First, design homework activities reasonably to promote the effectiveness of homework.
Effective hands-on practice requires students to be clear about "why to move" and know how to move, all of which require teachers to design operation activities reasonably.
(A) seriously study textbooks
Teachers must fully consider their own teaching objectives, student activities and other issues. "Teach what? When to teach? How to teach? How to help students with learning difficulties? " Wait a minute. When preparing lessons, teachers must accurately grasp the teaching materials and grasp the scientific system and logical structure of the teaching materials; Grasp the key content and non-key content of the textbook; Grasp the difficulties and doubts in the textbook. Then, on the premise of being loyal to and respecting the teaching materials, we will study relevant learning strategies and design various novel activities to make students learn easily, interestingly and effectively.
(2) Carefully select practical materials.
Mathematics studies the quantity and shape of things, not the external characteristics and attributes of objects. Therefore, the standard of choosing homework materials depends on whether homework activities are conducive to promoting students' understanding of activities, whether they can effectively complete teaching tasks and achieve teaching goals, and then consider their life, interest and openness. If teachers think too much about the latter, learning tools may become "toys", which is counterproductive and plays a negative role. In teaching activities, teachers should carefully select and provide materials related to revealing mathematical concepts and principles, which can stimulate students to explore, taking into account factors such as the size and color of materials, and on the basis of studying the characteristics of materials, let students practice freely. For example, when teaching the volume of a cone, the teacher organizes students to experiment in groups. Two groups of experimental materials are provided to each group. A group of hollow cylinders and cones with equal bottoms and equal heights; The other group is hollow cylinder and cone with different base heights. Then let the students experiment in groups with water, sand and other materials to explore the volume relationship between cone and cylinder.
(3) Dig deep into the thinking ability of homework materials.
Mathematics is the gymnastics of thinking. The main way of mathematics learning is not hands-on operation but mathematical thinking. All hands-on operations are a carrier for developing mathematical thinking. In a 40-minute math class, the types and time of operating materials that teachers can use are limited. On the premise of carefully selecting homework materials, we must dig deep into the value of each homework material to make it serve the development of students' thinking to the maximum extent.
For example, in the teaching of "Preliminary Understanding of Fractions", two teachers asked students to prepare square paper. A teacher did this. The teacher said, "Please fold the square paper in half up and down, then fold it in half left and right, and draw out one of them with a colored pen. Can you tell me how much of this paper is colored? " The students quickly completed the operation according to the teacher's requirements, and quickly said that the colored part was a quarter of this square paper, while the colored part of the students was exactly the same. Namely:
Another teacher did this and said, "Can you divide this square piece of paper into four parts by hand?" ? Colour one of them. How much is the color part of this paper? The students also quickly reached the correct conclusion according to the teacher's requirements, but the students' answers are several:
The same link, the same teaching AIDS, but the classroom effect is quite different. In the new teacher's class, students are just "operators" and square paper is just "props". All activities are carried out under the teacher's question, "the teacher's brain is the student's hand", and the students lack the time and opportunity to think independently. The development of mathematical thinking is limited to the mechanical understanding and application of fractions. In the second teacher's class, the students became "explorers" and the square paper became the "golden hoop" in their hands. Using it to transform different patterns, students' thinking sparks can bloom in these different operations. It is not enough to operate only in teaching. Teachers should also pay attention to the design, guidance and optimization of students' operation activities, give full play to the role of materials, make hands-on operation closely related to mathematical thinking, and have enough gold content, so as to achieve the purpose of real hands-on operation.
Second, seize the opportunity of students' hands-on operation to promote the effectiveness of the operation.
Primary school students' thinking is characterized by the dominant thinking in images and the gradual transition to abstract thinking. In the process of learning new knowledge, they should first observe with their eyes, operate with their hands and describe with their mouths, thus establishing the appearance of things, especially for junior students. According to their age characteristics and cognitive rules, teaching AIDS and learning tools are essential in classroom teaching. However, we can often hear the teacher say something like this at the beginning of the class in order to ensure the classroom order and complete the teaching task: "Put ... (learning tools) in the corner of the table, and don't move, it's more obedient than whose little hand." Learning tools should be used by children to solve problems consciously when they encounter problems, but now they have become props controlled by teachers. When faced with problems that they can't solve, children choose to wait more and will not take the initiative to try with the tools at hand (unless the teacher has special instructions). Sometimes teachers lead children to practice, and basically arrange the same time first. The teacher first puts forward the operation requirements, and then the students strictly follow the teacher's instructions. On the surface, it looks very orderly, and the students are quite enthusiastic about it. But think about it carefully, why do you want to operate? Is it a demand put forward by students? In fact, in this process, students have no initiative to explore. The whole process is that students perform simple operations and calculations according to the teacher's instructions. The so-called inquiry, students just act as operators. Although it is necessary to arrange a directional guidance link before students begin to operate, it is also important to help students master the correct operation methods, but we must pay attention to the scale, leave appropriate difficulty for students' inquiry, enhance students' willingness to challenge and cultivate students' independent inquiry ability.
Third, create situations to attract students to practice and promote the effectiveness of the operation.
In the process of learning, primary school students often pay attention to it at will. In teaching, teachers should create teaching situations, induce learning motivation, attract students' involuntary attention to participate in learning, and guide students to actively think and explore mathematical problems, so as to achieve the purpose of mastering knowledge and developing intelligence.
For example, when learning "subtraction of abdication within 20 years", the teacher created a shopping situation and asked two people at the same table to play the role of salesman and customer respectively. There were 15 pencils in the shop, and 9 pencils were sold. How much is left? Students use sticks to explore the calculation method. Some open a bundle of sticks and take out 9 sticks, leaving 1 stick. 1 stick plus 5 sticks makes 6 sticks, and there are 6 sticks left. Some took a bundle apart, took out four pieces, made nine pieces out of five pieces and took them away, and finally there were six pieces left. Others counted out nine of them one by one and took them away, and finally got the result. Another example is when the teacher recognizes the number 7 in teaching. The teacher created the scene of seven dwarfs picking fruit in the cartoon Snow White. They picked seven big fruits and took two bags. Guess how they packed it. Stimulated the students' desire for autonomous learning, the students actively used their brains to find ways to replace seven fruits with seven small disks, seven small triangles and seven small sticks, and listed all possible results. Some methods of drawing fruits also got results.
According to psychology, a good mood will affect the choice of cognition, improve the enthusiasm of cognition, lead to the optimization of cognition, be conducive to the internalization of cognition, enhance the transmission of cognition, and achieve the realm of moistening things quietly. Therefore, by creating a relaxed, pleasant and interesting mathematical problem situation, students' initiative to participate in learning activities can be effectively mobilized. Let students enjoy the activities, learn relevant knowledge and truth in the activities, and make the hands-on activities become effective activities.
Fourth, choose the appropriate surgical methods to promote the effectiveness of the operation.
Although there is no unified mode and requirement for the operation method, it is not appropriate to come at will and engage in it rashly. After careful design and logical connection, the operation method can not only make students acquire knowledge more easily, but also help to improve their logical thinking ability.
For example, when teaching the cross-sectional area of a cuboid, some teachers expand the surface area as a whole to get a combined plane figure in the process of demonstrating the surface area of the cuboid, and then analyze and deduce the calculation method of the surface area of the cuboid; Some teachers tear off three groups of opposite faces one by one and stick them on the blackboard, and then analyze and deduce a calculation method of the surface area of a cuboid. I don't think these methods are suitable, because both understanding the concept of cuboid surface area and exploring the calculation method of cuboid surface area must be realized by means of three-dimensional space. When analyzing and exploring the area of the front and rear sides and the area of the left and right sides of a cuboid, students must intuitively see that the areas of these four sides are calculated by "length× width× 2" and "width× height× 2" with the help of the image or representation of the figure. However, if we leave the image of "body" and put the two groups of faces on the same plane for investigation and study, students will often feel dizzy-it seems that the area of the two groups of faces is "length × width× 2", so it is inappropriate and undesirable to explore the surface area of a cuboid by using the expansion method. Before demonstrating the calculation of the surface area of a cuboid, you should make an activity teaching aid (two opposite faces can be unfolded one by one and restored immediately). When operating, with the help of the image of "body", try to demonstrate and highlight the perceived object, and first expand a group of faces. When unfolded, this group of faces still does not leave the "body". After students see it clearly, they will immediately compound this group of faces on the "body". In this way, through operation, students can not only sum up the general method of calculating the surface area of a cuboid from part to whole, but also cultivate their spatial imagination and develop their thinking.
Fifth, cultivate students' habit of orderly practice and promote the effectiveness of operation.
Psychological research shows that primary school students' thinking is in the transition stage from disorderly thinking to orderly thinking. Therefore, teachers should actively guide and help students through this stage and cultivate the order of thinking. In operation activities, students' thinking follows the order of operation, and the operation program reflects the thinking process accepted by students and a certain logical order. If the operating procedures are confused, students can't form clear ideas in their brains. Orderly operation helps students to form clear and fluent ideas and develop their thinking. Analyzing, synthesizing, abstracting and summarizing students' thinking activities can improve students' thinking order. For example, when teaching carry addition of 9 plus 2, the teaching process is divided into three steps. The first operation: first take out 9 balls and put them in the box, then take out 2 balls and put them outside the box. Q: Now, how do you count 9 balls and 2 balls together? Step 2: There are 9 in the box. A few more will make a box 10? (plus 1) operation: divide the two outside the box into 1 and 1. Step 3: Pick up the 65,438+0 outside the box and put it in the box (students say: 9 165,438+0 = 65,438+00). The teacher will use gestures to indicate that the 65,438+00 inside the box and the 65,438+0 outside the box are merged (students say 65,438+00)
Six, correct guidance, so that students can gain practical experience and promote the effectiveness of the operation.
In the process of cultivating students' practical ability, teachers should not let students practice aimlessly, but should pay attention to guidance and guide students to abstract mathematical concepts and conclusions from concrete practical operations.
(A) let students practice before class and participate in the construction of knowledge.
In the study of many mathematics contents, students should not only know what life experience they have accumulated in a certain knowledge before class, but also practice before class to accumulate perceptual experience, paving the way for classroom teaching and allowing students to actively construct their own cognitive structure. For example, when teaching interest and interest rate, the teacher arranges students to take the initiative to go to the bank to investigate and understand the knowledge about deposit interest rate one week before class. With the practical activities before class, the study of this class will become vivid from boring, so that students can actively participate in the process of knowledge construction, cultivate students' habit and ability of collecting information, feel the fun of practice before class, and improve the efficiency of classroom practical activities.
(B) let students practice in the classroom, take the initiative to explore and acquire knowledge.
In classroom teaching activities, teachers should let students do more homework, think more and practice more in limited time and space, and become real explorers. For example, when teaching the formula for calculating the circumference, teachers can ask students to measure the circumference by using materials such as disks, traveler, ruler and ribbon prepared before class. When students explore different measurement methods, the teacher demonstrates (holding a rope with a small ball at one end and swinging the track in a circle at the other end) and asks questions; Can you still measure the circumference of this circle with the method just now? Then ask the students to guess what the circle may be related to. Then ask the students to compare the circumference and diameter of a circle to see what they want to do. Let the students cooperate to measure the circumference and diameter of a circle and calculate the ratio of the circumference and diameter of the circle. Through practical exploration, it is not difficult for students to find the multiple relationship between the circumference and diameter of a circle. In this way, students can naturally derive the formula of pi. It can be seen that students experience and practice by themselves with the help of independent operation of learning tools, and the formula of circumference obtained is more profound and easier to remember than the knowledge directly instilled by teachers.
(3) Let students practice after class and constantly innovate their knowledge.
Creation comes from practice, and practice is a continuous and complete process. It is not enough to be satisfied with the exercises before and during class. Teachers should also arrange students' practical tasks after class through practical homework. For example, in the teaching of cuboid surface area, after class, you can arrange such practical homework: the supermarket should pack 12 boxes of yogurt into a package for promotion. Please design several different packing methods. Which do you think is the best? Through this practical activity, students' practical ability is cultivated, and at the same time, students realize that the smaller the surface area, the better, and the more materials are saved. In this way, students can also appreciate the value of mathematics.
(D) Guide students to abstract mathematical conclusions from concrete practice.
In the teaching process, after students have carried out concrete practice, teachers should pay more attention to the internal quality of activities while paying attention to the external performance of activity design, that is, through continuous generalization, verbalization and simplification, they gradually turn into abstract thinking, thus deepening students' understanding and thinking level, truly mastering knowledge and helping students become thinkers of problems. Teachers should use language as an intermediary to help students abstract thinking in images into mathematical knowledge, and then apply it to practice to form their abilities. If you stay in the hands-on practice stage, students can only "understand", let alone master and use, let alone improve their hands-on ability. Therefore, teachers should often let students talk about the knowledge gained from practice in teaching.
Seven, improve the utilization rate of the results after the operation, and promote the effectiveness of the operation.
Since the implementation of the new curriculum, many changes have taken place in classroom teaching: teachers have less explanations and students have more activities; The classroom atmosphere is active and students have more opportunities to start work; The classroom is no longer the teacher's personal stage, but the students become the protagonists. It is in this context that homework activities are full of vitality in the classroom. How much of these operational activities are content, how much is form, and how effective are they? How to make good use of the results of surgery?
We know that language is the shell of thinking. People use language to summarize the acquired feelings, perceptions and representations, forming concepts, judgments and reasoning; Adjust and sort out your thinking activities through language expression, so as to gradually improve. Therefore, in order to promote operation and thinking, students must be fully allowed to describe the process and results of operation and express their own thoughts and understanding. At the same time, in order to understand students' thinking activities, teachers also need to let students express themselves in language. Different ways can be combined, such as roll call, group communication, and two people talking at the same table, so that students have the opportunity to express themselves orally. By listening to students' expressions, we can find the bright spots and existing problems in students' operation and thinking, and affirm or correct them. At the same time, pay attention to organize students to listen carefully to their classmates' narratives and participate in evaluating the correctness and rationality of their operation and thinking process. In this process, we should consciously encourage and help students with learning difficulties to speak, promote and promote their positive thinking, and gradually improve their language expression ability. For example, in the teaching of "Preliminary Understanding of Division with Remainder", teachers ask students to place numbers with their own sticks. How many such numbers can you put at most? How much is left? Then, according to the numbers they put, the students are interested in listing the formulas. The teacher asked the students to put pictures in front. He propped up an umbrella with four sticks. When he didn't finish playing, the teacher asked other students to guess how many might be left. Students guess that there may be 1, 2, 3 left? The teacher asked again, "Why is this?" The students quickly said that there should not be four or five left, because then they can continue to play small umbrellas, and the result will be that the sticks have just been used up or there is 1 left. Students can easily draw the conclusion that the remainder is less than the divisor and understand the reason.
Eight, evaluation and encouragement, pay attention to the development of students' practical operation ability, and promote the effectiveness of operation.
Paying attention to people's development has become the primary goal of the new curriculum standards. "Standard" points out: "Evaluation should not only pay attention to the results of students' learning, but also pay attention to their learning process ... pay attention to students' emotions and attitudes in mathematics activities, help students know themselves and build confidence. "This is the purpose of the new curriculum to encourage evaluation. Let students develop in activities is the foothold of all classroom activities, and it is also the yardstick to evaluate the effectiveness of student activities. Therefore, we should pay attention to the timeliness of guidance and evaluation, and guide students to summarize and reflect on the experience, understanding and gains in the process of activities; Guide students to learn to respect and share the achievements of others, and pay attention to using multiple evaluation methods to guide students to evaluate themselves, each other and others. For example, some teachers use encouraging language or admiring eyes and gestures to affirm students' activities, and some teachers skillfully guide students to comment on their own and others' activities in class ... all these make students gain positive and successful experiences. Through evaluation and encouragement, more students can gain self-confidence, develop skills, gain knowledge and experience in activities, and implement "learning in activities and developing in activities"
Edison said, "I have never made an accidental invention. All my inventions are the result of careful consideration and rigorous experiments. " Practice is the foundation of innovation, and the thinking of primary school students is in the transition stage from concrete thinking in images to abstract thinking. Hands-on practice is one of the important ways for students to learn mathematics. In teaching, students should establish concepts in familiar living environment, understand concepts in meaningful practical activities and deepen concepts in comprehensive application exercises. To advocate hands-on learning methods, we should emphasize students' active learning and give them enough time to operate and think around the set themes. Teachers can turn demonstration teaching materials into inquiry materials, closed questions into open questions, and final conclusions into process research, strive to design hands-on activities for students reasonably, grasp the opportunity of students' hands-on operation, create situations to attract students to practice, and choose appropriate operation methods. Cultivate students' hands-on practice habits in an orderly manner, correctly guide students to gain hands-on experience, improve the utilization rate of results after homework, pay attention to evaluation and encouragement, pay attention to the development of students' hands-on practice ability, create hands-on practice atmosphere, provide hands-on practice opportunities, cultivate hands-on practice habits, cultivate hands-on practice ability, and let students develop in activities, thus ensuring the effectiveness of hands-on practice. Therefore, only in this way can our teachers improve the effectiveness of hands-on practice in classroom teaching activities under the background of the new curriculum, and also maximize the effect of classroom teaching.