Reflections on Primary School Mathematics and Mathematical Thinking Methods 1 "Let reading become the habit of teachers and students, and let books infiltrate the hearts of all teachers and students" is the original intention of the first primary school in Junan County to advocate reading for teachers and students. In 20xx, the school put forward the concept of "six years affect a lifetime" and made great efforts to build a school with connotation development. As an important measure for the growth and development of teachers and students, the school started the construction of "scholarly campus". The school tried to combine long and short classes, set up large reading classes, and made a unified reading plan for students. According to the number of classes, it bought nearly 100 kinds of books such as basic reading bibliography for primary school students nationwide. From Tuesday to Friday afternoon, they read collectively under the guidance of the teacher, ensuring the reading time and effect. A series of various reading exchange activities, such as teachers' reading exchange meeting, teachers' and students' reading talent show, classic reading activities of Double Ninth Festival, theme education activities of "Learn from Me" and reading essay activities, have enriched the reading life of teachers and students and made reading a pleasure! Under the background that the country advocates "reading for all", on March 30th, the school held the launching ceremony of the "First Reading Festival", which opened a new starting point for school reading activities. As an important part of this activity, it embodies the feelings and thoughts of teachers during the winter vacation, and it is another witness to the happy growth of teachers' profession!
After reading Wang Yongchun's Primary School Mathematics and Mathematical Thinking Methods, I have a further understanding of primary school mathematics and mathematical thinking methods. The following is what I sorted out.
First, the understanding of primary school mathematics thinking methods.
Mathematical thought is the essence of mathematical knowledge and the essential understanding of mathematics. It is a new mathematical viewpoint extracted from some specific mathematical contents and the process of understanding mathematics, and it is the guiding ideology for constructing mathematical theory and solving problems with mathematical theory.
Mathematical method refers to various methods and means to put forward and solve problems from a mathematical point of view. There are differences and close connections between mathematical thought and mathematical method. Mathematical thinking is more theoretical and abstract, while mathematical methods are more practical. People often rely on certain mathematical methods to realize mathematical ideas; And people's choice of mathematical methods should be based on certain mathematical ideas. Therefore, the two are closely related. We collectively call it mathematical thinking method.
Mathematical thinking method is the soul of mathematics, so if you want to learn and use mathematics well, you must go deep into the "soul" of mathematics.
Second, the significance of primary school mathematics thinking methods.
1, which is beneficial to the establishment of modern mathematics education concept and the implementation of new curriculum concept.
"Mathematics Curriculum Standard (20xx Edition)" further puts forward in the overall goal: "Through mathematics learning in compulsory education stage, students can acquire basic mathematics knowledge, basic skills, basic ideas and basic activity experience necessary for adapting to social life and further development." The "Four Basics", goals and ideas are put forward for the first time, and mathematical thought is regarded as one of the basic goals of compulsory education, especially primary school mathematics education, and the importance of mathematical thought and its implementation is emphasized.
2. It is beneficial to improve teachers' professional quality and teaching level.
After the Standard (20xx edition) regards the basic idea of mathematics as one of the "four foundations", I face greater challenges. On the one hand, I lack professional knowledge about mathematical thinking methods, on the other hand, I lack the awareness, experience and strategies of mathematical thinking methods that should be possessed in classroom teaching.
3. It helps to improve students' thinking level. Cultivate "four abilities", improve cognitive structure, guide learning transfer and promote thinking development.
Therefore, consciously infiltrating some basic mathematical thinking methods into students in primary school mathematics stage can deepen students' understanding of the mathematical essence of mathematical concepts, formulas, laws and laws, and improve students' ability to find, ask, analyze and solve problems, which is also the real connotation of primary school mathematics quality education. At the same time, it can also lay a good foundation for junior high school mathematics learning.
Third, how to consciously infiltrate mathematical thinking methods in teaching?
1, pay attention to the implementation of the goal of thinking method.
2. Embody mathematical thinking methods in the process of knowledge formation.
3. Embody mathematical thinking methods in the application of knowledge.
4. In the arrangement and review, the mathematical thinking method is reflected in the general review.
5, subtle, clear presentation, long-term persistence
The following is the mathematical thinking method applied in the second volume of the fifth grade: 1, symbolic thinking. 2. The idea of classification. Step 3 collect ideas. 4. There are constant thoughts in change. 5. Limited and infinite thoughts. 6. induction. 7. analogy method. 8. Deductive reasoning. 9. Change your mind. 10, the idea of combining numbers and shapes. 1 1, the idea of geometric transformation. 12, substitution ideas. 13, model thinking. 14, optimization ideas. 15, statistical thought. Analytical method and comprehensive method. 17, exhaustive method. 18, comparison difference method.
Mathematical thinking method is different from general concepts and skills, and can not be mastered in short-term training. The teaching of mathematical thinking method should be a process of forming ideas and methods through long-term infiltration and influence.
Mathematical thinking method focuses on understanding, "sneaking into the night with the wind, moistening things silently", hoping that the teaching of mathematical thinking method can moisten students' hearts like spring rain.
Reflections on "Mathematics and Mathematical Thinking Methods in Primary Schools" 2 "New Curriculum Standards" puts forward in the general goal that students can acquire the necessary mathematical knowledge, basic skills, basic ideas and basic activity experience to adapt to social life and further development through mathematics learning in compulsory education. This sentence is familiar to our new teacher, but we really don't understand it. I didn't really understand this sentence until I read Wang Yongchun's Mathematics Thought and Mathematical Thinking Method in Primary Schools. It is better to teach people to fish than to teach them to fish. For students, mathematical knowledge is the second, and mathematical methods are the most important. In this book, Mr. Wang summed up the mathematical ideas contained in primary school mathematics knowledge for us, so that we can clearly know what mathematical ideas and methods are contained in these knowledge in our daily teaching, which provides guidance and help for our teaching.
This semester, I am a math teacher in grade three. The main ideas of the first volume of Grade Three are as follows: The units of length learned in Unit 3 "Measurement": decimeter (dm), millimeter (mm) and kilometer (km) are the application of symbolic ideas; Some exercises in Unit 7 "Rectangle and Square", such as "Case 2" on page 25 of this book, apply the idea of classification; The repeated learning of Unit 9 "Mathematics Wide Angle-Set" is the application of set thought; Unit 8 "Preliminary Understanding of Fractions" Students can use a square piece of white paper to fold into different shapes to express its 1/4. After students fully demonstrate, they can be guided to find that although the shapes and sizes are different, they all divide a square piece of white paper into four parts on average, and each part is its 1/4. In this teaching process, there are changes and the application of unchangeable concepts. Unit 8 "Preliminary Understanding of Fractions", Divide a circle equally. The more copies, the smaller the score. If you keep dividing, you can write an infinite number of fractions.
Life itself is a huge mathematics classroom, and there are a lot of valuable mathematical phenomena objectively in life. Instructing students to use mathematical knowledge to keep a diary can encourage students to actively observe life, think about life problems and make life problems mathematical. Pay attention to cultivating children's awareness of using mathematics in teaching and enhance students' ability to solve practical problems by using knowledge. It can be seen that mathematics is not taught by teachers, but is learned by students themselves under the guidance of teachers. In teaching, teachers should create scenes, provide opportunities for students, give students enough time and space, and let students actively explore new knowledge, discover laws and summarize laws in exploration. Therefore, in classroom teaching, we should leave more time for students to operate; Give students more time to express their views; Give students more time to ask questions. Ensure that there is enough time and space for students to communicate, discuss and ask questions in class.
This book teaches us a teaching idea and a teaching method. Reading is a good learning method, which will lead us to keep updating, keep pace with the times and become a good teacher with professional quality that students like.
Reflections on "Primary School Mathematics and Mathematical Thinking Method" 3 Why do I feel very benefited and moved after reading several pages of this mathematical thinking method? Because in the past, learning math well was only a natural choice, and the principle of subconscious action can be found here, which makes your behavior have a theoretical basis and the importance of thinking methods more clear. I just benefited from these ways of thinking, which I didn't realize before, and I suddenly realized after reading the book. Many things you take for granted understand the truth of this design. For example, why should we design the fifth and sixth grades of primary school? Why are the third and fourth grades and the first grade of junior high school a hurdle? The main difference is the development of abstract ability. Thinking does not play a particularly important role in the lower grades. The gap didn't show. From the author's implication, it can be seen that mathematical thinking method is the most important, but it is not the normal goal of classroom teaching, but an accessory of teaching. Some people have a high degree of understanding, capture more and develop well. Some people are insensitive and rob less. The gap came out.
But no matter from the experience of mathematics educators or our personal experience, mathematical thinking method is the most basic. It belongs to the understanding and rational understanding of the essence of mathematics.
Olympiad is to train mathematical thinking methods. But true and false olympiad numbers are different. Fake olympiad is just to teach you routines, just remember.
My own math study is also elementary. No guidance, no training. However, if someone gives advice, it will definitely be easier, or it can go further.
We often say that vocabulary is the basis of understanding in Chinese learning. In mathematics, concept is the basis of mathematics learning, the foundation and basic form of abstract thinking. Concept is probably equivalent to abstract words in Chinese reading, but concept is related to system. This explains what we usually say: lay a solid foundation and then expand. What is the basis? The foundation is the knowledge structure formed by the relationship between concepts.
Therefore, we naturally understand what we mean by "expanding" every day. On the basis of understanding the knowledge structure of the relationship between concepts, expansion means learning mathematics and solving problems by using thinking methods, model thinking and reasoning thinking.
Thinking about Primary School Mathematics and Mathematical Thinking Methods 4 In order to help primary school mathematics teachers change their concepts of mathematics education, improve their understanding and application of mathematical thinking methods, and then improve their professional quality, Wang Yongchun, the editor-in-chief of this book, published a monograph, Primary School Mathematics and Mathematical Thinking Methods, which was welcomed by the majority of primary school mathematics teachers once published. The teacher who participated in the learning activities wrote down his reading experience. Editor-in-chief Wang Yongchun compiled and published these vivid learning experiences and valuable teaching experience cases to form a book for more teachers to share popular and profound theoretical interpretation and practical experience of grounding gas.
Wang Yongchun, the author of this book, as the director of the primary school mathematics editing room of People's Education Publishing House, has been engaged in the compilation of primary school mathematics textbooks for a long time, devoted himself to the research of curriculum and textbooks, and deeply thought and explored the thinking methods of primary school mathematics. Based on a strong sense of responsibility to improve the quality of education and implement the educational goals, the author has written a series of articles and discussed the application of mathematical thinking methods in primary school teaching. On this basis, this book was formed.
This book is a front-line teacher's interpretation of mathematical thinking methods and a teaching case study of Primary School Mathematics and Mathematical Thinking Methods. Therefore, the content structure and content of this book basically correspond to "Primary School Mathematics and Mathematical Thinking Methods", and the contents of chapters 1 to 5 correspond to "Primary School Mathematics and Mathematical Thinking Methods". The sixth chapter, considering the uneven distribution of cases in different grades, divides the first and second grades into 1 and the third and fourth grades into sections. For students, mathematical thinking method is different from general concepts and skills. Concepts and skills can usually be mastered through short-term training, while mathematical thinking methods can only be formed through the long-term infiltration and influence of teachers. Teachers should reflect the teaching objectives of thinking methods in each class in a timely and appropriate manner, so that students can accumulate in a subtle way and learn mathematics well by improving their mathematics literacy.
Mathematical thinking method is different from general concepts and skills, and can be mastered through short-term training, while mathematical thinking method can only be formed through long-term infiltration and influence in teaching. As the old saying goes, "Taishan does not allow soil, so it can become big; Rivers and seas do not choose small streams, so they can be deep. " Teachers should reflect the teaching objectives of thinking methods in each class in a timely and appropriate manner, so that students can accumulate in a subtle way and learn mathematics well by improving their mathematics literacy. I hope that the teaching of mathematical thinking methods can moisten students' hearts like spring rain.
In fact, this book has been on the shelves for a long time, because there are many conceptual things in it, so it is not so interesting to read. After reading a few pages, I stopped reading.
The reason why I reread this book is because I watched Synchronous Classroom of Famous Teachers with my students these days. An experienced teacher, Lu, gave a math lesson to the sixth grade students on TV. I found that he paid special attention to the infiltration of mathematical thinking methods in his lectures, which was exactly what I lacked.
When explaining how to solve the problem of finding volume, Mr. Lu mentioned the idea of transforming one volume into another, casting a cube into a cylinder, putting pebbles into water, raising the water surface and so on. , embodies the idea of equal deformation.
Teacher Lu especially mentioned a mathematical thinking method, which is inferred by the solution of cylindrical volume, and proved by experiments that the solution of conical volume embodies the analogy thinking method. Analogy refers to the idea of transferring the known attributes of one type of mathematical object to the other based on the similarity between the two types of mathematical objects.
Teaching methods are more important than imparting knowledge. As a math teacher, it is necessary to have a systematic understanding of math thinking methods. So I thought of this book on the shelf. To tell the truth, reading this book is a bit boring. If you don't think about the problems in the book, you may just read the words.
On the cover of the book "Primary School Mathematics and Mathematical Thinking Methods", it reads:
Mathematical thinking method is different from general concepts and skills, and can not be mastered in short-term training. The teaching of mathematical thinking method should be a process of forming ideas and methods through long-term infiltration and influence. Teachers should reflect the teaching objectives of thinking methods in each class in a timely and appropriate manner, so that students can accumulate in a subtle way and learn mathematics well by improving their mathematics literacy.
This book is divided into two parts. The first part introduces various thinking methods, and the second part introduces the embodiment of various thinking methods in each textbook. This book can be used as a reference book when preparing lessons. For example, in the process of summing up the deduction of addition, subtraction or multiplication formulas in ten minutes, we all embody the function idea. As teachers, we don't need to let students know what the function thought is, but we should understand that it embodies the function thought and consciously infiltrate the thinking method into students, so that students can associate this thinking method to solve problems when they face similar problems in the future.
It only took me two or three days to finish reading the book in a hurry. Some ideas or contents in the book are not well understood in some places and need to be understood slowly, but I know that when preparing lessons and designing teaching in the future, we must think about one question: What ideas and methods are embodied in this class? What ways of thinking should students be infiltrated? Think longer for the students.