Self taught math methods. How to teach yourself math?

It's doable! You should buy a book about the derivation of important formulas in high school and college, you must not learn mathematics to death if you are studying software development! This time I didn't learn mathematics so that I didn't have to rush for the exam, so you can learn it leisurely, as long as you understand a formula derivation, you have mastered a logical thinking ability.

To be honest, I actually don't think there is much connection between the subjects in junior high school and high school along the way. Of course, you have to learn the basic math.

Putting aside the argument that as long as the deep iron pestle is sharpened into a needle, mathematics is really difficult. I was honest and clear in class every day, but it was still very difficult to do the questions. Even if she can't give the problem to the teacher, she has to study it for a long time, so the problem of mathematical solid geometry or something is really not very simple.

If it were so easy to learn on your own, there would be no students who would go to school and hire tutors.

But if you are so confident, of course you need to buy a high school math book, and it is better to buy a teacher's book, where there are many explanations. Take your time.

The key is to find the method of doing the question and some conclusive arguments from the exercises.

Well, mathematics is counting and learning, if you want to learn mathematics well, you must first confirm your learning attitude, and secondly, you must determine your own mathematical level to set your own goals. I think you have already worked, you should start with the basic texts, expand on the basis of the textbook, and do more math when doing problems, but not blindly. Be sure to learn to summarize and think.

Buy a few practice books to do, and you can learn the basics of self-study. If you want to solve the problem, you need to use your brain. I want to ask the master.

Online classes, 53 workbooks, detailed explanation books, column mind maps, several ways to cooperate. I'm in my second year of junior high school, and mathematics used to be very good, but for a while, it was a bit decadent and caused mathematics to be very average now, so I wanted to make amends, and by the way, I studied mathematics for the next semester by myself, and I think this method can be used as a reference.

If you have a good idea, you should start with the basics, math is like building a building. If you still have a textbook, it is best to read the most basic knowledge of the textbook first, write the formula often, and then do the exercises at the back of the textbook, in order to deepen your understanding of the textbook's theorem formula. If you still have material from previous exercises, such as basic training, etc., cover the answers and do it.

You can also watch online classes, just look for free ones, because there is a certain chance that the paid ones are deceptive.

To be right, for composite functions with quadratic functions, the monotonicity of composite functions is generally judged according to the position of the axis of symmetry. But the specific method does not have to be so troublesome, the following ideas are for reference:

For a composite function, it is not difficult to first determine the domain in which it is defined. In this example, we only need to consider x 2-3x+2>0, so that the domain of the composite function is x2

For a composite function, the second thing to do is to specify its composite type. If g(x)=x 2-3x+2 (whose domain is still x2) and h(t)=log1 2(t)(t=g(x)>0), then y=log1 2(x 2-3x+2)=h[g(x)], that is, the composite function is composed of h(t) and g(x), where g(x) can be called the inner function (inner function) and h(t) is called the outer function (outer function).

For a composite function, its monotonicity depends on the monotonicity of the inner and outer functions, and an important principle is "the same increase and different subtraction", that is, if the inner and outer functions are both increasing functions or both subtracting functions, then the composite function will be an increasing function; Correspondingly, if one of the inner and outer functions increases and the other is a subtraction, then the composite function is a subtraction.

Specific to this example:

Obviously, h(t)=log1 2(t)(t>0) is a subtractive function (the questioner is wrong to say "subtractive on r", because the domain of the function is not r). g(x) is a quadratic function, and it has no monotonicity on r, but if the definition domain is divided into two according to its symmetry axis, then the quadratic function presents a definite monotonicity in the two intervals. For the monotonicity of a quadratic function that is not defined on r but with a defined interval, the focus is on the position of the axis of symmetry with respect to the interval.

Going back to this example, the definition domain of g(x), although it is an interval, contains two open-ended intervals (i.e., one end to - and one end to +) and it is clear that g(x) still has no monotonicity over the entire defined domain. Look at its axis of symmetry, x=3. Then when x3, g(x) is the increment function (note that g(x) opens upwards).

Thus, it can be found that the defined interval x2 spans the two intervals (x3) on both sides of the axis of symmetry, i.e., g(x) still has no monotonicity in the defined interval x>2. The next step is to subdivide the definition interval x>2 according to the axis of symmetry: divide it into 23 (of course, you divide it into 23 and g(x) as an increasing function.

Taken together, g(x) is an increasing function on the defined interval x3.

First, "the world's martial arts, only fast is not broken", self-experienceThe so-called "fast" refers to learning in advance before the teacher lectures, paying attention to learning, not previewing, making a study plan, and insisting on completing it every day. Semester textbooks should be completed about two months in advance. Let the teacher's lecture follow you.

After quickly finishing the first study of the Envy Qingcheng textbook, what is the rest of the time to do - quickly enter the review.

Clause.

Second, the whole textbook should be reviewed several times, and the number of "times" wins. The first self-study should be detailed and fast, and it should be faster than the teacher's lecture. When the teacher lectures, he should listen carefully, and take the teacher's lecture as the first review, which should clarify all questions, so as to achieve "true knowledge", and leave no doubts, thoroughly understand the knowledge points in the textbook, and never leave dead ends.

When completing the first self-study of the textbook, self-study can not stop, start the first review of self-conduct, and at the same time, follow the teacher's lecture brother and sister to review, for the study of the textbook should not be less than five times, especially all kinds of examples, formulas, definitions should be reviewed more than five times. Textbook learning is the foundation, and it is necessary to lay a solid foundation.

Third, we should do more problems in mathematics and win by doing more problems. While studying and reviewing, you must do more questions, and you must pay attention to the wrong questions in the process of doing the questions, and keep in mind that the current wrong questions are the points to be raised in the future exams.

For the questions that you have done wrong, you should carefully study and summarize them to find out the reasons for the mistakes.

Regarding the selection of practice questions, it is recommended to first choose the mid-term, final and monthly test questions of the previous years in the province and city of Zaiqi, preferably in the past ten years. Secondly, you can choose the mid-term, final, and monthly test questions of the high school entrance examination and college entrance examination in major provinces.

In fact, the above three points are not only suitable for the study of mathematics, but also applicable to physics and chemistry. The above learning perspectives are only personal learning methods.

I hope you can learn from it.

How to self-study math in high school is as follows:Leap from Thinking Methods to Rational Levels: Another reason why high school students have math learning disabilities is that the thinking methods of high school mathematics are very different from those in junior high school.

In junior high school, many teachers have established a unified thinking model for students to solve various problems, such as solving fractional equations in several steps, factoring what to look at first, and then what to look at. Therefore, junior high school learning is accustomed to this mechanical, easy-to-operate way, while high school mathematics has produced great changes in the form of thinking, and the abstraction of mathematical language has put forward high requirements for thinking ability. This change in ability requirements makes many freshmen feel uncomfortable, so it leads to a drop in grades.

Understand and master commonly used mathematical ideas and methods in a timely manner: To learn high school mathematics well, we need to master it from the height of mathematical ideas and methods. There are several mathematical ideas to be mastered in middle school mathematics learning:

Gathering and corresponding thoughts, classifying and discussing ideas, combining numbers and shapes, moving ideas, transforming ideas, and transforming ideas. After having mathematical ideas, it is necessary to master specific methods, such as: commutation, undetermined coefficients, mathematical induction, analysis, synthesis, counterproof, and so on.

Among the specific methods, the commonly used are: observation and experiment, association and analogy, comparison and classification, analysis and synthesis, induction and deduction, general and particular, finite and infinite, abstract and general, etc.

Gradually form a "self-centered" learning model: mathematics is not taught by the teacher, but under the guidance of the teacher, it is acquired by one's own active thinking activities. To learn mathematics, it is necessary to actively participate in the learning process, develop a scientific attitude of seeking truth from facts, and have the innovative spirit of independent thinking and exploration. Correctly deal with difficulties and setbacks in learning, not discouraged in defeat, not arrogant in victory, and develop a positive and enterprising, indomitable, and frustration-resistant excellent psychological quality; In the process of learning, we should follow the laws of understanding, be good at using our brains, take the initiative to discover problems, pay attention to the internal connection between new and old knowledge, not be satisfied with ready-made ideas and conclusions, often carry out multiple solutions to one problem, change one problem, think about problems from multiple aspects and angles, and dig out the essence of problems.

To learn mathematics, we must pay attention to "live", it is not good to only read books and not do problems, and it is not good to only bury your head in problems and not summarize and accumulate. For textbook knowledge, we must not only be able to drill into, but also be able to jump out, and find the best learning method based on our own characteristics.

Study the textbook to understand the concepts, do more exercises, and be able to draw inferences from one another.

1.Return to the textbook and memorize the table of contents to understand the framework.

If you want to improve your math scores, many students will ignore textbooks and buy a lot of extracurricular teaching materials to "add food" to themselves, which is actually putting the cart before the horse, losing watermelon and picking up sesame seeds.

Textbooks are written by countless teachers according to the syllabus of mathematics education, which can be said to be the compass for college entrance examination questions.

Therefore, before students go to do extracurricular tutoring questions, they may wish to read the textbook several times, memorize the table of contents, and do the textbook exercises several times to understand it thoroughly, so that they can lay a good foundation and then do "high-level questions", and the effect will be twice the result with half the effort.

2.Memorize classic questions.

In the impression of most students, there is such a "stereotype": that is, mathematics needs to be understood and does not need to be memorized.

In fact, it is not the "on-site comprehension ability" that depends on the exam, but precisely the memorization ability, you need to keep the knowledge points and the type of solution in your own mind, and use it directly from the brain during the exam, rather than "understanding what this question is tested and how to solve it" at the exam site.

In the compulsory education stage, the types of questions involved in mathematics knowledge points are limited, what we have to do is to memorize these classic question types, and when we encounter similar questions during the exam, we will set them according to the question types we have memorized. It sounds clumsy, but it's practical.

When Duan Nan, the top student in liberal arts in Beijing, shared his learning experience, he mentioned memorizing example questions. By memorizing classic examples, he went from failing to excelling in mathematics.

3.Build a set of mistakes and review them regularly.

The topic of building a set of mistakes is actually a bit of a cliché. Many teachers will ask students to create a problem book, but often there is no latter one, that is, to regularly review the example problems they have organized.

According to the Ebbinghaus memory curve, we will constantly forget what we remember, and only through continuous review can we turn knowledge into permanent memory.

A good memory is not as good as a bad pen, and students must not save the step of sorting out the wrong questions. Regularly reviewing and reviewing the wrong questions can effectively make up for your knowledge weaknesses and improve your grades.

Self-learning mathematics is to understand the example problems by yourself, memorize the formulas and theorems, figure out the methods, and use them flexibly.

Well, if you want to learn by yourself, it's best to learn live classes online on software such as MOOCs, and then do the exercises by yourself offline, so that it will be more difficult to learn.

Mathematics is very profound, computers, mobile phone programs must use mathematics, in addition to memorizing formulas, more practice, but also know how to apply practically, so as to cultivate interest in order to learn well.

Personally, I think that mathematics is to memorize various formulas and then apply them in practice.