Chinese is a language subject, but at different stages, we can accurately quantify the learning requirements with numbers. For example, in the first study period, the total amount of extracurricular reading materials in grades 1 ~ 2 is 50,000 words, and in the second study period, it is 400,000 words in grades 3 ~ 4. There are also specific requirements for reciting ancient poems in each learning period.
But the mathematics curriculum standard is not like this. Mathematics, as a subject mainly dealing with numbers, has almost no quantitative requirements, and is generally a qualitative description. There is a special appendix at the end of the mathematics course, which explains in detail the definitions of "behavior verbs" and "process verbs", that is, understanding, mastering, using, experiencing, experiencing and exploring, and the differences between them.
The reason is that language learning pays attention to accumulation. As long as you reach the number, the problem will basically not be too big. For example, how many extracurricular books you have read and how many ancient poems you can recite can be quantified. Of course, it is also important to master the necessary reading methods.
What about math? You won't be asked to read the book many times and do many problems. It's about repeating what you know, what concepts you understand, what theorems you have mastered and what problems you have solved. It can be seen that mathematics still focuses on understanding. All you have to do is understand. You can get the problem right, which means you have mastered it. Being able to use knowledge flexibly and comprehensively shows that you can apply what you have learned.
Secondly, mathematics is the basis of scientific research. The science we usually talk about is mathematics, as well as physics, chemistry and biology. Learning mathematics well is also the basic ability of these subjects. Moreover, mathematics and these subjects are similar in learning methods.
Scientific learning is more about reasoning from the known, exploring the unknown, and trying to solve unknown problems according to known theorems, axioms and formulas. The topic of science is ever-changing. Just change a condition or a few numbers, and it will be a brand-new topic. Therefore, brushing the questions can't be finished, and blindly brushing the questions can't directly and effectively improve the grades. The real purpose of brushing questions is to test the mastery of basic knowledge.
If you can't do the problem, please go back to the textbook and make clear the relevant knowledge points. Especially its basic concept and theorem derivation process. Only by mastering the basic knowledge can we persistently solve the ever-changing problems.
Therefore, parents can guide their children to be familiar with textbooks, consolidate basic knowledge and attach importance to the understanding of the derivation process.
Third, mathematics comes from life, but it is higher than life. In mathematics curriculum standards, there are always more than 60 "situations" and more than 60 "lives", which shows that mathematics knowledge comes from life first. Of course, mathematics is higher than life, because mathematics is actually abstract from life, and the word "abstract" has appeared more than 20 times.
Abstract ability, with the development of students' thinking and understanding ability, the requirements will be higher and higher. At the beginning 1 ~ 3 grades, many examples close to life are introduced to guide students to understand the connotation of mathematics step by step. In grades 4 ~ 6, a large number of application problems are generally related to life. In grades 7-9, junior high school, the abstraction and thinking ability at this stage is actually a big step forward.
Therefore, in primary school, parents can still take their children to experience life, introduce mathematics, learn mathematics, and use mathematics in life. Plane geometry and solid geometry can also be done by hand, which can understand mathematics more concretely, vividly and vividly.
Fourth, it is best not to study in advance, and parents' counseling should be moderate. Now many parents call it "Chicken Baby", mainly because they study in advance. As I said just now, science learning is based on understanding, so children's understanding ability needs to be considered. Generally speaking, the arrangement of teaching materials takes this factor into account, so it is best not to study in advance, especially not to study significantly in advance.
Instead of wasting time on advanced learning, it is better to save time and let children do more extended learning on the basis of existing learning content. For example, in grade one, you mainly learn addition and subtraction, and in grade two, you learn multiplication in grade one. Why in the second grade? Some people say that they will continue to study in the third grade.
The problem is that the same knowledge points will definitely be taught by schools in the future, and school teaching is a relatively systematic process. If you teach yourself, sometimes it is not systematic. Children think they can learn, but they may not be able to study patiently, which leads to a weak grasp of basic knowledge.
And it's not to scare you. If you look back at the curriculum standards, you will know that more than 95% of parents in junior high school have forgotten math, and I belong to that 95%. I got 126 (full mark 130) in the senior high school entrance examination and 138 (wrong question) in the college entrance examination, but I think I can't remember many concepts of junior high school mathematics now.
Therefore, one is that the later you get, you really can't teach unless you learn it all over again.
On the other hand, children may not learn a lot of knowledge that we take for granted at school. Sometimes when we explain some topics to our children, we often use the later knowledge, which your children may not understand. One is that you take it for granted, and the other is that children are less knowledgeable and easily frustrated.
In science study, parents had better retreat behind the scenes as soon as possible and let their children learn independently. The process of children repeatedly changing their thinking and solving a difficult problem is a process of thinking, understanding and application, which is irreplaceable by others. Ask others for advice whenever you encounter problems that you can't do, which is not conducive to the improvement of children's thinking ability.
Fifth, protect children's interest in learning and attach importance to the foundation. Another main way of "chicken baby" is to do difficult problems, partial problems and strange problems, while mathematics is mainly to learn Olympic mathematics.
In the mathematics curriculum standard, the author noticed that mathematics learning is difficult for some children, so in the preface, he particularly emphasized that "everyone can get a good mathematics education, and different people can get different development in mathematics".
In the proposal of compiling teaching materials, it is also said that "the compilation of teaching materials should be oriented to all students and take into account the differences in students' development." On the premise of ensuring the basic requirements, we should show some flexibility to meet the different needs of students, so that different people can have different development in mathematics, and it is also convenient for teachers to play their own mathematical creativity. "
Learning mathematics can make people more organized and improve their logical thinking ability. But on the other hand, it is really not very useful for students who study humanities and social sciences in the future.
Therefore, not only compulsory education, but also the mathematics test questions in the senior high school entrance examination and even the college entrance examination generally meet the proportion of easy, medium and difficult, which is about 7:2: 1.
Emphasize the basics and learn the basics well. If you can do the basic questions without losing points, there will be no big problem if you score more than 150 on the paper 120. Don't force your child to learn olympiad, unless he really likes olympiad and has a certain talent, he can try to learn more mathematics.
Sixth, mathematics is a very easy subject to divide.
In the past, our traditional subjects were Chinese, mathematics and English. Chinese and English are both language subjects, so it is difficult to widen the differences. Few people learn well, and there are not many high-level people. Most of them get good grades in the range of 1 10 ~ 120 (total score 150), and English may be higher; Most of the students who didn't do well in the exam were around 90.
But relatively speaking, there will be more people with high mathematics level and a larger span. /kloc-there are relatively more people above 0/30, and the poor score will be lower. Generally speaking, students who learn math well will not do too badly in the exam. Students who are not good at math generally don't get very good grades. Therefore, we must attach great importance to the subject of mathematics.
The following officially begins the dismantling and interpretation of mathematics curriculum standards.
Directory:
Mathematics curriculum standard volume 132 pages, with the front 7 1 page as the text and the back part as the appendix.
There are two appendices. One is the explanation of behavioral verbs, that is, "knowing, understanding, mastering and using" and "experiencing, experiencing and exploring" which appear repeatedly in curriculum standards. The former is a behavior verb, and the latter is a process verb. Basically, the requirements in the back are higher than those in the front. It can be understood that "application" means mastering better, and more bluntly speaking, it is the key knowledge content of the exam.
The second appendix is an example, giving many examples to help you understand this concept. Because mathematics mainly needs examples, otherwise it can't be described clearly by language alone.
In the text, "course objective" and "course content" are very important. But many people can't understand the knowledge points of junior high school when they see nouns, just know what they are.
The first part, preface: The preface consists of four parts, and the last part is "Curriculum design ideas".
0 1, general:
At the beginning, I said that mathematics is mainly a science that studies quantitative relations and spatial forms. Mathematics in compulsory education can be simply classified into algebra and geometry. Although statistics and probability, synthesis and practice are also included in the following course content, these four parts are expounded together, but the latter two are rare.
The part of numbers, starting from integers, gradually goes to decimals, fractions, odd numbers, even numbers, rational numbers, irrational numbers, etc. Of course, it also includes the operation of numbers, addition, subtraction, multiplication and division, and square root.
There is also a big chunk of primary school mathematics, such as unit and conversion of quantity, unit of length, unit of time, unit of area, unit of volume and so on. The latter two are studied together with geometry.
Algebra, in a nutshell, is to represent numbers with unknowns, but it is not completely accurate. Numbers can be represented by letters or symbols, indicating that abstract thinking needs a big step. I don't know if you have any impression of factorization. Factorization is the core of algebra, that is, elimination and reduction. Equation is an introduction to algebra, and function is a difficult point in junior high school mathematics.
Let's start with geometry. The first phase 1 ~ 3 grades mainly know graphics; In the second stage, grades 4-6, points, lines, surfaces, the sum, parallelism, intersection, area, and the projection of the unfolded diagram are all involved; In the third period, did it rise sharply? The main requirements are to prove the similarity and congruence of triangles, the tangency, translation, rotation, axial symmetry, coordinate axis, parabola and so on. In graphics, triangles and parabolas (quadratic functions) are difficult points.
What are the next few words? Just get to know them in general.
Mathematics is an abstract summary of objective phenomena and the foundation of natural science and technical science, especially after the development of computer technology, the role of mathematics is more significant. Mathematics in primary schools and junior high schools, on the one hand, is to master the necessary mathematical knowledge and skills in life, on the other hand, it is a basic tool for other natural disciplines.
Mathematics is mainly to cultivate people's thinking ability and innovation ability.
02. Nature of the course:
03, the basic concept of the course:
Everyone can get a good math education, and different people get different development in math. Content presentation should pay attention to hierarchy and diversity. Therefore, mathematics learning is hierarchical. If math has little to do with your future life, study and work, or you don't like it very much, it is good to master the foundation.
The content should be close to the students' reality, which is conducive to experience, understanding, thinking and exploration. Paying attention to process, intuition and direct experience requires us to let students feel and experience mathematics in real life, learn and understand mathematics, and use and explore mathematics. Moreover, it is important to understand mathematical ideas. Results and conclusions do not come out of thin air, but to understand the formation process of results.
Students are the main body of learning mathematics, and teachers should pay attention to enlightening and interesting, stimulate students' interest in learning, trigger mathematical thinking and encourage creative thinking.
Students can learn mathematics through various forms. Listening, thinking, practicing, exploring and cooperating are all important learning methods. Students can choose their own learning methods according to their own characteristics.
Observation, experiment, guess, calculation, reasoning and verification are all very important, so there should be enough time and space for students to explore. Don't just do the problem! ! Teaching should pay attention to inspiration and guide students to think independently.
Because different people have different development in mathematics, the goals are diverse and the evaluation methods can be diverse. Examination is not the only means! !
Because of the progress of technology, these technical means can be used more. For example, if you study geometry, you can make more use of 3D models to help you understand.
There are two parts with two exclamation marks in front, which are written according to my own understanding. Don't just do the problem! ! Examination is not the only means! !
Because our first impression of mathematics is all kinds of problems and exams. Can students not be bored? Especially those students who find mathematics difficult to learn.
Of course, exams are inevitable. I just want to say that teachers and parents should let students experience more happiness and interest in learning mathematics.
04, curriculum design ideas:
This part of the content seems to be more and more important, especially the math ability part.
The general idea is to conform to students' cognitive laws and psychological characteristics, and it is very important to start from interest and trigger mathematical thinking. You know, mathematics is not imaginary, but based on real life and production background.
The learning period is divided into four learning periods, namely 1 ~ 2, 3 ~ 4, 5 ~ 6 and 7 ~ 9. Mathematics is divided into three learning periods, 1 ~ 3, 4 ~ 6 and 7 ~ 9.
It is said that the math teacher summed up a jingle, called: Senior one is equal to Senior two, and Senior three and Senior four are obviously layered behind Five or Six. I added another sentence at the back, called: Junior high school began to go to heaven and go to earth.
I have indeed heard some parents say that from the third grade, children's learning, good or bad, can be roughly known.
Explain what? First, the study habits and knowledge accumulation in grades one and two began to change qualitatively in grade three; Secondly, from the beginning of the third grade, the difficulty of content began to increase. However, it is not up to us to decide whether it is difficult or easy. It must be not difficult for those who are willing, and not difficult for those who are difficult. If you ask different people, you will get different answers. However, I still remind parents whether it is meaningful to pay attention, and you should pay attention yourself.
The course objectives have been mentioned twice before. If you have the heart and want to study the curriculum standards very seriously, you can print this page. For every knowledge point, it involves the vocabulary of this mastery level. In different courses, the course content will involve these four parts, which are fully introduced here:
Numbers and algebra: understanding, representation, size, operation and estimation of numbers; Letters represent numbers, algebraic expressions and their operations; Equations, equations, inequalities, functions, etc.
Graphics and geometry: the understanding of basic graphics in space and plane, the nature, classification and measurement of graphics; Translation, rotation, axial symmetry, similarity and projection of graphics; Proof of the basic properties of plane graphics; Coordinate is used to describe the position and movement of a graph.
Statistics and probability: collecting, understanding and describing data, simply sampling, sorting out survey data, drawing statistical charts, etc. Processing data, calculating average, median, mode, variance, etc. Extract information from the data and make simple inference; Simple random events and their occurrence probability.
Synthesis and practice: comprehensive application to solve practical problems; Cultivate problem consciousness, application consciousness and innovation consciousness; At least one teaching activity is guaranteed every semester.
In fact, this place has been greatly simplified. I'm sure I can't understand it in a few words, but I can get a general idea. The course content will be introduced in detail later. Mathematics ability, I think this piece is a key point of the whole mathematics curriculum, and it is a module that parents need to pay special attention to.
Although I don't approve of learning too much knowledge in advance, such as learning addition and subtraction in Grade One, multiplication and division in Grade Two, decimals, fractions and negative numbers in Grade Two. But this ability and cognition can be integrated into daily life and cultivated in advance. We should remember that mathematics is an abstraction of some phenomena in life, so we can basically find the real scenes of these mathematical thinking abilities in life.
For example, the sense of digital symbols and computing ability, many families will have some games to encourage rewards and punishments, remember the sun and stars, do something to earn stars, and change stars. For example, children get five stars according to their homework today, which is "+5".
Jump rope 100, but only one star can be changed every four, that is, "100÷4", and then "+25". A star can play iPad 1 minute. Now if you want to play iPad 10 minutes, you need to use 65438 first. Children can record and calculate by themselves. This is a real scene in life.
For example, the concept of space and geometric intuition, many boys like to spell Lego, and he can spell it himself according to the instructions. Isn't this the ability of spatial imagination? You can also do more manual work. What do triangles, quadrilaterals and cookie boxes look like after cutting? Isn't it just a three-dimensional graphic expansion?
The concept of data analysis, this also has many practical examples. For example, how many students are there in the class, and how many boys and girls are there? I caught the doll 10 times. How many times have I arrested? Hit the balloon with an air gun, 20 bullets, how many?
Reasoning ability, there are also many. The most typical examples are some puzzle games. If you play with them, your child can master some skills and discuss with him. How did you find the rules? Are there any other rules? Model idea, the model here is not what we usually call car model and plane model, but can be understood as a kind of summary and induction, that is, discovering regularity.
Actually, don't think too deeply about this. I think it is a mathematical model to use "digitalization" to express cases in life. Including the simplest addition, it can also be understood as a mathematical model. Applied consciousness is to use and exert mathematics more in life, make necessary and timely connection between mathematics and real life, and let children use mathematics to solve real life problems. Innovative consciousness, do not feel the need to make new discoveries, put forward new theorems is innovation.
The innovation here is to ask questions, analyze problems, think about problems and solve problems. Even the existing knowledge, if discovered and summarized by the child himself, is also an innovation, at least for him.
The second part, curriculum objectives:
0 1, the overall goal. In this part, the curriculum standard puts forward four main points, namely knowledge and skills, mathematical thinking, problem solving and emotional attitude. Finally, the curriculum standard emphasizes that these four parts are not independent and separated, but an organic whole that is closely linked and blended with each other. Then let's see what these four points are.
First, knowledge and skills are still four modules: number and algebra, and the ability of abstraction, operation and modeling.
Graphics and geometry, abstraction, classification, discussion of properties (such as what is a square, what are its characteristics? ), motion and position determination (such as folding, rotating, flipping, coordinate system, etc. ). Statistics and probability, collect and sort out data, analyze data, solve problems with data analysis, and obtain new information. Integration and practice, comprehensive use of mathematical knowledge, skills and methods to solve simple problems.
Second, mathematical thinking can also be understood as the above mathematical ability:
The sense of number, symbol and space have initially formed geometric intuition and operational ability, and developed image thinking and abstract thinking. This is the mathematical thought of algebra and geometry. Understand the significance of statistical methods, develop the concept of data analysis, and feel random phenomena. This is the mathematical thinking needed by statistics.
Participate in mathematical activities such as observation, experiment, guess, proof and comprehensive practice, and develop the ability of rational reasoning and deductive reasoning. This is the mathematical thinking of synthesis and practice, which allows students to experience the whole process of a concept from putting forward to solving it. Learn to think independently and understand the basic ideas and ways of thinking of mathematics.
Here I want to talk about the two ideas and two inferences mentioned above. Two kinds of thinking, namely image thinking and abstract thinking. Thinking in images is human instinctive thinking, and it is a concrete image or image. Childhood is generally thinking in images, such as tables. What he can imagine may be your own table at home, because he has seen this table.
Abstract thinking is starting from concrete things, abstracting concepts and thinking with the help of symbols. When we talk about tables, we think that a table board with four legs is a table. Table boards are generally rectangular and round, table legs are generally long cubes, and some have some radians. Let's talk about two kinds of reasoning, perceptual reasoning and deductive reasoning.
Reasonable reasoning refers to induction and analogy. Induction is the example we gave above. Through many different tables, it is concluded that a table with a table board and legs is a table; For example, you want to buy a table of three. The table of a family of three has a round table top and foldable legs. You should find a similar or similar watch.
Deductive reasoning is based on the concept of tables you form. You will see a new table. You know, it is also a table, although you have never seen the leg design of this table before. Learning mathematics is to gradually improve our abstract thinking ability, extract enough things we see and form concepts.
If you are a designer and you design a table, first of all, you will recall and imagine some specific tables you have seen before. This is thinking in images. Then you think, as long as there are table boards and legs, it is a table. This is abstract thinking and inductive reasoning. Then you start from this abstract concept and design a new table style, which is deductive reasoning.
Any "concept" and "definition" are the result of inductive reasoning and abstract thinking. Using these concepts and definitions to solve new problems is deduction. This is the basic process of mathematics learning.
Third, solve the problem:
Initially learn to find and put forward problems from the perspective of mathematics, comprehensively use mathematical knowledge to solve simple practical problems, enhance application awareness and improve practical ability. Get the basic methods of analyzing and solving problems, experience the diversity of problem-solving methods, and cultivate innovative consciousness. Learn to cooperate with others.
Initially form a sense of evaluation and reflection. Asking questions and solving problems are both manifestations of ability. In our previous education, there was too much indoctrination and too little inspiration, and students' ability to ask questions and solve problems was relatively poor. But after we take part in the work, we will find that there are very few ready-made problems waiting for you to solve, and it is more for you to find and solve the problems yourself.
Fourth, emotional attitude:
Take an active part in mathematics activities, and have curiosity and thirst for knowledge. Experience the fun of success, exercise the will to overcome difficulties and build self-confidence. Understand the characteristics of teaching and the value of mathematics. Develop the habit of serious study, independent thinking, cooperation and communication, reflection and questioning.
Adhere to the truth, correct mistakes, rigorous and realistic scientific attitude. Science subjects have this * * * nature. If you can't learn well, you can't even understand the questions, and you can't write the exam at all. Many people are more afraid of learning and give up directly. Therefore, to understand the value of mathematics, we must have curiosity and thirst for knowledge.
When doing the problem, you can also experience the joy of success, exercise the will to overcome difficulties and build self-confidence. After all, if you find math difficult, don't lose interest completely. The latter two are for those students whose academic performance is not bad. We should be serious and diligent, think independently, cooperate and communicate, reflect and question, adhere to the truth, correct mistakes, and be rigorous and realistic. Because mathematics is a rigorous subject, it must have the ability of seeking truth, being pragmatic and questioning.