First, create a situation to stimulate students' desire to explore independently
Modern teaching theory holds that teachers are always organizers and guides of students' learning activities, while students are always discoverers and explorers, and teachers' teaching should serve students' learning. Therefore, in teaching, teachers should be good at creating concrete and vivid teaching situations, opening the "floodgates" of students' thinking, making students enter the realm of "thinking impassability", stimulating their enthusiasm and interest in actively exploring knowledge, and forming a powerful driving force for independent exploration.
(A) the creation of problem situations to stimulate interest in inquiry.
"Learning begins with thinking, and thinking begins with doubt". Students' thinking often begins with problems, which arise from the exploration of the unknown. Students can only explore when they have problems, and they can only create when they take the initiative to explore. Problem situation is the driving force for students to build a good cognitive structure and an important measure to guide students to learn independently. In teaching, teachers should start with the objects and facts that students like to see and hear according to the age characteristics, knowledge and experience, cognitive rules and other factors, and provide students with rich background materials. Use questions and answers, storytelling, games, competitions and other forms to create vivid and interesting question situations, arouse students' doubts and stimulate their interest and desire for independent exploration.
For example, when discussing what the position of the circle is related to in the teaching of Understanding the Circle, you can play a video in the courseware: raindrops hit the lake and ripple around, forming circles of different sizes, which are very beautiful. Inspired by this beautiful artistic conception, students immediately have a deep understanding of the problem that the center of the circle determines the position of the circle.
(2) Create suspense situations and form the motive force of inquiry.
If the question is the material of exploration, then suspense is the driving force of exploration? Teachers should not only ask questions for students to think about, but also create suspense situations, so that students can be in the situation and ask questions actively, thus creating the demand for independent inquiry. Suspense can produce the most direct desire to explore, and it is also one of the most effective ways to stimulate students' interest in learning. When introducing new knowledge, if teachers can properly set suspense, they can quickly stimulate students' desire to explore knowledge and arouse their enthusiasm for learning.
For example, when teaching multiplication formula, the teacher showed a formula of 7 8 continuous addition and asked, "Who can say this number in 2 seconds?" The students were busy, and as a result, no one gave an answer quickly. The teacher said, "The teacher 1 second can say 56. Can you believe it? You are counting yourself. " It took the students three minutes to work out the figure, and the result was 56. "The teacher is really amazing!" Several students are whispering to each other. The teacher asked, "Does anyone know why the teacher calculates so fast? Want to learn this skill? " "Yes!" The students said in unison.
At this time, students are surprised and have a strong interest and desire to explore, eager to know the mystery, so that students will take the initiative to explore knowledge and find the law.
Second, optimize the process to make the inquiry activities more mathematical.
Mathematics teaching is the teaching of mathematics activities and the process of interactive development between teachers and students. On the one hand, we should give full play to the role of teachers as organizers, guides and collaborators, stimulate students' enthusiasm for learning with clear inquiry goals, provide students with opportunities to fully engage in mathematics activities and provide inquiry support for students' inquiry activities; On the other hand, we should boldly let go and explore with students as the main body, let students actively participate in activities such as observation, conjecture, experiment, operation, communication and reflection, help them truly understand and master basic mathematical knowledge and skills in the process of independent exploration and cooperative communication, gain rich experience in mathematical activities, and cultivate their exploration ability and innovative spirit.
(A) bold speculation, positive verification
Paulia once said, "I want to make a little suggestion. Can students guess the result or part of the result before doing the problem? " . Once children express whether some guesses are correct, they will take the initiative to care about this problem and the progress in class, so they will not take a nap or make small moves. "Guess is the embryo of mathematical theory. Many great mathematicians have discovered the truth that others have not discovered through guess. The new curriculum standard of mathematics also holds that students should "experience mathematical activities such as observation, experiment, guess and proof, and develop rational reasoning ability and preliminary deductive reasoning ability". It can be seen that guessing is one of the important ways to develop mathematics and learn it well. The mentality after guessing is eager to confirm, which makes the process of confirming guessing become students' desire and greatly strengthens students' initiative and enthusiasm in exploring new knowledge.
For example, when exploring the transverse area of a cylinder, the teacher first asked the students to guess what the transverse expansion of the cylinder would be. At first, due to the influence of book knowledge, students can only say that the expansion diagram is rectangular, and then through the guidance of the teacher, "Think about what graphics might appear if you don't expand along a height?" Students immediately became active, jumped out of the original mindset, made reasonable guesses and verified their guesses through personal operation, and got various unfolded graphics. This not only enhances the students' consciousness of using the transformation thinking method to solve new problems consciously, but also creates an atmosphere of "everyone participates, everyone experiences and everyone succeeds" through the process of "intuition-guess-verification-application".
(2) Hands-on operation and independent exploration
Friedenthal, a famous mathematician, emphasized that "the only correct way to learn mathematics is to practice and re-create". He thinks mathematics is a human activity, just like swimming. If you want to learn to swim in swimming, you must also do all mathematics in mathematics. In the process of exploring mathematics content, students sometimes stop some exploration activities because of their mature thinking or strangeness to the problem situation. In this case, teachers need to transform more abstract thinking materials into concrete operation materials through activity design in time, mobilize students' multiple senses to touch mathematics and participate in mathematics re-creation activities.
For example, when exploring the volume of a cuboid, guide students to do experiments: make different cuboids with a small cube with a volume of 1 cubic centimeter.
1. Fill in the table with the relevant data of cuboids with different postures in the group.
long
extensive
high
The number of small cubes
Volume of cuboid
2. Observe the above table. What did you find?
Let the students operate in groups, explore independently and communicate fully, and see how the number of small cubes contained in this cuboid is related to its length, width and height. Finally, let the students summarize the calculation formula of cuboid volume through observation, induction and reasoning. Practice has proved that guiding students to fully engage in mathematical activities and experience the formation process of knowledge can greatly enhance the effectiveness of inquiry activities.
Third, pay attention to guidance and teach students effective methods of inquiry.
Especially in group inquiry, we often see this phenomenon. It seems that everyone is actively participating, but the effect is very poor. Some groups even use the prepared materials as toys, and some students undertake all the tasks of group exploration. Some reports seem to be "singing and dancing", but in fact, they are all floating clouds and water, and they can't get to the point ... Thinking about these phenomena and problems, although there are many reasons, is mainly the lack of pertinence and effectiveness of teachers' guidance and intervention. Therefore, it is very important for teachers to guide students to explore in time and properly.
(A) the church method using reasonable methods to explore, is one of the prerequisites for the success or failure of inquiry activities.
Thinking is the gymnastics of mathematics. Giving students the method of mathematical thinking in teaching is like giving them the "golden key" to open the door of mathematical wisdom. Commonly used inquiry methods include operation-discovery method, analysis-induction method, analogy-transfer method and so on. For example, the operation discovery method is more suitable for deriving the area of geometric figures, the analytical induction method can be used to derive the concept of divisibility and perimeter of logarithms, and the analogy migration method can be used to derive the multiplicative commutative law and quotient invariance. In the usual teaching, these methods are often infiltrated and used, and students will gradually develop the habit of choosing reasonable methods to explore, so as to carry out effective exploration.
(2) Being good at guiding effective inquiry activities is not an independent individual behavior of students, but an interactive behavior between teachers and students. Through the timely, necessary, cautious and effective guidance of teachers, students' inquiry will leap to a deeper level.
1, role intervention.
The new curriculum standards clearly put forward new requirements for our teachers. Teachers are no longer "preachers" and "dispellers", but should change their roles, from the roles of "preachers", "teachers" and "dispellers" who used to focus on imparting knowledge to the roles of close partners who organize and lead students to explore science independently. Teachers go deep into various inquiry groups, mix with students as participants in group inquiry, and appear among students as learners and helpers.
First of all, teachers can keenly observe the confusion that students encounter in their inquiry. Sometimes students may face unknown fields that teachers have not set foot in, and there is no ready-made answer, which requires teachers to mobilize all their wisdom to be a "pioneer". However, in the process of students' independent inquiry, teachers should correctly grasp the "degree" of guidance, and teachers should grasp the temperature of "introducing without making, jumping like it". Students should be guided to feel that the conclusions drawn from the inquiry are the result of their own group cooperation.
Secondly, because of the participation of teachers, students will feel safe, practical and relaxed, and the atmosphere of cooperative inquiry will be more harmonious, and the effect of inquiry will complement each other.
Third, teachers have the "privilege" that every group can participate in. Grasping this "privilege", teachers can let themselves participate in inquiry activities more fully like students and experience the success of inquiry. Teachers can "think what students think and provide what students need", so that when preparing lessons or designing classroom teaching in the future, how many parts students have mastered when exploring can be considered first? What is the most urgent problem to explore? What kind of design ideas and guiding ideology should be adopted in design teaching? What knowledge can students learn through the specific inquiry process? What do you want to learn? …
In short, students have more ways to explore and have flexible minds. Teachers have also tried the concept of "curriculum standard" and the sweetness of quality education, which is easy to accumulate valuable experience for guiding students' exploration in the future.
2. Guide intervention.
The so-called guidance means that teachers must give targeted guidance to students' inquiry activities. There are many situations that need the guidance and intervention of teachers. When students encounter difficulties (or shallow levels)-guidance, when students are controversial-listening, when students explore mistakes-correcting, when students succeed-appreciating.
For example, when students study the basic properties of scores, through observation and comparison, they explore that the numerator and denominator of scores expand or shrink by the same multiple (except 0) at the same time, and the size of scores remains unchanged. The inquiry activity seems to have been successfully completed, and then the teacher said, in this way, the numerator and denominator can only be multiplied or divided by natural numbers other than 0 at the same time, and the size of the score remains the same, right? At this time, the students were silent. A few seconds later, a classmate asked in a low voice, can you divide them all by a decimal? The teacher took over his topic: Can you divide everything into decimals? What should I do if I can do it or not? At this time, there are more students' voices: check again! The teacher said: ok, divide into groups and verify it again. After a while, the students raised their hands and gave birth to 1: I still take 1/2 as an example. Multiply the numerator and denominator by 0.5 at the same time, and it becomes 0.5/ 1. According to the relationship between fraction and division, 0.5 divided by 1 is still equal to 0.5, so it is equal to. Health 2: I also take 1/2 as an example. When the numerator and denominator are divided by 0.5 at the same time, it becomes 2/4, and the value is still 0.5, and the values are equal ... At this time, the teacher asked: How can I speak more completely? ..... In this way, when students' inquiry activities only stay at a shallow level, teachers' appropriate "touch" will expand students' thinking and make students' inquiry practice constantly improve and perfect.
Fourth, change the way, leaving time and space for students to explore independently.
Any art form attaches great importance to blank space, which is to give viewers full play to their own space. In excellent works, what can most impress the viewer is often not the content described in the works themselves, but the space left by the viewer in his mind to develop himself and create himself. The same is true of math learning and math classroom.
Mathematics learning is a self-and meaningful construction based on students' existing knowledge and experience. Effective mathematics learning cannot rely solely on imitation and memory. Hands-on practice, active exploration and cooperative communication are important ways for students to learn mathematics. Undoubtedly, students need enough time to observe, experiment, guess, verify and communicate with each other. Therefore, teachers should take appropriate measures to give students enough time to explore, experiment and verify in the learning process.
For example, students can get opportunities to try and explore by "posing", "thinking" and "talking". Many teachers can guide students to explore in class to adapt to the new curriculum concept. But basically, it's just a point-to-point, which prevents students from thinking off topic, wasting time and failing to complete teaching tasks. Often, they just let students explore independently, and then quickly guide students back to their own teaching ideas, unwilling to spend time on their own exploration. This kind of teaching is still a superficial and formal independent exploration, and it has not achieved real independent exploration. Therefore, students should be given enough time to really explore independently.
For example, let students explore the method of calculating division, which is the focus of the teaching of multiplication formula for quotient. In the past, the teacher explained 15 minutes and instilled the calculation method into the students. The new curriculum concept advocates students to explore independently and acquire knowledge actively. Teachers should be willing to take the time to let students try it themselves, and use experience and methods to let each student solve new problems individually and create different algorithms. The allocation of teaching time can be adjusted to 25-30 minutes of independent exploration, and 10 minutes can be extended. Even though students' algorithms may sometimes be complicated, teachers should not deny them. On the basis of students' independent exploration, organize exchanges and discussions, and guide students to experience various algorithms, so as to realize that finding quotient by formula is the simplest calculation method.
Five, positive evaluation, experience the fun of exploring success.
Feedback evaluation is very important to realize effective teaching, and truly effective teaching feedback must be reflected in the whole process and all elements of inquiry activities. Teachers should allow students to put forward their own ideas on the existing information, analyze problems in their favorite ways, draw conclusions, verify conclusions and solve problems. In the process of inquiry, students should be allowed to fully express their thoughts, attitudes, opinions, wishes and feelings freely. In the evaluation, (1) should appreciate the courage of students to question, encourage students to question boldly, guide students not only to study, but also to be teachers, and create an atmosphere of free questions and free answers. (2) It is necessary to affirm students' active and serious attitude and scientific and reasonable inquiry methods in the process of inquiry, so that students can gain emotional experience of actively exploring knowledge and enhance their confidence and motivation. (3) It is to encourage students of different levels to make little achievements or make little progress in the activities. (4) Guide students to reflect and experience the inquiry process, and gradually form inquiry learning strategies to lay the foundation for sustainable development.
The famous educator Bruner pointed out: "Inquiry is the lifeline of mathematics. Without inquiry, there will be no development of mathematics. " In mathematics classroom teaching, teachers should create situations to stimulate students' desire to explore according to the internal relationship and development law of mathematics knowledge; Teach students the method of inquiry, and guide students to explore and learn actively; At the same time, teachers should leave enough exploration time for students and give them positive comments, so that students can experience the fun of successful exploration. Through students' effective independent exploration, students can feel the occurrence and development of knowledge in the organic combination and transformation of cognition and practice, internalize mathematical knowledge, form mathematical skills, acquire mathematical ideas and methods, and completely change students' learning methods, thus effectively improving the effectiveness of classroom teaching.