First of all, the idea of letter algebra
Replacing numbers with letters is the first mathematical idea that junior high school students come into contact with, and it is also the most important and basic mathematical idea in elementary algebra and even the whole mathematics.
In junior high school mathematics, letters are used to replace numbers, and various quantities and their relationships and changes, as well as reasoning and calculus between quantities, are all expressed in symbolic forms (including numbers, letters, graphs and charts, and various specific symbols), which is an ongoing set of formal mathematical languages. For example, ∣a︱ represents the absolute value of a number,-a represents the reciprocal of a number, an represents the product of continuous multiplication of n A's, s=40t represents the relationship between distance and time, and a pair of ordered real number pairs (x, y) represents the position of a point in a plane rectangular coordinate system.
Chapter 3, Chapter 7 (1) explains that letters replace numbers, that is, when students have just changed from primary school students to junior high school students, they begin to calculate numbers and numbers instead of letters for reasoning and calculation, which requires an adaptive process for most students. Therefore, the new textbook of Jiangsu Education Edition guides students to gradually master the mathematical thought of replacing numbers with letters in some rich and close situations. Representing numbers with letters is the basis and starting point of algebra, and it is also one of the main manifestations of "symbol sense". In fact, people often use symbols to express some meanings in their daily lives, such as weather forecast icons, traffic signs, staff and so on. Starting from this situation, it helps students feel that "in mathematics, letters are often used to represent numbers".
Representing numbers by letters is an important turning point from arithmetic to algebra, but its learning is based on arithmetic learning. Teachers should let students observe and summarize the rules through specific numerical operations, and form an understanding of the necessity of "representing numbers with letters". In fact, the knowledge of algorithms (exchange rule, combination rule, distribution rule, etc.). ), the area of simple geometry, travel problems, etc. It can explain the significance of using letters to represent numbers: universality, universality of application, etc.
In short, to learn junior high school mathematics well, we must first master the mathematical idea of replacing numbers with letters.
Second, the idea of conversion.
Transformation is transformation and belonging. Through the transformation process, the problems to be solved or unsolved are reduced to familiar normative problems or solved problems, so as to obtain the idea of solving problems.
In the long-term study and practice of applied mathematics, people have made a lot of achievements and accumulated rich experience, and many problems have also formed fixed method models and established steps. People call this problem with prescribed solutions and procedures a normative problem, and the process of transforming an unknown or complex problem into a normative problem is called problem reduction.
For example, for integral equations (such as linear equations with one variable and quadratic equations with one variable), people have mastered the basic properties of the equations and the theory of finding roots. Therefore, the solution of integral equation is a normative problem, and the process of transforming fractional equation into integral equation with denominator is the standardization of the problem.
In order to realize "transformation", "substitution" is often used in mathematics, also called transformation. In algebra, there are identity transformation, equation and inequality transformation with the same solution; Congruence transformation, similarity transformation and equal product transformation in geometry. Transformation is a means, and revealing what cannot be changed is the purpose. Exploring the transformation means for the unchangeable purpose constitutes the thinking and skills of solving problems. For example, given that x2+y2+2x-6y+ 10 = 0, find xy. For junior high school students, this problem cannot directly solve the binary quadratic equation about X and Y, but if we start with the complete square formula, the known condition can be transformed into (x+ 1) 2+(y-3) 2 = 0. And because the even power is negative, that is, (x+ 1)2≥0 and (y-3) 2 ≥ 0, (x+ 1)2=0 and (y-3) 2 = 0, so x =- 1 and y =
Third, the idea of decomposition and combination.
When a mathematical problem cannot be solved in a unified form, the range involved can be decomposed into several local solutions of the problem. Then the solutions of each part are combined to get the solution of the original problem. This idea is the idea of decomposition and combination, and its method is called classified discussion.
Decomposition and combination are one of the important mathematical ideas. For complex calculation problems, proof problems, etc. Using the thinking method of decomposition and combination can help students to think and analyze comprehensively and rigorously, so as to obtain reasonable and effective methods to solve problems. For example, the lengths of two sides of an isosceles triangle are 4 and 5 respectively. Find the circumference of this isosceles triangle. To solve this problem, firstly, we discuss it by classification: ① If 4 is the bottom, then 5 is the waist, and the lengths of three sides are 4, 5 and 5 respectively, which can form a triangle, and the circumference at this time is14; ② If 5 is the base, 4 is the waist, and the three sides are 5, 4 and 4 respectively, a triangle can be formed, and the circumference at this time is 13.
Fourthly, the idea of equation function.
The idea of equation and function is an important idea to deal with constant mathematics and variable mathematics, and it is of great significance to solve general mathematical problems. In junior high school mathematics, equations and functions are extremely important, and all kinds of equations and simple functions are systematically studied. For a complicated problem, it is often only necessary to find the equivalence relation and list one or several equations (equations) or functional relations, which can be solved well.
For example, a lighting store purchased a batch of energy-saving lamps of a certain model and used 400 yuan. In the process of handling, five lights were accidentally broken. The store sold all the remaining lamps at a high price in 4 yuan, and then used the money to buy a batch of such energy-saving lamps at the same price as last time, but the number of lamps purchased was 9 more than last time. Ask about the purchase price of each lamp.
Fifth, the idea of combining numbers with shapes.
The combination of numbers and shapes not only makes geometric problems a powerful algebraic tool, but also makes many algebraic problems obvious and intuitive. The combination of numbers and shapes is a very important idea in junior high school mathematics, which has a unique strategic guidance and adjustment function in solving mathematical problems. For example, the image solution of binary linear equations transforms the problem of quantitative relationship into the problem of graphic properties; A road with a length of 100 km will be built between A and B, and C is a 50 km nature reserve in Fiona Fang, with point C as the center. A is in the southwest of C, and B is 30 degrees east of C. Will highway AB pass through the nature reserve?
Of course, junior high school mathematics involves more than these five mathematical ideas. The above is just my humble opinion on several common mathematical ideas in junior high school mathematics. In the future teaching practice, I will pay more attention to and strengthen the mathematicization of students' mathematical thoughts, improve students' problem-solving ability and cultivate students' mathematical literacy.
Teaching summary: several common mathematical ideas in junior high school mathematics. In the past semester, I carefully prepared lessons, attended classes, attended classes and evaluated classes. I corrected my homework in time, commented on my homework, provided after-school counseling, and extensively dabbled in all kinds of knowledge, forming a relatively complete knowledge structure, strictly demanding students, respecting students, and promoting teaching democracy, so that students can constantly learn and improve, constantly improve their teaching level and ideological consciousness, and successfully complete the education and teaching tasks.
The following are my teaching experiences and lessons.
1, the key to improving teaching quality is to have a good class. In order to have a good class, I have done the following work:
⑴ Preparation before class: Prepare lessons.
(1) study the textbook carefully, understand the basic ideas, concepts, every sentence and word of the textbook, understand the structure, key points and difficulties of the textbook, master the logic of knowledge, be able to use it freely, know what information to supplement and how to teach it well.
② Understand the quality of students' original knowledge and skills, their interests, needs, methods and habits, and what difficulties they may have in learning new knowledge, and take corresponding preventive measures.
(3) Consider the teaching methods and solve how to teach the students the textbooks they have mastered, including how to organize the textbooks and how to arrange the activities in each class.
(2) the situation in the classroom.
Organize classroom teaching, pay attention to all students, pay attention to information feedback, mobilize students' intentional attention, maintain its relative stability, stimulate students' emotions at the same time, make them have a happy mood, create a good classroom atmosphere, the classroom language is concise and clear, overcome the repeated problems in the past, ask questions to all students in class, pay attention to stimulate students' interest in learning mathematics, combine teaching with practice in class, assign homework, and reduce students' burden.
2. To improve the quality of teaching, we should also do a good job of after-school counseling.
Junior high school students are active and playful, lack self-control ability, and often can't finish their homework on time. Some students copied their homework. In order to solve this problem, we should do a good job in students' ideological education, and make this work be used to guide students' study. At the same time, we should also do a good job in students' guidance and help, especially in the transformation of underachievers, and try to be friendly to them, for example, holding his hand and touching his head. From the beginning of praise, all people are eager for understanding and respect from others. Therefore, when talking with poor students, we should show deep understanding and respect for their situation and ideas, talk about our own shortcomings first, and then criticize the students.
3. Actively participate in lectures and evaluation, and learn teaching methods from peers with an open mind.
Learn from others and improve the teaching level.
4. Cultivate a variety of hobbies, read widely in the library, constantly broaden the knowledge and inject fresh blood into the teaching content.
5. "No one is perfect when he enters the classroom", which is inevitably flawed in teaching. For example, the classroom language is mild, there are few exams at ordinary times, and the language is not vivid enough.
Entering the 2 1 century, the society has higher requirements for teachers' quality. In the future education and teaching work, I will be more strict with myself, work hard, develop my advantages, correct my shortcomings, forge ahead and contribute to a better tomorrow.
Summary of ideological work
Over the past six months, with the kind care and enthusiastic help of the leaders and teachers of our lesson preparation group, especially my tutor, Mr. Sun Ning, I have worked hard to do a good job in education and teaching. Now I will summarize my work in the past six months as follows:
First, the performance of teachers' morality
Usually actively participate in faculty meetings, class teacher meetings and various educational and teaching activities. Attend the flag-raising ceremony on time every week, attend attendance on time, always adhere to the idea of "teachers have no discipline, educate people in everything", usually pay attention to their own teacher image, set an example, respect teachers, obey the unified arrangement of the school, and have a harmonious relationship with colleagues.
Second, the teaching work
From the 20** to the 20 * * school year, the school arranged for me to teach math classes in Class 10 and Class 10 in Senior Three. In teaching, I try to do the following:
(1) Prepare lessons carefully and try to be scientific. Accurate. It's tight
As I just joined the work, I have no teaching experience. Therefore, in the process of preparing lessons, in addition to carefully studying the textbooks and consulting various related books, I also actively consulted the old teachers of the preparation group, such as Mr. Sun, in order to deeply understand the textbooks and accurately grasp the key points and difficulties. At the same time, I also pay attention to the careful preparation of teaching plans and constantly sum up the experience and lessons in teaching.
1, highlighting new textbooks, new ideas and new methods.
To improve the quality of teaching, we should also do a good job of after-school counseling. Primary school students are playful and lack self-control. They often fail to finish their homework on time, and some students can't finish their homework. In order to solve this problem, we should do a good job in students' ideological education and implement this work in students' learning guidance. We should also provide students with guidance and help in their studies, especially the transformation of underachievers. For example, we should try to be friendly to underachievers. From the beginning of praise, all people are eager for understanding and respect from others. Therefore, when talking with poor students, we should show deep understanding and respect for their situation and ideas, talk about our own shortcomings first, and then criticize the students.
Actively participate in teaching and research group activities such as attending lectures and evaluating classes, learn teaching methods from peers with an open mind, learn from each other's strengths and improve teaching level.
Cultivate a variety of hobbies, read widely in the library, constantly broaden the scope of knowledge, and inject fresh blood into the teaching content.
"There is no shortage of gold, no one is perfect", and there are inevitably defects in teaching. For example, the language in class is mild, there are few exams at ordinary times, the language is not vivid enough, and the attitude towards underachievers is often impatient. All these require me to improve gradually in my work and treat every student seriously.
In the new century, society has put forward higher requirements for teachers' quality. In the future education and teaching work, I will be more strict with myself, work hard, develop my advantages, correct my shortcomings, forge ahead and contribute to a better tomorrow.