The first part of primary school mathematics application thesis
Simple application problem teaching is the beginning of application problem teaching and the basis of the whole application problem teaching. How well students master the structure, basic quantitative relationship and problem-solving thinking method of simple application problems in this stage of learning will directly affect the future application problems learning. Therefore, we must start with the basics and do a good job in the teaching of simple application problems in lower grades.
Primary school mathematics; Simple application questions; Teaching strategy
Application problem learning plays a very important role in primary school mathematics learning and is an important teaching content of primary school mathematics. The level of children's solving practical problems not only represents their mastery and understanding of basic mathematical knowledge, but also represents their ability to solve practical problems in real life by using existing mathematical knowledge and skills. Therefore, the research topic of solving students' mathematics application problems has been paid more and more attention by mathematics educators and psychological researchers. The most prominent function of simple application problem teaching is its basic function. Any compound application problem is composed of several simple application problems. Simple application problems are the beginning for primary school students to learn application problems. Therefore, in the first and second grades, we should attach importance to the teaching of simple application problems and lay a solid foundation. It can be said that cultivating students' ability to solve simple practical problems is the basic content and important way to enable students to solve simple practical problems by using their learned mathematical knowledge, that is, by solving simple practical problems, students are encouraged to connect their learned mathematical knowledge with real life and some simple scientific and technological knowledge, thus initially developing their ability to solve practical problems by using their learned mathematical knowledge. In the current curriculum standards, application problems are no longer regarded as an independent unit, but distributed to all parts of teaching. This is not to cancel application problems, but to strengthen the important role of application problems in developing students' mathematical thinking, which really needs to improve students' problem-solving ability. Therefore, it is of great significance to reform the existing teaching methods, further systematically analyze the teaching status and existing problems of simple application problems, and explore more reasonable teaching strategies, so that the teaching of simple application problems can really improve students' problem-solving ability.
1. There are different opinions on the definition of teaching strategies for simple application problems in primary mathematics, and different scholars have put forward different opinions from different angles and levels. The comprehensive definition of teaching strategies can be roughly divided into three categories: first, teaching strategies are specific teaching methods and methods used to achieve teaching goals. For example, Gao Wen believes that teaching strategy is a teaching method adopted as a way to achieve the predetermined teaching purpose. Secondly, it is considered that teaching strategy is a behavior policy and scheme to achieve teaching objectives and solve teaching problems. For example, Zhang Dajun and others define teaching strategies as: "In a specific teaching situation, teaching plans and teaching implementation measures are formulated to achieve teaching objectives and meet students' cognitive needs. "The third view is that teaching strategy is a kind of knowledge about how to achieve teaching goals and solve teaching problems. For example, Huang Gaoqing and others define teaching strategies as knowledge of methods, operating principles and procedures for effectively solving teaching problems.
It can be seen that the first definition focuses on the operability and purpose guidance of teaching strategies, but this definition is easily confused with teaching methods; The second definition is easily confused with the teaching mode; The third definition starts with the existing form of teaching strategy in people's minds, and thinks that it is a kind of knowledge about operating principles and procedures, and it also has the disadvantages that are difficult to distinguish from other concepts.
2. The application of the teaching strategy of simple application problems in primary school mathematics In algebra teaching, teachers should consciously guide students to learn to use quantifiers correctly and do a good job in enlightening simple application problems. Teachers can first guide students to tell the contents of the pictures, sum up two known conditions and a question, and then teachers can describe these two conditions and questions completely, and then let students repeat what the teacher said. Step by step, slowly train students to look at the pictures and say what the conditions and problems are. In the classroom, teachers' own teaching language should be concise and clear, and the observation requirements for students should be clear, so as to attract students' attention to valuable information. Slowly, students can learn to observe pictures from a mathematical point of view and find useful mathematical information to solve practical problems. Teachers guide students to draw line segments from the lower grades, so that students can consciously draw line segments before solving problems, and the abstract quantitative relations in problems can be vividly and clearly displayed, making complex application problems simple and solving problems easy. The purpose of creating situations is to let students learn knowledge and cultivate their ability to solve problems. When creating situations, we should consider whether the creation of situations is conducive to the realization of teaching objectives and grasp targeted problems, and we should not create situations for the sake of creating situations.
However, the simple question-and-answer between teachers and students sometimes can't make teachers fully understand students' thinking. It is necessary for teachers to organize students to discuss and cooperate in time in the form of group communication. Each student in the group tells his own thinking process, complements each other and recognizes other students' analytical methods, which can also help the teacher to observe the students' thinking process more comprehensively and deeply in the collision of various ideas. In addition to group evaluation, teachers can also show simple application problems. After the students answer, they can guide the whole class to discuss complementarity and brainstorm, so that students can gain more comprehensive knowledge. At this time, teachers do not judge, but guide students to discuss, express their views on known and unknown quantities, and evaluate others' opinions. Therefore, students not only clarify the thinking of solving problems, consolidate the knowledge they have learned, but also cultivate their oral expression ability and further improve their thinking ability. If we persist in this guidance for a long time and draw a concrete picture in students' minds over time, students will consciously find out the contents related to mathematics and form the habit of looking at problems from a mathematical point of view. As long as teachers teach students the correct evaluation methods, combine teaching with the training of speaking and calculation, and infiltrate the idea of self-evaluation in the teaching of lower grades, it is completely feasible to first evaluate the students' thinking process of solving problems, then transition to the students' self-evaluation under the guidance of teachers, and finally complete it independently by students.
This paper analyzes some problems existing in today's teaching, and forms preview strategies, problem-solving strategies, mathematical application ability training strategies and self-evaluation and reflection strategies for these problems. More educators and front-line teachers need to work together, which is a process of continuous exploration and progress, and this work is of great significance to improve the problem-solving ability of primary school students.
The second part of primary school mathematics application thesis
Math application problems in primary schools focus on cultivating students' application consciousness, problem consciousness, exploration ability and innovation ability, so that the educational goals of knowledge and ability, emotion and attitude are integrated and complement each other, creating a good environment for personalized education. According to incomplete statistics, there are about 30 types of mathematical application problems in primary schools, which determines the diversity of problem-solving strategies, but they are always the same, that is, teachers' teaching methods and teaching means.
Keywords: primary school mathematics; Application problem teaching; Examining questions; Comparative analysis; Expand thinking
Application problem teaching occupies a very important position in the primary school mathematics syllabus, but some students are afraid to solve application problems, and they are at a loss when they look at the problems, and they don't know where to start. There are many reasons for this situation. The author talks about how to carry out the teaching of mathematical application problems in primary schools.
First, the current problems in the teaching of mathematical application problems in primary schools and their causes.
According to the principle of finding the cause according to the result, the present situation of application problem teaching is inseparable from many teachers' pursuit of "colorful" teaching methods, especially some open classes as models, which pay attention to the form of classroom and ignore the essence of mathematics.
1. Overrendering of the situation. "Creating situations" has become an arduous task for mathematics teachers at present. In a class or an open class, the teacher is worried about what the audience will think of this class if the situation is not created, and always digs into it. Creating vivid and interesting situations makes the classroom more dynamic, but some teachers ignore the purpose of creating situations, regardless of the content, unilaterally pursue situations, and even regard shopping as an essential situation, which is divorced from the teaching content and teaching objectives. 2. The textbook is inaccurate. In new textbooks, application problems are often regarded as the first situation, but in actual teaching, some teachers only regard the first situation as a means of "introduction" or as a stepping stone. We can't grasp the role of application problems in the process of students' establishing mathematical models. Some teachers only want the process of activities and do not guide students to build mathematical models. In this way, every activity of students is only an isolated case, and there is no need to "sort out" and "integrate" in time, so it is impossible to guide students to explore and build mathematical models through problem situations. 3. Total negation of tradition. After the implementation of the new curriculum, teachers' teaching ideas have changed greatly, but many teachers completely deny the essence of traditional teaching, and teaching often starts from a new stove. Some teachers didn't make clear their own goals when studying textbooks and designing schemes. Some teachers dare not apply the essence of traditional classroom to their own classes, especially in open classes, for fear that others will say that they are backward in ideas and lose themselves in practice, which is actually a blasphemy against the new curriculum reform.
Second, the new teaching strategy of primary school mathematics application under the new curriculum standard
1. Teach students to learn to examine questions, and cultivate students' habit of carefully examining questions. The difficulty of application questions depends not only on the amount of data, but also on the complexity of plot interweaving and the quantitative relationship of application questions. At the same time, the narrative in the topic is written language, which will make it difficult for junior students to understand, so the first link and premise to solve the problem is to understand the meaning of the topic, that is, to examine the topic. You must read the question carefully. Understand the meaning of the question through reading and master the content of the question. What happened? What was the result? Find out what conditions are given in the question by reading. What are the questions that must be asked? Practice has proved that students can't do it because they don't understand the meaning of the problem. Once you understand the meaning of the problem, its quantitative relationship will be clear. So from this perspective, a reasonable understanding of the meaning of the topic is equivalent to doing half of the topic. Of course, students should learn to think while reading.
2. Strengthen the analysis and training of quantitative relations. Quantitative relationship refers to the relationship between known quantity and known quantity, known quantity and unknown quantity in application problems. Only by understanding the quantitative relationship can we choose the appropriate algorithm according to the meaning of the four operations, transform mathematical problems into mathematical formulas and solve them through calculation. Therefore, the quantitative relationship of simple application problems in lower grade teaching is actually the arithmetic and structure of four operations. Therefore, from the beginning of application problem teaching, we should focus on analyzing the quantitative relationship. Therefore, we should first attach importance to analysis and reasoning in teaching. This is because not only the calculation process of the solution should be found through the analysis of the quantitative relationship, but also the calculation process itself embodies the arithmetic of solving the problem. Therefore, we should attach importance to teaching students the significance of connection operation, transform the plot language described in the application problem into mathematical operation, and describe it in students' own language on the basis of understanding. For the algorithm of each problem, the teacher should carefully reason, let the students reason, let the students abstract the quantitative relationship from the plot of the application problem and integrate it into the existing concepts.
3. Teach students how to solve problems. It is very important to master certain problem-solving methods when solving application problems, especially those with more than two or three steps of calculation. This is the general steps to solve the application problems summarized in the seventh volume of the primary school mathematics textbook (experimental version), namely: ① find out the exhausted problems, find out the known conditions and problems; (2) Analyze the relationship between the quantities in the problem, and determine what counts first, then what counts, and finally what counts; (3) Determine how to calculate each step, list formulas and calculate numbers; (4) Check or check and write the answer. The general steps to solve application problems mentioned here are not to ask students to do so from here, but to pay attention to guiding students to do so when talking about application problems. This is just a summary based on the previous work, so that students can answer the application questions more consciously according to this step. 4. Contrastive analysis of confusion. Some related and confusing application problems can guide students to make comparative analysis, such as what is a fraction of a number and a fraction of a known number, and the application problems of this number are often confused by students. First, they can't tell whether to use multiplication or division; Second, there is no need to add parentheses when calculating.
So you can arrange the following group of questions for comparative teaching. ① There are 240 pear trees in the orchard, and apple trees account for 1/3 of the pear trees. How many apple trees are there? ② There are 240 pear trees in the orchard, accounting for 1/3 of the apple trees. How many apple trees are there? ③ There are 240 pear trees in the orchard, with fewer apple trees than pear trees 1/3. How many apple trees are there? ④ There are 240 pear trees in the orchard, less than apple trees 1/3. How many apple trees are there? ⑤ There are 240 pear trees in the orchard, and there are more apple trees than pear trees 1/3. How many apple trees are there? There are 240 pear trees in the orchard, more than apple trees 1/3. How many apple trees are there? When comparing two numbers, the latter number is the standard number and the former number is the comparison number, that is, who is the standard number compared with (usually the standard number is 1).
Given a number, find its score and the score of the known number, and find this number. The similarities between these two types of application problems are: (1) the fraction of the known comparison number to the standard number; The difference is that the former seeks the comparison number from the known standard number, while the latter seeks the standard number from the known comparison number. Questions 1, 3 and 5 are all comparisons between apple trees and pear trees. The number of pear trees is the standard number, the number of apple trees is the comparison number, and the number of pear trees is already known. Therefore, they belong to the former category through multiplication. Questions ②, ④ and ⑥ are all comparisons between pear trees and apple trees. The number of apple trees is standard, the number of pear trees is comparative, the number of apple trees is standard, the number of pear trees is comparative, and the number of apple trees is unknown. Therefore, it belongs to the latter category according to the division. The scores of comparison numbers in 1 and 2 questions in the standard number are known, so "brackets" are not used in the calculation, and the scores of comparison numbers in 3, 4, 5 and 6 questions in the standard number are unknown. You need to add the score of 1 and subtract the score of 1 to get it, so "brackets" are needed in the calculation.
5. Introduce open questions to expand students' thinking. For the development of students, the learning value of problem solving lies not only in obtaining the conclusion or answer of the problem, but also in forming strategies through teaching activities and empirical methods of problem solving.
In the teaching of practical problems, we should not focus on the answers, but should pay more attention to the methods and strategies in the process of letting students experience the problems. The stability and formation of these methods and strategies will gradually become an important part of students' way of thinking, and it will also be the value of mathematics education to let students examine and solve various problems in real life from the perspective of mathematics. However, traditional application problems are mostly well-structured, with unique answers and clear directions, which can be solved by repeatedly applying the formulas and quantitative relations that have been learned.
Application problems in primary school mathematics are difficult for students to learn, which requires our teachers to adopt some flexible teaching strategies, consciously adopt various forms, and gradually cultivate students' logical thinking ability, so that students can actively participate and play an active role in order to achieve better teaching results.