(A) the basic ideas under the guidance of the concept of mathematics curriculum
The teaching content of junior high school mathematics should not only reflect the foundation, popularization and development of compulsory education; It should also reflect the instrumental, linguistic, creative and cultural nature of mathematics.
The traditional junior high school mathematics curriculum overemphasizes the scientific nature of mathematics and ignores the educational function of mathematics, and excessively pursues the rigor of logic and the formalization of the system. Therefore, the learning content is "complicated, difficult, biased and old", which leads to the situation that junior high school mathematics curriculum and junior high school mathematics education can not meet the needs of society and causes many junior high school students to be afraid of mathematics.
In the process of formulating the mathematics curriculum standard of compulsory education, someone once selected 9 classes from 9 ordinary middle schools, made a preliminary investigation on junior high school students' mathematics learning, and had a direct communication with them. The survey shows that students find some math content too difficult to learn and it is useless to learn it. The general view of mathematics content is that "there are too many concepts and formulas to remember"; "There are many and complicated data in the calculation problem"; "Application problems and geometric proof problems are too difficult"; "I am puzzled by this drawing problem;" I don't understand the function problem. 2 1.5% students like geometry the least.
Regarding what kind of mathematics should be taught to students in junior high school mathematics and how to guide students to know mathematics, the basic idea puts forward that "everyone should learn valuable mathematics; Everyone can get the necessary mathematics; Different people get different development in mathematics ","Mathematics is an indispensable tool for people's life, labor and study ". This spirit is embodied in the textbooks of Hunan Education Edition. For example, the algebraic expressions 2. 1, 2.2 (page 75) and 2.3 (page 82) in the second chapter of the first volume of grade seven, all introduce problems from real life. It emphasizes the practicality, inquiry and cooperation of mathematics.
(2) Development-oriented teaching concept and learning concept under the guidance of basic concepts.
In the traditional junior high school mathematics teaching, vivid and rich mathematics content is replaced by mechanically boring theorem definitions and formulas; Mathematics learning means that teachers ask students to listen, memorize theorems and formulas, and memorize all kinds of questions. Teachers can teach until they die, and students can learn until they die, so math learning is boring.
The new curriculum requires establishing a new concept of teachers' teaching and students' learning;
1. Teachers' teaching philosophy: "Students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning".
2. Students' view of learning: "Hands-on practice, independent exploration and cooperative communication are important ways to learn mathematics", "Learning activities should be a lively, proactive and personalized process". For example, the paper-cutting method of p. 105 in the first volume of the seventh grade of Hunan Education Edition; Obtain different information from statistical data; P. 19 1 step to collect data. It embodies this new teaching concept.
(C) the evaluation view of mathematics education under the guidance of basic ideas
According to the basic idea, the core of the new evaluation idea is: "the learning process of students should be brought into the evaluation field of vision;" Expand diversified evaluation objectives and methods; Teachers should be urged to improve teaching. "The traditional junior high school mathematics education evaluation is characterized by quantification. In the practice of education and teaching, this quantification has evolved into a queuing examination characterized by "deduction". This "queuing" has a positive side (enlightening students), but it focuses on "screening" and "selection". Constantly queuing with scores to evaluate students' advantages and disadvantages will easily make students who are enthusiastic about learning begin to doubt themselves and their abilities and become less confident after falling behind once or twice for some accidental reasons. The enthusiasm for learning fades and loses with the "falling behind", which leads to the fear and even disgust of mathematics learning.
According to the basic concept, the curriculum standard puts forward five evaluation suggestions for junior high school mathematics education:
1, pay attention to the evaluation of students' mathematics learning process.
2. Appropriate assessment of students' basic knowledge and skills.
3. Pay attention to the evaluation of students' ability to find and solve problems.
4. The evaluation topics and methods should be diversified.
5. The evaluation results should be presented in a qualitative and quantitative way.
The second question: How to have a good junior high school math class in combination with my own teaching practice?
Mathematics curriculum standards set up new ideas and put forward new requirements for mathematics teaching. Mathematics teaching in middle schools is undergoing great changes. Middle school mathematics teachers should actively and quickly reflect on past and present mathematics teaching, understand new mathematics curriculum ideas and establish a new concept of middle school mathematics teaching.
(A) the establishment of diversified teaching objectives
"The mathematics curriculum in compulsory education emphasizes starting from students' existing life experience, allowing students to personally experience the process of abstracting practical problems into mathematical models and explaining and applying them, so that students can gain an understanding of mathematics and make progress and development in many aspects such as thinking ability, emotional attitude and values. Based on this concept, mathematics curriculum has set diversified teaching objectives from four aspects: knowledge and skills, mathematical thinking, problem solving, emotion and attitude. Mathematics teaching should not only attach importance to knowledge and skills, but also attach importance to emotional attitude. It also puts intellectual factors and non-intellectual factors in the same important position. Mathematics teaching should not only pay attention to problem solving, but also pay attention to mathematical thinking process. Also put the result and the process in the same important position.
(B) the establishment of teacher-student interaction.
Mathematics teaching is the teaching of mathematics activities and the process of communication, interaction and common 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). In traditional teaching, the focus of teachers' goal is to change students, promote learning, form attitudes, cultivate personality and promote skills development, and complete the task of socialization. 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 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 teachers 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; Ask teachers to discuss and explore with students, encourage students to think, ask questions, choose and even act freely, and try to be students' consultants and active participants when exchanging opinions; Teachers are required to establish emotional friendship with students, so that students feel that teachers are their bosom friends.
Once the roles of teachers and students are changed and a new relationship between teachers and students is established, we can clearly feel that classroom teaching is carried out and completed in the interaction between teachers and students. Establishing a good interaction between teachers and students requires teachers to think more about how to let students learn relevant knowledge and skills through their own study when preparing lessons. Respect students in class, respect their experience and cognitive level, let students ask questions boldly, take the initiative to explore, and mobilize students to actively participate in the discussion and solution of problems; We should change roles flexibly, look at problems with "childlike eyes", think with "childlike innocence", solve problems with "childlike interest", participate in students' learning activities together, and become students' intimate friends and learning partners.
(C) the introduction of life-oriented learning situations
"Curriculum Standard" points out: Mathematics curriculum "should not only consider the characteristics of mathematics itself, but also follow the psychological laws of students learning mathematics, emphasizing starting from students' existing life experience ... Mathematics teaching activities must be based on students' cognitive development level and existing knowledge and experience. "That is to say, mathematics teaching activities should be based on students' development, and students' personal knowledge, direct experience and real world should be regarded as important resources for mathematics teaching. For example, if a teacher is in Jiaxing, how big is 1 million? Ask the students first: "Our Jiaxing Wufangzhai Food earned nearly 590 million US dollars during the two sessions. Do you know how big $590 million is? ""... ""So who has seen such a big number elsewhere? "This way of speaking is easy for students to accept. When it comes to local specialties, students naturally feel cordial and proud, and then connect them with similar large numbers that are common in daily life, introduce nature, kindness and closeness to life, and establish a democratic, scientific, harmonious and pleasant learning atmosphere for learning new knowledge. This vivid and interesting situation is helpful to stimulate students' interest in learning, make learning a pleasure and become students' conscious behavior.
(D) the choice of 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-ended questions, such as: for example 1, a middle school engages in greening and wants to build a flower bed on a rectangular open space. Now the design scheme is collected, and it is required that the design scheme is axisymmetric (it can be composed of circles, squares or other figures). How to design? (This is an open-ended question) Example 2, there is a kind of crab that can only survive for two days at most after being caught from the sea. If kept in a pond, the survival time can be prolonged, but a certain number of crabs die every day, and the individual weight of crabs remains basically unchanged during the stocking period. At present, a dealer bought 1000 kg live crabs at the market price and kept them in the pond. At this time, the market price is 30 yuan per kilogram. According to estimates, the market price per kilogram of live crabs has increased by 1 yuan every day since then. However, stocking them 1 day requires various expenses, 400 yuan, with an average of 10 kg of crabs dying every day. Assuming that all the dead crabs are sold on the same day, the price is 20 yuan per kilogram. (1) If the live crabs are sold at one time after X days, and the total amount of 1000 kg crabs is Q yuan, please write the functional relationship between Q and X; (2) How many days after the dealer hoards the crabs and sells them, can he get the maximum profit (profit = total sales-acquisition cost-expense)? What is the maximum profit? This is a project exploration question. This conditional open question gives different methods (cases) required in the question, and seeking the best method (case) is helpful 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. Therefore, a good open-ended question should meet all or several characteristics such as unconventional, participatory, interesting and challenging, open and exploratory. Secondly, learning materials should not be limited to textbooks, but life events, practical activities and growth experiences can all be used as learning materials.
(E) Adopting diversified teaching methods
The new curriculum standard emphasizes that students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning. Teachers should stimulate students' enthusiasm for learning, provide them with opportunities to fully engage in mathematical activities, and help them truly understand and master basic mathematical knowledge and skills, mathematical ideas and methods in the process of independent exploration and cooperative communication, so as to gain rich experience in mathematical activities. In other words, teachers are required to adopt diversified teaching methods in teaching. It can be summarized into four categories: teacher guidance, practical operation, independent inquiry and cooperative communication.
Teacher guidance. Although middle school students have certain life experience and knowledge base, they learn more from the indirect experience of human civilization; Although they are in the dominant position in learning, this does not weaken the role of teachers in teaching, but puts forward higher requirements for teachers' organization and guidance ability. Such as "parallel axiom" and "four operations", as established indirect experience, if students are allowed to explore by themselves, it may be time-consuming, laborious and inefficient, and teachers only need proper guidance to solve it.
Practical operation. The thinking of middle school students depends largely on indirect experience and intuitive feeling. Sometimes simple operation activities and practical experience can help them understand abstract mathematics, such as the understanding of unfolding and folding, the use of calculators and looking from different directions. It's better to move than to say a hundred words. Teachers should be good at organizing students to carry out practical activities.
Independent investigation. The process of learning is a process of internalizing external knowledge, and it is very important to give full play to students' independent inquiry ability. As an important way for students to learn under the concept of new curriculum standard, teachers should fully give students this right. If you learn to understand equations, you will find that the basic properties of fractions and ratios are closely related to knowledge. If the teacher lets go, you will get better results, and students can communicate with each other more independently and effectively, and build a good knowledge structure.
Cooperation and exchange. The teaching process is a process of cooperation and communication. In teaching, teachers should deal with the relationship between teachers and students, treat every student equally, make more use of group learning and activity games to promote students' cooperation and communication. On the one hand, it can promote learning to be more efficient, on the other hand, it can cultivate cooperative habits and communication skills in the learning process, and better promote the development of students.
(six) to carry out participatory teaching process.
The new curriculum standard not only attaches importance to knowledge and skill goals, but also emphasizes process goals, and pays attention to students' learning experience and exploration feelings. Therefore, it is necessary to fully develop the process of students participating in learning. In order to carry out this process smoothly and effectively, I think we should do these three things well: improve the sense of autonomy, encourage the main body to participate, and attach importance to active evaluation.
Improve self-awareness. The premise of the development process is that students should actively participate in the process, which requires students to have a strong sense of autonomy and regard learning as their own subjective behavior. To achieve this goal, teachers should respect students' subjectivity, give students opportunities for individual activities, experience feelings, enjoy success and harvest in activities, which is also the teaching requirement emphasized in the Standard.
Encourage the main body to participate. Students' learning is not a process of indoctrination, but a process of active acquisition. Only by encouraging students to participate in the learning process can we get better learning results.
Attach importance to active evaluation. As a lever, evaluation not only determines the results of students' learning, but also determines their learning behavior. As the main body of learning, students' interest in learning depends not only on teachers' evaluation, but also on students' self-evaluation. In learning, teachers should give students the opportunity to participate in the evaluation of learning process and the right to participate in the evaluation of results. Students' active participation in the evaluation of learning process and results can enhance the initiative of learning and make learning a conscious and happy action.