Keywords: independent and harmonious guidance of interests
Mathematics teaching should stimulate students' enthusiasm for learning, help students really understand and master basic mathematics knowledge and skills, mathematics ideas and methods in the process of autonomous learning activities, and gain rich experience in mathematics activities. Therefore, in mathematics classroom teaching, teachers' guidance should break through the superficial limitations of textbooks, guide students to think, analyze, understand and comprehend from the process of solving mathematical problems, master mathematical laws and mathematical thinking, and improve students' ability to solve practical problems by using existing mathematical models. Therefore, teachers' guidance is not only to guide students to solve a mathematical problem, but also to guide students to explore deeper things through mathematical problems and to guide students' thinking to a broad space for mathematical exploration.
1, interest guidance. Stimulate students' internal drive.
Good learning mood is indispensable to promote students' intellectual development, stimulate their interest in learning and form a classroom "learning field". As we all know, interest is an important factor that constitutes the internal driving force of cognition. If students have a good learning mood, they can stimulate a strong interest in learning. There are many ways to guide emotions, and the open strategy of paying attention to teaching is conducive to students' curiosity. Students' psychology is still in a semi-mature state, but the cognitive internal drive is developing rapidly. They are curious about all kinds of things and have a strong thirst for knowledge. Teachers should make full use of students' positive psychological factors, design a lead that can stimulate students' cognitive drive to introduce new courses according to different teaching contents, narrow the distance between teaching materials and students' life experience, and create a strong teaching atmosphere from the beginning. For example, when teaching "Simple Data Arrangement", the teacher first plays the game of "scissors, stone and cloth" with his classmates, and then asks three students to count the number of students' "scissors", "stone" and "cloth" and fill them in the table on the blackboard (the table is abbreviated). Then the teacher explained that this is a statistical table. Let the students speak freely and talk about the characteristics of the statistical table.
Originally, the course of data statistics was easy to make students feel boring, but the teacher introduced games that students were familiar with, which aroused students' interest and curiosity, so students were focused, thinking positively and the classroom effect was very good. In addition, it is also important to establish a good relationship between teachers and students. In classroom teaching, teachers should not appear in front of students as "authorities and supervisors", but should think and discuss with students as "participants", and provide students with "suggestions" first when encountering problems, rather than guiding students to do something, so as to reflect the equality between teachers and students and the participation in the teaching process. Harmonious teacher-student relationship helps to maintain and enhance students' self-esteem and self-confidence in exploring knowledge, stimulate students' enthusiasm and creativity in learning, and create a "competitive psychology" that allows students to play their potential advantages and strive to catch up with others, thus enabling students to realize a "psychological change" from passive acceptance to active participation.
2. Activity guidance to stimulate students' learning motivation.
The diversity of classroom activities is conducive to students' thinking. Due to the constraints of various factors in practical teaching and the characteristics of existing teaching materials, teachers often only pay attention to refining and essential logical conclusions in the formation and development of students' mathematical knowledge, and the formation process is simplified, so it is difficult for students to understand the ins and outs of knowledge. Therefore, in daily teaching, teachers should actively guide students to understand the occurrence and development process of knowledge, so that students can know how mathematical knowledge is produced and how it occurs, and how to use what they have learned to solve practical problems. In this way, students' mathematical knowledge will not become a tree without roots and passive water, and they will truly experience and understand the true source and significance of mathematical knowledge. For example, when teaching "Calculation of parallelogram area", the teacher can draw several parallelograms with different shapes and sizes on the grid diagram, so that students can count the base and height of the parallelogram by counting squares, and then observe and guess that the area of the parallelogram is related to its base and height, and the area is the product of the base and height. Whether this conjecture is correct or not, the teacher does not tell the students directly, but asks such a question: "What method can you use to prove this conjecture is correct?" This naturally leads students to use the mathematical idea of transformation, and the calculation formula of parallelogram area can only be deduced through experiments. Students really understand and master the ins and outs of parallelogram area calculation formula and the derivation process of the formula through hands-on and brain exploration activities.
3, thinking guidance, to stimulate students' thinking ability
It is necessary to provide students with rich and typical intuitive background materials, create environments and conditions that can activate the connection between knowledge, and show the process of knowledge generation, digestion and application, so that students' thinking and knowledge accumulation can all be devoted to the challenge of analyzing problems and understanding mathematical connections, so that mathematical thinking methods can be integrated with all kinds of knowledge. Give full play to the guidance, association and transformation functions of mathematical thinking methods in finding and solving problems, and flexibly use various mathematical knowledge and methods to analyze and solve problems. For example, for some questions, we should guide students to comprehensively use various mathematical knowledge and methods as much as possible, look for mathematical laws and connections, seek the best answers from different ways, and cultivate students' broad thinking. A teacher showed such a situation when teaching multiplication estimation: the school cafeteria bought 58 Jin of meat every day, with an average of per Jin 12 yuan. Please estimate how much it costs to buy meat in this canteen every day. After listing the formulas, the teacher asked everyone to think about how to estimate the product of 58× 12 quickly and leave more time for students to express their ideas.
Health 1: I take 58 as 60, and then 12 as 10. Use 60× 10=600, and use about 6O0 yuan every day.
Health 2: We can regard it as 50× 10=500, that is, more than 500.
Health 3: I take 58 as 60 and use 60× 12=720, so I can't reach 720 yuan.
Health 4: Only regard 12 as 10, and use 58× 10=580, which must be above 580 yuan.
Health 5: You can use 58× 10+60×2=700, which is probably 700 yuan.
Health 6: Use12× 60-12× 2 = 696 or 10×58+2×58=696. The exact number is 696, which is about 700 yuan.
The students speak freely and the teacher praises them from time to time. Finally, the teacher concluded: estimation is commonly used in our daily life. When encountering calculation problems, it is best to have estimation consciousness. Estimating approximate figures can reduce errors. There are many ways to estimate a topic, some of which are better. Now please discuss which of the above methods is better and give the reasons. Obviously, the teacher's teaching focus is not only on training "rounding" estimation, but also on the basis of estimation, highlighting the process of students' active inquiry and cultivating students' innovative spirit of diligent thinking and daring to seek differences, which is very important for their future development.
4. Question guidance to stimulate students' curiosity.
The characteristic of the "problem-oriented" teaching design process of primary school mathematics is problem-oriented. The questions that teachers should answer in each link are as follows: ① Reading the textbook for the first time, analyzing the teaching content and its logical starting point: What is the teaching content of this section? How many parts can it be divided into? What mathematical thinking methods are included in the teaching content? What knowledge, experience and thinking methods do students have to learn this section? (Logical Starting Point) Learning this section will provide a basis for students to acquire knowledge, experience and mathematical thinking methods in subsequent learning. ② Analyze and understand students' knowledge, experience and mathematical thinking methods, and determine the starting point of teaching: What teaching contents have students mastered or partially mastered in this section? How many people have mastered it? What is the degree of mastery? What don't you have? What content is closely related to students' real life and what content students lack of life experience? Do students already have the knowledge and skills needed for new study? Is the starting point of students' realistic learning consistent with the starting point of logical learning, and what are the gaps? ③ According to the teaching objectives and students' reality, adjust the teaching content and its presentation: Is the teaching content necessary to achieve the teaching objectives? What else do you need to add? What has nothing to do with the goal? What else is closely related to this section that students should know, or what students need in their lives but are not in the textbook? Is the presentation of teaching content in the textbook conducive to students' choice of learning methods such as independent exploration, cooperation and exchange? What adjustments need to be made? Can the arrangement order presented in the textbook be directly used as the teaching order? What adjustments need to be made? Imagine students' activities and solutions to problems, design teachers to adjust teaching plans and form preliminary teaching plans.
5. Use guidance to stimulate students' combination of learning and application.
The process of human cognition is a "perceptual-rational-perceptual-rational" cycle, which is progressive and spiraling. It is not the end of students' cognitive activities that teachers organize students to construct corresponding mathematical models from specific problems, but also organize students to restore abstract mathematical models to concrete mathematical intuitive or sensible mathematical reality, so that the established mathematical models can be continuously expanded, promoted and rooted in the process of returning from abstract to concrete. For example, after teaching engineering problems, you can design the following exercises: Teacher Zhang wants to make a set of furniture and is going to ask two masters from the furniture factory to cooperate. The furniture factory provided such a table (table outline) for students to help Mr. Zhang make suggestions. Which two masters are more suitable for cooperation? After some discussion among the students, the following three schemes were worked out:
① The cooperation between Party A and Party D can save time: 1 \u(+)
② Party A and Party C can save money by cooperating: (600+500)×[ 1÷(+)]
③ The cooperation between Party A and Party B saves money and time: (6O0+700)×[ 1 small (+)]
According to the actual situation of Mr. Zhang's family, you can choose different types of combinations. Such problems not only make students experience that reality is full of mathematical problems, but also solve practical problems, increase the space for students to explore and enrich classroom teaching.
Finally, the function of the teaching process is not single. Every class and every class activity will have a lot of influence on students. In fact, even if teachers pay attention to one aspect, students' feelings are varied. When teachers only pay attention to knowledge, students will feel bored and tasteless in emotion and attitude. This is also the impact on students. Based on this, it is necessary to:
(1) Choose a reasonable learning guidance method. In the process of implementing learning guidance, teachers need to design, implement and reflect according to new ideas and new requirements. Always remind yourself: how to teach in the past, how to teach in general, whether there is a better method, what characteristics this method has, where students are in learning, whether it meets the standard concept, and so on.
(2) Correctly handle possible differences. "Different people get different development", which is recognized and advocated by the standard. It is a fact that there are differences among students. Let every student receive education, instead of letting everyone start from the same starting line and rush to the same destination. Under the new concept, we should provide every student with room for development and put forward different requirements for different students. Some students get the most basic development, while others get more development. Really teach students in accordance with their aptitude, instead of just paying attention to students' knowledge and ability, and comprehensively guide students' temperament and personality to perfection.
(3) Put yourself on an equal footing with students. Teachers and students are people with independent personality values. Their personalities are equal, their values are equal, and there is no distinction between high and low strength. In the communication with students, we should establish a humanistic, harmonious, democratic and equal relationship between teachers and students. Only in this way can the students' vitality be displayed.
Teachers should fully understand their position and role, correctly understand their relationship with students, give full play to the role of guides, and guide students' mathematics learning to the realm of autonomy, harmony, pluralism and aesthetics.