Some bad phenomena in "wide angle" mathematics teaching.
In recent years, we often see "regulars" of various teaching and research activities, wide-angle and open courses, and "darlings" of high-quality courses! Processing, because the general teaching content can be regarded as an independent, do not need to consider the progress, but also follow the trend, feel more fashionable, and best reflect the curriculum concept. However, I found many shortcomings and improper behaviors, and the teacher was also confused about the wide angle of mathematics in teaching.
& lt/( 1) misconduct in teaching objectives. The understanding of teaching materials is not in place, and the goals are biased. Some teachers put the wide angle of mathematics into the practice and comprehensive application of this field as a "practical class". Mathematical thinking
(2) not sure. Mastering the "degree" of mathematical thinking is an inaccurate phenomenon and a high-grade requirement. There is a teacher's second album "Simple Arrangement and Combination" in the teaching, which embodies the innovative and unique teaching examples and exercises in Grade Three. The second level and the third level, in the case of "simple arrangement and combination", have the same content, but different teaching requirements. Although they can be adjusted appropriately, they can't help each other.
A teacher is teaching "Problems", asking students to abstract "Multiplication Principle" and "addition principle" and compare their combinations in detail, and arrange the concepts from the last requirement. Because of the Olympic math class.
It seems too low, and the effect of solving a problem, even after a class, only stays at the level of blindly pursuing intuitive experimental operation, ignoring the rise. From the intuitive abstract process, this also ignores the mathematical thinking mode emotionally and aims at low. For example, for teaching problems, some teachers make content (such as two coats and two games) and ask students to draw a picture, which is a lesson to be answered. From the beginning to the end of the class, the strategy of solving problems stays in an intuitive state. It is not enough to think intuitively and abstractly in mathematics, but to lack the infiltration of mathematical thinking methods.
(3) The activity process is a mere formality. Many classroom activities, rather than the beautiful courseware process, make the classroom a dazzling "flying courseware". Whether the students' mathematical thinking activities really support the experience in the activity process is a mere formality and the difficulty is effective.
(4) The handling of materials is too simple. In the experimental textbooks of the new curriculum, many teachers will encounter such confusion: how to deal with the design of simple textbooks? This simple material, many teachers' business processes often need to deal with narrow mechanized and simplified textbooks, such as the overlapping design of teachers' problems:
The department made a list of textbooks and asked, "What did you observe?"
Student: I observed the boys and girls on duty taking part in math interest group activities.
Department: Boys and how many people? How many girls are there (student: 8 boys and 7 girls)
Co: the total number, boys and girls? (Born in: boys and girls, fifteen in total).
Teacher: Are boys and girls really 15 in the observation table?
Healthy boys and girls 3 overlap, three overlapping ones are repeatedly forgotten, and there are always some things that should not be 15.
Teacher: Ask the type of people's column.
Health column: 8 +7-3 = 12 (person)
":Why is it always not equal to 15, but equal to 12? What if two round figures of boys and girls represent students? Easy hands.
Student: Students open their books and fill in the names of male and female students in two groups.
However, how to use the two obvious rings in the number of these two interest groups is still unclear to most students.
The teacher felt very helpless and pointed it out himself: ○○○○○○○○○○○○○○○○○○○○○○○○○○○96
As we know, due to the limitation of space, mathematics textbooks are often refined, focused on introduction and rich in mathematics content. Teachers should make every effort to play a leading role in the development of teaching materials and teaching organizers, and understand students' psychological background in combination with laws. By post-processing the teaching materials, the content of the corresponding teaching materials will become simple and static, and the design will become rich and vivid. In the process of teaching content, students can experience the occurrence and development of mathematical knowledge and gain rich experience in mathematical activities, thus promoting positive development. However, under the above circumstances, teachers collect simple layout patterns, textbooks and teaching materials for simple teaching.
In this case, students' learning activities are set up to give them the opportunity to explore and practice in person, but they can't see and hear mathematics by themselves. This is based on mathematics, experience and indirect mathematics, while ignoring the activities of doing math problems, guessing math and discovering math, and accumulating rich direct experience, which leads to students' lack of depth and transparency in mathematics and difficulty in establishing real mathematics. These simple teaching designs make students understand the significance of simple column calculation, and it is difficult to deeply understand and flexibly use them, which limits the cultivation and development of students' mathematical literacy.
(5) excessive pursuit of life prototype. The close relationship between mathematics and life is a new concept advocated by the new curriculum. However, in mathematics teaching, the excessive pursuit of daily life leads to the phenomenon that mathematics interest is diluted and the cart before the horse is put.
For example, a teacher created a breakthrough in the case of "digital coding class, postman and courier", which led to a long video about postal code and introduced a letter published by the post office. The process of making ID cards introduced in the second half is very easy for students to listen to, and there is no necessary mathematical thinking, just like a common sense class!
Another example is that a teacher teaches "Looking for Rules" (watching) class, and students look for painted rules, draw a picture, and paste a theme map set according to law. Secondly, according to the law based on the experience of afterplay music rhythm, there is a lively rhythm ocean in the classroom. In fact, the class in the first half of this year is the "art class" of the music class in the second half.
So many teachers often give lectures and sigh: "This lesson is too ugly, they may not be confused!" "
Characteristics of wide-angle arrangement of mathematics in PEP.
"Mathematical Wide Angle" is the specific content of the textbook published by People's Education Press, and other versions of the textbook "Mathematical Wide Angle". Although the wide angle of mathematics is involved in the formation of other versions of primary school textbooks from grade one to grade six, like the textbook of People's Education Press, it is a system and a complete system, but other versions do not, which has become an aesthetic feature.
The significance of "mathematical wide angle" arrangement.
The textbook "Wide Angle of Mathematics" published by People's Education Press is systematic, and the thinking mode of mathematics is permeated systematically. The important ideas of mathematical methods can be tried to solve the problems in life in the simplest form and in an interesting way, which is easy for students to accept and understand. Through observation, operation, experiment, guessing, reasoning and communication activities, the role of mathematical thinking mode with wonderful initial feeling and mathematical thinking training make students gradually form an orderly and rigorous thinking consciousness, and at the same time make them gradually form an interest and desire to explore mathematical problems and discover and experience the feeling of mathematical beauty.
The Content Structure Arrangement of "Mathematics Wide Angle"
In order to facilitate the learning of wide-angle mathematics, the author arranges the teaching contents of wide-angle mathematics in the whole PEP textbook into the following table:
The content of mathematical thinking method of copy number
Book two, finding the law, reasoning in grade one, series
The second album of the problem
Logical reasoning permutation and combination
reason
The second volume discovers a series of methods in the second year, reasoning.
And sorting out the third grade books
The problem of overlapping the second volume of grade three
The same number replaces the set.
Equivalent substitution
Fourth grade books, pancakes, tea,
Waiting for Tian Ji horse racing optimization
The future is in the fourth grade. Mathematical modeling of tree planting problem
Digital coding of fifth grade books
Find out the defective optimization of the second volume of the fifth grade.
BR/>； Sixth grade books chicken and rabbit cage hypothesis
Sixth grade, book 2, pigeon coop principle, pigeon coop principle
As can be seen from the table, it fully embodies the mathematics curriculum standard of "wide angle of mathematics": important mathematical concepts and mathematical thinking should gradually spiral up. "The idea.
The thinking mode of permutation and combination mathematics, such as the first and second experimental textbooks, arranges students to get in touch with a little permutation and combination knowledge for the first time, and finds the simplest thing through observation, speculation and experiment, and through the permutation and combination of the number of students. The arrangement and combination of two-digit words, such as a digital card with three children and two two-way handshakes. The textbook in the book is in the third grade of primary school. Continue to learn the arrangement and combination of content. But the goal is to let students continue to find out the arrangement and combination of numbers through observation, speculation and experimental activities on the basis of existing knowledge and experience. Equipped with some different math problems, there are two more tops than 3, and the textbooks of Volume 2 and Grade 3 are more systematically and comprehensively arranged and combined. The same arrangement also appears in the "law" of content. Secondly, the wide angle of mathematics in the whole 12 textbook reflects the progress of students' thinking level from low to high, step by step, from concrete to abstract, and gradually penetrates these mathematical methods to think, in order to conform to the law of mathematical cognition.
3. "Wide-angle mathematics learning materials.
The design of "Mathematics Wide Angle" learning materials embodies the concept of mathematics curriculum standards, and strives to solve the problems in life, easily accepted by students and familiar with the form, and feel the thinking mode, materials and space of mathematics.
For example, the shirts that everyone wears every day, the arrangement and combination of bottoms; Thinking permeates ordinary schools, participates in interest groups, collects statistical data of guests' home-brewed tea, permeates optimization ideas, permeates mathematical modeling and coding ideas, and adopts tree planting and postal coding. Yes, in the background, the choice of materials for these examples or exercises, whether familiar living materials or materials for solving life problems, not only stimulates students' interest in exploring knowledge, but also feels the magical mathematical thinking mode, which is closely related to real life.
4. Different from classmates, students have different requirements for "mathematical wide angle".
"Mathematics Wide Angle" has different requirements in each learning period. To meet the needs of work practice, considering the relatively scattered reserves, the first paragraph has enough rich life experience and students' mathematical knowledge at this stage. It is necessary to guide students to explore through the operation method of activities, so that they can experience the hidden mathematical knowledge in real life and their preliminary training in observation, operation, induction and reasoning. Abstract modeling in the second academic year needs to take into account that after the first stage of study, students have certain mathematical knowledge and experience in solving some simple problems, and also have certain logical thinking ability, so they continue to emphasize practice and experience and strengthen the requirements of "abstract modeling". Not only let students understand and master the concepts and models of mathematics, but also strive to improve students' ability to solve practical problems in mathematics, and gradually form orderly and rigorous abstract thinking consciousness and habits.
The characteristics of mathematical wide-angle scheduling give us a lesson.
(1) Close contact with life. It is not difficult to find that the life stories from students are familiar. This layout embodies the idea that students' mathematics learning content should be realistic, meaningful and challenging, which makes mathematics closer to children's real life, helps to stimulate their curiosity and thirst for knowledge, helps them to build knowledge and deepen their understanding, and also enlightens us that effective mathematics learning activities should be based on students' existing life experience, and teachers' teaching should be based on students' life experience.
(2) Let students experience the process of exploring mathematical knowledge. Focusing on the solution of this problem, let students experience the mathematical process of exploration, and let students gain the infiltration of mathematical thinking methods and the cultivation of mathematical thinking ability. This is a major functional layout of "Mathematics Wide Angle", an experimental textbook for primary school mathematics published by People's Education Press.
We know that mathematical thinking mode is based on the fact that mathematical knowledge is higher than implicit mathematical knowledge, mathematical knowledge and students' thinking about ideas, especially concrete images. Therefore, if we do not pay attention to teaching and guide students to experience the whole process of mathematical inquiry, it may lead to the phenomenon that most of the work will not be completed by students. Therefore, in teaching, we should pay attention to the teaching platform of students' cognitive starting point and foothold, establish personal experience for students, solve problems by observing and exploring mathematical knowledge, expand business, guess, experiment, reason, exchange mathematical activities, feel mathematical thinking methods, and improve students' mathematical thinking ability and problem-solving ability.
(3) The image role of students in learning mathematics and strengthening intuitive thinking.
"Mathematics Wide Angle" is a very intuitive way, which can help students understand the situation, think about problems and emotional thinking, and improve learning efficiency, such as the arrangement of the third textbook, putting digital cards and shaking hands background, reflecting simple arrangement and combination; The fifth volume of teaching material cohesion helps to deal with the principle of underwear order. The sixth volume of teaching material collective circle 2 intuitively expresses the asset-liability relationship of extracurricular groups and helps students change their thinking when they encounter the same amount. Volume 18 shows the general law of tree planting. 10 books draw abstractions to help students analyze how to find defects. BR/>；
Characteristics of children's thinking: primary school students who mainly think in concrete images and gradually transition to abstract logical thinking. Intuitive ways to support your own ideas or direct perceptual experience, pictures link to the required materials. Visual thinking, which is often neglected, makes students feel that mathematics is boring, boring, difficult to understand, enthusiastic and inefficient. Attach importance to students' thinking in images and help them learn under the premise of abstract mathematical knowledge. Explain that we should often use intuitive language teaching methods such as objects, teaching AIDS, charts, life experiences and humor to help students learn mathematics.
/& gt； 3 "mathematical wide-angle positioning.
The teaching goal of "mainly in the wide angle of mathematics" is to gradually learn the ideas of mathematics.
"Mathematics Curriculum Standards" clearly states: "According to students' past experience, characteristics, laws and psychological development, as well as some important mathematical concepts and ideas they have learned, we should adopt gradual infiltration and deepen the spiral writing of teaching materials. On the basis of arranging the wide angle of mathematics, the significance of the experimental teaching materials of People's Education Press mainly allows students to solve some important mathematical ideas and actively try to find strategies to solve problems through some simple examples. In the process of looking at problems from a mathematical point of view, guessing, experiments and reasoning in the process of mathematical exploration activities are infiltrated, thus gradually improving students' experience in solving practical problems and the experience and ability of some important mathematical ideas.
Therefore, infiltrating important mathematical ideas is the wide-angle goal of "Mathematics" teaching. The ideal infiltration is "moistening things silently".
2. The relationship between width and traditional application problems in mathematics teaching.
"The wide angle of mathematics is different from the applied problems in traditional teaching, such as the wide angle of mathematics in some traditional applied problems, such as" chicken and rabbit in the same cage "and" planting trees ". The problems of traditional applications focus on practice, but the only answer to the main problem is often the lack of openness. Traditional application problems also attach great importance to students solving simple problems. Ability, but mainly as a means to help students understand mathematics knowledge, present the answers to the questions in this book. More attention should be paid to cultivating students' ability to solve problems. To a great extent, students' problem-solving process is the process of becoming the model of "understanding the relationship between numbers-searching memory structure-using the corresponding mathematical wide angle". The process of emphasizing experience and abstraction has become more open and challenging. In the process of solving problems, students should not rely on simple imitation and memory, but should actively think and constantly process and process information. They improve their mathematical thinking level through observation, operation, conjecture, experiment and abstract mathematical activities, and meet some important mathematical ideas.
3, mathematical wide-angle Austrian mathematical relationship.
Although: wide-angle mathematics is the initial olympiad. "pigeon cage principle", "finding defects", "finding rules" and so on. Mathematical wide angle and mathematical olympiad.
In essence, Olympiad Education, an elite education student with superior intelligence, is faced with the right of wide-angle mathematics for all students, public education and the difficulty of Olympic Mathematics. The focus of Olympic Mathematical Thinking Training is mainly to instill teaching methods. The wide-angle focal length of problem routine mathematics teaching permeates mathematical thinking methods, and heuristic teaching is adopted to guide students to learn actively, develop their intelligence and improve their mathematical literacy. Mathematical Olympics allows students to learn various problems and determine the types of methods to solve them. Students can't do, can't teach, can't practice, and teachers don't teach more questions. Mathematics is wide-angle, so that students can learn to draw inferences from others, master it, stimulate their interest in learning, broaden their perspectives, experience, experience and feelings, and moisten things silently.
4. Mathematical wide angle pays more attention to mathematical thinking.
The standard knowledge and skills, mathematical thinking, solution, emotion and attitude of full-time compulsory education mathematics curriculum are the overall goals of compulsory education mathematics curriculum, and our goals are four closely related and inseparable organic whole.
Mathematical thinking is to face all kinds of problems, especially to find mathematical problems and problems-related phenomena from a mathematical point of view, and to solve problems with mathematical knowledge and methods, that is, to let students observe the world with their eyes. "From the perspective of applying mathematics, we can think about the world in our minds with mathematical thinking." Mathematical thinking, is there any real mathematics learning? Mathematical thinking should be the main mathematical thinking. Of course, it is not only the training of thinking, but also the consciousness and ability to discover and apply mathematics.
The teaching content of mathematics, teaching mathematics wide angle, should achieve four goals: knowledge, skills, mathematical thinking, problem solving, emotion and attitude. Of course, the weights of the four goals will not be the same. Obviously, the idea of high-content mathematical wide-angle content has unique conditions for realizing the goal of mathematical thinking. Therefore, in the wide-angle teaching of mathematics, we should pay more attention to the realization of the teaching goal of mathematical thinking and how to achieve it. In particular, there should be clear requirements and accurate judgments on the level of mathematical thinking ability, which should not be too low or too high.
Fourthly, improve the effectiveness of "wide angle" mathematics teaching strategy.
1, accurately grasp the teaching objectives.
To grasp the teaching goal of wide-angle vision, we must first position mathematics teaching. Through mathematical activities, let students experience the mathematical way of thinking and learn how to try to solve problems, experience and solve problems with the mathematical way of thinking.
Mathematics wide angle is the way of thinking that all students infiltrate mathematics. Its purpose is to make each student's mathematical thinking training gradually form their interest and desire to explore mathematical problems and discover the consciousness of appreciating the beauty of mathematics. Therefore, in order to prevent the "excellent" wide-angle Olympic Mathematics training class in educational mathematics, more creative practical activities are needed for all students to observe, study and think, and pay attention to activity emotion.
Logistics thought and game theory are arranged with more systematic and abstract mathematical thinking. The textbook only allows students to experience logistics ideas and countermeasures to solve practical problems through simple examples, cultivate their application awareness and improve their ability to solve practical problems. Students solve problems from various schemes and find the best one. The initial experience can optimize the thinking of application, and students are not required to look at the best solution to the problem from the best angle. Teachers should not use mathematical language to describe logistics, optimization and countermeasures in teaching.
2. Reasonably develop and integrate the teaching content.
As a teaching carrier, mathematics defines the space of educational content and theme from a wider angle, and the way of thinking of mathematics is its soul and core. As the users of curriculum resources, teachers should deal with the problems of careful analysis of mathematics textbooks, formulation of teaching objectives, clarification of clues, students' participation in mathematics activities and effective organization of teaching. Textbooks need time to adjust and trade the contents for sale. With the development of resource materials, teachers should read the combined teaching content and curriculum objectives, consciously choose and integrate curriculum resources, and the curriculum content should be more closely coordinated with students' mathematical activities to better reflect the infiltration and cultivation of ideas.
The story of Tian Ji's horse racing in Wide Angle of Mathematics introduces the application of game theory, and both sides of the game theory research can beat it by whatever measures they take. Students may have known the story of horse racing in Tian Ji, but they didn't understand it from a mathematical point of view. We hope that students can experience the application of game theory in practice.
The teacher made a teaching attempt: at the beginning of the class, the teacher told the students that the coach of the Hunan women's badminton team skillfully defeated the Guangdong women's team and won the championship. The Guangdong women's team is very strong, but unfortunately it is foolhardy and leads to defeat.
What about the Hunan team's countermeasures? Have you heard the story of horse racing in Tian Ji? Let's review the process of horse racing in Tian Ji. When describing this story, the teacher asked a question: "Why are different horses still horses, and what is the result of the race?" By guiding you to think, you can draw a conclusion: "Choose different tactics and you will often get different results in the game."
In the teaching process, through the preliminary experience of game theory with specific examples in badminton team competition, students are guided to solve practical problems, stimulate their desire for learning, and lay a good foundation based on learning.
For another example, a teacher teaches third-grade mathematics wide-angle volume two because there are only seven. Examples and exercises in supplementary materials for teachers and students' cognitive level, so that students can experience the materials of mathematical thinking, such as: the weight of a puppy is equal, the weight of two kittens and four kittens is equal to the weight of two rabbits, and the weight of a puppy is equal to the weight of several rabbits? Another example: In the first group, Wang You 12 people did two questions of the first question, and 10 people did at least one question. How many people have done both questions? The subjects that these students are familiar with are easy for students to master, but they are also easy to think, so as to experience the collection of mathematical thinking.
3. Feel and think through positive experience.
The way of thinking in mathematics is a hidden form, which is more abstract mathematical knowledge. .