The first phase (grade 1 ~ 3)
I. Teaching suggestions
Mathematics teaching is the teaching of mathematics activities and the process of interactive development between teachers and students. Mathematics teaching should be closely linked with students' real life. Starting from students' life experience and existing knowledge, we should create vivid and interesting situations to guide students to carry out activities such as observation, calculation, guessing, reasoning and communication, so that students can master basic mathematical knowledge and skills through mathematical activities, initially learn to observe things and think about problems from the perspective of mathematics, and stimulate students' interest in mathematics and their desire to learn mathematics well. Teachers are the organizers, guides and collaborators of students' mathematical activities; According to the specific situation of students, the teaching materials are reprocessed and the teaching process is creatively designed; It is necessary to correctly understand the individual differences of students, teach students in accordance with their aptitude, and let each student develop on the original basis; Let students have a successful experience and establish self-confidence in learning mathematics well.
(1) Let students learn mathematics in vivid and concrete situations.
In this period of teaching, teachers should make full use of students' life experience and design vivid, interesting and intuitive mathematics teaching activities, such as telling stories, playing games, intuitive demonstrations and simulated performances, so as to stimulate students' interest in learning and let students understand and know mathematics knowledge in vivid and concrete situations. For example, teachers can instruct students to play the following games.
Example 1 Two students play a guessing game in pairs.
A: I thought of a two-digit number. Can you guess what it is?
B: Is this number greater than 50?
A: That's right. B: Is it less than 70? A: That's right. B: Is it greater than 60? No. B: Is it bigger than size 56? ……
Teachers can use the above games to guide students to engage in interesting mathematical activities, so that students can learn an effective problem-solving strategy while experiencing the size of numbers, which contains the simple idea of gradually approaching with "interval sets".
(2) Guiding students to think independently, cooperate and communicate, practice independently, explore independently and communicate cooperatively is an important way for students to learn mathematics. In this period of teaching, teachers should let students think independently in specific operational activities, encourage students to express their opinions and communicate with their peers. Teachers should provide appropriate help and guidance, be good at choosing valuable questions or opinions among students, and guide students to discuss in order to find the answers to questions.
Example 2 When rotating the turntable (see the right), is it more likely that the pointer will fall in the shadow area or the white area?
In teaching, the teacher can first group the students, let each student guess in advance which area the pointer will stop, and then start to turn the turntable. In the process of personally rotating the turntable, students realize that it is uncertain whether the pointer falls in the shadow area or the white area before the turntable stops. After many rotations, students gradually realize that the number of times the pointer falls in the shadow area is different from that in the white area, and the number of times the pointer stops in the white area is more than that in the shadow area, that is, the possibility of the pointer falling in the white area is greater than that of the pointer. On the basis of students' hands-on operation, teachers can guide students to discuss and exchange their feelings. In the teaching of "Space and Graphics", teachers should design colorful activities, so that students can further understand their own space and know some common geometric bodies and plane graphics through observation, measurement, folding and discussion. For example, in the teaching of identifying cuboids, cubes, cylinders and spheres, teachers should select materials from objects familiar to students (such as basketball, table tennis, beverage bottles, kaleidoscopes, chalk boxes, toothpaste boxes, globes, etc.). ), and encourage students to observe, touch and classify, thus forming an intuitive feeling of related geometry. For another example, the following activities can be designed in teaching: let four students sit in four directions and observe the same object (such as kettle, teacup, etc.). ), draw what they see first, then organize students to communicate and guess who drew a picture and where he sat. Through observation, comparison and imagination, students realize that what they see in different directions is different, and gradually develop the concept of space.
(3) Strengthen estimation and encourage diversification of algorithms.
Estimation is widely used in daily life. In this stage of teaching, teachers should seize the opportunity to cultivate students' estimation consciousness and preliminary estimation skills.
Example 3 Xiaoming earned 243 yuan from raising chickens and 479 yuan from raising pigs. What is the estimated income of these two items?
Different students may have different estimation strategies. Some students think that "200 plus 400 equals 600, 43 plus 79 is greater than 100, so their sum is a little more than 700"; Some students' estimation methods may be: "243 is less than 250 and 479 is less than 500, so their sum is less than 750;" Some students may say that "this number is more than 200+400 and less than 300+500", which is correct. Teachers should organize students to exchange estimation methods, compare estimation results, and gradually cultivate students' estimation consciousness and strategies.
Because students' life background and thinking angle are different, the methods used are inevitably diverse. Teachers should respect students' ideas, encourage students to think independently and advocate diversification of calculation methods. For example, students can use various methods to calculate the problem of 34+27, and the methods listed below should be encouraged.
( 1) 3 4 (2) 34+27 + 2 7=34+20+7 6 1
=54+7 =6 1 (3) 30+20=50 (4) 34+27
4+7= 1 1=34+6+2 150+ 1 1=6 1=40+2 134+27=6 1=6 1
Teachers should not be eager to evaluate various algorithms, but should guide students to choose their own methods by comparing the characteristics of various algorithms. For another example, when solving the problem that "at the parent-teacher conference, each bench can hold up to 5 people, and 33 parents need to prepare at least several benches", students' thinking methods may be diverse. Some students use learning tools, sticks represent benches, and disks represent parents. It is concluded in the operation that at least 7 benches should be prepared. Some students judged that at least 7 benches should be prepared by calculating 33÷5. Some students use multiplication, 5× 7 = 35, 35 > 33, 5× 6 = 30 30 < 33, so at least 7 benches should be prepared. Teachers should encourage these methods, provide opportunities for students to communicate, and let students constantly improve their methods in mutual communication. This can not only help teachers understand the learning characteristics of different students, but also help to promote the development of students' personality. At the same time, teachers should always ask students to think about such questions: What do you think? What did you do just now? What if? What's the matter? Which method do you think is better? ..... so as to guide students to think and exchange solutions to problems.
(D) Cultivate students' initial application awareness and problem-solving ability.
In this period of teaching, teachers should make full use of students' existing life experience, guide students to apply what they have learned to life at any time, solve math problems around them, understand the role of mathematics in real life, and realize the importance of learning mathematics. For example, teachers can guide students to solve the following open questions.
Example 4: 27 people go to a place by bus. There are two kinds of vehicles available for rent, one can take eight people and the other can take four people.
(1) Give more than three car rental schemes;
(2) The rental of the first car is 300 yuan/day, and the rental of the second car is 200 yuan/day. Which scheme costs the least?
Practical activities are an important way to cultivate students' initiative exploration and cooperation spirit. In this period, teachers should organize students to carry out lively and interesting activities, so that students can experience the process of observation, operation, reasoning and communication.
Second, the purpose of evaluation suggestion evaluation is to fully understand students' learning situation, stimulate students' learning enthusiasm and promote students' all-round development. Evaluation is also a powerful means for teachers to reflect and improve teaching. The evaluation of students' mathematics learning should not only pay attention to their understanding and mastery of knowledge and skills, but also pay attention to the formation and development of students' emotions and attitudes. We should not only pay attention to the results of students' mathematics learning, but also pay attention to their changes and development in the learning process. The means and forms of evaluation should be diversified, and the process evaluation should be the main one. The description of evaluation results should use encouraging language to give full play to the incentive function of evaluation. Evaluation should pay attention to students' personality differences and protect students' self-esteem and self-confidence. Teachers should be good at using a lot of information provided by evaluation to adjust and improve the teaching process in time.
(1) Pay attention to the evaluation of students' mathematics learning process. The evaluation of students' learning process in this period should examine whether students actively participate in mathematics learning activities, whether they are willing to communicate and cooperate with their peers, and whether they are interested in learning mathematics. Teachers should also pay attention to the process of understanding students' mathematical thinking, and let students talk about his thinking process when solving problems.
Take a test with 1 How far can you throw the solid ball
In the above activities, we should first examine the degree of students' participation, and understand whether students can independently propose measurement schemes, cooperate with others to solve problems, and communicate their own methods and problem-solving processes with others. At the same time, we should also understand how students use knowledge to solve problems and think mathematically in activities. Students may have the following performances: (1) Measure according to the method instructed by the teacher; (2) come up with other measurement methods (such as step measurement, rope measurement, meter measurement, tape measurement, etc.). ); (3) Explore various measurement methods and exchange different measurement methods through group cooperation; (4) Measure by various methods, and simply explain the rationality of the measurement method. For example, if a student throws a distance of more than 3 meters, there will be some errors in measuring this distance with a meter ruler, because the measuring process may not be a straight line, but it will be more accurate to measure it with a tape measure. Teachers can analyze and evaluate students' performance in the process of activities. When evaluating students' learning process, a growth record bag can be established to reflect students' progress in learning mathematics and increase their confidence in learning mathematics well. Teachers can guide students to include important materials reflecting their learning progress in the growth record bag, such as the most satisfactory homework; Favorite small production; Impressive problems and solutions; Experience in reading math books; Wait a minute.
(b) Appropriate evaluation of students' understanding and mastery of basic knowledge and skills.
The evaluation of basic knowledge and skills in this section should follow the basic concept of standards, and take the knowledge and skills objectives in this section as the benchmark to examine students' understanding and mastery of basic knowledge and skills. It should be emphasized that the semester goal is the goal that students should achieve at the end of this semester, and some students should work hard for a period of time and gradually achieve it with the accumulation of knowledge and skills. For example, the requirements for calculation listed in the following table are not to be met by all students immediately after learning the corresponding content, but by the end of this semester, and attention should be paid to grasping the scale when evaluating.
Learning content
Speed requirement
Addition and subtraction within 20 and multiplication and division in oral table
8 ~ 10 questions per point
Addition and subtraction within three digits
2 ~ 3 questions per mark
Multiply two digits by two digits.
1 ~ 2 questions per point
Divider is the division of one digit, and the dividend does not exceed three digits.
1 ~ 2 questions per point
Students in this period often need to use concrete things or physical models to complete their learning tasks. Therefore, when evaluating students, we should pay attention to students' understanding of the practical significance of what they have learned in combination with specific materials. The evaluation of logarithmic and algebraic contents should be combined with specific situations to examine children's understanding of logarithmic meaning. For example, the understanding of the meaning of fractions can be examined in the following situations.
Example 2 (1) What percentage of the whole figure is shaded?
(2) Please show it graphically.
The evaluation of space and graphic content should be combined with intuitive materials and life situations to evaluate students' understanding of graphics. For example, the following questions can be used to examine students' concept of space.
Example 3 There is a car as shown below.
Xiaohong looked down at the car from the air. Which of the following pictures is the shape that Xiaohong sees?
The evaluation of statistics and probability content should be combined with life situation to examine students' preliminary statistical consciousness and ability to solve simple problems. For example, when preparing for class activities, in order to determine the types and quantities of fruits to be purchased, students can investigate the favorite types of fruits in the class and the corresponding number of people. In the evaluation, we can mainly examine the following aspects: whether students can collect the number of people who like to eat various fruits with the guidance and help of teachers; On the basis of collecting data, can we classify, sort out and describe these data (for example, it can be said that "the people in our class like apples the most, and the people who like pears are less than half as fond of apples". ); Can you confirm your purchase plan?
(3) Pay attention to the evaluation of students' ability to find and solve problems.
To evaluate students' ability to find and solve problems, we should pay attention to whether students can find and ask simple math problems from their daily lives under the guidance of teachers. Can you choose a suitable method to solve this problem? Willing to cooperate with peers to solve problems; Can you express the general process and result of solving the problem? For example, teachers can ask students various questions from their daily lives: who has more pencils, who is tall, and whose home is near the school ... Teachers can give qualitative evaluation according to the quantity and quality of questions raised by students.
(d) Evaluation methods should be diversified.
Children in this learning period have just entered school, and their feelings about mathematics are very important for whether they like mathematics learning in the future and whether they can learn mathematics well. Therefore, teachers' evaluation of children should be guided as positively as possible to confirm what children know and master. When evaluating students, teachers' evaluation should be combined with peer evaluation and parent evaluation. The evaluation of students' learning situation should pay attention to the combination of various evaluation forms, and adopt classroom observation and after-class interview. Work analysis, operation, practical activities and other forms. Each evaluation method has its own characteristics, which should be selected in combination with the evaluation content and the characteristics of students' learning. For example, teachers can choose the way of classroom observation to examine students from four aspects: the seriousness of learning mathematics, the mastery of basic knowledge and skills, problem solving and cooperative communication. Teachers can also understand students' learning attitude and awareness of cooperation and communication from learning activities, students' mastery of computing skills from their usual homework, and the development of students' ability to ask questions and solve problems from their growth records.
(5) The evaluation results are presented in a qualitative way.
According to the characteristics of students in this period, the evaluation results should be presented in qualitative description and encouraging language to describe students' mathematics learning. The following is an example of a comment: "Xiaohong has been able to finish every homework carefully in this semester's math study, actively participate in group discussions, and is willing to listen to other students' speeches." "Willing to ask questions, I can often come up with different ways to solve problems from my classmates. The correctness of the calculation needs to be further improved. " Such comments are mainly encouraging, but they also point out the direction that students need to work hard.