I. Types of homework
Students' homework can be roughly divided into three types.
The first type: preview homework.
Preview can improve the efficiency of students' listening in class and change the situation of students' passive learning. Mathematics is abstract, and the knowledge continuity is very strong. Without preview, it is not easy to quickly enter the thinking field guided by the teacher after class, which is not conducive to the understanding of new knowledge. Preview can find your own shortcomings in knowledge and make them make up and correct in time. Preview can cultivate self-study habits and improve self-study ability.
The second type: class assignments.
Classroom assignment is a powerful injection for students to master knowledge in time after teachers impart knowledge. Generally speaking, it is to strike while the iron is hot, so that the information of teaching and learning can be given immediate feedback and avoid "mending after the sheep is dead".
The third type: after-school homework (commonly known as homework).
Homework after class is the catalyst for students to master the knowledge taught by teachers. In the process of completing homework, students deepen their understanding and memory of what they have learned, and gradually turn what they have learned into skills in practical application. It can be said that it not only increases knowledge, develops thinking, but also improves the ability to analyze and solve problems.
Second, homework
(a) Basis of transfer
The homework assigned by the teacher is rich in content and there are various methods to assign homework. However, whether it is rich in content or varied in methods, there must be a foundation, that is, teaching materials and syllabus. As teachers, we should not only delve into the contents of textbooks, but also fully understand the meaning of primary school teaching objectives. There are "three" teaching purposes in the newly compiled syllabus. (1) enables students to understand and master the most basic knowledge of quantitative relations and geometric figures; (2) To enable students to have the calculation ability of integers, decimals and fractions, cultivate their initial logical thinking ability and spatial concept, and be able to solve simple practical problems by using what they have learned. (3) Enable students to receive ideological and moral education.
(b) The operation should define a relationship.
One relationship that teachers should make clear when assigning homework is: "The relationship among knowledge, ability and intelligence is dialectical unity.
The teaching purpose of the new syllabus puts students' understanding and mastering the most basic mathematical knowledge in the first place, and puts the cultivation and development of students' ability and intelligence in the second place. This shows that the new syllabus expresses the view that knowledge teaching is the basis of ability and intelligence development in primary school mathematics teaching. The development of ability and intelligence is helpful to improve the quality of knowledge teaching. The purpose of teaching is not only to make students understand and master systematic knowledge, but also to fully develop students' ability and intelligence. The two are complementary, mutually promoting and dialectical unity.
(3) Homework should enable students to understand and master the most basic mathematical knowledge.
The new syllabus puts forward clear and specific teaching requirements, and according to students' cognitive characteristics and thinking development law, different teaching requirements are put forward in stages for different teaching contents. Teachers should follow these specific requirements when assigning homework, so that students can successfully complete these learning tasks.
When assigning homework, teachers should also fully realize that primary school students can't understand and master the basic knowledge at one time, and generally have to go through the process from individual to general, from concrete to abstract, and gradually deepen. Teachers should find out the depth of knowledge in each stage and grasp the stage and continuity of relevant teaching requirements, so as to ensure that students can understand and master the basic knowledge of mathematics step by step. For example, for the calculation methods of the features and areas of plane geometry, only the features and areas of each plane geometry are arranged first, and then the homework to understand the relationship between the features of various plane geometries and the connection between plane calculation methods is arranged, so that students can gradually deepen their understanding of plane geometry.
(4) Homework should be closely related to teaching requirements, with clear objectives and strong pertinence.
From the teaching point of view, the teaching of every knowledge should meet the requirements of the teaching objectives stipulated in the syllabus. For example: multiplication in table, the syllabus requires students to master oral calculation skillfully, so the homework exercises arranged in the teaching formula should be closely related to the teaching requirements to ensure that students can blurt out, otherwise it will affect the following multiplication teaching.
From the perspective of students' learning, if the content of homework is closely related to the teaching requirements and the purpose is clear, they can take the initiative to grasp learning. Judging from the age characteristics of primary school students, due to the abstraction of mathematical knowledge, although teachers provide them with some perceptual materials in the process of understanding knowledge, the perceptual basis on which students understand knowledge is still poor. Therefore, when they practice with knowledge, their ability to distinguish knowledge is weak, and their thinking is prone to negative transfer, which leads to mistakes of one kind or another when solving problems. For example, after learning, use the additive associative law to calculate: 25+47+75+53, and then let students calculate 89+1-89+11,and they also use the additive associative law to calculate and get the wrong result. When assigning homework, its content should not only be closely related to teaching requirements, but also be targeted.
(5) homework should be carefully selected, practice forms should be diverse, and the amount of practice should be appropriate.
After the lecture, students' exercises are mainly carried out in the classroom, and the number of exercises should be appropriate to meet the needs of different students. After learning new knowledge, primary school students will soon forget it if they don't arrange homework consolidation exercises in time. Therefore, classroom homework, on the one hand, allows students to correctly understand the knowledge in their minds in time, on the other hand, it also allows students not to make mistakes.
Knowledge can be corrected in time under the guidance of teachers. In this way, we can avoid spending too much time after class to check the missing parts and improve the efficiency of teaching and learning.
The homework exercises after class are mainly to consolidate knowledge. The design of exercise questions should be meticulous, and attention should be paid to grasping the essence of knowledge, highlighting key points and breaking through difficulties in content. Pay attention to the questions from imitation to variation, and the order of the questions is from shallow to deep, from easy to difficult. Whether in class or after class, the assigned homework questions should reflect:
1. correlation
Homework must be targeted. That is, the purpose is clear. On the one hand, we should aim at the teaching objectives, on the other hand, we should aim at the actual situation of students. Assigned homework, starting from the teaching objectives of this class, should carefully analyze what concepts, formulas and methods students should master, what kind of ability they should cultivate and what kind of learning level they should achieve, and then select and write topics. At the same time, according to the actual situation of students' knowledge in this class, such as which concepts are difficult to establish, which knowledge is easy to be confused, which aspects are easy to make mistakes, which skills are poor, and the methods, speeds and habits of students to solve problems, the selection or design is targeted and moderately difficult, so that most students can complete the assigned homework within the specified time.
Second step
According to the content of the textbook, from easy to difficult, from simple to complex, from simulated questions to comprehensive questions, from basic questions to changing questions, homework is arranged step by step to gradually increase the difficulty, and some exercises related to old knowledge are widely and consciously equipped to increase feedback, so that old and new knowledge can communicate with each other and form a new cognitive structure.
3. Diversity
Diversity refers to the variety of types of homework and methods of answering questions, so that students can practice seriously from different angles with some basic knowledge and skills, and the homework exercises designed with some basic knowledge, basic definitions, rules and basic skills combined with the content of this course are easy to form singleness and produce mindset. Once the conditions or conclusions change, students will be at a loss, stuck, and unable to find a solution to the problem for a while. It is not conducive to the cultivation of students' thinking quality, but also to the cultivation of thinking ability. Therefore, the content of homework and the design of exercises should be flexible and diverse, and open up ideas for solving problems. Especially after learning a unit of knowledge, we should pay more attention to the diversity of homework exercises. Cultivate students' good habit of examining and analyzing every question from time to time.
Enlightening
Assigned homework topics should be enlightening. The topics designed or selected can stimulate students' enthusiasm for learning, their interest in learning and their strong thirst for knowledge. For example, a changeable topic with multiple solutions, a topic to solve practical problems. Students can do it both in the game and in actual operation. Draw line segments and schematic diagrams, and complete them in deep thinking. Such questions help students to concentrate, develop their thinking and enlighten their wisdom.
Step 5 be appropriate
The time for students to finish their homework is limited. If the amount of homework is too large, students will be bored and the teaching information will not be fed back in time. It not only affects the whole teaching process, but also increases the learning burden of students, which is not conducive to the healthy growth of children. If the amount of homework assigned is small, the purpose of practice will not be achieved. Over time, students' ability will become lower. Therefore, teachers should assign homework according to the content of teaching materials and the actual situation of the class.
6. operability
Operation exercise is to let students explore, discover or verify some mathematical laws, rules or formulas of geometric shapes through practical activities such as measuring, cutting, spelling, posing, drawing and folding. Assigning such homework can mobilize students' multiple senses to participate in learning. This kind of participation can make students' interest soar, and the knowledge gained is impressive, memorable and vivid, which not only improves their learning ability but also exercises their practical operation ability.
7. Discriminatory
Assign homework and pay attention to the discrimination of exercises. Discriminatory exercises require teachers to choose accurate topics, which are closely related to the knowledge imparted that day. The number of questions should not be too much, and the completion time should be limited, not too long. After the practice, teachers should guide students to make a proper summary and generalization in theory. This kind of homework exercises generally appear in the form of judgment questions and multiple-choice questions. This kind of homework has certain depth, breadth and difficulty. Teachers must encourage students to explore actively. Compared with basic training exercises, this kind of exercise is more flexible, inspiring, thoughtful and discriminating. These exercises not only paved the way for the follow-up study, but also concentrated on developing students' thinking ability.
8. merger
The homework assigned every day is consolidated, and the homework assigned after class should be strengthened. Practice should focus on key knowledge and main ability requirements, with clear purpose and accurate direction, so that students can draw inferences from one another. Because the focus of review is the induction and arrangement of knowledge, the practice of question types should be less and more precise. The topic of design should be big and comprehensive.
9. comprehensive
After summarizing and sorting out the knowledge of each stage and unit, we should arrange some comprehensive homework exercises to guide students to deepen and consolidate what they have learned, comprehensively apply what they have learned to solve difficult and complicated problems, and make students by going up one flight of stairs in knowledge and ability.
10. Teaching students in accordance with their aptitude
Design exercises and homework should start with most students. Around the teaching content, design some basic exercises that most students should and must master. At the same time, we should implement the principle of "teaching students in accordance with their aptitude". For poor students or students with temporary learning difficulties, individual guidance should be strengthened in the process of completing homework, and efforts should be made to make them meet the basic requirements stipulated in the syllabus. Students who are full of energy and spare capacity for learning can do more comprehensive and thoughtful topics, arouse their enthusiasm, show their talents and develop their talents. When practicing, we can adopt the method of asking good, medium and poor students respectively and arrange different levels of exercises for them. It enables students to learn knowledge properly, and at the same time reduces the learning burden of students to varying degrees.
(6) Assigning homework should reasonably allocate practice time, pay attention to practice methods, and improve the quality of homework practice.
When assigning homework, we should pay attention to the age characteristics of students while allocating practice time. Too much homework and long-term practice will bring fatigue and boredom to students, distract their attention and increase the error rate. If the form of homework practice is single or the topic is too difficult, it will reduce the enthusiasm of students to complete homework, not only affect their confidence in completing homework, but also affect the improvement of their grades. For important basic knowledge and knowledge that must be mastered skillfully, you can concentrate your time on practice appropriately. For example, the prime factor decomposition of numbers, finding the greatest common divisor and finding the least common multiple in knowledge, let students master the essence of knowledge, basic thinking methods, problem-solving steps, writing format and so on. Concentrate on practice, and then practice separately until the students master it. This can save the time to finish homework and improve the learning efficiency. You should pay attention to the practice method when practicing. Different exercise forms and methods are adopted according to the content of the textbook. Observation, comparison, hands-on operation, graphic method, game method, audio-visual teaching method and other entertaining methods enable students to actively explore knowledge in the process of completing their homework. It can be seen that reasonable allocation of time to complete homework and emphasis on practice methods play an extremely important role in reducing the excessive burden on teachers and students and improving teaching quality.
(seven) in-depth excavation of intellectual factors in the operation.
It is very important to train logical thinking in the process of students' homework in a planned and purposeful way.
Thinking is the generalization and indirect reflection of objective reality by human brain. It reflects the essence of things and its inherent regularity. Logical thinking is definite and consistent. Systematic and well-founded thinking. The formation of pupils' initial logical thinking ability is by no means a one-off event, but the result of teachers' purposeful, planned and long-term training with knowledge as the carrier. Therefore, teachers should consciously combine the contents of teaching materials, cultivate logical thinking in different grades and different teaching links, and at the same time, it should be reflected in homework. When the assigned homework has a certain depth, it will be just right to really tap the intellectual factors in the textbook. Students' initial logical thinking ability can be continuously improved, which teachers must not ignore when assigning homework.
To sum up, it can be seen that how teachers assign homework is very important for students to master knowledge.
Third, correct homework.
Primary school mathematics is the most basic part of mathematics, and the teaching content of primary school mathematics is the simplest and most basic knowledge in mathematics. But primary school mathematics also has the characteristics of high abstraction, strict logic and wide application. These characteristics are in contradiction with the age psychological characteristics of primary school students. Therefore, after the teacher assigns homework, he must check and correct it in time. Because of the different requirements for the content and form of homework, teachers have different methods to correct homework.
(A) the conventional correction method
The conventional correction method is to correct any homework problems left over, so that every problem that students do can be affirmed, whether it is correct or not. For primary school students' homework, this correction method is particularly important, and it is also a common correction method for teachers.
(B) Teacher-student mutual inspection and correction method
After receiving the students' homework, check it first, tick the wrong ones and send them to me immediately, so that they can check it again, find out their own problems, find out the reasons for the mistakes, and then correct the wrong questions. For example, find the greatest common divisor of two numbers by short division;
68 and 102 and 102.
The divisor is 2. The number is 2× 17=34.
52 and104,68 and 102.
The divisor is 2×2=4. The divisor is 2×2× 13=52.
Some even returned it two or three times until it was correct. These students said: 52 and 104 are multiples, and their greatest common divisor is the smaller number 52. This question can tell at a glance who is the greatest common divisor, so there is no need for short division. This kind of correction not only cultivates students' good habit of careful observation and homework, but also cultivates their spirit of independent thinking and develops their thinking ability.
(3) Mutual inspection and mutual recognition method
Teachers ask questions and students check and correct each other. For example, which of the following numbers are composite numbers? What is a prime number?
9、26、2 1、29、55、7 1、78、9 1、 1 14、 129、 182
Through cross-examination, we found the following problems: some students regard 9,21,9 1, 129 as prime numbers; Some students take 4,91as prime numbers when they decompose composite numbers into prime factors.
36=3×3×4(×)
182=2×9 1()
Some students decomposed 1 14 and wrote the product formula:
2×3× 19= 1 14。 Through mutual examination and approval, students not only strengthen their understanding of the three concepts of prime number, composite number and prime factor decomposition, but also deepen their understanding and application.
(four) the correction method of combining collective discussion with individual discussion.
We only look at people, things and things from one angle, which is too limited. If you look at it from multiple angles, you will see through the problem objectively and comprehensively, and so will learning mathematics.
Through drawing, students can find several connections and list different formulas from different angles. Through collective and individual discussion, reasoning, evaluation and revision, students can get solutions from different angles. Although this kind of correction takes up a certain amount of time, it is many times more effective than the teacher making a partial correction for the students alone. With this grading method, students are eager to try. Interpreters talk endlessly about ideas; If you don't understand, sit and listen; The doubter is suddenly enlightened. This kind of correcting method cultivates students' ability to observe and solve problems from different angles, which not only enables students to learn, but also enables students to learn and be good at learning.
Fourth, the evaluation work
Evaluation homework is an important part of primary school mathematics teaching, which is completed through bilateral activities between teachers and students. Teachers use textbooks and various methods to comment on homework, so that students can meet the teaching objectives and requirements stipulated in the syllabus. The main target of correcting homework is students. Therefore, the overall function of class evaluation activities is ultimately focused on the progress and achievements made by students in all aspects. The principles of homework evaluation are: distinguish between primary and secondary, and combine evaluation with evaluation; Control time and ensure key points; Solve problems and strive for accuracy.
The content and forms of homework are various, so the methods of homework evaluation are also various.
(1) Comments of the day
Students should do some homework in class every day. In order to ensure the quality of homework, they should correct it and comment immediately after correcting it, so that mistakes can be eliminated in the bud.
(2) Special opinions
Teachers' comments on a certain item or a certain kind of problem in students' homework. Such as rewriting and ellipsis of numbers, general division, reduction and so on. This evaluation task is single and not easy to be confused. It is easy to correct mistakes and see the results.
(3) Block comments
Block evaluation is to evaluate according to the knowledge unit. The arrangement of knowledge in each unit is from simple to complex and from easy to difficult, which can be evaluated according to the level of knowledge arrangement. When commenting, you should prioritize, don't hide, and grab your eyebrows and beard.
(4) classified comments
Classification evaluation is based on the knowledge content and classification of assignment. Such comments can string the same type of knowledge into a string, turn it into a chain and form a knowledge network, which is convenient for students to understand and remember. For example, the constant property of quotient→ the basic property of fraction-the basic property of ratio. Another example is the calculation of knowledge area of plane geometry, formula derivation and so on. Through classification, knowledge is more systematic and organized.
(5) Comprehensive comments
Comments on more complicated knowledge after practice. For example, complex application problems, calculation problems, and conceptual problems with large knowledge coverage must be transferred and transformed by comprehensive evaluation. In commenting, it is necessary to break through the difficulties and let students find ideas and methods to solve problems, and never adopt the method of topic commenting.
(6) * * * opinion
Students will encounter some problems in the process of completing their homework. Teachers should be good at classifying problems and distinguish which ones are * * * and which ones are individual. If it is a * * * topic, you must take the time to comment, and you can't delay it, which will affect the learning of the later knowledge. For individual problems, it is necessary to teach students in accordance with their aptitude.
(7) It is difficult to question and comment.
There are all kinds of problems in homework, and it is impossible to complete the task of commenting only by the teacher's mask. Students should be encouraged to question and ask difficult questions, so that what they have learned can be properly placed and obstacles in progress can be removed.
(8) comments.
The new knowledge learned by students is closely related to the old knowledge, and students' cognition and memory are not at the same level, so this reflects that students forget the old knowledge in their homework. What can we do? Teachers can only seize the opportunity to comment on homework, make comments to fill gaps and connect old and new knowledge. This kind of comment not only makes up for the deficiency, strengthens the students' memory and understanding of knowledge, but also makes the new knowledge develop well.
Modern mathematics evaluation theory holds that teaching evaluation is an evaluation centered on promoting students' development and realizing teaching objectives. And isn't it an evaluation to comment on students' homework? Therefore, the evaluation homework not only pays attention to measuring students' knowledge, but also pays attention to measuring students' ability, intelligence, habits and morality. Teachers should not only pay attention to summative evaluation, but also pay attention to formative evaluation when reviewing students' homework; It is not only used to evaluate students' learning, but also used to evaluate teachers' teaching and educational effects. In other words, it not only measures, analyzes and evaluates the basic knowledge that students understand and master, but also measures, analyzes and evaluates the ability and intelligence level that students have achieved.