First of all, use information technology in math class.
(A) help to cultivate students' mathematical thinking ability
Mathematics pays attention to logical reasoning and cultivates students' abstract thinking ability. The animation demonstration supported by information technology and the scene reappearance of mathematical problems in life can enable students to think and learn mathematics step by step through their own discovery and exploration, from concrete problems to abstract concepts, from special problems to general laws.
In the production of the courseware "Axisymmetry in Life", I used the network to show a large number of axisymmetric figures in life, and attracted students' attention with the video of butterflies flying, and then enlarged a butterfly into a plane figure; When teaching polyhedron expansion diagram, students and teachers can make full use of objects and mark the six faces of the cube with letters A, B, C, D, E and F. However, due to the opacity of objects, it is inconvenient for students to observe. So I made a cube with a geometric sketchpad, marked six faces with different colors and letters, which can be seen through, and then combined with physical objects to teach. This process makes students directly feel that mathematics comes from nature and is abstract from practice, which creates a good situation for mathematics teaching, constructs an ideal learning environment, and receives an ideal teaching effect, so that students naturally accept mathematical concepts, broaden their horizons and help cultivate divergent thinking.
(B) is conducive to increasing classroom capacity and improving classroom efficiency.
The use of information technology creates a good cognitive environment for students and provides a shortcut for students to master new knowledge. To construct students' cognitive structure, mathematics teaching must only focus on students' knowledge accumulation, and judge the quality of teaching by mastering the "quantity" of knowledge, ignoring that students can grasp the present situation of mathematical knowledge structure from the internal relationship of mathematical knowledge.
For example, when learning Pythagorean Theorem, teachers can collect some information related to Pythagorean Theorem, such as aliens, Pythagorean Theorem, etc., so as to create a scene to stimulate students' interest and enthusiasm in learning Pythagorean Theorem, and then ask the following questions: What is the content of Pythagorean Theorem? Tell me about its origin. What are its proof methods? What problems can it solve in our lives? Pythagoras number, etc. Secondly, discuss and analyze the above problems, and then solve them in groups and tasks. Third, after the students have made clear their goals, they will collect relevant information through online independent search with questions. Fourth, guide students to carry out various forms of collaborative learning through the Internet, give full play to their intelligence and imagination, sum up solutions, and communicate through email, Tencent QQ live chat or posting on BBS to discuss its feasibility and whether the collected information is effective. Fifth, after students collect the information about Pythagorean Theorem, they summarize the information, complete the project summary and print it into a book, and get the history of Pythagorean Theorem, Pythagorean and Pythagorean Theorem, the proof method of Pythagorean Theorem, the application of Pythagorean Theorem in life, and the research status of Pythagorean number. Finally, the team members will make a written report to all the students and ask them to recall and explore. Reflect on how to extract mathematical knowledge from problems, how to find needed information, how to choose useful information, what quantitative relationship to use to solve problems, whether it is pleasant to cooperate with team members, which learning partners are worth learning, and how to apply these mathematical knowledge and learning methods in the future. Through this process, all students basically have a good grasp and understanding of Pythagorean theorem and its application.
(3) Stimulate students' enthusiasm for autonomous learning.
German educator Steward pointed out: "The mystery of education lies not in teaching, but in inspiration, arousal and encouragement." With its novelty, interest and artistry, we attract students' attention through intuitive and vivid teaching methods and create a teaching situation that conforms to students' psychological characteristics, which is an interpretation of the art of inspiring, awakening and encouraging teaching. Creating situations in teaching, stimulating students' cognitive drive and activating students' thinking will make students feel cordial. Applying information technology to teaching can make the teaching form interesting, novel and vivid, thus sprouting their feelings for mathematics and generating their enthusiasm for autonomous learning.
For example, when I was studying inverse proportional function, I used flash to set up the story of "The Trouble of Cylinders-How to Lose Weight" to create suspense: There was a king of cylinders, which was filled with all kinds of cylinders, including a cylinder with a large bottom area and a high waist. He was proud of his brawniness, but recently he was very worried and suddenly became inferior. Why did he ask? It turns out that other slender columns are laughing at it, saying it is too fat. Amy's column not only wants to keep the space advantage unchanged (volume unchanged), but also wants to make herself thinner and taller. It tried its best, but failed to realize its wish. Smart students, can you help the column to relieve troubles? In this way, students are guided to explore how to solve practical problems with inverse proportional function.
Such witty fairy tales can stimulate students' curiosity, quickly dispatch students' emotions, stimulate students' thirst for knowledge, activate students' knowledge reserves, and let students actively think and study in the mathematics kingdom, so as to achieve the goal of getting twice the result with half the effort, saving time and being efficient.
(D) The difficulties that help students to master and remember mathematical knowledge.
For junior high school students, they are in the transition stage from thinking in images to abstract thinking, and the advantages of thinking in images are greater than that of abstract thinking. Things or images are more convincing than abstract language and formulas. In addition, they are active and curious, easily attracted by intuitive and interesting things, and their short time and poor persistence often affect the teaching effect and quality, so multimedia information technology is of great use. Because animation technology is one of the advantages of information technology, it can be introduced into the classroom and participate in teaching. Its image is concrete, dynamic and static, and it is full of emotion. Therefore, if properly used, it can turn abstraction into concreteness, mobilize the synergy of students' various senses, reduce the difficulty of teachers' teaching, and break through important and difficult points, so as to effectively realize intensive and concise teaching.
1, from abstract to intuitive, to promote students' understanding of mathematical knowledge.
For example, when learning the concept of function, in order to make students have a clear and intuitive impression of the concept of "for every value, there is a unique value corresponding to it", I use the intuitive characteristics of multimedia to intuitively display "for every value, there is a unique value corresponding to it" in the form of sound and animation. It not only aroused students' pride, but also had a thorough understanding of the concept of function.
2. From static to dynamic, let students truly feel the formation process of knowledge.
For example, in the chapter of "Circle", all knowledge points are dynamically linked, the positions of many graphs have changed, and the laws and conclusions contained between graphs remain unchanged. Teachers who are familiar with the geometric sketchpad will invariably demonstrate the "power theorem of a circle" with the geometric sketchpad, that is, the intersection theorem → secant theorem → secant length theorem. When the mouse moves, the conclusion appears immediately, and the effect is quite good. In fact, theorems that need to be proved by knowledge, such as "vertical warping theorem", "central angle, arc, chord and chord center distance theorem", can be dynamically revealed through the geometric sketchpad.
3. Simplify the complexity and reproduce the process of knowledge development.
For example, when studying the properties of quadratic function, I used the software "Geometry Sketchpad" to explore the properties of quadratic function, which is very intuitive. In this class, I asked students to draw the image of quadratic function on draft paper with basic methods and steps. This is the basic method that students can master and understand. Next, I will use the Geometry Sketchpad to input parameters,,,,. Compare the function image obtained on the computer with the image drawn by the students themselves, and then stimulate the students' strong desire for knowledge. Of course, the focus and difficulty of this section is not the function image, but to let students clearly understand the nature of quadratic function. In the dialog box "Motion Parameter Properties of Operation Action Button", I changed the parameters from "to" to guide students to observe the different changes of images. In this way, students can clearly, intuitively and quickly observe the different changes of function images. "The parameters have changed, the parameters have changed, and how will the image change?" I throw this question to my classmates, who will find it and summarize it themselves. In this section, I use the advantages of information technology, with the help of geometry sketchpad software, vividly show the dynamic process of image changes caused by parameter changes in front of students. This kind of dynamic simulation not only solves the difficulties in mathematics teaching, but also makes students feel the advantages of solving practical problems with computers, mainly to stimulate students' curiosity and interest in learning.
4. Solve the shape by number, and reveal the relationship between number and shape intuitively.
For example, in the teaching of "the image of inverse proportional function", there are two difficulties in traditional teaching: one is the formation of hyperbola, the other is the understanding of hyperbola and the infinite approximation of two coordinate axes. In order to break through these two difficulties, I changed the traditional teaching mode of "teacher demonstration-student imitation-teacher-student discussion", brought students into the computer classroom and provided them with a drawing software. Then, with the guidance and help of the teacher, I asked the students to use this media technology to "draw" hyperbola by giving more different values to the independent variables, and finally found and summarized the inverse proportional function. This mathematical activity is not to solve numbers and shapes independently, but to calculate numbers and shapes naturally, which deepens students' understanding and mastery of the image and essence of inverse proportional function.
(E) conducive to the implementation of hierarchical teaching.
Mathematics is a basic subject, which is the basis of learning physics, chemistry and other disciplines well. It requires a person's logical thinking ability and understanding. Due to individual differences, students have different levels of understanding and mastery. This makes students have many different problems in the process of learning mathematics. If we follow the traditional teaching method, it is difficult to give consideration to students of different levels, and it is especially easy to form "full house irrigation" The integration of information technology and mathematics curriculum has unique advantages in hierarchical teaching.
For example, when I explain the judgment of triangle congruence, I make this section into a web page, which is divided into judgment theorem, example analysis, knowledge exploration, magic question and answer, and senior high school entrance examination questions. "Bullknife quiz" and "senior high school entrance examination" are two parts, and the topics are from easy to difficult. Students can choose different levels of questions according to their mastery of knowledge, and the questions and answers have hyperlinks, which students can click freely. This will enable students to get feedback in time, make students at different levels have a sense of accomplishment, and let students explore independently. Learning in this network environment breaks the non-replicability of traditional classroom teaching content, allowing students to focus on solving their own difficulties according to their own needs, thus realizing hierarchical teaching.
Second, how to better integrate information technology into mathematics teaching
(A) Change "Listening to Mathematics" to "Doing Mathematics"
The essence of education lies in participation, that is, fully mobilizing students' enthusiasm, initiative and creativity, allowing students to participate in teaching to the maximum extent, and allowing students to actively acquire knowledge with their own way of thinking. In junior high school mathematics experiment teaching, students can truly experience the formation process of mathematical knowledge by operating computers, and discovering mathematics by doing mathematics is not only conducive to students' understanding and mastery of mathematical knowledge, but also conducive to stimulating students' potential sense of inquiry and innovation.
For example, when studying the relationship between the angle of circle and the angle of center, I made the following design: As shown in the figure, sum is the angle of the angle of circle and the angle of center relative to the same arc, and measure the size of the two angles.
Question 1: Move the points and guess the relationship between them?
Question 2: When moving a point, do you find that when it is fixed, the circumferential angle of the arc is fixed? Students move the position of the point through hands-on experiments.
Question 3: When moving a point, what is the positional relationship between the central angle and the peripheral angle?
Students use the geometric sketchpad to measure the size of two angles, observe and guess through the size of the change, and find the same through the position of the moving point in the change, and get the conclusion about the fillet they want to learn, that is, the fillet surrounded by an arc is half of the central angle it surrounds. Observing the position relationship between the fillet and the central angle paves the way for the next theorem proof and case proof, and the classroom introduction is natural and smooth.
(B) the use of multimedia to make abstract mathematical concepts concrete
Give full play to the role of modern educational technology, and pay more attention to the generation and development of mathematical definitions, the application of knowledge and the infiltration of mathematical thinking methods in the design and teaching of mathematical software. Mathematics is a discipline with high abstraction and strict logic, especially mathematical concepts. The understanding of primary school students is mainly manifested in the concrete thinking of images. Therefore, it is difficult to understand and master mathematical concepts. Especially the concept of geometry, because students are young. Lack of basic concept of space. This concept is difficult to understand. Some students only master the description of the concept in form and can't use it at all. Therefore, there is no formula to calculate the area during homework, and the fill-in-the-blank questions are always wrong. Judgment and multiple choice questions depend entirely on luck, which directly affects the quality of teaching. Concepts come directly from life and from concrete things, and teaching concepts should also start from concrete things. Using multimedia can solve this problem well, make it concrete and organized, and make it easy for students to understand and master.
For example, when I teach the course Understanding Corner, the most common mistake that students make is that "the size of the corner is related to the length of the two sides that make up the corner". In order to overcome students' misunderstanding, we designed such a teaching situation: displaying a group of pictures with two equal angles but unequal sides and two equal angles but unequal sides on a computer screen, and asking students to judge the size of each diagonal? Results 70% of the students came to the wrong conclusion that the side length is too big. At this point, I didn't deny it immediately, but let the students discuss it in groups of four. The students verified it together by drawing, comparing, measuring and discussing, and got the correct answer. At this time, in order for students to further intuitively verify and show the cognitive process, a high-brightness "corner" is displayed on the computer screen, and students are required to pay attention to what happens to the size of the corner when the two sides of the corner change. The students witnessed the two sides slowly extending without changing the angle. Through discussion and observation, they learned the truth and unified their understanding, which not only stimulated students' interest in learning, deepened their understanding of scientific knowledge, but also developed their thinking.
(C) to guide students to take the initiative to solve problems
In the information technology environment, "multi-contact representation" has been fully exerted, providing an interactive learning environment for students. Many computer softwares are not only multimedia demonstration tools, but also tools to help students explore and understand, enriching and expanding the content and form of mathematics activities. Teachers can guide students to measure and calculate through experiments, put forward assumptions and prove or deny them, from mathematical model establishment to demonstration, from performance prediction to law exploration, so that students can learn to ask questions, analyze problems and then solve problems.
For example, for the question "connect four midpoints of an arbitrary quadrilateral in turn to form a midpoint quadrilateral. What quadrilateral is it?" Try to prove the solution of your conclusion. I instruct students to explore as follows: ① Drawing: Students use the "Geometric Sketchpad" to make any quadrilateral (four vertices can be dragged at will) and its midpoint quadrilateral; (2) Inquiry: drag a vertex of the quadrilateral arbitrarily to change its shape, and find that the shape of the quadrilateral also changes; ③ Guess: What properties of the original quadrangle determine the shape of the midpoint quadrangle? ④ Verification summary. This will leave more room for students to think, let them solve problems on the basis of existing knowledge, and constantly find new problems and put forward new conclusions, which will help to cultivate students' reflective consciousness and problem-solving ability.
(d) Improve the effectiveness and credibility of practical feedback, consolidate new knowledge and assist teaching.
Whether a class is successful or not, the practice link is also very important. How can we stimulate students' enthusiasm for doing problems and make every student interested in doing them? In teaching, we can design exercises including animation, graphics and sound, give full play to the remarkable characteristics of human-computer interaction and instant feedback, and design different levels of exercises for students at different levels, including "trying", "practicing", "comparing" and "testing you", from easy to difficult, step by step, to stimulate interest, thus effectively prompting them to actively participate and develop independently.
For example, in the exercise class teaching of trigonometric function application, auxiliary lines are added by computer preset, right triangles and rectangles are constructed, the contents of trigonometric function application problems are solved and several examples are displayed, and the key points are highlighted step by step from all directions and angles, so that students can sum up important methods and skills to solve problems, thus improving their ability. When we talk about the understanding of various cylinders, cones, platforms and spheres in solid geometry and the calculation formulas of area and volume, we can use various animation forms such as division, combination, rotation, combination, movement, cutting and display of space graphics, and combine relevant necessary explanations and beautiful music to make students immersive and have a three-dimensional sense. At the same time, through enlightening questions, guide students to actively develop their thinking and self-awareness. Introduction of formula. Animation simulation can not only completely change the tradition: imagination, specious and difficult to understand in teaching? Bitterness can also fully stimulate students' initiative in learning: observation, turning passivity into initiative, and producing unique teaching effects.
Thirdly, some thoughts on the integration of information technology and mathematics curriculum.
(A) teachers should not become a mere formality, but should always play a leading role.
The intervention of information technology should embody a new educational concept, which is not only the increase of teaching content, but also the novelty of means. The subject of classroom teaching activities is people. Teachers should not only impart knowledge, but also sow and irrigate the occurrence and development of knowledge and set an example for students to do things. Flexible adaptability, rigorous learning attitude and rigorous logical thinking all depend on telepathy between teachers and students, teachers' own personality charm and interesting explanations, emotional integration between teachers and students, and mobilizing students' active participation. We should not let "man-machine dialogue" replace the emotional communication between people, otherwise, modern media will become teaching machines and teachers will become keyboard players. Classroom teaching must proceed from the teaching objectives and technical characteristics, combine the teaching content, implement the principle of seeking truth from facts, and adopt it selectively and timely on the premise of ensuring the basic skills training of mathematics, stressing necessity, moderation and effectiveness, not pursuing form, and synthesizing for the sake of synthesis.
(B) the production of multimedia courseware should not be fashionable, but practical.
The application of courseware should be integrated into classroom teaching content. For mathematics teaching with abstract thinking and logical reasoning as the training purpose, the contents stored in the courseware should be concise, the pictures should be concise, the explanation and deduction should be guided by teachers and completed independently through cooperative inquiry. In order to help solve the difficulties in the combination of numbers and shapes in mathematics and understand the mathematical ideas abstracted from practice to guide practice, we think that we should make full use of the interactive function of information technology according to the characteristics of mathematics to design courseware into some relatively independent and interrelated modules, so that teachers can flexibly call the contents of each module, design their own teaching process and express their own teaching style according to their own needs of organizing teaching materials and different teaching ideas.
(3) The network electronic classroom should be an ideal place for mathematics education.
Under the guidance of teachers, students can operate by themselves, observe by themselves, find problems by themselves, study problems by themselves, and look up mathematical data in the network by themselves, thus forming a model of "doing mathematics" for students. Students become the masters of learning, no longer regard learning mathematics as a burden, enhance their confidence in learning mathematics well and enjoy the fun of learning mathematics. Students' hands-on operation will make their hands-on ability, observation ability and induction ability get a good exercise, which is more helpful to cultivate their thinking ability and innovation ability.
Of course, when we use information technology to serve teaching, we should pay attention to scientific and effective use. Although the integration of information technology and mathematics can expand the amount of information and questions for teachers and students, we should also pay attention to trade-offs. In classroom teaching, we must never forget the dominant position of teachers, otherwise it will be difficult to achieve good educational results if students are allowed to play their subjectivity.