The cultivation of basic knowledge and ability plays a vital role.
What kind of mathematics classroom should be under the new era and new concept? What ability does learning mathematics cultivate? Why are all countries in the world?
Does basic education include and attach importance to mathematics learning? What should teachers do in the classroom during the six-year primary school mathematics education that students have experienced?
What? What should I do?
I think the teaching material is the carrier, the students are the center, the classroom is the position, and the concept is the foundation. Ten years have passed, and the new textbooks carry more new teaching.
The concept of education and teaching is more of a help to personnel training and more of an effective guide to educators. Let me talk about what I have done in the past few years.
In the process of curriculum reform, how to correctly grasp new ideas, correctly interpret new textbooks, use new textbooks scientifically and creatively.
Practical research and generation reflection.
First, a correct interpretation of textbooks can enable students to learn new mathematics.
10 years ago, we were all teachers, and the students we trained only accepted learning. How can we cultivate our own ability? Since the promotion of new teaching materials and new curriculum reform, I have
Through a lot of study and research, students gradually change from "teaching" to "educating people"; From "Teaching Mathematics with Textbooks" to "Using"
Textbooks for teaching mathematics. "We gradually understand that teaching materials are the carrier of teaching, not the only standard. In the full implementation of the new curriculum reform
In the process of implementation, higher requirements are put forward for teachers. Only teachers can examine and control the current textbooks from a historical and developmental perspective.
Only by correctly interpreting the new textbooks can students learn new mathematics.
Then, a principle that must be followed in correctly interpreting new textbooks is: having curriculum standards in mind, textbooks in mind and students in mind. The power of teachers
It is necessary to read the curriculum standards intensively, study the teaching materials deeply and study the students seriously.
The case links to the teaching fragment of the example of "estimating two numbers with two numbers"
Estimation is the teaching content of calculation that needs to be strengthened in the Standard. Because estimation is widely used in daily life and has important application value,
At the same time, it is of great significance to cultivate students' sense of numbers.
Content Description: The textbook presents a situational diagram, and asks students to solve the question "There are 350 students in the class. Can you sit down?" problem Below the situation map
There are different estimation methods: ① treat two factors as integers close to them, and then determine the range of their products through oral calculation; (2) Among them
Think of a factor as an integer close to it, and then determine the range of their products by oral calculation.
Case generation
Teacher: Look at the information, look at the problem and solve it quickly. (The students' answers are inconsistent, so slow down. )
One of the students suggested that this question need not be so clear, just a rough calculation.
Teacher: How are you going to make a rough calculation?
Health: I regard 22 and 18 as 20 times.
Teacher: You can estimate the nearest integer of two digits and multiply it. This is the method of estimation.
Teacher: Are there any other estimation methods? (other students were inspired by this classmate and came up with several other estimation methods.
The teacher instructed the arrangement of several methods. )
Teacher: It seems that these three estimation methods can solve this problem, so what are the similarities between these three methods?
Student: They all multiply two digits as the nearest integer.
Teacher: Do you think we get more or less than the exact number of words through estimation?
(Some students talk less, some students talk more, and some students talk about the same. )
Teacher: Why? How did you know?
Health: Because 22 is regarded as 20, the factor is underestimated, so the estimated result is smaller than the accurate result.
……
Teacher: Really? Let's have a look! The estimate of 18 is 20, which is overestimated, so the final result is greater than the exact number of words. If 22 is estimated to be 20, it is estimated that
If it is low, the final result will be less than the exact number of words.
So, how to compare the results obtained by estimating 18 and 22 to the nearest integer ten with the exact number of words?
(Students react together: almost. )
Teacher: Why is it almost the same?
Health: Because one factor is underestimated by two and the other factor is overvalued by two, it is even.
Teacher: It seems that we can have many kinds of estimation methods when solving problems, which one depends on the specific problem.
Case interpretation
When listening to the examples taught by teachers, I clearly realized that these estimation methods are not difficult for students.
Students can say that you don't have to teach this course, and they will all solve this problem. So what do students need in this course?
And then what? What do they need to develop?
What students need is to learn reasonable analysis and comparison in the process of estimation, so that estimation can really play its own significance and value.
Can solve the problem. Therefore, in example teaching, pen and ink should not only focus on learning multiplication and estimation methods, but also guide learning according to specific problems.
Students analyze and compare the results according to the specific estimation methods, so as to get the required answer to this question. Therefore, in the next teaching.
In this process, I adjusted the pen and ink, and no longer downplayed the analysis and comparison. Students are guided by teachers, which leads to "estimated height" and "estimated height"
The conclusions of "low" and "almost" are the embodiment of students' ability to analyze problems. This is an essential analysis when solving problems with estimation.
Estimation is different from oral calculation and written calculation, which is also a feature. This kind of thinking training cannot be realized in accurate calculation. Learning in estimation teaching
The cultivation of students' estimation consciousness and ability is gradually formed, as long as we consciously and systematically provide students with the opportunity to estimate and let them move.
Solve problems with estimation, realize the necessity of learning estimation in practice, the awareness of estimation will gradually form, and the estimation ability will gradually improve.
Students' analytical ability is greatly improved while forming their awareness and ability of estimation. When facing new problems, students need to open their minds.
Good analytical skills as support. Mathematics class should not only cultivate the ability of analysis and judgment, but also cultivate the difference from the old textbooks.
One of the highlights is that the new textbooks enrich the training points of students' abilities, students will learn new mathematics, and students' abilities will fully serve students.
Live.
Second, the innovative use of teaching materials can promote the development of students' ability.
Mathematics class must have the taste of mathematics. Incorrect or incomplete interpretation of the textbook will make the new math class obsolete. The so-called mathematical interest is a kind of rationality.
Thinking, such as logical thinking, analysis and judgment, spatial imagination, etc. These abilities are indispensable and important for talents needed by social development. If you want to learn
Students' promoting the development of students' ability in math class also requires teachers to use new textbooks creatively. Teachers can teach creatively and students can learn with interest.
As long as you are interested in learning mathematics, your ability will gradually form.
Taking the arrangement and review of division in Volume 2 of Table 2 of Senior Two as an example, this paper discusses how teachers create teaching materials for the development of students' ability.
New use, use.
Arrangement and review of case links "Division in Table 2"
Description: Two questions are given in the arrangement and review of division in the second volume of Table (2) of Senior Two. The first question raised the children's discussion.
Regarding the classification method of division formula in the table, students express their opinions, some think that it can be divided according to the number of formulas, and some are the same according to divisor.
The formula should be divided, and some questions can be divided? The second problem is to solve the problem together. Then I divided into two classes and tidied up. first
One kind arranges the calculation part, and the other arranges the problem-solving part.
I will ask students to give examples of which division formulas in the table they have learned. The teacher should put these formulas on the blackboard when the students speak.
Written on the blackboard, the positions of these formulas should be the positions of the division table in the table. For example, if a student says 20÷4=5, I will first write this formula on the blackboard.
Row 5, column 4; When the students say 9÷9= 1, I will write it in the ninth column 1 on the blackboard; When the students say 16÷4=4, I will write it on the fourth row of the blackboard.
Cylinders ... in the list of many formulas, middle school students will now feel how the teacher scribbled the formulas, one in the east and the other in the west, and then slowly discover the rules.
Will accurately guess where the teacher will write this formula on the blackboard and why. In this process, the enthusiasm of the whole class is very high, because
Because there are some riddles in it, students will feel that simple formulas become mysterious. In the whole process of completion
Students have gone through a series of processes, such as induction, sorting, guessing, reasoning and enumeration, which are helpful to the development of students' thinking. And the students themselves summed it up: When?
When the dividend and divisor are the same, the quotient is1; When the divisor is 1, the divisor is the same as the quotient; What is the divisor? Dividend is quotient.
Times; What is quotient? The divisor is several times the divisor ... The inductive language of students made me not think of mine when preparing lessons.
Presupposition is to let them go through such a process of induction and arrangement, and feel from it and express it in their own childish language.
My own understanding is enough, but the students' incisive induction has opened my eyes, which shows that students are also going through such a process.
The climate is efficient, and students have been comprehensively improved in this process.
Case interpretation
In the treatment of the first class, the textbook does not list the division formula table in the table, but presents it in the form of group discussion among students.
My understanding of this kind of writing is that students should have their own thinking process, which can be arranged according to certain rules.
It is not necessary for students to sort out the division formula table completely, but it is quite difficult for second-year students to summarize and sort out the division formula table. but
What we should challenge and improve in each review lesson is the students' ability of sorting and summarizing. Difficulties don't mean that they won't learn it.
It is difficult to experience difficult challenges before thinking is improved. Therefore, my understanding of textbooks is that not only students themselves
Teachers should give students some guidance according to certain laws, and in the process of guidance, let students find out the arrangement of the division table in the table.
Regularity, so as to be able to learn the effective method of this arrangement.
Therefore, we should not only fully understand the presentation of teaching materials, but also thoroughly understand them. This kind of writing is not limited to books, but a living learning.
Students are closely linked and need teachers' correct and scientific support, so that teaching is efficient and students' development is possible.
Effective and comprehensive.
Being able to teach new textbooks is a skill, and creatively teaching new textbooks and combining the ideas and concepts contained in new textbooks is another ability.
Teaching materials are transformed into teaching practice through development and achieved results, which is a foundation. Teachers should use their brains on the basis of respecting teaching materials, and don't
Limited to teaching materials, flexible use of teaching materials, innovative use of teaching materials according to the actual situation of schools and students, so as to achieve student-oriented development, which
Only by truly implementing the new curriculum reform and new ideas can students develop scientifically.
Third, the scientific interpretation of teaching materials can promote the formation of students' mathematical thoughts.
Everyone wants to be a creator and inventor, especially our students. Once our education was to obliterate students' innovative consciousness and ability to learn.
Students become passive learning and problem-solving machines. New ideas try to change this situation, trying to make students
After many successful innovations and inventions, it gives students a desire to explore and a habit of thinking, which is exactly what we need in mathematics.
Quality.
When teaching the knowledge of assembly circle, students experience Wayne's creation of this circle. For students, this is to improve their mathematics quality.
It is also the best time to form the ability.
Case Link "Fun Circle" Teaching Fragment
Content abstract: Set theory is the most basic idea in mathematics, and it can even be said that set theory is the foundation of mathematics. Starting with students' study.
Mathematics, in fact, is already using the set thinking method. For example, students learn to count, using 1 person, 2 flowers and 3 pencils as one.
A closed curve is circled, which means that the mathematical concepts expressed in this way are more intuitive and vivid, leaving a deeper impression on students. Take me for example.
The classification ideas and methods that students have learned are actually the basis of set theory.
Example of this unit 1 With the help of students' familiar subjects, infiltrate the relevant ideas of set, and calculate the total number of two groups in an intuitive way.
In this example, the list of students participating in the Chinese group and the math group is listed through statistical tables. As can be seen from the statistics, students who participate in the Chinese group
There are 8 people in the group and 9 people in the math group. But in fact, the total number of participants in these two extracurricular groups is not 17, which causes students' anxiety.
Cognitive conflict. At this time, the textbook directly uses the direct diagram to show the relationship between the two extracurricular groups. As can be clearly seen from the figure.
There are three students in both groups, so the total number of students can only be calculated once.
Case generation
The information given by the teacher is that there are 8 people in the Chinese group. There are nine people in the math group.
Ask a question: How many people are there? Students list the formula: 8+9= 17 (person)
Teacher: Please stand up and let's see if there are 17 people.
(Students found the problem, and there were no 17 people, only 14 people. The teacher instructed the list of statistical tables to check, and the students seemed to find that statistical tables carried weight.
A complicated phenomenon. )
Teacher: Let me tell you something! In order to make everyone see more clearly, we invite these students to come up separately, and we will count them in groups!
(1) Please join the China Group and stand here! Count, is it eight people?
(2) Please join the math group. Stand this way!
(among them, repeat students want to come to the math group and the teacher will guide them. )
Teacher: Yes! Aren't you in the China Group? Please stand over there and don't run around!
At this time, the three students who participated in the two groups had no choice but to cope with the teacher's humor. They hesitated, but they still wanted to come over.
. )
Teacher: In order to show that all eight of you are in the Chinese language group, we will circle you all with this red circle, and you are not allowed to run around!
So, you are all in the math group. There should be nine people in the math group. Why are you three short?
The student is anxious: there are still three of us!
Teacher: Then come here!
Student: But teacher, you won't let us out of this circle!
At this time, contradictions and conflicts aroused the students' strong desire to find a solution. Finally, some students couldn't sit still, and some learned.
The students chimed in to get these three people together, but the other students didn't quite understand. A student finally ran to the podium.
Finally, an operation was carried out: he arranged the repeated three people in the middle and crossed two circles to form the repeated three people, so that the three students
Stand in the red circle and the basket. )
Case interpretation
This result is inevitable. Now many teachers treat textbooks in this way. Why? It is because of this kind of teaching that it is given to students.
Space for thinking and desire for exploration. The intersection of this circle is not what everyone wants, but we students did come up with it.
It is not because students read textbooks in advance or their parents taught them, but because students try their best to solve such contradictions and conflicts.
This question. Wayne is not a special genius. Many of our students have experienced Wayne's creative process, and this kind of learning is exactly the same.
The concept of education and teaching permeated in the new textbook allows students to experience, understand, stimulate and creatively solve contradictions. With this kind of creation,
In this process, students not only gain something in thinking, but also meet their psychological needs, and a great sense of accomplishment arises spontaneously-
I can be an inventor myself!
There are many examples like interesting circles in the new textbook. What the teacher needs to do is not directly give the students how to fill in and draw Wayne circles, but
It is to let students really get the space to think, consciously walk into contradictions, and let themselves create in the ocean of mathematics.
In our actual mathematics teaching, we should really understand new ideas and new teaching materials, and design our teaching scientifically with the development of students as the center.
study Let students give full play to their wisdom in the classroom and learn excellent mathematics quality and excellent mathematics in tens of thousands of posts.
The generation of learning ability is inevitable.