The essence of mathematics teaching is to let students understand the close relationship between mathematics and nature and human society, understand the value of mathematics, learn to observe and analyze real life with mathematical thinking mode, solve problems in daily life and other disciplines, enhance the awareness of applied mathematics, establish good feelings for further study and lay a good foundation for students' lifelong sustainable development. Therefore, students' real life and mathematics learning should be closely linked. The author thinks that instructing students to write mathematical papers is a good method and way to guide students to carry out research-based learning, a new way of communication between teachers and students, and a very novel research topic. The so-called "math thesis" is to let students describe their math problems and their solutions in the form of diaries, which is a written record of students' math learning experience. It can be students' understanding and evaluation of a certain mathematical problem, their true mentality and thoughts in mathematical activities, the problems encountered in comprehensive mathematical practice activities, and the process of solving mathematical problems in life by using the learned mathematical knowledge.
First, the role of mathematical papers
"Mathematics thesis" is a new way for teachers to understand the individual differences of students' psychological, thinking and non-intellectual factors in mathematics learning, and a new way for students to analyze and evaluate themselves, which can improve students' mathematics ability and cultivate their self-confidence in learning mathematics.
1. Cultivate students' ability to find, analyze and solve problems, and develop their autonomy and creativity. Students' learning activities are based on finding and solving problems. The writing of mathematical papers can effectively enhance students' problem consciousness. Math papers are not restricted by textbooks or bound by teachers. It is written by students who comprehensively apply what they have learned in mathematics, make bold attempts and explore problems independently. It is helpful to cultivate students' ability to find, analyze and solve problems and develop their personality.
2. Cultivate students' practical ability, improve students' interest in learning mathematics and love life. To carry out writing activities of mathematical papers in primary school mathematics teaching requires students to do a lot of hands-on practice. Psychological research shows that such activities can open students' thinking, increase their interest in learning mathematics and give full play to their potential in learning mathematics. Because the acquisition of knowledge is the result of students' own efforts to explore, students can fully experience success and have a strong interest in mathematics. By writing papers on mathematics, students can gain more mathematical knowledge from life, increase their mathematical talents, and have the opportunity to apply the knowledge and skills they have learned to life. Therefore, while they understand the origin of mathematics, they will also love mathematics and life more.
3. Helping teachers to understand students' emotions in mathematics learning is helpful for teachers to reflect on teaching and improve teaching. Teachers can see students' attitudes, beliefs, frustrations and sense of achievement in mathematics learning in students' articles, reflect and improve their teaching behavior on the basis of understanding students, conduct mutual trust and exchanges between teachers and students, and establish friendly feelings between teachers and students.
Second, the multi-dimensional perspective and rich content of mathematical papers
Mathematics thesis arouses students' curiosity and thirst for knowledge through students' observation and discovery of mathematics problems in life, makes students realize that mathematics is close to life, thus arousing their enthusiasm and interest in learning mathematics; By guiding students to practice what they have learned in class, students can feel the practicality of mathematics and improve the actual effect of mathematics learning; By exploring interesting and intelligent questions, students can broaden their horizons and cultivate their flexibility and profundity of thinking. Based on the author's teaching practice, this paper talks about several specific writing methods of mathematics papers.
1. The solution to a math problem. It is mainly a simple or unusual answer to a challenging topic (including multiple answers to a topic). For example, the thinking questions at the back of the book, the Olympic math questions, the wisdom questions assigned by teachers or parents, the challenges in math publications, and the problems I usually encounter in doing problems. By solving these problems, students not only develop their thinking, but also experience a strong sense of accomplishment, which will be a great motivation for his future mathematics study.
2. Analyze realistic problems from a mathematical perspective. It mainly means that students observe, calculate and analyze practical problems from a mathematical perspective and get a rational thinking. For example, a student wrote: If everyone saves 1 gram of water every day, 1.300 million people in China can save1.300 tons of water every day, sending out the feeling that "if everyone saves a drop of water, the desert can become an oasis"! Some students wrote: If everyone who goes to the bank to deposit money can donate 1 cent for the "Hope Project" every time, how many poor students can realize their dream of going to school with the money donated by so many savings points across the country! Students can think about social significance through mathematical calculation from these angles, and its value can far exceed the mathematical research itself.
3. Mathematical problems in life. It is mainly used to record situations about mathematics that students are interested in and have personal experience in life. There are many topics to write in this kind of math paper. For example, some students wrote why the RMB is only 1 yuan, 2 yuan and 5 yuan, but not 3 yuan, 4 yuan, 6 yuan, 7 yuan, 8 yuan and 9 yuan. For another example, a student wrote that there are 24 stairs on each floor of the building where his family lives, so how many stairs should he climb from 1 floor to the fifth floor? These are ordinary things that students have to experience every day, but once students observe and think about these seemingly ordinary life problems from the perspective of mathematics, they will build a bridge between mathematics and life and feel that there is mathematics everywhere in life.
4. Math problems in class. Mainly refers to students' own thinking and discovery in the process of classroom mathematics learning. This is very helpful for students to learn mathematics. For example, when a student is learning to draw the height of a triangle, he finds that the book introduces three heights of an acute triangle and a right triangle, while an obtuse triangle only introduces one height. After class, she drew the other two heights of the obtuse triangle through her own thinking and trying. After being affirmed by the teacher, she was overjoyed and quickly wrote a math paper "I found the other two heights of an obtuse triangle".
5. Problems in mathematical practice. Mainly refers to the students' doubts, inspirations and conclusions in the process of practical activities through their own hands-on practice. For example, a student read a book by himself before the teacher had a practical activity class, touched it with red and blue pencils according to the contents of the book, and explored and verified the law by himself. Afterwards, she wrote an article about her experience and wrote out her thoughts and experiences in the process of hands-on practice, which made her feel very happy.
6. Mathematical fairy tales. It mainly means that students use their rich imagination to record the mathematical world they see in the form of fairy tales (including mathematical exposition). This is a good integration of Chinese and mathematics. The unique perspective and vivid language description make the teachers feel refreshed.
Third, some problems that should be paid attention to in guiding students to write mathematical papers.
1. Pay attention to the actual level of students, step by step. When you start writing, don't start too high. The choice of writing content and form should not only consider students' actual ability and level, but also consider whether students have the ability and conditions to observe, test and experiment. Without practical and reliable material data, it is impossible to write articles with scientific value. The value of a math paper has little to do with the size of the topic, and a small topic can still write a big article. Beginners had better discuss one problem at a time. The topic is time-consuming and laborious, and it is not easy to make it clear, so it is often impossible to write it. The topic is narrowed, the argument materials are easy to collect, and the writing difficulty of the article is also reduced, which is conducive to students' participation.
2. Pay attention to the practical mathematics around students and make it practical. Primary school students have limited mathematical knowledge, energy and time. Teachers should pay attention to closely combining students' study and life reality when instructing students to write math papers. Teachers can guide students to choose some topics, so that students can write according to their own personal experiences, which is easy for students to accept and understand and is conducive to writing. For example, after learning the area unit and the area of rectangle and square, let the students measure and estimate the area of desks and classrooms themselves, and write the process of practical activities into mathematical papers. For another example, in order to educate students to save food, students can investigate and count how many kilograms of food are wasted in the school cafeteria every day, and what can be used for the food saved by the school in one year. Only in this way can students have activities, thinking and content to write.
3. Pay attention to cultivate students' sense of participation, and let students actively write math papers. The subject of teaching is students. Only when students actively participate and turn math papers into conscious actions can this activity achieve the expected results. The purpose of writing is to improve students' learning enthusiasm, change passive learning into active learning, and cultivate students' autonomous learning ability and innovative consciousness. Due to the limitation of primary school students' knowledge and ability, most students are unlikely to write high-level compositions. For students, the greatest significance of writing mathematical papers is participation. In the process of participating in writing activities, students' ability is improved and their talents are displayed.
Fourth, take a math paper as an example.
Mathematical problems in RMB
One day, my mother and I went shopping. Mom went into the supermarket to buy things and let me stand at the place where I paid. I have nothing to do, just watch the assistant aunt collect money. After reading it, I suddenly found that the money collected by the assistant aunt was 1 yuan, 2 yuan, 5 yuan, 10 yuan, 20 yuan and 50 yuan. I feel very strange: Why isn't RMB from 3 yuan, 4 yuan, 6 yuan, 7 yuan, 8 yuan, 9 yuan or 30 yuan, 40 yuan or 60 yuan? I ran to ask my mother, and my mother encouraged me to say, "Think hard and calculate well. My mother believes you can figure out the reason." I calmed down and thought it over. After a while, I jumped up happily: "I know, because as long as you have 1 yuan, 2 yuan and 5 yuan, you can form 3 yuan, 4 yuan, 6 yuan, 7 yuan, 8 yuan and 9 yuan at will, and as long as you have 10 yuan, 20 yuan and 50 yuan, you can also form 30 yuan and 40 yuan." Why 2 yuan and 5 yuan? "I said," it is not convenient to use 1 yuan to form a larger number. "Now my mother showed a satisfied smile and praised me for observing more and thinking more. I am really more comfortable than eating my favorite ice cream.
Here, I also want to tell other children: in fact, there are math problems everywhere in life. As long as you pay more attention to observation and thinking, you will find many unexpected discoveries. Try it if you don't believe me!