The big aspect of mathematics literacy is related to students' growth direction and development goals, while the small aspect is related to people's learning attitude and habits. Mathematics literacy refers to the unity of learning orientation, reality and rigor formed by students in the process of learning. It includes learning purpose, learning attitude, learning method, logical thinking mode and logical, intuitive, connected and developing thinking method.
Learning objectives, learning attitudes and learning habits have been widely recognized and understood by educators. Therefore, I will focus on four issues.
(1) Seeking truth and being pragmatic, cultivating students' rigorous thinking quality We often find such a thing in teaching: Some students write the plus sign as a minus sign, reverse the divisor and dividend, and write the correct result wrong. Many teachers attribute these to "carelessness", but it is not entirely true. I think the key is that students have not yet formed a rigorous thinking quality. As a teacher, we should understand students' learning psychology, find out the bad qualities of students, even accurately predict possible problems when teaching specific content, and actively take measures to cultivate and correct them, thus forming a stable mentality. The cultivation of this quality runs through the whole teaching activities.
When teaching the content of "proportional distribution", I first ask a question before the new lesson: divide 12 trees into two groups, and how many trees will each group divide?
Careful observation and analysis will reveal that the answer to this question is not unique. For me, it is of unusual significance to show this question to students in class.
After I asked the question, the whole class answered in unison without thinking: "6 trees!" " ""Do you have any different opinions? " I asked. At the same time, eyes quickly passed from each classmate's face. Suddenly I found a student named Sun frowning and staring out of the window. According to my understanding of this student and my special intuition formed over the years, I keenly feel that he must have different ideas and may find a breakthrough in him. So I reminded everyone: "You should seriously consider it. Some students may have overturned your answer. "At this time, the students suddenly became alert and reconsidered my question. Then several students raised their hands and asked to speak, and the classmate surnamed Sun also raised his hand. I immediately asked him to talk about his thoughts and looked at him with encouraging eyes. He stood up and said, "teacher, six trees in each group may be wrong." "
"Why?" I quickly inserted a question mark to attract everyone's attention.
"Because the topic didn't say how to divide. If the scores are average, then each group can get 6 trees. If the score is not average, there are many ways to divide it. "
I immediately praised: "Good! He's quite right. We used to learn the average score, that is, equal division. Today, we are going to learn uneven scores. " Then, I immediately wrote "proportional distribution" on the blackboard.
The students seemed to be awakened in the gloom and suddenly cheered up. When you look at the topic I wrote, you all want to know how to divide the "proportional distribution" when you think of the uneven score proposed by Sun. In this way, I skillfully extended the single thinking activity to multiple thinking from my understanding of children's habits.
It's a stone that stirs up a thousand waves. This doubt made the students pay special attention and their mood was particularly high. Everyone is eager to try and start the new lesson with passion.
What exactly is proportional distribution? Let me give you an example: there are 12 trees, which are divided into two groups according to three equal parts for planting. One and two groups give one and two in turn. How many trees do each group give? Under my guidance, students understand the concept of "proportional distribution" and master the operation method. Finally, I have further doubts. What is the relationship between "proportional distribution" and "average score"? The students' thinking is active again. After discussion, everyone finally realized that both distribution methods are conditional. "Proportional distribution" comes from "average score", and "average score" is "proportional"
A special case of distribution.
In my mathematics teaching, I often encounter such problems: setting difficult problems, seeking truth from facts in exploration, cultivating the depth and breadth of students' thinking, and guiding students to think carefully and rigorously when analyzing and solving problems. (2) Study hard and cultivate students' spirit of exploration, which is the content of non-intellectual factors. I attach great importance to the cultivation of students' non-intelligence factors in teaching. I think intellectual factors and non-intellectual factors are the two wings of children's growth, and either one will affect the take-off and development. Nowadays, primary school students are all only children, and most parents only attach importance to intellectual development and ignore the cultivation of non-intellectual factors, which leads to the uncoordinated development of intellectual factors and non-intellectual factors in many children, especially the lack of diligent study and exploration spirit. This is a big problem in mathematics teaching.
I believe that studying hard and pursuing tirelessly is not only a strong perseverance, but also a sense of exploration, a tenacious and thorough learning perseverance.
When I was teaching the content of "Understanding Area", I learned what area is by letting students see, touch and think, and then drew three interesting questions from the many questions raised by students: (1) Which surfaces have you seen are flat? Which is the flattest? (2) Is the sea flat? Why?
(3) What has no edge? How to make it have edges?
Isn't it "profound" for sophomores to discuss these issues? Yes, it's deeper. But these questions are of interest to students and can be fully understood by the teacher's "point" and "dial". I just want to induce students to study actively through "depth", open up knowledge fields and cultivate students' excellent learning morality. The students had a heated discussion. "The concrete floor of our classroom is the flattest," said a student. "Uneven, because there is a place to store water when I sprinkle water." Immediately, a student retorted, "I said that the surface of the glass blackboard is the flattest."
"No, the flattest side can't be written!" A student's strong retort amused everyone. "So, the glass sold in the shop is the flattest." Another student put forward a new idea.
The classroom was quiet for a while, and no one asked questions for two seconds. Suddenly, a tall girl stood up and said, "The surface of the glass is not flat, because if you put two pieces of glass together, dust will also enter the middle." "It's so beautiful!" I praised. I asked my classmates to keep looking for the flattest face, and everyone was a little embarrassed. So I concluded: "in practical things, there is no absolutely flat surface, and flatness is compared with each other." The plane mentioned in the math textbook is just an imaginary plane in our minds. It can be seen that the faces of several geometric figures we have seen are not absolutely flat. "
Everyone began to answer the second question-is the sea flat? Why? This issue is also hotly debated. A student said, "The sea is flat, because that's how it is drawn on the map." Another student said, "The sea surface is not a plane, but a curved surface, because the sea on the globe is a curved surface." Who is right after all? I pointed out the direction of thinking for my classmates: "Then think again, what is the actual shape of the earth?" Everyone found the answer at once. Now is the time to solve the third problem.
"What has no edge?" When I mentioned the boss, many students rushed to answer: "ball", "dirt" and "egg"
"The surface of this ball has no edges." A student hit the nail on the head.
"Without the edge of the surface, how can the area be calculated? We must find ways to give it an advantage! " I deliberately said to the students with an embarrassed face. A student said, "If we cut it in half, won't there be edges?" I shook my head. "This method will destroy good things. Besides, some things can't be cut! This method is not very good. "
Another student stood up and said, "Teacher, I have a good idea-draw a seal on it and the problem will be solved?" "Well, this idea can. We only need to mark it with lines to find the edge of the surface. " I affirmed it in time. Then I took out another egg and drew a closed curve on it with chalk. At this time, a classmate immediately put forward a difficult problem: "Teacher Zhao, how to calculate such an area?" That's how my students like to get to the bottom of it. In my opinion, students can constantly ask new questions and use their brains to solve problems in their studies, which is a manifestation of the spirit of exploration. Students ask questions one day earlier, which means they have a sense of exploration one day earlier; Never ask, you will never have the spirit of exploration. Ask the teacher one day earlier and you will succeed one day earlier. I wish I could be asked by my classmates. (3) Clear the direction and cultivate students' awareness of adapting to the needs of social development.
When I was teaching percentage application problems, I did some exercises about interest rate and exchange for students, and many people were puzzled. In recent years, the overall reform experiment and mathematics teaching I presided over, based on the needs of future social development and economic construction, closely combined the needs of people's own development with the needs of social development, taking improving the quality of talents as the breakthrough and foothold. My idea is: 2 1 century is an era of rapid economic development, and today's primary school students are talents for economic construction in 2 1 century. People's quality is directly related to the degree of economic development. No matter which department or industry, it is inseparable from mathematics, especially the mathematical knowledge closely related to production and life. Therefore, we must cultivate primary school students' awareness and ability to cope with future challenges from an early age, adapt to the needs of social and economic development, and better serve the society. In teaching, teachers should consciously combine the contents of teaching materials to help students gradually clarify their learning direction and understand their position and role in future economic construction.
I actively advocate students to learn microcomputer. The economy is more and more developed, and high-tech talents are more and more needed. Let students learn microcomputer from childhood, not only to master a basic skill needed by society, but also to make students understand that 2 1 century is a high-tech era, so they should study hard from childhood to meet the needs of society and make better contributions to society in the future. In other words, students should be allowed to link their current study with social and economic development and set lofty learning goals. (d) Cultivate students to see the world from the viewpoint of dialectical materialism.
In my opinion, primary school students should know not only why, but also why. In other words, we should not only know algorithms, but also know arithmetic. The most important thing is arithmetic. As a teacher, we should strive to improve students' mathematical literacy, master the basic mathematical thinking mode and thinking, and then understand that mathematics is a science that studies the relationship between number and quantity, time and space, and form and form. The contents in mathematics are inextricably linked with each other and full of dialectical materialism. The establishment of this view depends on the excavation and inspiration of teaching materials.
When I was teaching "1", while reviewing my decades of practical experience, I noticed the profound mathematical ideas contained in the teaching content and made them concrete.
After class, I wrote the word "1" clearly on the blackboard.
"Students, who knows'1'?" The children swished up their little hands. "okay. Who can tell me what'1'means? "
The children rolled their eyes, some raised their hands, and some slowly withdrew. I unfolded the wall chart again: "Who can tell me what is drawn on the picture?" The students all replied, "A child is sitting on a stool and writing on the table. There is a book and a pencil box on the desk. " -This is the first step for children to know "1" by looking at pictures. Then I held up a small stick: "What does this stick look like?" "For example,'1'."
"Is it straight or curved?"
"It's straight, and there is no bend at all."
"good! Let's practice and see who writes straight and fast. " The students are writing carefully.
This is the second step for students to write "1" with the help of physical images.
Then, I asked the students to list what "1" stands for. The students scrambled to say: a lecture table, a blackboard, a tree, a flower, a plane, a moon, and the imaginary wings of a galaxy student unfolded. While the students were talking excitedly, I asked another question: "Can you finish everything represented by'1'?"
The student replied, "I can't finish talking." I went on to say, "That's right. What'1'represents is endless and infinite. " In my lectures, I skillfully abstract the concept of the number "1" from various concrete things, and in turn give the number "1" practical meaning through things, thus combining numbers with quantities and combining finiteness with infinity. In teaching, I have infiltrated the dialectics and extreme thought of mutual transformation between the whole and the part, making the teaching of "1" richer and more attractive, and achieving the purpose and effect of killing many birds with one stone.
Reflections on Cultivating Middle School Students' Mathematical Literacy
The word "mathematical literacy" first appeared in the junior high school mathematics syllabus in China, which marked the inevitable trend of the transformation of China's mathematics education goal from exam-oriented education to quality education. Improving students' mathematical literacy in mathematics teaching is an important task faced by mathematics teachers in compulsory education stage, and it is also an urgent problem for mathematics workers to explore and solve. First, the connotation and performance of mathematical literacy
Mathematical literacy refers to the literacy of mathematical knowledge, skills, abilities, concepts and qualities acquired by people through mathematical education and their own practice and cognitive activities. It mainly includes: basic knowledge, ability and quality of mathematics.
The expression of mathematical literacy in daily life;
1, learning good personality qualities formed in mathematics, such as realistic spirit, serious attitude, tenacious perseverance, agile thinking, etc.
2, can consciously use mathematical knowledge and mathematical thinking methods to observe, analyze and deal with the surrounding life and production problems; 3. The language expression is accurate, concise and logical, and has good mathematical language communication skills. Second, pay attention to the cultivation of mathematical knowledge literacy and improve students' ability to solve practical problems by using mathematics.
Solving practical problems with mathematics is a weak link in middle school mathematics teaching at present, so improving students' ability to solve problems with mathematics is the key to improve mathematics literacy. In actual teaching, we can start from the following aspects:
1, to actively show the occurrence and formation process of mathematical knowledge. Such as the formation of concepts, the derivation of theorems and formulas or the process of discovering, thinking and analyzing problems, so that students can understand the historical and realistic background of knowledge, and then understand knowledge more widely, from multiple angles and in many aspects;
2. In order to avoid talking about knowledge, we should put knowledge into the network of knowledge structure for teaching. We should not only understand the provisions and significance of knowledge content itself, but also connect it with other knowledge content at any time, so that the knowledge we have learned can be connected up and down, forming a dynamic network of knowledge and thinking.
3. Pay attention to the teaching of the evolution process of mathematical concepts. Mathematical concept comes from practice, which is the result of high abstraction of practical problems, and can reflect the essence of science more accurately, which has universal significance. But it is this generalization and abstraction that makes mathematics
There is an insurmountable gap between learning and mathematics application, which makes students learn a lot of knowledge but don't know how to use it. This requires that the principle from practice to practice can be embodied in the teaching of mathematical concepts, so that students can understand the occurrence and development process of mathematical concepts and the prototype of concepts in reality, so that they can trace back to the source and remain unchanged.
4. Develop model teaching and mathematical modeling ability. When using mathematical knowledge to solve practical problems, we should first establish the mathematical model of practical problems, then find out the results with mathematical theories and methods, then go back to practical problems to solve problems, and finally in turn promote the establishment and development of new mathematical theories. As for the cultivation of students' modeling ability, it is a gradual process. We should start with simple problems, teachers and students should jointly create models, guide students to master the methods of describing and constructing models in mathematical forms, and cultivate students' awareness of active participation and courage to create. With the increase of ability and experience, students can analyze and discuss each model in the form of internship or activity group, analyze the effectiveness of each model, put forward suggestions for revision, cultivate students' confidence in continuous creation, and correct their one-sided understanding of mathematical knowledge. Third, attach importance to the cultivation of mathematical ability and determine the core position of the cultivation of mathematical thinking ability.
Cultivating students' mathematical ability and forming good thinking quality are the premise and guarantee to improve students' mathematical literacy. Mathematical ability literacy can be manifested as: computing ability, logical thinking ability, spatial imagination ability, and the ability to analyze and solve practical problems. Among them, the cultivation of students' mathematical thinking ability is the core of the cultivation of mathematical ability literacy. Therefore, it is necessary to clarify the core leading position of cultivating mathematical thinking ability and strive to improve students' ability and literacy in an all-round way. To this end, we should pay attention to the following aspects:
1, create thinking situations, pay attention to thinking induction and cultivate exploratory thinking. According to the teaching idea of "guiding but not introducing", students have some time and space to imagine freely in class and explore and solve problems independently in new situations. Through discussion, question and answer and procedural homework, let students participate in defining and giving conclusions, find ideas and methods to solve problems, sum up the rules and steps to solve problems, and let students participate in more teaching exploration activities.
2, overcome the mindset, pay attention to multi-directional thinking, and cultivate the flexibility of thinking. In the process of thinking and solving problems, we should sum up some conventional solutions to problems, so that there are "laws" to follow and "roads" to be feasible when encountering problems. But more importantly, we should strive to overcome some wrong thinking patterns of students, pay attention to multi-angle thinking, and cultivate the flexibility and comprehensiveness of students' thinking.
3. Grasp the essence of the problem, tap the implied conditions and cultivate the profundity of thinking. Some students often can't grasp when solving problems.
The essence of the problem, we can't dig out some hidden conditions in the problem, and our thinking is at a shallow level. When guiding students to think, teachers should pay attention to the analysis of the essence of the problem, dig out hidden conditions through layer-by-layer analysis, expose the essence of the problem and cultivate the profundity of thinking.
4. Strengthen comparison and association, guide multiple solutions to one question, and cultivate the broadness of thinking. In teaching, teachers should combine the contents of teaching materials to guide students to associate new knowledge with old knowledge, this kind with other kinds, vertical and horizontal, and clarify the relationship between knowledge, so as to broaden students' knowledge and broaden their thinking.
Fourth, pay attention to the cultivation of mathematics quality and cultivate students' pragmatic personality.
Mathematics literacy is the spiritual temperament and personality characteristics that students should have in learning knowledge and engaging in research or work in the future. It embodies the strength of personality and is the crystallization of mathematics and quality. It is clearly pointed out in the mathematics teaching syllabus that "it has the correct learning purpose, strong learning interest, tenacious learning perseverance, scientific attitude of seeking truth from facts, independent thinking, innovative spirit and good study habits." It is the goal and requirement of cultivating students' mathematical quality. In a sense, the cultivation of students' mathematical literacy has far-reaching significance and greater value than the teaching of mathematical knowledge.
In mathematics teaching, combined with the characteristics of mathematics itself, we should highlight or strengthen the following aspects:
1, cultivate students' rigorous and realistic personality. Mathematics is a science that makes people's creative thinking rigorous and its theoretical system rigorous. Learning mathematics must be meticulous and down-to-earth. Even if the proposition is created by some imprecise methods such as imagination, intuition and analogy, it must be proved by strict logic before its authenticity can be confirmed. Therefore, it is also very important to cultivate students' rigorous and realistic spiritual quality through mathematics teaching, which can be maintained and extended to other fields and play an effective role;
2. Cultivate students' persistent pursuit and innovative spirit. Mathematics has gradually developed into a "mathematical family" with many branches from the generation and evolution of numbers. Teachers can use the development history of mathematics and the establishment process of mathematical concepts, theorems and formulas in teaching materials to cultivate students' spiritual qualities of being brave in pioneering, persistent in pursuit and innovation.
3. Cultivate students' abstract generalization ability and master the necessary personality qualities. Mathematics is a highly abstract science. The original concepts such as natural numbers and simple geometric figures are abstracted from the real world, and even some problems that seem irrelevant at first are exactly the same in mathematical essence, such as the relationship between area and mass, speed and tangent slope. place
Therefore, in mathematics teaching, we should infiltrate this spiritual quality into students and cultivate their ability to grasp the abstract generalization of the essential characteristics of problems through superficial phenomena when dealing with problems in mathematics or other cities.
4. Cultivate students' quality of optimizing problem-solving methods. In today's society, all walks of life are pursuing benefits. Such as investment, stocks, securities, profits, etc. Are closely related to people's daily life, and these "best, minimum, maximum and minimum" problems are actually optimization problems. In mathematics, the idea of optimization runs through the whole process of mathematical development. It can be seen that cultivating students' awareness and ability to optimize problems is not only the need of mathematics teaching, but also the requirement of contemporary social development for talent training planning. Its purpose is to make students consciously apply the optimized consciousness and quality to practical problems.
In a word, cultivating middle school students' mathematics literacy is a systematic project, which requires not only the efforts of our mathematics education circles, but also the care and support of our whole society. For middle school mathematics teachers, only by continuous practice and exploration can they improve their teaching level and adapt to the needs of this situation, so as to cultivate students' mathematical literacy more effectively in mathematics teaching.