Second, teaching methods
In teaching, I use heuristic teaching, create scenarios under the guidance of teachers, inspire students to think through the setting of open questions, and experience the mathematical methods contained in the formation of mathematical concepts in thinking.
Third, study law.
Encourage students to take the initiative to participate, be willing to explore and be diligent, and cultivate students' ability to collect and process information, acquire new knowledge, analyze and solve problems, and communicate and cooperate. "Mathematics is one of the core courses of basic education. Changing students' mathematics learning style is not only conducive to improving students' mathematics literacy, but also conducive to promoting the change of students' overall learning style. Guided by constructivism theory, supplemented by multimedia means, heuristic teaching methods based on students' exploration and research are adopted to discuss and summarize with teachers and students.
5. Examples of teaching plans in the first volume of senior three mathematics.
First, the guiding ideology.
Study new textbooks, understand new information, update ideas, explore new teaching modes, strengthen teaching reform, pay attention to unity and cooperation, face all students, teach students in accordance with their aptitude, stimulate students' interest in learning mathematics, cultivate students' mathematical quality, and fully promote the improvement of teaching effect.
Second, the basic situation of students.
In the new semester, I teach math in two liberal arts classes in Grade Three, namely 10 class and 1 1 class. Most of these students have weak basic knowledge, no habit of self-study, poor self-control, inattention in class, easy distraction, poor ability to finish homework independently after class, and serious laziness, so the whole review task in senior three is quite arduous.
Third, work measures.
1. Seriously study the exam instructions, study the college entrance examination questions, and improve the efficiency of the review class.
"Exam notes" are the basis of proposition and preparation. College entrance examination questions are the concrete embodiment of "examination instructions". Therefore, it is necessary to carefully study the examination questions in recent years, so as to deepen the understanding of the examination instructions, grasp the new trend of the college entrance examination in time, and understand the guiding role of the college entrance examination in teaching, thus helping us to accurately grasp the important and difficult points of teaching, select targeted examples, optimize teaching design and improve review quality.
2. Teaching progress.
According to the teaching plan of senior three mathematics group and the actual situation of this class, the first round of general review for senior three is expected to be completed at the end of February and the beginning of March. Cooperate with the monthly exam held by the school and reflect on teaching in time.
3. Understand students.
Through classroom display, students' communication and interaction, correcting homework, marking examination papers, writing on the blackboard in class and the change of students' modality, we can deeply understand students' situation, observe, discover and capture information about students in time, so as to adjust teaching methods and make teachers serve students to a certain extent. For students with weak foundation, we should encourage and guide them to study law more and enhance their confidence and courage in learning.
4. Prepare lessons carefully.
Prepare lessons carefully, strive to improve classroom efficiency, usually listen to teachers in the same subject, learn good teaching methods from old teachers, and strive to improve their teaching ability.
5. Optimize exercises.
Improve the effectiveness of practice: the consolidation of knowledge, the proficiency of skills and the improvement of ability all need to be achieved through appropriate and effective practice. Exercise questions should be carefully selected, the amount of questions should be moderate, and attention should be paid to the typicality and hierarchy of questions to adapt to students of different levels; The exercises should be revised in batches, and the students' mistakes should be counted well. For more wrong questions, find out the reasons for the mistakes.
The evaluation of exercises is an important part of mathematics teaching in senior three. Don't say what you shouldn't say, but what you should say must be thoroughly explained. For typical problems, let students show and explain, fully expose their thinking process, and strengthen the pertinence of teaching. Do more exercises and pay attention to synthesis. Select the topic of "small problem, skillful method, flexible application and wide coverage" to train students' adaptability.
6. Pay attention to the guidance of learning methods and mathematical methods.
We should strengthen the review of mathematical thinking methods, such as reduction and reduction, function and equation, classification and integration, combination of numbers and shapes, special and general ideas, possibility and necessity, etc. And some basic mathematical methods, such as collocation method, method of substitution method, undetermined coefficient method, induction method, mathematical induction method, analysis method, etc., should be consciously reviewed and implemented according to students' learning reality.
According to the specific situation of students, we should give guidance on the learning methods of review, so that students can develop good study habits and improve the efficiency of review. For example, ask students to set up the wrong question book, especially after the exam, so that students can develop the habit of reflection; Cultivate students' habit of intuitive thinking with graphics; Cultivate students' expression norms and the habit of answering questions according to the necessary steps and writing formats.
7. Pay attention to psychological adjustment and test-taking skills training.
Test-taking skills and psychological training should start from the first class of grade three and run through the review class of grade three. Good psychological quality is an important link in the success of college entrance examination. Our math teacher mainly exercises students' psychological quality in lectures, especially in exams. We educate students to treat every exam with a normal heart.