Learning method of mathematical function in senior one.
First, pay attention to the requirements of this part in the exam instructions.
1. function (1) Understand the elements that make up a function, and find the definition and value range of some simple functions; Understand the concept of mapping. (2) In actual situations, we will choose appropriate methods (such as image method, list method and analytical method) to represent functions according to different needs. (3) Understand the simple piecewise function and apply it simply (the function is divided into no more than three segments). (4) Understand the monotonicity, maximum (minimum) value and geometric meaning of the function. Understand the meaning of functional parity. (5) Using basic elementary functions to analyze the properties of functions.
Second, pay attention to the learning process of function concepts.
When learning the concept of function, by learning the concept of junior high school function and several different functions such as? Direct proportional function, inverse proportional function, linear function, quadratic function? Review and consolidate the contrast, and understand the connotation and extension of the concept. Highlight the learning process of function concept, analyze and understand the concept sentence by sentence with examples, and experience the function in examples. Three elements? Besides, combining? Mapping? Understanding is more important than the concept of function? Corresponding? .
Third, pay attention to the learning method of function concept.
When learning the concept of function, we must master such a method, that is? Combination of numbers and shapes? Is it determined according to the topic? Use form to help numbers? Or? Use numbers to help shape? .
Fourth, pay attention to the expansion and generation of related knowledge of function concepts.
What does the concept of learning function involve? Function domain, value domain, correspondence? And then what? Interval? We should understand them one by one, expand the types of test questions according to the corresponding topics, and improve the degree of knowledge generation. Here is an example.
1. The method of finding the domain of common basic elementary functions is extended to abstract functions.
The denominator in the (1) fractional function is not equal to zero. (2) Even root functions are opened in a way greater than or equal to 0. (3) The domain of linear function and quadratic function is R .. ..
(3) The function domain in practical problems should not only make the analytical expression of the function meaningful, but also consider the constraints of practical problems on the independent variables of the function.
Bad habits of high school students in learning mathematics.
(1) lax thinking.
Some students transplanted their learning ideas from junior high school to senior high school. I simply think that I didn't study hard in Grade One and Grade Two, but I was easily admitted to high school two or three months before the exam in Grade Three. So, I think high school is so much. Senior one and senior two don't need to study so hard, but as long as they study hard in senior three, they will be admitted to an ideal university. If you have this idea from the beginning, I'm afraid it will be too late to realize the seriousness of this problem. Tall buildings have risen from the ground? Without the foundation of senior one and senior two, the college entrance examination is empty talk, and finally it will be empty talk in a daydream, remember! Remember! !
⑵ Learn mathematics by memory.
Junior high school teachers teach knowledge points carefully when giving lectures. Because there is enough time and less content, students practice more and practice makes perfect, so they will certainly achieve good results. However, the audience teacher will talk about many concepts, examples and problem-solving methods in one class, and time is tight. If you don't concentrate on understanding the content in class, then the homework after class can't be completed smoothly, and it will inevitably affect your grades over time.
⑶ Rely on teachers and neglect self-study habits.
After entering high school, many students still rely on it as much as junior high school, follow the teacher's inertia, and have no initiative in learning, which is manifested in not taking class notes, taking error correction notes, making summaries, making study plans, waiting for classes, not previewing before classes, and being confused in classes. These practices are unscientific.
(4) There is no mathematical knowledge system in mind, and only the isolated knowledge points are concerned.
There are 140 knowledge points in high school mathematics. There are a lot of mathematical thinking methods and problem-solving skills in the process of knowledge formation, and there is a strong connection between knowledge points, which are often ignored by students. What to learn depends on the content of which section, and I don't know the relationship between chapters and sections. You only pay attention to the superficial characteristics and are not good at digging deeply, which makes the knowledge you have learned fragmented and one-sided.
5] Only attach importance to conclusion and memory, not to the formation process of knowledge.
Senior high school mathematics concept course is rich in content. Students often disdain these courses and lack a deep understanding of the occurrence and development of some concepts. They only stay at the level of generalization and memory, and can't grasp the concept from the connotation. For example, when students study the chapter of series, they will recite the formula of series, but when they encounter the problem of series, they can't start, because they didn't understand the mathematical thinking method produced in the process of concept formation when they were studying the concept of series, and they couldn't transfer this thinking method to specific problems.
[6] There is no habit of self-reflection and self-summary.
Students are only satisfied with understanding what the teacher teaches in class, but they don't digest and summarize carefully after class, and they don't form the habit of self-reflection and self-summary. Many students think it is useless to take reflective notes, but it is not. If you want to go to a college that focuses on this, it is possible as long as you are smart enough. If you want to go to a good university, it is impossible to take special notes without reflection and summary (this book specifically explains how to do it)
Some Suggestions on Mathematics Learning in Senior High School
(A) to develop the habit of preview before class
The meaning of preview
Preview is to learn the content of the new lesson independently before the teacher gives a lecture, to get a preliminary understanding, and to make good knowledge and psychological preparation for class (usually the school will give it in the form of a study plan). The significance of preview has the following three points: ① cultivate good study habits, learn to study independently, master self-study methods, and lay the foundation for the learning of all beings; Preview helps to understand the main contents and difficulties of the next class, remove some knowledge obstacles for class, establish the connection between old and new knowledge, and help to systematize knowledge; (3) it is helpful to improve the efficiency of attending classes; Teachers can be clear-headed, positive, focused and easy to understand for the problems they don't understand in preview.
2. The basic steps of preview
Thinking while reading: Mathematics textbooks are divided into introduction, mathematical concepts, laws (including laws, theorems, reasoning, nature, reasoning, etc. ), pictures, examples, exercises. The introduction is generally based on students' existing experience and familiar common sense of life, and the content is familiar and specific, so that students can have a perceptual understanding of what they have learned. After the reform of new textbooks, mathematical concepts and theorems are generally guided by mathematical activities such as observation, thinking and exploration. It is very operable to understand and master the basic knowledge of mathematics through personal practice and positive thinking, from concrete to abstract, from special to general activities, which is the biggest change of teaching materials after the new curriculum reform. When you teach yourself examples, you should: distinguish the steps of solving problems and find out the key to solving them; Find out the key to each problem-solving step, form the habit of asking why in each step, and use the above knowledge as much as possible; Note that some examples are accompanied by graphics. Even if there is no graph, we should try our best to understand the example from the angle of graph, analyze the standard and format of solving the problem, see if there are other examples to solve, and finally do several exercises according to the format of the example.
Draw while thinking: Under normal circumstances, students can basically grasp the key points of a lesson in the process of self-study. Drawing the key points of this section in the process of self-study will help students master knowledge and use it in places of doubt. Mark, in the course of the teacher's explanation the next day, solve doubts and improve the efficiency of class.
Thinking while writing: there is a big gap in every page of the new textbook. In the process of self-study and teacher's explanation, you can record your own views and experiences in the blank space, such as the interpretation of concepts, the thinking of solving problems, the analysis of error-prone points, the changes of example conditions and conclusions, etc. This will always help students to fully grasp the content of this section. Some schools will be equipped with self-made study plans, which will reduce the difficulty of preview and is also a good way to preview.
(2) Listen carefully, ask questions actively and take notes carefully.
? Is it enough to know after learning? The key to understanding and mastering the basic knowledge, skills and methods in class is to listen to how the teacher breaks through the difficulties, key points and key points, what can't be understood in the preview process, and how the teacher analyzes and summarizes the problems or exercises in a class. Some students like to write down the teacher's blackboard word for word, so there is no need to do so. Classroom notes are to record some important knowledge points, conclusions and some classic solutions and problem-solving skills supplemented by teachers. As long as you remember the problem-solving process and sort it out slowly in your spare time, you must deal with the contradiction between attending classes and taking notes, and don't lose sight of one thing.
After the new teaching reform, higher requirements are put forward for teachers' teaching methods and students' learning methods, and students' main role is emphasized. Teachers should actively encourage students to participate in the classroom. There are some problems in the classroom that the teacher can't explain, but let each student think positively, show his own ideas and explore more ideas and solutions. Putting forward ideas is sometimes more important than solving a problem, because it brings about ideological changes (I don't think we can abandon traditional teaching methods, it depends on the content).
(3) Earnestly finish the homework and do a good job of review and summary.
We should think independently, analyze and solve problems while finishing our homework seriously, so as to further deepen our understanding of new knowledge and master new skills. However, the reality is not optimistic. Most students have the habit of copying homework, and what's more, almost all of them do. Of course, some factors are caused by unscientific assignment, so homework is also a test of students' perseverance. Through homework exercises, students can understand what they have learned. what's up Arrive? Cooked? In addition, we should attach importance to homework ideologically, and don't take homework as a burden, because homework is work.
Reviewing in time and summarizing systematically is another important part of efficient learning (this book specifically explains how to take notes in math learning). By reading textbooks repeatedly and consulting relevant materials in many ways, we can strengthen our understanding and memory of basic concepts and knowledge systems, link the new knowledge we have learned with the old knowledge, make analysis and comparison, and arrange the review results in a notebook while reviewing, so as to learn the mental knowledge we have learned from the meeting. When reviewing and summarizing, based on textbooks and systematic review, referring to notes and materials, through analysis, synthesis and generalization, the internal relationship between knowledge is revealed, so as to achieve the purpose of mastering the knowledge learned.
(4) Pay attention to the wrong questions
There is a simplified understanding that mistakes are caused by lack of knowledge. In fact, there are more than one kind of mistakes in solving problems, and mistakes will also occur after knowledge. Since there are knowledge factors, ability factors, experience factors and emotional factors in successful problem solving, unsuccessful or failed problem solving will also be related to these factors, which can be summarized as: knowledge errors, logical errors, strategic errors and psychological errors.
Knowledge error
Mainly refers to the mistakes caused by the defects in mathematical knowledge, such as misunderstanding the meaning of the problem, unclear concepts, wrong rules, wrong theorems, wrong methods and so on. The core is whether the content involved conforms to the mathematical facts. For example, when students learn the formula of trigonometric function, they often make mistakes because of confusion.
logic error
Logical errors mainly refer to errors in reasoning or argumentation caused by violation of logical rules. For example, false argument, inability to deduce, stealing concepts, circular argument, etc. It is often manifested in the confusion of four propositions, the confusion of necessary and sufficient conditions, and the unreality of reducing to absurdity. The core is whether reasoning conforms to logical rules. For example, when students study the content of mathematical induction, they often think that n=k+65438+ is derived from the assumption of n = K.
There are both connections and differences between intellectual errors and logical errors.
(1) Knowledge errors are related to logical errors.
Because mathematical knowledge and logical rules are often interdependent, in a broad sense, we can't exclude logical knowledge from mathematical knowledge. Therefore, logical errors and intellectual errors often coexist, and the analysis from which angle depends on the size of the proportion and the needs of teaching. In the above example, we see that when we say that it has an intellectual error, it does not rule out that it also has a logical error; Similarly, we say that it has logical errors, but we do not rule out that it also has intellectual errors.
(2) There is a difference between intellectual error and logical error.
Knowledge error mainly refers to whether the proposition involved conforms to the facts (whether it conforms to definitions, laws, theorems, etc.). ), and the core is the authenticity of the proposition; Logical error mainly refers to whether reasoning conforms to logical rules, and the core is the effectiveness of reasoning. Although the truth value of mathematical proposition is related to the logical validity of reasoning, mathematics is not logic after all, and it is much bigger than logic after all. In the basic position and main trend of knowledge blind spots, it is still necessary to distinguish between knowledge errors and logical errors.
Strategic error
This is mainly because of the deviation of the direction of solving problems, which leads to the obstruction of thinking or the long length of solving problems. For the exam, even if it is done correctly, if it is time-consuming and laborious, it will lead to potential or implied loss of points, and there are strategic mistakes. In the process of solving problems, it is inevitable that thinking will be blocked or tortuous, so it is difficult to completely eliminate strategic mistakes in the exploration stage.
For example: inequality x2+ax+1>; 0 is in x? Shangheng holds, and the range of the number A is realistic. Most students
Everyone thinks that it is complicated to solve the problem by constructing a quadratic function and determining the moving axis interval of the quadratic function. If the separation constant method is used to solve the problem, the problem will be easily solved and the process will be simple and clear.
Psychological error
This mainly refers to the problem-solving errors caused by some psychological reasons, such as order psychology, detention psychology, potential assumptions, misreading questions, copying wrong questions, forgetting to write, etc., although the subject has the necessary knowledge and skills to solve problems. Will it be right, right and incomplete? Open the distance between admission and failure. Is this it? Big problem? Question:
(1) Yes, but it's wrong. Some candidates are not helpless, but thinking in the wrong way, or thoughtless, or lax in reasoning, or inaccurate in writing, and the final answer is wrong. It's called. Could it be wrong? .
(2) Yes, but not all. Other candidates, the thinking is generally correct, and the final conclusion has come out, but they are forgetful or lack of main steps, and a logical point in the middle can't pass; Or a special case is omitted, and the discussion is not complete enough; Or a potential hypothesis, or a partial generalization, what is this called? Correct but incomplete? For junior high school students, it is very important to realize the importance of error correction first.
(5) Active learning, good at comparison and association.
In class, students should actively listen to the teacher's ideas, actively use their brains, hands and mouths, actively participate in classroom teaching, and cultivate their abilities in all aspects. From perceptual knowledge, which mainly perceives the external characteristics of things, to rational cognition, which analyzes and comprehensively understands knowledge, and from more specific thinking in images to abstract logical thinking, thus cultivating the initiative, independence and flexibility of thinking and improving thinking ability. Under the guidance of teachers, through their own observation, experiment and exploration, they exchange their own conclusions in cooperation with others, and cultivate their own innovative spirit, cooperative spirit and practical ability in the process of research-based learning.
Students are good at associating Chinese medicine in the whole learning process and learn to draw inferences from others. For example, the association between plane geometry knowledge and space geometry, mathematical language and geometric figures, and general problems and special problems. Comparison can deepen the understanding and mastery of knowledge. If we compare exponential function with logarithmic function, we can see that their image positions are different, but the discussion of cardinality is the same, so that we can establish a reasonable knowledge structure and understand knowledge systematically and comprehensively.
Learning mathematics must work hard on three words:? Exquisite, thorough and lively? You can't just read books without doing problems, and you can't just bury your head in sea tactics without summing up and accumulating. We can not only get into the textbook knowledge, but also jump out and find the best learning method by combining our own characteristics. The methods vary from person to person, but the four steps (preview, class, homework and review) and one step (study notes) are indispensable.
For an ordinary mathematics educator, it is his lifelong pursuit to transcend the simple and narrow thinking mode, look farther, broaden his horizons and promote the all-round development of students as much as possible.
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