The new curriculum standard points out that "everyone should learn necessary mathematics, and everyone should learn practical mathematics", which closely links mathematics with real life, and takes finding problems, analyzing problems, solving problems and putting forward new problems as the main links in classroom teaching. Cultivating students' ability to solve problems is an important link in the teaching process. Problem solving means that students solve various problems they face under the guidance of teachers. In this process, students should actively participate in classroom teaching, and finally form a good habit of thinking with practice through the combination of speaking, doing and thinking, and change passive problem solving into active problem solving.
This requires teachers to have clear goal orientation and strategies to guide the problem.
First, "solving problems" should have a clear goal orientation. In solving mathematical problems, we should first make clear the directionality of the problem goal, that is, what kind of final state to achieve, and then let students know what to do in order to achieve the problem goal. If they can't do it, they will fail. In a math class, the more questions, the better. How teachers guide students to ask "mathematical questions" with exploratory value is the starting point for the success of this course. However, valuable mathematical problems are not easily produced, and are often influenced by many factors such as classroom teaching environment, learning materials, effective guidance of teachers and so on. Therefore, I think teachers should follow the following three aspects when designing problem objectives:
(A) the problem objectives should be targeted. Under the background of new curriculum, mathematics classroom pursues an open, democratic and harmonious teaching atmosphere. Students are required to actively explore, boldly question and ask their own questions, which also implies that teachers must combine the classroom teaching content with a clear goal when designing the goal of the problem, and give students a clear direction to solve the problem. If the problem goal is not targeted, it will easily lead to the deviation of classroom teaching from the preset teaching goal before class, which will lead to the deviation of the focus of teaching content and affect the scheduled teaching tasks. For example, when teaching area and area unit, some teachers introduced it before class. The teacher asked the students to "simulate the same" books, exercise book covers and classroom desktops, so that students could compare which area is larger. The problem designed by the teacher is: let's make a model of the book, the cover of the exercise book and the desktop of the class, and see what we find. In this way, students find more: some write fluently; Rough desktop; There is an exercise book cover without a text cover and so on. Although this kind of question design is open, it is not targeted, misleading students' thinking, making the classroom lead-in time too long and failing to reach the teacher's questioning goal. On the contrary, the views put forward by the students have not been solved, so the teacher has to draw a hasty conclusion, pull the students back to the initial state and guide them to think: "which area is big?" In fact, this question can be put forward directly from the beginning: "Everyone is exactly the same, let's see which side is bigger, OK". It quickly solved the problem.
(2) The goal of the problem should be gradual. The design of mathematical problems should be hierarchical, from shallow to deep, from easy to difficult. Actively follow the principle of gradual progress, so that students will have a sense of pride, satisfaction and accomplishment when solving a problem psychologically. In this way, we can experience the happiness brought by learning mathematics in solving one problem after another. For example, in the process of teaching the meaning of proportion, in order to make students grasp the meaning of proportion, they must first understand what proportion is. How to find the proportion? After students understand the ratio and the ratio, they can form a ratio by further guiding two ratios that are equal, so that students can naturally grasp its meaning quickly: two equal ratios are called ratios. Understand that equality here refers to equality. Some students will also think about how to make up the proportion of two division formulas with equal quotient. This shows that when we solve problems, we should consider going from simple problems to gradual deepening, so that students can feel psychologically that "solving problems" is not terrible, but a pleasure of experiencing success.
(3) The goal of the question should be open. In class, sometimes valuable math problems cannot be put forward at once. Students need to reflect and evaluate themselves, or teachers and students need to reflect and evaluate each other, so as to solve the problem better. For example, when I was teaching fractional division, I summarized the calculation rules of fractional division: A divided by B equals the reciprocal of A multiplied by B. Let the students discuss in groups, judge right and wrong, and explain the reasons. When reporting in groups, most groups thought it was not feasible. The reason is: 1 This solution can only represent fractional division in which both numerator and denominator are multiples. 2. This solution violates the law of calculating scores. 3. What if numerator and numerator, denominator and denominator are inseparable? When students put forward these views, one student in one group raised his hand and replied that he disagreed with this view, especially for reason 3. He said that if the numerator and numerator, denominator and denominator are not multiples, they can also be divisible. That is, first find out the least common multiple of the numerator and denominator of the divisor, and then expand the numerator and denominator of the dividend at the same time according to the basic properties of the fraction, so that it can be divisible. If we can find out that the least common multiple of 2 and 5 is 10, and then expand the dividend, numerator and denominator by 10 times at the same time, can't we divide the numerator by numerator and divide the denominator by denominator? This will get the same result. It's really good for students to do more questions. In this way, by asking open questions, under the guidance of teachers, students' divergent thinking can be stimulated, problems can be solved, and innovation can be realized.
Second, "solving problems" is obviously strategic.
(1) Pay attention to group cooperation. Compared with the traditional teaching form, group cooperative learning has many similarities in teaching steps, but it also has certain particularity. When teachers ask students to cooperate in groups, students should first understand the task, learning content and objectives of cooperative learning. How to complete the task? What are the evaluation criteria (how the group's tasks are completed, how the individual's learning results are, etc.)? )? At the same time, teachers should also stimulate students' learning enthusiasm by creating situations or asking interesting and challenging questions; Inspire students to be good at using existing knowledge and experience to solve problems and promote the transfer of learning. When students understand their learning tasks, they enter the stage of group exploration. During this period, teachers should actively guide students to find possible problems and help students improve their cooperation ability through inspections. When each group gets the solution to the problem, what is needed next is the exchange of group reports, and teachers and students combine the reports of each group to summarize. Finally, the methods to solve the problem are summarized. Cultivating students' cooperative consciousness is one of the good ways to solve problems in mathematics classroom teaching. It has better improved students' awareness of participation, cooperation and language expression.
(2) Pay attention to inspiration. Often, in mathematics teaching class, in order to solve the problems raised, teachers need to be good at combining with the reality of life and gradually inspire students with simple life examples to solve problems. For example, when teaching multiplication distribution rate, we can organize teaching by looking at simple life examples. A is equivalent to an apple, and B and C are equivalent to two brothers and sisters. The students certainly don't agree that apples can be given to their brothers or sisters respectively. Everyone's request is that if my brother shares the apple, so does my sister. Is it wrong for the teacher to go further? The multiplicative distribution rate is like this. A is assigned to B, and A is also assigned to C, which is only the sum or difference of the products. In this way, students can quickly grasp the key to the multiplication distribution rate.
(3) pay attention to finishing. Mathematical problems are often not single and unchangeable, and different problems can be raised under the same conditions. Especially for application problems, we constantly change the known conditions and problems, but we are good at induction and sorting out, and we will find its universal characteristics: 1, fractional application problems and percentage application problems are not the corresponding scores of standard quantities = corresponding quantities; 2, the distance problem is not speed time = distance; 3. The engineering problem is not work efficiency × working hours = general trade unions, and problems such as price and output all have their fixed quantitative relationships, and one of these quantities is needed, or the quantitative relationship is taken as an equation and solved by the equation; Either it is deduced according to the quantitative relationship and solved by arithmetic method. Of course, this does not mean that as long as our teachers seem to understand, the most important thing is that students should learn to summarize and sort out, so that they can understand in their hearts and solve such problems naturally.
(D) Pay attention to the integration and sharing of resources. At present, the content of distance education resources is rich and colorful, with many excellent classroom records, excellent courseware and excellent teaching cases of teachers. All these can help us to solve classroom problems well. But no matter how good things are, they should also be combined with the local reality, so this requires teachers to be good at blending and eventually turn other people's things into their own and use them for me. For example, if a teacher teaches to understand the surface area of a cylinder and combines courseware with objects, the effect will naturally be very different. When the circles on the upper and lower surfaces appear on the screen, they will gradually smooth the bottom surface and finally overlap. Students will soon understand that the circles on the upper and lower surfaces are as big as each other. Students will naturally understand the shape of the side of the cylinder when they see the side slowly unfolding into a rectangle (square). In this way, students will quickly solve the problem in this lesson by combining physical observation and feeling, that is, the surface of a cylinder consists of two equal circles and sides (rectangles or squares).
Third, "solving problems" focuses on evaluation. Mathematics under the new curriculum concept pays more attention to teachers' evaluation of students, embodies students-oriented and builds a harmonious classroom. Therefore, in classroom teaching, teachers should evaluate students like this: "There are more rulers and more talents; One more angle, one more beautiful view; One more emotion, one more world. " Only in this way can our classroom teaching be more colorful and better reflect students' thinking of seeking differences. The purpose of asking questions in class is to solve problems. How do students actively participate in solving problems? Of course, an important factor is that students are interested in the questions raised. Students who are interested in problems will take the initiative to solve them. At this time, students can actively express their views, and the teacher's evaluation of students becomes more important. But at this time, the student answered irrelevant questions, and the teacher killed him with another stick, still looking at him coldly. This is the strangulation of students' feelings. This can not only solve the problem, but also survive new problems in the problem. That's the next class, the students didn't learn anything ... so it is particularly important for the teacher to evaluate the problems in the class, talk about methods and talk about art.