Courseware of exponential function
The vivid and interesting courseware makes the classroom no longer boring. Although it is the teacher who plays the leading role in classroom teaching, courseware only plays the role of auxiliary teaching, but it does not mean that we can despise the problems that should be paid attention to when making courseware. The following small series for you to bring exponential function lesson courseware, for reference only, hope to help you.
Courseware of exponential function
1¡¢ Textbook analysis
1. The position, function and characteristics of exponential function in textbooks
"Exponential function" is the sixth section of "function" in the second chapter of high school mathematics (Compulsory) Volume 1 of pep. It is arranged after learning the section of "index". Through the study of this lesson, we can not only consolidate and deepen the concept of exponents and functions, but also lay a solid concept and image foundation for the further study of logarithm and logarithmic functions, especially the study of the properties of logarithmic functions by using the relationship between the images of reciprocal functions, Because exponential function is the first systematic research function encountered by students after entering senior high school, it has laid a good learning foundation for studying logarithmic function, trigonometric function and other complete function knowledge in senior high school stage, and preliminarily cultivating the application consciousness of function. Therefore, exponential function is not only the key content of this chapter, It is also one of the main research contents in senior high school, which plays an irreplaceable role.
In addition, the knowledge of exponential function is closely related to our daily production, life and scientific research, especially in cell division, calculation of loan interest rate and dating in archaeology. Therefore, learning this part of knowledge has extensive practical significance. One of the characteristics of this section is that it is conceptually strong, and the other is that it highlights the important role of mathematical graphics in the study of function properties.
2. Teaching objectives, key points and difficulties
Through the study of junior high school and the systematic study of set and function in senior high school, students have constructed a certain cognitive structure of the relationship between function and image, which is mainly reflected in three aspects
Knowledge dimension: have a preliminary understanding of the simplest function concepts and properties, such as positive proportional function, inverse proportional function, first-order function, quadratic function, etc., and be able to understand the function from the perspective of junior high school movement change to the view of set and corresponding.
Skill dimension: students have basically mastered the method of using "point tracing method" to describe function image, and can be prepared for studying the nature of "exponential function".
Quality dimension: from observation to abstract mathematical activity process, we have some experience, and have a preliminary understanding of the idea of combination of number and shape.
In view of the analysis of students' existing knowledge base and cognitive ability, according to the requirements of the "Syllabus", I determine the teaching objectives, teaching key points and difficulties of this course as follows:
(1) knowledge objectives: 1) master the concept of exponential function; ¢Ú Master the image and properties of exponential function; ¢Û The concept of exponential function can be used to solve practical problems;
(2) skill objectives: ¢Ù infiltrate the basic mathematical thinking method of combination of number and shape; ¢Ú cultivate students' ability of observation, association, analogy, guess and induction;
(3) emotional goal: ¢Ù experience the learning law from special to general, understand the universal connection and mutual transformation between things, cultivate students to see problems from the perspective of connection; ¢Ú promote the emotion of teachers and students through teaching interaction; stimulate students' interest in learning; improve students' ability of abstraction, generalization, analysis and synthesis; ¢Û understand the application value of mathematical science.
(4) teaching emphasis: image and properties of exponential function.
(5) teaching difficulties: the relationship between the image property of exponential function and base a.
The key to break through the difficulties is to find the growth point of new knowledge, establish the connection between the old and the new knowledge, fully combine the image on the basis of understanding the concept, and clear the obstacles by combining the number and shape.
2¡¢ Teaching method design
Because of the special position of exponential function, in the teaching method design of this lesson, I try to make students not only understand and apply the knowledge of exponential function, but also lead students to master the general ideas and methods of studying the image quality of elementary functions, so as to prepare for the study of other functions in the future, In order to achieve the purpose of cultivating students' learning ability, I combine the two teaching modes according to my own understanding of the teaching mode of "inducing thinking and inquiry" and "situational teaching mode", which mainly highlights the following aspects:
1. Create problem scenarios. According to the actual background of exponential function in life, two examples are given to fully mobilize students' interest in learning, stimulate students' inquiry psychology, and successfully introduce the topic. These two examples are just ready for the study of the image with the base greater than 1 and the base greater than 0 less than 1 in the exponential function.
2. Strengthen the concept of "exponential function". Guide students to sum up the definition of exponential function by combining the relevant concepts of index, and point out the formal characteristics of exponential function to students. Ask students to think about whether the base number a needs to be restricted, and if not, what problems will arise. This will avoid students' unclear classification of the range of base a, It also paves the way for studying the image of exponential function.
3. Highlight the role of images. In the process of mathematics learning, graphics are always an important auxiliary means we need. A mathematician once said that "the number out of shape is less intuitive, and the shape is difficult to be refined". When studying the properties of exponential functions, the properties are directly obtained from the observation of images. Therefore, images play an important role.
4. Pay attention to the connection between mathematics and life and practice. The essence of mathematics comes from life and serves practice. In the introduction of classroom teaching, the explanation of examples and the expansion of extra-curricular knowledge, the life problems closely related to exponential function are introduced, trying to make students understand the role of mathematics as a basic discipline, and cultivate students' awareness of mathematics application.
3¡¢ Learning method guidance
This lesson is arranged after learning the concept and operation of "index". According to the actual situation of students, I mainly try in the following aspects:
1. Reproduce the original cognitive structure. After introducing two life examples, students are asked to recall the concept of index to help them reproduce the original cognitive structure and prepare for understanding the concept of exponential function.
2. Understand common mathematical thinking methods. When studying the properties of exponential function with the help of images, we will encounter some basic mathematical thinking methods, such as classification discussion, combination of number and shape, which will run through the whole high school mathematics learning.
3. Develop through mutual communication and independent inquiry. In the classroom introduction of life examples, the study of the nature of exponential function, the examples and training, the small sections in class and other teaching links have arranged students' discussion, grouping, communication and other activities, so that students can change passive acceptance and memory of knowledge to actively construct the framework and system of new knowledge in the fun of cooperative learning, so as to complete the internalization process of knowledge.
4. Pay attention to the gradual learning process. In the process of concept, image, nature, application and development, the students can feel challenge and gain by leaping and reaching. The design of different difficulty topics will take into account the individual differences of students in the classroom.
In the process of designing the teaching of this lesson, in line with the principle of following the cognitive law of students and letting them experience the formation and development of knowledge, I designed the following teaching procedure to inspire students to gradually discover and understand the image and nature of exponential function.
1. Create scenarios and introduce new courses
Teacher's activities: ¢Ù show two examples with computer. The first is the problem of computer price falling, the second is the example of cell division in biology. ¢Ú divide students into odd and even series.
Student activities: 1) write the relationship between computer price y and month x, and the relationship between cell number y and division number x, and communicate with each other; ¢Ú The concept of recall index; ¢Û The concept of exponential function is summarized; ¢Ü The necessity of discussing the base number of exponential function and the classification method are analyzed.
Design intention: stimulate students' learning motivation through living examples, clear up knowledge barriers caused by unclear concepts, cultivate students' thinking initiative, and prepare for breaking through difficulties;
2. Inspire, induce and seek new knowledge
Teacher activities: 1. Give two simple exponential functions Study Draw their pictures. 2. Draw the images of the two exponential functions on the prepared blackboard. 3. Write the properties of the exponential functions on the blackboard.
Student activities: ¢Ù draw two simple images of exponential function; ¢Ú communicate and discuss; ¢Û summarize the aspects involved in the study of function properties; ¢Ü summarize the properties of exponential function.
Design intention: let students do simple image of exponential function, which can promote students' deep understanding of the content of this lesson. After students complete the basic drawing, the teacher will use the small blackboard which has been listed before class and established coordinate system to show accurate drawing methods, so as to further standardize students' drawing habits, Then, with the help of "function plotter" and multimedia, the image of exponential function is generalized to the general situation. Students will naturally summarize the properties of exponential function by observing the image, and at the same time, the discussion of the base number becomes logical.
3. Consolidate new knowledge and feedback feedback
Teacher's activities: ¢Ù blackboard example 1; ¢Ú blackboard example 2: Question 1; ¢Û introduce the expanded knowledge of archaeology.
Student activities: ¢Ù learning the standard steps of solving problems; ¢Ú completing the second and third questions of example 2; ¢Û completing group exercises; ¢Ü expanding the field of vision; and experiencing the application value of mathematics.
Design intention: the design purpose of this link is to realize students' preliminary application of exponential function knowledge, complete the process of students' learning "practice recognition practice", and strive to cultivate students' good problem-solving habits through the teaching of examples and standard blackboard writing, so as to play the exemplary role of teachers The third question is to consolidate students' understanding and Realization of the nature of exponential function. They can use the property of exponential function to solve mathematical problems. Through three group exercises, teachers're guidance and students' gradual improvement can be realized. The exponential function is closely related to the calculation of loan interest rate, the calculation of half-life in chemistry and the modern application of archaeological technology. The "Application of 14C in chemistry in Archaeology" introduced in this link not only broadens the students' vision, but also lays the groundwork for the next study of "calculating the interest rate of installment payment".
4. Summarize and deepen the goal
Teachers' activities: 1) guide students to summarize the classroom knowledge and complete the induction of mathematical methods such as classification discussion and combination of number and shape; ¢Ú Arrange homework after class and expand
Students' activities: complete the in class summary of the concept and nature of exponential function, and further deepen the learning objectives through homework after class. Students with the ability to complete the online survey and exchange the achievements of China's 14C archaeology with students in the next class.
Design intent: the teacher guides students to sort out the knowledge of exponential function, deepen the knowledge and skill objectives, and consolidate the objectives through homework.
5. Blackboard writing design
Considering the function of blackboard writing in the teaching process, I designed a blackboard composed of three plates in this lesson. The proportion of the blackboard is 2:1:1. The first plate contains two parts: one is the definition of exponential function; the other is the small blackboard with coordinate system and table prepared before class; The second part describes the first question of example 1 and 2; The third part is composed of the last two questions, exercises and class summary of example 2.
5¡¢ Teaching evaluation
The timely and effective teaching evaluation can mobilize the atmosphere of the classroom, infect students' emotions, and play a positive role in promoting classroom teaching. Therefore, I will run through the teaching evaluation in each teaching link of this class. For example, the expression evaluation of scene introduction, the memory evaluation of recall index knowledge, the inductive evaluation of the concept of exponential function, the accuracy evaluation of drawing, the normative evaluation of problem-solving, and the expressive evaluation of summary. In students' communication, discussion, exploration and other links, we should encourage students to complete the mutual evaluation of knowledge and ability. Through a variety of evaluation methods, more students can gain self-confidence in learning, and complete the teaching and learning tasks of this class in a relaxed and harmonious classroom evaluation atmosphere.
Of course, teachers will get a more comprehensive evaluation of students' knowledge and Reflection on the classroom effect by correcting students' homework, and revise the classroom design scheme in the follow-up time to achieve the expected teaching effect and realize the development of students' ability. The above is my design and thinking of exponential function class, please criticize and correct!
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