Mathematics Curriculum Standard points out that students' learning materials must be realistic and challenging. However, there are at least some problems in the traditional exercises in the "91" textbook, such as monotonous and outdated forms and lack of application in exercises. The exercises lack the connection with practical problems or other disciplines, and are basically pure mathematical problems. The so-called application problem can only be solved by mechanically distinguishing and imitating formulas or related mathematical models, and it is not a real application problem. Students can't see the actual background of mathematical problems and can't solve practical problems by mathematical means, which is extremely unfavorable for students to establish a positive and healthy view of mathematics and master mathematical modeling methods.
The exercises in the curriculum standard experimental textbook have greatly changed the arrangement form and content selection of previous mathematical exercises. Instead, according to the psychological characteristics of students, it is designed as an open homework with diverse forms, realistic and interesting content, rich thinking, strong inquiry and strong operability.
First, give full play to the exercise function and let students improve in practice.
The exercises in the new textbook have many advantages. As a teacher, how to use them to give full play to the function of exercises, so that students can improve and practice wonderfully? To this end, I made a preliminary attempt in practice.
(A) fully tap the role of examples and lay a good foundation for learning.
Examples in textbooks are a bridge for students to learn knowledge. The exploration of learning methods and the demonstration of problem-solving methods can play a role in infiltrating knowledge, inducing methods, mastering skills, cultivating abilities and developing thinking. However, in teaching, many teachers often blindly change the presentation of examples in textbooks and ignore the due role of examples.
1. The tentative function of the example.
The so-called exploratory role means that teachers first grasp the internal relationship between old and new knowledge according to the content characteristics of examples, carefully select presentation materials, and start with carefully designed preview exercises, so that students can make tentative answers in inquiry. For example, the first example in the multiplication teaching of zero (to prepare for the following knowledge) is: 0+0+0+0 = 0, 0× 7 = 0 7× 0 = 0 (; Then give an example of 6: 508× 3 =
In teaching, because students already have the relevant knowledge and ability foundation, they can solve the first example independently and directly pave the way for Example 6. Then, with the help of the connection between problems, it plays a positive role in migration. Then the teacher only needs to look at the results of the answers, and make a targeted and instructive analysis of the examples to help students sort out the reasons and clarify the algorithms. This not only enables students to master new knowledge unintentionally, but also forms the habit of consciously exploring knowledge.
2. The transformation of examples.
We should give full play to the transformation function of examples, that is, after the teaching of examples, we should use a variety of questions to make the knowledge comprehensive and the methods students have learned flexible. For example, teach four arithmetic (page 10 in the second volume of grade four): "Tourists in the ice sculpture area 180 in the morning and 270 in the afternoon. If every 30 tourists need a cleaner, how many more cleaners will be sent in the afternoon than in the morning? " When the students master the solution of the example, then the teacher turns the question into "How many cleaners do you need this day?" In this way, the knowledge of how to think and calculate with or without brackets in the formula is consolidated in time, and students are prevented from learning one thing, thus cultivating the good habit of carefully examining questions and carefully analyzing them.
3. The extension function of the example.
Giving full play to the extended function of examples is actually to extend the knowledge learned appropriately, so as to develop thinking, deepen knowledge and nurture subsequent knowledge. For example, after teaching the example of "Preliminary Understanding of Fractions (Fractions)" (page 92 of the first volume of Grade Three), students can use the paper prepared by the teacher with exactly the same size to fold out their favorite scores, and the partners in the same group can talk about the meaning of the scores with each other, and then compare the sizes, which is intuitive, vivid and rich in content, directly paving the way for the comparison of the scores. To give full play to the extended function of examples, we must master the basic knowledge and skills of this lesson, otherwise it will be counterproductive. Of course, the extension should also consider the reality of the students who teach the content, so that the difficulty is appropriate, the extension is natural, and the teaching benefits of further consolidating knowledge and developing thinking are received.
4. The diversified educational function of role models.
The presentation of examples in the new textbooks has changed the disadvantages of the previous textbooks, integrated boring mathematics learning into specific life situations, accumulated the flavor of the times, organically combined the exploration of methods with the solution of problems, and skillfully carried out a variety of education. For example, the theme map of students planting trees on page 24 of the second volume of grade two and page 33 of the second volume of grade four subtly educates students to plant trees and protect their homes; Example 3: The theme map of mineral water bottles is collected on page 42 of the second volume of grade two, and the students are educated on the idea of waste utilization and recycling; The first volume of the third grade 15 page theme map for environmental education; The first volume of Grade Two 16 shows the theme map of Beijing's successful bid for the Olympic Games, which educates students in patriotism and inspires their pride ... Teachers can kill two birds with one stone by properly carrying out corresponding ideological education in teaching, but we should pay attention to properly grasping the degree of combination of mathematics teaching and moral education in teaching, and don't spoil mathematics class!
(2) Strengthen the "trial" and give immediate feedback.
"Try to do it" means "do one thing" after learning something new. It is a bridge between examples and exercises, with proper division of labor, mutual connection and coordination. What can be done to fully reflect their functions?
1. Enlighten, enlighten and practice hard.
The topics in "Do One Thing" are mostly the reappearance of new lessons, with the intention of trying to imitate them. Therefore, before class, students should read textbooks with specific questions, use old knowledge to perceive new knowledge, explore new knowledge and try to "try". For example, when teaching the law of addition and association (page 29 of the second volume of grade four), let students preview in three steps: the first step is to independently complete the examples in the textbook and compare several groups of formulas. What did you find? Step 2, read aloud the dialogue between the elf and the little girl; The third step, according to the knowledge learned from the examples, try to do:
425+ 14+ 186=425+( + ) 168+25+75= ( ) + (+ )
In this way, students are guided to try to practice in thinking, proceed in an orderly way in exploration, and cultivate their autonomous learning ability.
2. Information recovery, timely feedback
"Do it" provides timely feedback materials. After students finish "doing one thing", they urgently ask the teacher to judge the results of their exercises. At this time, the teacher can let the students check and correct each other after self-examination, and the teacher can patrol to understand the trial situation, collect feedback information and correct it in time.
(3) Grasping thinking questions skillfully and training students' thinking.
An important goal of mathematics learning is to train students' thinking and promote the development of their thinking ability. The characteristics of primary school students' thinking development are: from concrete image thinking to image association, and then from image association, they gradually form abstract logical thinking ability for simple things. In order to speed up the transition from concrete thinking in images to abstract thinking and develop students' thinking ability at an early stage, it is a practical and effective method to train students with thinking problems in textbooks.
1. Train students' thinking direction.
When answering thinking questions, we must choose certain goals and make clear what we should think in order to teach students to think. For example (page 26 of the first volume of Grade Three): Fill in the appropriate numbers in the box.
It is difficult for children in grade three to solve this problem if they blindly guess and think hard. Therefore, we should guide students to find a breakthrough from the relationship between the number of digits and the size of numbers.
2. Train students to think methodically and logically.
By answering some thinking questions, train students to analyze and think in a certain order. Find out what to think first, then what to think, let them know that such thinking is not easy to repeat and omit, so as to get all the answers, and at the same time use logical thinking skills such as analysis, comparison, judgment and reasoning. For example (page 92 of the fifth grade): 36 may be the least common multiple of which two numbers? How many groups can you find?
Students can be guided to think by finding the least common multiple of two numbers: first, consider the factor of 36, analyze the relationship between the two factors from its factor, and find out that 36 is the least common multiple of 36 and one of them; If two factors of 36 have a coprime relationship, then their least common multiple is also 36; Finally, consider the case that the minimum common multiple of two defenders who have neither multiple relationship nor coprime relationship is 36. Such orderly thinking can easily lead to multiple correct results of this problem.
3. Cultivate students' divergent thinking.
For thinking about different solutions, teachers should guide students to explore various solutions from different aspects and angles, and find out novel and unique simple solutions. For example (8 1 page in the second volume of Grade 3): on a square paper with a side length of 10 cm, cut out a rectangle with a length of 6 cm and a width of 4 cm. What's the rest of the circumference?
General solution: divide the remaining irregular figure into two rectangles, find the sum of their perimeters, and then subtract the sum of repeated side lengths.
(6+10) × 2+(10-6+4) × 2-4× 2 = 40 (cm)
Novel solution: directly move the 6 cm line segment upward and the 4 cm line segment to the right to form a new square (in fact, the circumference is the same as the original square).
10×4=40 (cm)
4. Train students to think comprehensively.
Some thinking questions have many conditions, so students should be taught to consider them comprehensively when seeking solutions to problems, and all the conditions in the questions should be considered, instead of taking one thing into consideration and generalizing it. Such as (grade 5, page 2 1): in
Fill in a number so that it is both a multiple of 2 and a multiple of 3.
2 4 2 465 12
When solving problems, guide students to give consideration to all aspects. Because it is a multiple of 2, the unit of each number must be a multiple of 2. In order to satisfy the condition of multiple of 3, the sum of each number must be multiple of 3. This can train students to take care of each other and meet the requirements of the topic.
5. Train the flexibility of students' thinking.
The flexibility of students' thinking should be trained and cultivated in solving problems. When analyzing and thinking about problems, teachers should inspire students to determine reasonable and flexible solutions according to the structural characteristics of the topics.
For example (page 2 1 in the first volume of Grade 3): Use only the number 8 to form five numbers, and fill them in the box below to make the equation hold.
( ) + ( )+ ( ) + () + ( ) = 1000
When solving problems, we should choose the thinking method reasonably and flexibly according to the characteristics of the data and formulas of the questions.
Second, optimize the use of textbook exercises and improve the utilization rate of exercises.
Although the exercises in the textbook have been recognized by experts, teachers should still choose appropriate exercises according to the actual situation of students' knowledge and skills to give full play to the role of each exercise.
(A) the choice of practice should be "one in a hundred"
Mathematics exercises are rich and varied. How to do correct exercises from numerous mathematical exercises requires us to work hard on the word "essence".
1. The purpose of the selected exercises should be clear and targeted. In other words, the selected exercises can suit the remedy to the case. For example, when I finished teaching the unit "The Meaning and Nature of Fractions" (the second volume of the fifth grade), I found that students were somewhat confused about the knowledge of general fractions and approximate fractions, so I immediately practiced the comparison between general fractions and approximate fractions. This helps students to clear up the ambiguity of knowledge points in time.
2. The demonstration effect of multiple-choice questions is better. Choose a question that can represent a piece.
3. The difficulty of multiple-choice questions is moderate, that is, multiple-choice questions can exert their comprehensive efficiency. For example, after teaching "Reciprocity of Fractions and Decimals", you can choose such an exercise: fill in the appropriate numbers in () and explain the reasons.
3÷4 =()24 = 24÷()= () (fill in decimal places)
This topic communicates the invariance of quotient and the basic nature of fraction from the horizontal aspect, and also communicates the relationship between division and fraction, as well as the knowledge of reciprocity between fraction and decimal.
(B) the use of exercises "take one as a hundred."
The design and application of mathematical exercises can not only satisfy one problem and one solution, but also answer one question and one answer. We need to pay attention to the word "live" when designing and using exercises.
1. Ask more questions. The same question, ask questions in many ways, let students think about the problem, you can "practice one question with a string."
2. Multiple solutions to one problem. Teachers can combine students' reality, inspire students from different aspects, guide students to think from different angles, answer in various ways and develop students' thinking.
3. One question is changeable. The same topic, different narrative methods, reflect the depth of the problem is also different You can design forward and backward exercises, or seek the same sex and the opposite sex, or similar exercises and comparative exercises. In the structure of questions, we should also pay attention to diversity, such as filling in the blanks, judging, choosing and combining, so as to improve students' ability and thinking quality.
Third, skillfully design exercises to actively mobilize students' emotions
Although the exercise design in the new textbook has changed to some extent the limitations of the previous textbooks, such as inflexible exercise form, inability to fully mobilize students' emotions, unified requirements and inability to meet the learning needs of students at different levels, in the process of using exercises, teachers should also skillfully design exercises according to students' learning reality, fully mobilize students' emotional factors and promote students to complete their learning tasks better.
(A) practice to be "new" to stimulate interest in learning.
Psychology believes that interest is the tendency of people to like certain activities or try to understand something, which is related to certain learning contents and forms. This requires us to design exercises in new ways, strengthen intuition, simplify the complex, add interest and stimulate interest.
(two) for all, to promote active participation.
Ausubel, a famous modern American cognitive psychologist, pointed out: "The most important factor affecting learning is what students already know, so we should design exercises to pave the way for knowledge and design the process of all students actively participating in knowledge acquisition. Let students have a sense of success in practice, let them succeed, help them succeed, and cultivate students' good learning psychology.
(3) Pay attention to differences and meet the learning needs of students at different levels.
Teaching practice and research have proved that students have obvious differences in heredity, culture, background, cognitive style and ability development. Therefore, it is particularly important to give play to the principle of teaching students in accordance with their aptitude and meet the needs of students at different levels.
The new curriculum provides a brand-new stage for teachers and students. If we want to make good use of new textbooks and give full play to the role of exercises, it is closely related to teachers' understanding and processing ability of textbooks. As long as we dig deep into the teaching materials and give students a broad world and a free space, I believe every class can be full of wonderful growth of teachers and students!