Solving application problems is a complex thinking activity. The teaching task of application problems in primary schools is to guide students to correctly answer all kinds of application problems and cultivate their thinking ability. The cultivation of good thinking quality is a powerful guarantee for the high efficiency of thinking training. In the face of students' "distress" about application problems, I have been exploring teaching methods in this area. Now I will talk about how to better activate students' thinking in the teaching of mathematical application problems in primary schools based on my own experience.
First, contact the reality of life and stimulate interest.
Compile all kinds of knowledge commonly used in life into practical problems suitable for students to learn and explain or practice them. This kind of application problem from students is full of interest in life. Students use their own knowledge to solve problems, further stimulating students' interest in solving application problems.
For example, after learning decimal addition and subtraction, students can make up some examples of decimal addition and subtraction in their own lives and write representative examples on the blackboard for everyone to enjoy. For example, a bucket of instant noodles, 3.5 yuan, and a pack of biscuits cost 2.45 yuan. How much is a * * *? The student's column solution is 2.45+3.5=5.5 (yuan). There is something wrong with the calculation. It may be because students only consider rounding up ten or adding up when they see the last number, and ignore whether the two "5" numbers are on the same number. If they are vertical, this problem will not occur. Therefore, when beginners learn decimal addition and subtraction, they should emphasize column-vertical calculation until they are proficient. Just after the sports meeting, we can make use of sports events to compile some decimal addition and subtraction, so that students can appreciate the value of decimal calculation and improve their interest in learning. For example, in long jump, high jump, 400-meter running, relay race and other projects, the calculation of decimals is everywhere. Let students find the gap in the calculation, find the gap and clearly analyze the reasons, and make their own efforts and goals according to the size of the gap, so that students can realize the importance of decimal addition and subtraction. In order to let students see the gap between this class and other classes in the mid-term exam, I show the average score of each class in the form of a table, so that students can calculate the gap between the average score of this class and that of other classes, see the position of this class in the seven classes in the calculation, and then analyze the reasons, know the direction of future efforts, and establish a sense of collectivism honor.
Through students' self-writing and teachers' guidance, students can fully realize the wide application of decimals in life, further improve their deep understanding of decimals, and more importantly, let students realize the importance of learning decimal addition and subtraction. Learning is to better solve the problems encountered in life, stimulate their interest in learning mathematics, and apply what they have learned. This is the key to learning mathematics.
Second, associate the situation when examining the questions, and combine boring mathematical knowledge with solving practical problems.
The teacher helps students form the habit of reading questions and associating them. I often say this: If you are the person mentioned in the question and you are one of them, how can you solve such a problem? Try to externalize the narrative in the title into vivid images. First, imagine what kind of life scene is mentioned in the title. This scene should be clear enough to "see" and "touch" as if it were there; Closely link mathematics with life, let students feel that mathematics knowledge comes from life everywhere, reflect the value of mathematics, and improve their interest in learning mathematics.
For example, when I explain the law of addition and association, I will give you a few examples first: Uncle Wang traveled by bike, riding 88 kilometers on the first day, 104 kilometers on the second day and 96 kilometers on the third day. Ask uncle Wang how many kilometers he rode in these three days? After reading the questions and understanding the meaning, ask the students to list different formulas. I have a choice on the blackboard. Equation1:88+104+96; Equation 2:104+96+88; Equation 3: 88+( 104+96). I asked the students to observe the similarities and differences between formula 1 and formula 3, and the students summed up the following points: first, the arrangement position of the three addends remained unchanged (indicating that there was no exchange of addends, so additive commutative law was not applied); Second, although the listed formulas are different, the final sum remains the same; Third, the operation sequence is different. At this time, I will follow the trend and tell the students which calculation method you like, and the students will be different. Students will draw a conclusion from the calculation, because the third calculation order is 104+96, which makes the calculation easier. ) At this time, I wrote Equation 1 and Equation 3 as Equation (88+104)+96 = 88+(104+96). Then show two sets of equations in the book: (69+172)+28 069+(172+28),155+(145+207) ○ (155+) Ask the students to calculate the sum of each group of formulas, and use ">" < or "=" to let the students experience the two operation sequences in the calculation and feel the simplicity brought by one of them. Adding two numbers into an integer will make the calculation simple. Then I asked the students to form an equation according to the above three examples, and the students appeared the situation of addend exchange. At this time, I asked students to observe that there are three addend positions in the first three groups of equations that have not changed, and then fill in the equations that meet the requirements as required. Finally, observe the difference between the left-handed formula and the right-handed formula of these four groups of equations. Which method do you prefer to calculate? Finally, to sum up the knowledge system, the positions of the three addends in the left and right formulas of the equation are unchanged, and the sum is unchanged, that is, the operation order has changed. I guide students to grasp the key point: there are only two operation orders for three identical addends. Let the students observe the left and right formulas and try to sum them up by themselves: add three numbers, or add the first two numbers and then the third number; Either add the last two numbers first, and then add the first number, and the sum of the two numbers remains the same. At this time, I told my classmates that this is actually the law of addition and association we learned today. There are only two operation orders in the law of addition and association of three numbers, but we have to choose an operation order that can make the calculation simple and convenient, which is the significance of applying the law of addition and association. In the future calculation, the additive combination law can be used to make the calculation simple and improve the speed and accuracy of the calculation. The laws of addition and association are represented by letters. I designed it this way: I expressed a+b+c=a+b+c, and asked students to quickly put brackets around (a+b)+c=a+(b+c) according to the rule that three numbers have only two operation orders.
By learning the law of additive association in such a situation, students not only learn the method of solving problems, but also subtly reflect the application of the law of additive association in solving problems, which makes them impressed and thoroughly understood.
The nature of subtraction is also used in this unit, but it is also used to help my son with his homework. It is a pure formula connection. For example: formula 1: 86-37- 13, formula 2: 86-(37+ 13), formula 3: 86-(37- 13) and formula 4: 86-37+. At this time, I gave my son a life problem to help him understand. For example, in response to the formula 1: 86-37- 13, I explained that there were 86 extra-curricular books in the class, 37 of which were borrowed for the first time and 13 for the second time. How many books are left in the classroom now? First of all, we can guess which formula is reasonable and correct according to the actual figures. This kind of problem is easy to understand, and it is 86-37-13 = 86-(37+13). Comparing these two different solutions, the one on the right is simpler than the one on the left, which also permeates the application of subtraction in solving problems. What is the relationship between Equation 4 86-37+ 13 and Equation 3 86-(37- 13)? I made up the question like this: Of the 86 extracurricular books in our class, 37 were borrowed on the first day and returned the next day 13. How many extracurricular books are there in our class now? Equation 4 is the most commonly used method to solve this problem, and Equation 3 can solve this problem, indicating that the level of thinking has reached a higher level. How to help children understand? This is how I interpret 86-(37- 13). What does 37- 13 in brackets mean? (It means that only 24 books have been lent out, and then subtract 24 books from the 86 books of a * * * * which is equal to the remaining books. In this way, you can get 86-37+13 = 86-(37-13), so that children can understand the relationship between the two formulas. In fact, it is the embodiment of two solutions to a problem. Not to tell him that there is a MINUS sign outside the brackets, and the brackets should be changed. Is to let him know the truth and know the truth.
Third, the use of teaching AIDS, line diagram intuitive demonstration, simplify students' problem-solving ideas.
Imagine the relationship between quantities in an event. This relationship requires students to reach the level of "seeing and touching". Teachers can ask students to associate line drawings or schematic diagrams when reading questions. Students already have certain spatial thinking ability. First of all, teachers can concretize the situation with the help of line graph. From operation demonstration to line drawing, it is a transitional process from image thinking to abstract thinking. When instructing students to draw line drawings or schematic diagrams, we should pay attention to the training level: at first, follow the teacher → draw by yourself according to the meaning of the question → draw a simple schematic diagram → "draw" in your mind. In other words, students only need to come up with a "line diagram" that reveals the quantitative relationship in their minds. Solve problems with the strategy of painting. The problem of planting trees in the fourth grade of compulsory education curriculum standard experimental version 1. "Students plant trees along the path, with a total length of 100 meters, and plant one tree every 5 meters (both ends should be planted). How many seedlings does a * * * need? " First of all, the teacher guides the students to draw a line graph through the interval of fingers; Students may get 100÷5=20 (tree) through discussion. At this time, teachers should guide effectively, because teachers' keywords can arouse students' thinking. Teacher: "There are 20 sections here, so how many trees should be planted in a * * *"? According to the finger spacing just now, the students thought of 20 intervals and should plant 2 1 tree. The generation of the classroom will appear at a clever moment. We teachers should seize the resources generated in the classroom and make good use of them to teach effectively. Therefore, in the teaching of mathematical application problems, we can use teaching AIDS and charts to demonstrate intuitively and train students to describe the known conditions and problems in mathematical language. After knowing each known condition intuitively, we can describe the quantitative relationship. Use teaching AIDS and line diagrams to let students demonstrate intuitively, so that students can better understand the meaning of the problem and get solutions to the problem. In this way, over time, when students read the questions again, they will come up with related line diagrams or schematic diagrams in their minds, thus developing students' spatial thinking ability and improving their ability to solve applied problems, thus improving their ability to solve applied problems.
Fourth, reasonably imagine, explore in many directions and cultivate the flexibility of thinking.
In order to cultivate the flexibility of students' thinking, I pay attention to guiding students to develop reasonable imagination and reasoning according to different situations. Let students master conditions and conditions, conditions and problems, deeply understand the quantitative relationship, flexibly use what they have learned, and seek various solutions from different starting points and angles, which can also promote the flexibility of students' thinking. For example, there should be 10 potted flowers around the square wooden platform of osmanthus tree. How many potted flowers do you want? By showing the beautiful scenery of campus, creating situations, leading to mathematical problems in life and stimulating students' desire to explore. ) 1: 40 pots, 2: 36 pots,
Teacher: Is it 36 or 40 pots? Want to know which answer is right, what should I do?
(Let the students argue with each other) Please verify how many pots you need in your own good way. Think independently first, and then talk about your method in the group. Giving students the initiative to learn, allowing them to think freely, draw freely and talk freely, and activating their existing life experience not only satisfies students' desire for expression, but also cultivates students' awareness of independent exploration and group cooperative learning. )
Feedback: What do you think? (Show all the students' methods first, and then comment on each method)
Health 1: 10× 2 = 20, 8×2= 16, 20+16 = 36;
Health 2:10-1= 99× 4 = 36;
3,10-2 = 88× 4+4 = 36;
Health 4:10× 4-4 = 36;
Teacher: Can you explain your idea? Let the students talk about their own ideas. Through multimedia projection, which part of students' thoughts are displayed intuitively, and students' desire to explore is stimulated. )
Through training, students learn to think in many directions, so as to broaden their thinking, make their thinking agile, and achieve the goal of mastering knowledge and drawing inferences from others.
5. Self-assessment, compare the accuracy of identification, and cultivate thinking.
A few students have a little knowledge of the quantitative relationship in application problems, or there are some problems that are difficult to think about. Some excellent students always ask the teacher after solving the problem, right? Both cases belong to the answer, but I don't know whether it is correct or not. In order to put an end to this phenomenon, I ask students not to be busy calculating the results after determining the calculation steps and listing the formulas. They must first explain the calculation to see if it conforms to the meaning of the question, whether it correctly reflects the quantitative relationship and whether their thinking is reasonable and correct.
Although some questions have calculated the results, students should also be asked to test whether the results are reasonable according to the meaning of the questions.
For example, there is a topic in the workbook: "When two brothers and sisters buy a book, the difference between the money for the elder brother to buy this book is 3.60 yuan, the money for the elder sister to buy this book is 4.80 yuan, and the brother and sister together buy this book for 2.40 yuan. What is the price of this book? " This question is very difficult for most students, but some students don't know if their answers are correct when they work it out. At this time, I asked the students to bring the answers into the conditions and check whether they are consistent with the descriptions in the questions. If they are exactly the same, they must be right. The correct answer to this question is: 3.60+4.80+2.40= 10.80 yuan (yuan) search process: according to "my brother's money is still 3.60 yuan short of buying this book", it can be concluded that my brother originally had 10.8-3.60=7.2 yuan, and according to "my sister's money is still 4 yuan short". Every condition brought by the obtained answer is completely consistent, so that the correctness of the answer can be fully verified. By teaching students the method of verification, students can judge for themselves whether their answers are correct or not, without asking teachers, thus cultivating students' autonomous learning ability.
Due to the emphasis on cultivating students' self-evaluation ability, students have a thorough understanding of various topics, their ability to analyze and solve problems has been greatly improved, and the correctness of their thinking has been obviously enhanced.
6. Ask more questions for one question, so that students can ask some novel and reasonable mathematical questions in all directions according to the known conditions.
For example, example 3 on page 6 of the textbook, I didn't show it directly according to the original title in the book, but let the students think independently. Who are you going to "World of Ice and Snow" with? Calculate how much it costs to buy a ticket. After the students finished their work independently, they reported their ideas one after another. Student 1: I'm going with my parents. The formula is 24+24+24÷2. The teacher guides the students: What else can I do? Students supplement 24× 2+24 ÷ 2; Student 2: I'm going with my father, mother, grandfather and grandmother. The formula is 24× 4+24÷2. Inspired by the method of "student one", "student two" directly uses simple formulas to achieve the purpose of inspiration and mutual learning. Student 3: I want to play with my father, mother and brother. The formula is: 24× 2+24 ÷ 2× 2; In order to make students think from different angles, I then asked the students: Are there any different ways? The students listed the formula in this way; 24×3, I asked him, why is this arrangement? He explained: the fare for two children is only one adult ticket, so it is equivalent to buying three adult tickets. Inspired by this classmate, another classmate listed this formula: 24÷2×6, that is, two adult tickets are equivalent to four children's tickets, and two children's tickets are used, and one * * * is equivalent to buying six children's tickets. ..... By designing such open-ended questions, students can report their own activities and calculations independently, experience the extensive application of mathematics in daily life, and cultivate students' expressive ability. Students can experience the calculation process according to their own life experience, clarify the operation order, closely combine the problem-solving ideas with the operation order, and naturally form a correct representation in the process of solving problems, instead of the teacher telling students what the operation order is, and solve the problems entirely by students themselves.
Example 4 on page 10 of the textbook, I only give the known conditions in the question (tourists in the ice sculpture area in the morning 180, 270 in the afternoon. If every 30 tourists need a cleaner, emphasize that a cleaner only works for half a day), don't give ready-made questions directly, let the students fill in the questions themselves. I ask students to add a problem that requires more than two steps of calculation. This requirement slightly increases the difficulty of students. Students should think for a moment and raise their hands to report their thoughts. Student 1: How many cleaners do you need in the morning and Monday afternoon? Then let all the students answer in columns. Ask students to use different methods and try to answer with comprehensive formulas (being able to answer with comprehensive formulas is the teaching requirement of the first unit of the textbook and the difficulty of this unit). The list of most students is as follows: 270÷30+ 180÷30, and the list of some students: (180+270) ÷. Learning to use parentheses correctly is the key and difficult point of this lesson. At this time, I will use this wrong example 180+270÷30 to let students analyze: according to the formula of addition, subtraction, multiplication and division I learned before, what is the operation order? Students also know to calculate division before addition. Therefore, according to the thinking of solving this problem, the first step must be addition and the second step must be division. What should you do? At this time, parentheses are needed to change the operation order. Therefore, the formula for calculating which step to take first is enclosed in brackets. So the correct formula is (180+270)÷30. In this way, in the comparison of old and new knowledge, students understand why brackets should be added, and the role of brackets breaks through the important and difficult points of this lesson. Then let the students ask different questions. Question 2: How many more cleaners were sent in the afternoon than in the morning? Inspired by the question 1, the whole class can write 270÷30- 180÷30 or (270- 180)÷30, and most students will answer correctly with simple methods with brackets. In this way, instead of giving students ready-made questions, students ask their own questions and solve them themselves. Because the questions are put forward by students themselves, students are willing to answer them themselves, which improves the enthusiasm and efficiency of solving problems.
Through the teaching of the above two examples, we mainly want to explain that the problems we design should be open, so that students can play freely and reflect their individual thinking. Give students more time and space to think, show them their opportunities, and let them feel the joy brought by success and have a certain sense of satisfaction. In class, students are the main body. Students explore and try by themselves, and then the teacher guides them to correct their mistakes. Students inspire each other and learn from each other, so as to achieve the goal of * * * improvement. I believe that every student will like autonomous classes and make their own decisions in their own classes. This is what students expect, and we should create such opportunities for students.
In a word, the purpose of mathematics application problem teaching in primary schools is not only to impart knowledge, so that students can learn, understand and master mathematics knowledge, but also to pay attention to teaching students learning methods and cultivating students' thinking ability and good thinking quality. Moreover, it is necessary to guide students to understand the meaning of the topic, focus on analyzing the relationship between quantity, grasp the conditions and problems of the application topic, draw inferences from others and practice more. In the process of solving mathematical application problems in primary schools, I pay attention to cultivating students' ability to understand the meaning of problems, analyze and summarize, judge the types of problems and calculate and reason. Therefore, teachers should carefully set exercises, through thinking training such as multiple solutions to one question and changeable questions, and persevere in teaching, so as to achieve the purpose of cultivating students' thinking ability.