Keywords:: elementary school mathematics teaching simple application problem application problem teaching
Application problem is an important content of mathematics teaching in primary schools. Solving application problems can enable students to apply the basic knowledge and basic quantitative relations in number recognition and calculation to practice, deepen their understanding of the meaning of the four operations, not only cultivate students' ability to analyze and answer questions, but also develop their logical thinking ability, and also enable students to receive ideological and moral education. Simple application problems are the basis of compound application problems and occupy a very important position in junior high school mathematics textbooks. The author now talks about some views on the teaching of simple application problems.
First, grasp the key points and establish contacts.
The quantitative relations in simple application problems can be summarized as sum, difference, product and quotient, and can be roughly divided into four groups.
The first group is related to the rest of the application problems, which are directly related to the meaning of addition and subtraction. The key point is to guide students to understand the meaning of the question, master the structure of simple application questions, clarify the quantitative relationship in the questions, and contact the algorithm to determine the meaning of addition and subtraction. For their variant problems, such as finding an addend, a minuend and a minuend, we should try our best to communicate their connection with summation and remainder application problems in teaching, so that students can master the thinking method and solution correctly.
The second group is an application problem reflecting the relationship between two numbers and their differences, which needs to be considered indirectly through addition and subtraction. Teaching should focus on helping students to establish a correct concept of difference and analyze the relationship between known number and unknown number, so that students can clearly understand who is more than who, who is more than who and who is less, and which two parts a larger number can be divided into, so as to establish a relationship with addition and subtraction significance and determine the algorithm. For the application problems of finding a number less than another number, finding a number less than a number and finding a number greater than (less than) a number, the key point is to guide students to use the idea of transformation, communicate the relationship between old and new knowledge, and cultivate students' transfer ability.
The third group is three kinds of application problems directly related to the meaning of multiplication and division, that is, finding the sum of several identical addends, dividing a number into several parts to find out what a number is and how many other numbers a number contains. The key point is to guide students to think about the significance of multiplication and division on the basis of clarifying the problems.
The fourth group is an application problem that reflects the relationship between two numbers and their multiples, which needs to be considered indirectly by using the meaning of multiplication and division. In teaching, we should pay attention to correctly establishing the concept of "multiple" and convey its connection with the meaning of multiplication and division.
Second, proper infiltration, early pregnancy
For the first-grade pupils, the enlightenment teaching of application problems refers to the proper infiltration of application problems in mathematics teaching and early pregnancy. Its task is to speak and calculate by looking at pictures. The application problems represented by pictures include the transition between the application problems with pictures and words and the application problems with words, so that students can gradually understand the structure of the application problems, understand the relationship between conditions and problems in the application problems, and master the thinking methods and answering steps. Generally can be divided into three stages.
The first is the incubation stage, that is, look at the picture and keep your word. At this stage, teachers should be good at inducing, step by step, and consciously go ahead. Generally speaking, students can be trained to say a complete sentence from the "preview class", and then gradually train students to say two or three sentences. On this basis, students can be guided to try to change the third sentence into a question in combination with specific topics, and gradually become familiar with the quantitative relationship in the topics.
The second is the preparation stage, that is, the application problem represented by teaching pictures. At this stage, you can take the following steps for training: (1) Understand the meaning of the problem, what is said in the problem, what you want, and initially conceive the structure of the application problem; (2) Guide students to determine the algorithm according to the meaning of addition and subtraction; (3) Formula calculation.
The third is the transitional stage, that is, teaching practical problems with pictures and words. Students should be guided to understand terms such as "conditions" and "problems".
Further understand the structure of application problems, according to the relationship between conditions and problems, contact the algorithm to determine the meaning of addition and subtraction, thus laying a good foundation for the study of word application problems.
Third, observe the experiment and stimulate interest.
The psychological characteristics of primary school students in lower grades are active and curious, and their thinking also has the characteristics of preschool children, which is often inseparable from specific images. Therefore, the teaching method of observation experiment is not only beneficial to stimulate students' interest in learning, but also enables students to learn knowledge from a large number of perceptual materials.
1. Attach importance to operational activities and let students actively participate in the learning process.
In teaching, we can make full use of "preview questions" and related examples to let students think, put forward, speak and participate in the process of knowledge formation.
2. Strengthen language expression and develop abstract thinking.
People think with the help of language, and the language expression we require mainly means that students should not only express their own operating process, but also express their own thinking activities, and internalize external actions into their own intellectual activities, which requires a long-term process and must be trained as soon as possible. As mentioned above, cultivating students' ability to say one sentence or even three sentences and turning the third sentence into a question is nothing more than that. In operational activities, teachers should strive to cultivate students' expressive ability.
Fourth, strengthen the whole, clear thinking.
As mentioned above, simple application problems can be roughly divided into four groups in terms of quantitative relationship, and the same group of application problems is closely related. For example, the application problem of phase difference relationship in Volume II includes three situations. The quantitative relationship is the same, but the known and unknown have changed. If you don't understand this, there will be interference, so that the quantitative relationship will be chaotic and the analysis will be impossible. It can be seen that it is very important to understand the similarities and differences of this kind of application problems for correctly analyzing the quantitative relationship.
Fifth, pay attention to training and cultivate ability.
The improvement of students' problem-solving ability is by no means a one-off event, and it needs a process. Therefore, teachers can take different forms of training. In addition to the general conventional form, the following methods can be adopted:
1. Practice of filling in conditions and asking questions;
2. Various exercises, such as changing one of the conditions or problems;
3. Expressed in simplified mathematical language, such as how many red flowers there are, and how much is three to five;
4. Contrast exercises;
5. Judgment exercises;
6. Editing exercises, etc.
Some students' problem-solving difficulties are caused by the lack of appropriate problem-solving strategies, which requires teachers to be good at studying and summarizing problem-solving strategies for different types of questions and giving appropriate guidance and guidance to students.
(1) Get rid of stereotypes. The reason why students are confused about some application problems lies in thinking set's influence. At this time, the teacher should guide the students to change their thinking angle and make their thinking clear. For example, Zhang Ming scored an average of 76 in Chinese, foreign languages and science in the final exam. After his math scores were announced, his average score increased by 3 points. What's Zhang Ming's math score? According to the conventional solution, it can be seen that Zhang Ming took four courses at the end of the term and asked for math scores. You can subtract the total score of three courses from the total score of four courses. Because the average score of four courses is 3 points higher than that of three courses, the average score of four courses is 76+3=79 (points), the total score of four courses is 79×4=3 16 (points), and the total score of three courses of Chinese, foreign languages and science is 76×3=228 (points), so Zhang Ming's mathematics. If you think about it from another angle: suppose Zhang Ming got 76 points in math, then the average score of four subjects is still 76 points. However, the average score of the actual four courses is higher than the average score of the three courses, which is just allocated to all subjects, and each subject is increased by 3 points, so that * * * is 3×4= 12 (points) more.
(2) clear thinking. In teaching, optimizing the teaching of mathematical application problems in primary schools can better develop students' logical thinking ability and cultivate their good thinking quality. In order to achieve this goal, it is necessary to create life-oriented scenarios, cultivate students' ability to analyze the structure of questions, and guide students to use various problem-solving strategies flexibly. As long as we grasp the structural characteristics and connections of simple application problems, strengthen the use of intuitive means, strengthen the analysis of ideas and attach importance to the thinking process of acquiring knowledge, we will certainly improve students' ability to analyze and solve problems.