Analysis on the influence of primary school mathematics learning characteristics on teaching.
Primary school mathematics is the starting point of knowledge learning. Compared with human learning, primary school mathematics learning is more specific. Primary school students' learning of quantitative relations and spatial form knowledge is abstract, which requires students to think seriously. Based on the actual situation of students, this paper analyzes the knowledge level, ability level, emotional attitude and values that students have achieved before learning primary school mathematics, so that teachers can plan teaching plans according to the characteristics of primary school mathematics learning and provide theoretical basis for teaching. This paper discusses the influence of primary school mathematics learning characteristics on teaching from three aspects: learning content, learning process and learning methods.
First, learn the abstraction and visualization of content.
1. Abstract and visual features
Textbook writers transform abstract mathematical knowledge into intuitive mathematical knowledge that children can easily understand. Through transformation, mathematics is not only abstract, logical and rigorous, but also more vivid. Greatly improved students' interest in learning. The textbook presents mathematics knowledge to students in various ways through rich and varied pictures and stories. Let students want to learn and love to learn. Although the content of primary school mathematics learning is very abstract, it is presented in many ways, which makes the knowledge more visual. This method solves the contradiction between the characteristics of mathematical knowledge and the thinking of primary school students.
2. The influence of abstract and vivid features on primary school mathematics teaching.
Teachers should combine visualization and abstraction when explaining primary school mathematics, and visualize abstract mathematics knowledge through various teaching methods. Therefore, teachers need to properly solve the relationship between concrete and abstract, that is, to solve the following four problems: first, how to combine the visualization of learning content with the essence of mathematics; Second, how to abstract and summarize; Third, how to deeply understand mathematical knowledge into students' minds; Fourth, let students learn to describe math problems in their own language.
Second, the learning process of progressive system.
1. Progressive and systematic
The development and application of teaching mode is a process of continuous development with educational theory and teaching practice. It is gradual and systematic. These two characteristics follow the development law of primary school students, and knowledge learning is a cyclical and gradual process. In teaching, we should fully consider the characteristics of students' age and primary school mathematics learning, guide students to do more, use more brains and open their mouths in specific activities, mobilize all kinds of senses to participate in activities, and improve learning efficiency. Progressiveness and systematization are the characteristics of students' learning process, which are mainly manifested in the logicality and systematization of mathematical knowledge, the development of mathematical knowledge, and the mutual infiltration of various knowledge points to form comprehensive and systematic knowledge. Learn to draw inferences from others. Learn primary school mathematics step by step.
2. The influence of gradualism and systematicness on primary school mathematics learning.
According to the progressive and systematic characteristics of primary school mathematics, choose teaching methods reasonably. Follow the law of student development in the teaching process. Combine the gradual and systematic learning of primary school mathematics properly, so as to make an effective teaching plan and make the teaching of primary school mathematics planned and efficient. To adapt to this feature, we need to meet the following two aspects: the first aspect, learning according to the mathematics learning order formulated by the textbook for students; The second aspect is to systematize the learning process of primary school mathematics on the basis of learning principles.
Thirdly, the acceptability and exploration of learning methods.
1. The embodiment of acceptance and inquiry in primary school mathematics learning activities
There are two ways to learn mathematics in primary schools: acceptance learning and discovery learning. No matter what kind of learning method, it is a process for students to transform their existing mathematical knowledge into their own knowledge to improve their mathematical level. The process of transforming knowledge is not only the process of students' own discovery and exploration, but also the process of accepting the original knowledge. Through students' exploration of mathematics learning methods, primary school mathematics learning is manifested on the basis of acceptance, exploration and unity. The rediscovery of mathematics knowledge determines the exploration of mathematics learning in primary schools, and the transmission of mathematics knowledge determines its acceptance of learning. Acceptability and exploration are the necessary conditions for primary school mathematics learning.
In the teaching process, teachers should correctly understand and admit the differences between students, and let students develop on different bases through independent thinking and group cooperation and communication, so as to gain the joy of success from teachers' affirmation of each method. Students can choose their favorite calculation methods to communicate with their classmates, increase their interest in this course and improve teaching efficiency.
2. The influence of acceptability and inquiry on primary school mathematics teaching.
Acceptability and inquiry are characterized by the influence on primary school mathematics teaching through teaching and learning. Teachers should take students as the main body and play a leading role in mathematics teaching in primary schools. Teachers should use a variety of teaching methods to guide students to think, and choose appropriate teaching methods according to students' acceptance and mathematics knowledge, so that students can not only learn mathematics in a variety of ways, but also master knowledge. The progress of mathematics teaching in primary schools needs to be completed by various learning methods and advanced teaching methods, so that students can play their middle school, improve their interest in learning and achieve teaching goals. In the teaching process, we need to pay attention to the following three points: first, guide students to adopt a variety of learning methods; Second, in the teaching process, we should pay attention to cultivating students' ability to explore, discover and solve mathematical problems; Thirdly, according to the learning characteristics of primary school mathematics, we should adopt various teaching methods to improve students' initiative and enthusiasm in learning.
Four. conclusion
In the process of primary school mathematics teaching, we must attach importance to the characteristics of primary school students learning mathematics and adopt various teaching methods according to their characteristics. The teaching content should be vivid and abstract. In the teaching process, we should combine systematicness with gradualism, acceptability with exploration, follow the characteristics of primary school mathematics learning, master knowledge step by step and circularly, and achieve the expected teaching objectives. The characteristics of primary school mathematics learning are enlightening and exploratory to teaching. Only by fully understanding its characteristics can primary school mathematics teaching advance rapidly in a direction that is conducive to students' acceptance, thus improving teaching efficiency and achieving teaching objectives.
Analysis on the Development of Mathematics Derivative Teaching in Senior High School under the New Curriculum Reform
In recent years, with the rapid development of market economy in China, the society is constantly changing, and the level of science and technology in China has also reached a new level. In order to develop better, we also need to develop our natural sciences at the same time, so that we can better meet the needs of social development. As we all know, mathematics is an indispensable part of high school quality education. Mathematics has existed since the formation of China's education system. Therefore, mathematics plays a very important role in quality education, and derivative plays a very important role as a tool to help students solve difficulties such as function and sequence. After the implementation of the new curriculum reform, calculus has been included as the teaching content in senior high school mathematics textbooks, which puts forward higher requirements for students to master derivative knowledge. Therefore, under the background of the new curriculum reform, this paper studies how to improve students' ability to master derivatives through the improvement of teaching methods.
1. Present situation of mathematics derivative teaching in senior high school
(1) The teaching mode is single, and there is not enough guidance for students' learning methods.
Under the background of liberal arts, derivative is studied as an optional course in senior high school mathematics, which leads to the failure of liberal arts students to master the application of derivative and solve the problem of function parameters with derivative. At the same time, due to the implementation of the new curriculum reform, math class hours are compressed. In order to complete the contents stipulated in the syllabus in a short time, many teachers generally use the way of teachers giving lectures or writing on the blackboard in the teaching process. There is no doubt that students are passive in the whole teaching process, which greatly suppresses the activity of students' thinking and the enthusiasm of classroom participation to some extent. This causes students to lose their enthusiasm for learning because the derivative content is too difficult, which is even more unfavorable for mastering derivative knowledge and carrying out teaching activities.
(2) The teaching rigidity caused by the concept of exam-oriented education
For a long time, China's exam-oriented education system has a relatively stable position in the education system, and even now it has not been completely eliminated. Even after the implementation of the new curriculum reform, many teachers pay too much attention to the explanation and practice of examination questions in the teaching process, but neglect to help students correctly understand mathematical ideas and connotations, which leads to students mechanically reciting formulas purely for exams in derivative learning and unable to apply the derivative knowledge they have learned to life and other subjects' content learning, which is inconsistent with the concept of quality education advocated by the new curriculum reform. The difficulty in derivative teaching lies in students' lack of understanding of derivative and their difficulty in understanding its concept, which requires teachers to use physics subjects or scenes in life to have a deep understanding, instead of teaching students purely theoretical mathematical concepts? Duck education? .
Second, the measures to improve the teaching quality of mathematical derivatives under the new curriculum reform
(1) Help different students make different study plans.
Generally speaking, learning methods are the basis of students' effective learning and play a decisive role in students' learning to a certain extent. The correct learning method is the guarantee for students to effectively master the knowledge they have learned, which requires math teachers to understand students' mastery of derivative content through certain tests and exchanges besides explaining the classroom content. For students who have not mastered enough, they should help to make corresponding study plans. The purpose of the exam is not to get grades, but to master the students' learning situation, and at the same time make appropriate adjustments to the teaching plan according to the students' learning situation. If the follow-up study plan fails to keep up, then the exam will lose its meaning.
(2) Use cases to help students deepen their understanding of derivatives.
Derivative is too theoretical for senior high school students, which often leads to students' insufficient understanding and application of derivative. In this case, pure theoretical teaching will only lead to students' further incomprehension, which is very unfavorable to students' learning efficiency and teachers' classroom efficiency. Therefore, in derivative classroom teaching, teachers should pay attention to using derivative application cases to stimulate students' learning enthusiasm, such as the speed change and acceleration change of physical movement. This can not only help students better understand the connotation of derivative, but also make students actively think about the application of derivative knowledge in life while strengthening their understanding of other disciplines, which greatly improves the teaching quality and efficiency.
(3) Strengthen derivative skills and application training.
In normal teaching, students should be encouraged to use derivative content to solve related problems such as functions, which can further improve students' understanding and application level of derivatives. At the same time, teachers can also train students with more technical problems of derivative application, such as drawing images of second-order and third-order functions with derivative knowledge. Students need some skills to do such problems. With the increase in the number of answering technical questions, students will be more skilled in the application of derivatives. At the same time, in the initial stage of derivatives, because students' understanding of derivatives is not deep enough, teachers can give some questions with life cases for students to answer, such as adding the question of speed change when students ride a bike to the topic of derivatives, which can encourage students to actively think about derivatives knowledge, deepen their understanding of derivatives and lay the foundation for further study of derivatives in the future.
Third, the conclusion
To sum up, we can know that derivative teaching in senior high school mathematics has its uniqueness. The reason is that it not only has the strict logic of mathematics, but also has the abstraction that junior high school mathematics does not have, so teachers need to teach according to the characteristics of senior high school mathematics in teaching. The effective teaching of derivative in senior high school requires not only teachers to adopt active guiding teaching methods, but also students to cultivate mathematics learning thinking. Only through the joint efforts of teachers and students can derivative teaching in senior high school develop steadily and sustainably under the new curriculum reform.
On the cultivation of junior middle school students' consciousness of mathematical problems
First, the significance of cultivating junior high school students' problem consciousness
Question consciousness is the mental preparation to think actively and explore seriously in the process of subject learning, so as to put forward a certain problem. In math class, students are often afraid or unwilling to answer questions in class, and they are not or are not good at asking questions. Only a few students can always answer questions actively, and even fewer students can ask questions in class. Students' lack of question awareness and inability to ask questions is not conducive to the development of students' thinking and the further improvement of their learning ability. One of Zhu Yongxin's core ideas about the new curriculum is to teach students something useful for life. Students' habit of learning independently, being diligent and asking questions will definitely benefit students for life. Psychological research shows that realizing the existence of problems is the starting point of thinking, and it is a big problem for students to have no problems. Einstein, known as the father of modern science, once pointed out that it is often more important to ask a question than to solve it. ? The cultivation of junior middle school students' mathematical problem consciousness is an important aspect of the cultivation of learning habits and learning ability, and it is also the need of the new curriculum reform.
Second, junior high school students' problem awareness training strategies
How to cultivate students' problem consciousness? Through teaching practice, we have made relevant explorations and initially formed some strategies.
1, change the evaluation method and encourage questions.
There are many reasons for students' lack of problem consciousness. One of the reasons is that our evaluation orientation is not conducive to the cultivation of students' problem consciousness. Many times, we appreciate the correct answers to questions and high scores in exams, and lack encouragement and guidance for students with learning difficulties. A large number of students who follow the rules dare not and will not question it. The problems in students' study should have been raised by students themselves, but in actual teaching, students are often asked by teachers. How to change this situation? We can encourage students to ask questions in many ways. (1) Pay attention to the language of praise or encouragement, and gradually make students feel that being able to ask questions in class is as worthy of recognition and encouragement as being brave in answering questions. (2) Whether students take the initiative to ask questions in class is an important aspect of evaluating students. (3) Conduct some questioning contests and other activities purposefully.
2. Consolidate the learning foundation and let students ask questions.
In teaching practice, we realize that whether students can ask questions is closely related to their learning foundation, and students with better learning foundation are more likely to ask questions. Therefore, teachers should pay attention to consolidating the learning foundation, cultivate students' quality of learning to ask questions well, and make students' solid learning foundation become the soil for problems.
3. Create a relaxed learning atmosphere and let students dare to ask questions.
It is not without problems that students in math class don't ask questions. More often, I am afraid to ask questions because of nervousness and other reasons. Only in a relaxed and harmonious atmosphere can students maximize their thinking potential. In order to eliminate students' nervousness and fear in class, teachers need to create a relaxed, harmonious and democratic learning atmosphere as much as possible. Students can exchange questions in the study group first, and then ask or answer questions in the whole class. Teachers guide students with a smiling, peaceful, tolerant and encouraging attitude, communicate and discuss with students, help students build self-confidence, narrow the emotional distance between teachers and students, and let students ask whenever they want.
Mathematics teaching should teach students to think. Let students experience the process of observation, conjecture, operation, experiment and reasonable reasoning, which is not only conducive to cultivating students' independence, initiative and innovative spirit, but also helps students to eliminate nervous factors in a relaxed learning atmosphere and dare to ask questions when they have questions.
4. Teachers demonstrate and guide students to ask questions.
If a person has no problems, there will be no new discoveries and no real growth. Students without problem awareness will study passively and inefficiently, and teachers without problem awareness will hinder professional growth. If teachers want to make students have problem consciousness, they must first have problem consciousness themselves. Teachers' strong problem consciousness can play a good demonstration role and promote the development of students' problem consciousness.
Case 2. Teaching of triangular trilateral relations
(1) Ask the students to take out three plastic straws with different lengths prepared before class.
(2) put these three straws? End to end connection? What did you find? At this time, students found that some can form triangles, while others can't.
(3) The teacher continued to ask three questions: ① What are the lengths of your three straws? ② What is the relationship between the lengths of three straws? End to end connection? Form a triangle? (3) three line segments of any length are ok? End to end connection? Form a triangle?
In the above-mentioned inquiry process, it is the teachers who constantly ask questions and concentrate students' thinking, which leads to students' constant questions, in-depth thinking, constant results and constant surprises. In the long run, students will be good at asking questions.
5. Use modern media technology to urge students to ask questions.
Curriculum Standard for Compulsory Education (20 1 1 Edition) (hereinafter referred to as the Standard) points out that the design and implementation of mathematics curriculum should make rational use of modern information technology according to the actual situation and pay attention to the integration of information technology and curriculum. Take information technology as a powerful tool for students to learn mathematics and solve problems, effectively improve the way of teaching and learning, and make students willing to participate in realistic and exploratory mathematics activities. The application of modern information technology in mathematics teaching can achieve incomparable results in other ways, which is powerful for students' learning? Question space? Independent investigation. Teachers set the environment for students, provide the tools and resources they need, encourage students to ask questions and explore, stimulate students to answer questions, and realize students' self-construction of knowledge.
Modern information technology provides a vast world for the development of mathematical activities. As long as students participate in the process of using media software to do mathematics, they will inevitably find or raise various problems, which will lead to independent inquiry.
Third, the conclusion
In short, real education should be based on the development of students. Teachers should not only pay attention to how to teach, but also how to learn. We ask students to create a learning environment that can ask questions, dare to ask questions and be good at asking questions, and cultivate students' problem consciousness and innovative spirit.
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