The new curriculum reform has been going on for nearly ten years, and I always hear many teachers around me feel puzzled: there are only a few practice classes about solving practical problems in the textbook. After half a class and adding some topics, the final effect is not great, but it is still far from good ... Faced with these problems, I was very confused. In fact, comparing the new and old textbooks, you will find that the application problems in the old textbooks are basically given two. As long as students choose the right method to solve the problem, they will get the right answer. But in the lower grades, the only application problems are addition and subtraction and simple multiplication and division. In addition, with a lot of practice, students may not understand the meaning of the question, but they can also guess roughly. The questions were done correctly, but they didn't grasp them in essence. However, teachers have not fully understood these hidden situations. The new textbook is not like this. When solving a problem, two known conditions and one problem are not directly given. Students need to analyze, judge and choose useful information from the given information and correctly understand the meaning of the problem in order to solve the problem (which is more demanding than the old textbook). In this way, the teacher feels that the error rate of solving problems has suddenly increased, and it is of no help to increase practice after class. "New Curriculum Standard" points out that the application consciousness is mainly manifested in: recognizing that there is a lot of mathematical information in real life and that mathematics has a wide range of applications in the real world; In the face of practical problems, we can actively try to use the knowledge and methods we have learned from the perspective of mathematics to find strategies to solve problems; When faced with new mathematical knowledge, we can actively look for its actual background and explore its application value. The root cause of these doubts is that students have no strategy to solve problems. So, is it clear to talk to primary school students about strategies? Especially junior students, can you understand? I made some attempts in teaching, so let's talk about it:

First, the strategy of examining questions

Mathematics comes from real life and is used in life. Solving problems is a bridge to solve practical problems by using mathematical knowledge. Students who solve problems are afraid of learning, while teachers are afraid of teaching. The reason is that the topic in the textbook is written language, and it is difficult for students to understand the meaning of the topic, which is the basis of solving problems. The purpose of the examination is to make students understand the meaning of the topic, and the difficulty of solving the problem is determined by the complexity of the plot and the quantitative relationship of the actual problem. The process of examining questions is mainly to let students know the plot of the actual problem, and then understand the meaning of the problem through the plot.

As long as the "obstacles" of Chinese characters in practical problems are removed and the meaning of the problem is understood, the problem will be solved. There used to be a famous saying: "Understanding the meaning of the topic is equivalent to doing half of the topic", which makes sense. There is a famous saying in the book "Primary School Mathematics Teaching Method" of the former Soviet Union: "When students can't solve problems, it is enough to ensure the success of the solution by changing the subject matter of the actual problem and making the actual problem closer to the students' experience. "The learning strategy of examining questions is" one reading, two marking and three retelling ".

(1) Reading more is basically divided into three steps: initial reading, intensive reading and intensive reading.

1. Rough reading: Read the full text, get a general idea of the content of the example, and don't be busy thinking and answering specific questions. In the process of students' learning, I ask students to think about what the question said when they read it for the first time.

2. Close reading: Close reading sentence by sentence, combined with pictures. You can make symbols while watching, and basically understand all the problems. In the second reading, students are asked to draw what they told us and what they didn't tell us with straight lines and curves respectively. Sometimes when you lack words, you find what you need from there; If you encounter some complicated problems, think about the difficult points repeatedly and think in connection with similar knowledge you have learned in the past. For example, answer, "There are 36 students in our class, and there are 30 math exercise books and 5 Chinese exercise books in the class." Everyone will be given 1 this math exercise book, 1 this language exercise book. How many math exercise books and Chinese exercise books do you need? "Many students don't understand this question, so I will let them read it again and recall whether we have encountered similar problems before. Sure enough, after a while, one hand, two hands ... the students raised their hands one after another, and the idea was basically correct.

3. Intensive reading: On the basis of a basic understanding of various issues, I can deeply analyze some of them, put forward key issues, and express my views and ideas in my own language. After the third reading, some students can reach three sections. If we can describe what this section mainly talks about, what we should remember and what we need to know, teachers will collect reading information extensively in the process of students' "reading" and give guidance and guidance to common problems, even if students with learning difficulties keep up.

(2) Fine-stroke symbols

Being able to read does not mean understanding the meaning of the question, because students may inadvertently read the question; Drawing straight lines and curves is also a habitual action. On the basis of reading the questions carefully, let students understand the meaning of the questions, which can guide them to think, draw and mark. Circle the important content and key words in the topic.

(3), retelling

Let the students repeat the questions, which means a good way to understand the students' examination of the questions. In Chinese teaching, retelling the main idea of the text is used to test whether students really understand the content of the text. We can apply this experience to mathematics teaching and test whether students really understand the meaning of the topic by retelling the meaning of the topic. Retell the meaning of the topic and ask the students to give the meaning of the topic in their own words. Retelling is not the same as reciting. You can change words or not ask for specific figures, but the meaning of the topic must be clear. You can also ask the teacher, "Where did you see it? How do you know? " By training students to repeat the meaning of the questions, it is not only to solve the application problems, but also to cultivate students' mathematical reading ability.

The so-called "examining questions like thieves" means that students should read more, understand at different levels, and gradually understand and clarify the meaning of the questions. I believe that "read a book a hundred times and know its meaning" is also applicable in mathematics learning. Although this kind of examination is a bit slow, after a period of training, students' analytical ability has improved and the correct rate of solving problems has also improved.

Second, deepen the strategy.

After reviewing the questions and answering correctly, we should further deepen our understanding. Linking new materials with familiar materials, including internal connection strategy and artificial connection strategy, promotes the brain's deep understanding of information.

The deepening methods include homophonic method, representation method, comparison method, generalization method, example method, graphic method and symbol conversion method. Problem-solving learning strategies can be trained by representation, comparison, generalization, example and diagram. In the teaching of lower grades, there are many:

(A) the method of expression

Connect all the contents of the material to produce a representation, that is, to produce a clear and vivid picture in your mind. In order to make students understand the meaning of the question, let them think about the pictures and scenes at that time in combination with the content of the actual question. For example, "ⅹⅹ Primary School has two rows of classrooms, a row of four classrooms and a row of five classrooms. How many classrooms are there? " ? Let the students have a picture of "two rows of houses, 1 with four classrooms and the other row with five classrooms" immediately, and avoid the mistake of listing them as 2+4+5. For students who can't imagine, it is feasible to let them use learning tools (CDs, sticks, etc.). ) pose or draw.

(2) Comparative method

Compare the content described in the material with your existing study or life experience in order to understand and remember the content of the material. In teaching, I often find that students do not have the good habit of reading and examining questions carefully when answering practical questions, which is often clear at a glance. In this case, students should be guided to do comparative exercises.

1, Comparison of practical problems in addition calculation and subtraction calculation;

(1), there are 8 birds in the tree, and 2 have flown by. How many birds are there now?

There are eight birds in the tree, and two fly away. How many birds are there now?

Ask the students to compare the similarities and differences between the two questions. The same is true: the first condition is the same as the question; The difference is that the second condition, which is also the key to this problem, is here, one is "coming" and the other is "going", which leads to different solutions. In this way, students can not only understand the different meanings of addition and subtraction, but also educate them to read and examine questions carefully.

2. Comparison between practical problems of addition calculation and practical problems of addition calculation.

(1), there are 8 birds in the tree, and 2 have flown by. How many birds are there now?

(2) Xiaoming has 7 stamps and Xiaohua has 3 stamps. How many stamps do they have?

There are some birds in the tree, two of them fly away, and there are six left. How many birds are there in the tree?

This set of questions is mainly for students to compare: the same addition calculation, but the quantitative relationship is different. A is the part added on the original basis; B is the total number of stamps for two people; C is the practical problem of finding the minuend. Make students understand that there are different situations when using addition calculation, and make them think.

3. Comparison between the practical problems of subtraction calculation and the practical problems of subtraction calculation.

(1). There were 8 birds in the tree, and 2 flew away. How many birds are there now?

(2) There are 8 birds in the tree, some fly away, and 6 others. How many flew away?

(3) Xiaoming and Xiaohua have 10 stamps. Xiaoming has seven stamps. How many stamps does Xiaohua have?

This set of questions is mainly for students to compare: the same is calculated by subtraction, but the quantitative relationship is different. One is to solve the practical problems left over; B is the practical problem of subtraction: C is part of the total. Let the students experience different situations of the same subtraction calculation in order to distinguish them carefully.

In addition, we can also compare the practical problems of finding the minuend, finding the minuend and finding the remainder:

(1). There are 8 birds in the tree, and two of them have flown away. How many birds are there?

There are some birds in the tree, two of them fly away, and there are six left. How many birds are there in the tree?

(3) There are 8 birds in the tree, some fly away, and 6 others. How many flew away?

This group of questions can be compared from different angles, such as the expression order of three sentences, the relationship between 8, 6 and 2 used, what is known and what is sought, and the method of solving problems, so that students can have a profound understanding of three practical problems.

4. Comparison of practical problems in addition calculation and multiplication calculation.

(1), ⅹ There are two rows of classrooms in the primary school, one with four classrooms and the other with five classrooms. How many classrooms are there?

(2) The primary school has two rows of classrooms, each with four classrooms. How many classrooms are there?

Through comparison, students can understand that the similarity between addition and multiplication lies in summation, but the difference lies in that every part of addition is different, and every part of multiplication is the same, so the solutions are different.

5. Comparison between practical problems of multiplication calculation and practical problems of multiplication calculation.

(1), ⅹ Primary school has two rows of classrooms, each with four classrooms. How many classrooms are there?

(2) Xiaoming has seven stamps, and Xiaohua's stamps are three times that of Xiaoming. How many stamps does Xiaohua have?

This set of questions is mainly for students to compare: the same multiplication calculation, but the quantitative relationship is different. A is seeking the total; B is a multiple relationship. Let the students experience different situations calculated by the same method so as to distinguish them carefully.

6. Comparison of practical problems in multiplication calculation and division calculation.

The comparison between the practical problems of multiplication and division can be divided into two situations:

(1), ⅹ Primary school has two rows of classrooms, each with four classrooms. How many classrooms are there?

(2) There are 8 classrooms in the primary school, and every 4 classrooms are arranged in a row. How many rows can they be arranged?

(3) There are 8 classrooms in the primary school, arranged in 2 rows on average. How many classrooms are there in each row?

or

(1), Xiao Ming has seven stamps, and Xiaohua's stamps are three times that of Xiao Ming. How many stamps does Xiaohua have?

(2) Xiaoming has 7 stamps, Xiaohua has 2/kloc-0 stamps, and Xiaohua's stamps are several times that of Xiaoming.

The former communicates the connection of multiplication and division and deepens the understanding of the meaning of multiplication and division; The latter is a practical problem about "multiplication"

7. Comparison between practical problems of division calculation and practical problems of division calculation.

(1), ⅹ There are 8 classrooms in the primary school, and every 4 classrooms are arranged in a row. How many rows can they be arranged?

(ⅹⅹ There are 8 classrooms in the primary school, arranged in 2 rows on average. How many classrooms are there in each row? )

(2) There are 8 classrooms in the primary school, and every 3 classrooms are arranged in a row. How many rows can they be arranged? How many rooms are there?

(ⅹⅹ There are 8 classrooms in the primary school, arranged in 3 rows on average. How many classrooms are there in each row? How many rooms are there? )

This group of questions is mainly to let students communicate the connection between division without residue and division with residue, and deepen their understanding of division.

(3), graphic method

Graphic method is mainly used in the teaching of lower grades to help students understand practical problems such as finding difference, finding large numbers and finding decimals.

When solving practical problems in junior high school teaching, we should also pay attention to the number of problems in comparison. Because junior students' computing ability is limited and influenced by the progress of computing teaching, it is best to calculate the selected number no matter which method is chosen, so as to expose the real situation.

The learning strategy of "solving problems" in primary school mathematics requires both cognitive strategies. We also need self-awareness and monitoring cognitive strategies, that is, metacognitive strategies. "Solving problems" mainly includes using words to reflect practical problems in real life to talk about learning strategies. Combining problem-solving teaching practice, specifically, it is necessary to explore and summarize learning strategies suitable for children's psychological development, follow children's thinking characteristics and laws, effectively teach students mathematics learning strategies, and improve students' ability to answer and solve simple practical problems. Let students feel that mathematics is around us, and enhance their intimacy and familiarity with mathematics, so as to love mathematics and enhance their enthusiasm for autonomous learning.