The ability to examine questions is an extremely important ability in students' learning activities. In practical problem teaching, according to the cognitive psychological laws of primary school students, strengthening the training of problem judgment through "reading, searching, answering, thinking and speaking" can effectively cultivate students' problem judgment ability and promote the development of their intelligence. The application problem consists of two parts: the plot and the quantitative relationship. The process of examining questions is to examine the plot content and quantitative relationship of the topic, know what the topic is about and what the course looks like, and find out the problems with known conditions and requirements, so as to establish a complete impression on the conditions, problems and their relationships of the topic in students' minds and create a good prerequisite for correctly analyzing the quantitative relationship and solving application problems. In primary school mathematics teaching, application problems account for a large proportion. Our students often lose the most points on application problems, and some students don't get any points on application problems. This happens. On the one hand, students' foundation is poor, and more importantly, students can't judge problems, and most students do it at random after reading the questions. Therefore, it is necessary to strengthen the cultivation of students' problem judgment ability in primary school mathematics teaching. Let me talk about some of my own practices:
First, study.
Learning means reading the topic carefully and getting a preliminary understanding of the meaning of the topic. Examining questions is the first step to understand the content of questions, and it is also the beginning to cultivate the ability to examine questions. It is necessary to cultivate students' habit of repeating, carefully reading and examining questions. The first-grade teacher should read and guide the model essay. When reading questions, students should be trained not to add words, miss words, mispronounce words and keep sentences. In the second grade, students are trained to read independently, and gradually transition to silent reading, through which they form the habit of consciously understanding the meaning of the questions.
Second, find key sentences.
Language and writing are the ties of various relationships in practical problems, and they are also obstacles to solving problems. Therefore, like Chinese teaching, examination teaching should help students understand the meaning of every word, word and sentence in application questions and cultivate students' written language reading ability.
First of all, have a correct understanding of the mathematical terms in the expression of application questions. For example, if students don't understand these terms correctly, they can't understand the meaning of the question, which will hinder the establishment of quantitative relations.
Secondly, the key sentences that reveal the quantitative relationship in application problems should be scrutinized repeatedly to understand their true meaning, paving the way for correct problem solving. For example, "students make up books. I took 127 books in the fifth grade, 28 more than in the fourth grade. How many books did you take in the fourth grade? " Some students can't tell the difference between grade five and grade four at once, so we should grasp the key sentence of "make up 28 books more than grade four" and make this short sentence clear step by step, that is, "make up 28 books more than grade four", that is, "128"
Third, repeat the meaning of the question.
Retelling the meaning of the question, entering the situation, and retelling the meaning of the question in your own words can promote students to further analyze the plot of the application question, turn the content of the question into a vivid representation, and let students really enter the role. For example, "Xiao Ming has 35 chickens and 28 ducks. If each chicken can produce 13 kg of eggs a year, then each duck can produce 12 kg of eggs a year. How many kilograms of eggs can these chickens and ducks produce a year? " If students can repeat this: "Xiaoming has 35 chickens, and each chicken can produce 13 kg of eggs a year, and there are 28 ducks, and each duck can produce 12 kg of eggs a year. How many kilograms of eggs can Xiaoming's chickens and ducks produce a year? " This shows that students have really fully understood the meaning of the question.
Retelling the meaning of the question can accurately reflect students' understanding of the meaning of the question, and is also conducive to cultivating students' generalization ability and mathematical language expression ability, thus improving their ability to examine the question.
Fourth, pay attention to guiding students to understand the quantitative relationship.
Middle school students' abstract thinking ability has been developed, and they basically have the ability to classify what they have learned through learning. Through the study of lower grades, students have basically understood the basic structure and solving steps of application problems. Therefore, we should pay attention to the understanding of quantitative relationship in teaching.
1. Ask students to master common quantitative relations.
In the middle teaching, we should pay attention to let students master the conventional quantitative relations, such as speed, time, distance, unit price, quantity, total price, work efficiency, time and total workload, and ask them to skillfully use them, so that students can classify application problems according to the quantitative relations and derive application problems such as travel itinerary and engineering. In addition, you can solve problems by drawing and listing.
2. Cultivate students' comprehensive ability.
The middle grade is no longer a one-step application problem, and students are required to grasp the key points (commonly known as intermediate problems) in solving problems. For example, someone can travel 300 kilometers in five hours. According to this calculation, it is 240 kilometers from A to B. How many hours can this person drive? In the teaching of this problem, we should pay attention to let students master the invariant (speed). To grasp invariants, we must fully understand the meaning of "calculate according to this", so as to find the key to solving the problem. This two-step calculation of application problems requires the use of two quantitative relations in solving problems, and the correct use of them requires the improvement of students' comprehensive ability.
Five, two strategies to solve practical problems-analytical method and comprehensive method.
1, analysis method
The idea of analytical method is to start with the problem of application problems and find out the mathematical information needed to solve this problem according to the quantitative relationship Some of this information may be known, while others are unknown. Then, take the unknown information as an intermediate problem, find out the information needed to solve this intermediate problem, and reason step by step until all the needed mathematical information can be found from the topic.
2. Integrated approach
The idea of solving problems by comprehensive method is to change from known information to analytical method of problems. The analysis idea is: choose two known quantities and put forward the problems that can be solved; Then choose two known quantities (at this time, the calculated quantity becomes known quantity), put forward the problem that can be solved ... and deduce it step by step until the problem of the topic is solved.
Sixth, strengthen training to improve students' ability to "solve practical problems".
Students have mastered the basic knowledge of solving application problems and learned the thinking method of analyzing application problems. Can students solve application problems smoothly? The answer is no, it's like a chef who has mastered the theory of cooking, but can't cook delicious dishes without hard practice. This is true for chefs, and so is solving application problems. Therefore, strengthening training is the key to improve students' ability to solve application problems.
Although some students can solve problems correctly, they may not be able to explain the thinking process clearly. In teaching, some teachers only teach students how to solve problems and ignore the idea of letting students describe problems, which is not enough. Students' description of problem-solving ideas has several advantages: (1) is conducive to cultivating students' oral expression ability. (2) Teachers can know whether the students' thinking state is smooth; If the thinking is not smooth, where is the crux, the teacher can give targeted help. (3) Save time. The time of a class is constant. If we judge whether students can solve and analyze application problems only after they answer the questions correctly (a lot of calculations are needed in the process of solving problems), it will waste a lot of classroom time. Moreover, students do problems quickly and slowly, and students who do them quickly will waste a lot of time, such as doing them slowly. If students are allowed to analyze application problems orally, they can save a lot of time and practice will be greatly increased.
Throughout the ages, there are countless mathematical thinking methods, and each mathematical thinking method shines with the spark of human wisdom. There are many important mathematical ideas in primary school mathematics textbooks, such as the combination of numbers and shapes, limit ideas, set ideas, symbol ideas, transformation ideas, modeling ideas and so on. How to better infiltrate these mathematical ideas into students and make our mathematics classroom full of wisdom and effectiveness? The first thing a teacher should do is to study the teaching materials carefully.
In short, it is a long-term process to cultivate the ability to examine questions. Teachers should persevere and carry out targeted training. On the basis of teaching students the method of examining questions, cultivate students' habit of carefully examining questions and improve their ability of examining questions. Only in this way can students master the skills of solving application problems more skillfully and improve their ability to solve application problems.