1 How to improve the mathematics ability of senior high school students
Improve students' mathematical application ability
1. Pay attention to language expression ability. The rigor and conciseness of mathematical language is an important part and carrier of mathematical knowledge, and mastering mathematical language is the premise of solving mathematical problems. A math application problem can be clearly expressed by students through reading comprehension, which is equivalent to solving half the problem. In teaching, we should consciously cultivate students' language expression ability and pay attention to language communication between teachers and students in order to enhance understanding of problems.
2. Set up problem situations and enhance the awareness of applied mathematics. Knowledge comes from life, and different knowledge has different backgrounds. In the teaching process, we can use some familiar examples that contain quantitative relations or spatial forms to set up relevant problem situations, so that students can feel that knowledge really comes from reality, which is self-evident to enhance students' awareness of applied mathematics.
3. Making decisions by using mathematical problems can further improve the ability of applying mathematics. Applying what you have learned is the ultimate goal of learning. In order to further enable students to understand the important role of mathematics in solving practical problems, we can provide them with more opportunities to make some mathematical decisions.
Improve students' ability to examine questions
1. Attach importance to reading teaching. Practice shows that one of the factors that cause some students' difficulties in mathematics learning is poor reading ability, especially in reading and understanding the connotation of mathematics. Indeed, many students blindly touch the number according to the known conditions at a glance, without full consideration, which affects the formation of problem-solving ability. Therefore, it is of great practical significance to improve students' ability to examine questions and attach importance to mathematics reading.
2. Correctly understand and cultivate the accuracy of students' exams. Accurate understanding of the meaning of the question is the premise of examining the question. In the process of examining the questions, we should not only have a correct understanding of the conditions, definitions, concepts, theorems and formulas involved in the questions, but also grasp some key words to prevent the answers from appearing. In teaching, teachers should pay attention to guide students to correctly understand the meaning of questions, cultivate the accuracy of students' examination of questions, guide students to form good thinking quality, and thus cultivate students' examination ability.
3. Fully explore and cultivate the profundity of students' examination. The reason why many students make mistakes in solving problems is not that some questions can't be answered, but that the questions are not thoroughly examined and the hidden conditions are not fully explored. In teaching, teachers should pay attention to digging hidden conditions and cultivate students' profundity in examining questions on the basis of guiding students to grasp the problems as a whole.
2 Mathematics teaching methods
Establish an interactive relationship between teachers and students
Mathematics teaching is the teaching of mathematics activities and the process of communication, interaction and development between teachers and students. The interaction between teachers and students in teaching is actually a way for teachers and students to get to know each other with their own fixed experience (self-concept). The goal of students is to change themselves as much as possible and accept socialization through the prescribed learning and development process. Only by narrowing the difference in this goal can it be conducive to the achievement and realization of teaching goals.
This first requires us teachers to change three roles. From the traditional knowledge giver to the participant, guide and collaborator of students' learning; From the traditional teaching dominator and controller to the organizer, promoter and director of students' learning; From the traditional static knowledge owner to the dynamic researcher. Secondly, teachers are required to practice teaching in a new role. This requires us to break the old habit of respecting teachers and attaching importance to morality, establish an equal relationship with students in personality, walk off the platform, walk into the students' side and have an equal dialogue and exchange with them; We are required to discuss and explore with students, encourage students to think, ask questions, choose and even act freely, and strive to be students' consultants and active participants when exchanging opinions; We are required to establish emotional friendship with students and make them feel that we are their bosom friends.
Choose open teaching content.
The new curriculum reform of mathematics emphasizes that mathematics learning is not a simple problem-solving training, and realistic and exploratory mathematics learning activities should become an organic part of mathematics learning content. The openness of teaching content is first manifested in the application of open questions, which promotes the transformation of mathematics learning methods, makes up for the deficiency of open mathematics teaching, and cultivates students' subjective spirit and innovative ability. There are many types of mathematics open questions, for example, a middle school should build a flower bed on a rectangular open space for greening. Now collect the design scheme, and ask the design scheme to be symmetrical (it can be composed of circles, squares or other figures). How to design? This is an open question? It helps to examine students' divergent thinking and innovative spirit, and so on.
In the use of open questions, it should be noted that the events contained in open questions should be familiar to students, interesting in content and willing to learn, which is a feasible problem that can be solved by students' existing knowledge; Open questions should enable students to get answers at all levels, and the answers made by students can be different from each other; Open question teaching should reflect students' dominant position.
3 math classroom interest
In addition to its high abstraction and strict logic, mathematics is also widely used and ubiquitous in our lives. If divorced from real life, the content will appear empty and boring. Therefore, in teaching, we should try to shorten the distance between classroom and real life, create some life situations, let students study in their familiar life environment, and make them feel that mathematics is not abstract and difficult to understand. On the contrary, it exists around us and in our lives. Mathematical knowledge comes from life and ultimately serves life.
The close connection between mathematics and life is an important concept in the mathematics curriculum standard. It emphasizes that starting from students' existing knowledge and life experience, guiding students to observe, think and communicate, fully excavating mathematics materials in life, awakening students' life experience, closely connecting mathematics knowledge with real life, and introducing themes in social life into classroom teaching are important links to embody new ideas in mathematics teaching. When designing lesson plans, teachers should creatively use and adapt teaching materials to make them more practical and close to life, so that students can feel that there is mathematics everywhere in life, and mathematics is inseparable from life, thus becoming interested in learning mathematics. Pay attention to quoting practical problems in life in class, guide students to experience and discover mathematics around them, and let students use mathematical knowledge to solve problems in life, thus generating interest in learning.
Students' interest in mathematics often begins with discussing mathematical problems. Teachers should skillfully connect with students' real life, reasonably organize teaching content, turn abstract into concrete, and make students have a strong interest in the mathematics knowledge they have learned. For example, in the teaching of "inverse function", I first tell students the functional model of magic performance. The magician's performance process of guessing cards is as follows: the performer holds six playing cards (excluding trump cards and cards of the same brand), and asks six spectators to touch 1 card from their hands, and tells them to see and remember their own brand when touching cards. The number of cards is as follows: A is 1, J is 1 1, Q is 12, K is 13, and the rest are subject to the values on the cards. Then, the performers asked them to calculate as follows: multiply their brand number by 2 plus 3, then multiply it by 5, and then subtract 25. Tell the performer the calculation result (absolutely accurate), and the performer can guess exactly what card you are holding at once. Do you know why? Guide students to analyze and observe, let the number of brands be the independent variable X, and take the calculation method mentioned by the performer as the corresponding rule, and get the function y=5(2x+3)-25, that is, y= 10x- 10. (1) In terms of meaning, the domain is {1, 2,3,? , 13}, it is easy to calculate the value range of this function is {0, 10, 20,? , 120}。 By solving the inverse function of ①, we can get x==y+ 1, ② where y ∈ {0, 10, 20,? ， 120}，x∈{ 1，2，3，？ , 13}。 When you tell the performer to substitute the value of X into the function value Y obtained from the function formula ①, he will quickly get the corresponding value of X from the inverse function formula ②. It is your brand number. After listening to this, the students' interest immediately came, but I didn't expect to be able to explain it with mathematical knowledge. Linking textbook knowledge with students' life practice in time and integrating mathematics knowledge into students' favorite activities have deepened students' understanding of the definition of inverse function.
4. Cultivate divergent thinking in mathematics
Establish a new teacher-student relationship and create a relaxed thinking environment.
First of all, in order to let students actively explore knowledge and give full play to their creativity, teachers should aim at cultivating students' innovative ability, reserve their own thinking space for students, respect students' hobbies, personalities and personalities, treat students equally, inclusively and kindly, and let students truly become the masters of learning. Only in this atmosphere can students give full play to their intelligence and creativity. Secondly, guiding the class to brainstorm is conducive to multi-directional communication and mutual learning between students.
Consciously do a good job in cooperative teaching in classroom teaching, so that the roles of teachers and students are in a dynamic change of communication at any time; It is necessary to design collective discussion, complementarity and group work to train students' cooperative ability. Let students discuss some difficult problems in class, which is a concrete embodiment of creating a new environment and carrying forward teaching democracy. In a relaxed environment, students can speak freely, express their opinions, dare to express their independent opinions, or correct others' ideas, and combine several ideas into the best one, thus cultivating students' divergent thinking ability in the learning process.
Change the angle of thinking and train the thinking of finding the opposite sex.
One of the important points of divergent thinking activities is that it can change the habitual thinking pattern and think from multiple directions and angles in order to solve problems. From the perspective of cognitive psychology, it is often difficult for primary and secondary school students to get rid of the existing thinking direction because of their age characteristics in the process of abstract thinking activities, that is to say, the individual (or even group) thinking mode of students often affects the solution of new problems, thus creating illusions. Therefore, in order to cultivate and develop the abstract thinking ability of primary school students, we must pay great attention to the cultivation of heterosexual thinking, and extend and enhance it, so that students can gradually form multi-angle and multi-directional thinking methods and abilities in training.
For example, there are internal relations among the four operations. Subtraction is the inverse of addition, division is the inverse of multiplication, and the relationship between addition and multiplication is transformation. When the addends are the same, addition is converted into multiplication, and all multiplications can be converted into addition. There is an internal relationship between addition, subtraction, multiplication and division. For example, how many 9s can you subtract from 333? Ask students to think from different angles and consider the relationship between subtraction and division. This problem can be regarded as that 333 contains several 9s, and the problem is solved. This kind of training not only prevents one-sided, isolated and static view of the problem, but also sublimates the knowledge learned, from which we can further understand and master the internal relationship between mathematical knowledge, and also train the divergent thinking, and its divergent thinking will certainly be well developed.