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How to become a mathematician


A modern teacher needs to know and love his subject well, to be demanding and fair, patient and restrained to himself and to his students. This article discusses a set of examples and own experience in a large pedagogical practice

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Tkachenko Irina Anatolyevna - teacher of mathematics MBOU "ChSSh №1 named after N. Curls ", pos. Black Sea, Republic of Crimea

Resume: A modern teacher needs to know and love his subject well himself, to be demanding and fair, patient and restrained towards himself and his students. This article discusses a set of examples and own experience in a large pedagogical practice.

Key words: real teacher, self-exactingness, professional competence, complete dedication.


Tkachenko Irina Anatolievna - teacher of mathematics, MBEI "

How do future mathematicians learn today?

Recently a strong student came to me. The purpose of the classes was preparation for the exam in mathematics and subsequent passing the exam for admission to Mehmat Moscow State University. We studied vector algebra with it. Once I made up his homework for him in one of the sections of the additional textbook “Polyhedrons”. I gave him the book. What was my surprise when in the next lesson I found out that her student fully photocopied and in addition to my 8 tasks, I solved 10 additional ones from it. In almost every lesson, we sorted out questions on tasks outside of my D / Z (from different collections). The boy passed the internal exam in mathematics at Moscow State University for 100 points and received the coveted budget place.
This example shows a lot. No one will force a child to solve problems outside the plan if he does not have an internal orientation to learn mathematics. If a purposeful student is also engaged with a tutor in mathematics, then knowledge will come to him faster and to a greater extent.

Knowledge is always proportional to the time spent on it. The only difference is that a capable (ingenious) student is quicker to grasp the main thing, to see the solution progress several steps forward. But everything is in your hands. Any properties of objects can be independently verified or proved, and most of the movements of numbers can be revealed on paper. To solve complex issues there are specialized textbooks and, in the end, a tutor. If you wish, you can always figure out anything. The main thing to do, not laziness.

Most students do not withstand significant mental stress when studying mathematics. However, I myself know that perseverance is stronger than any complex topic.

How did I become a mathematician myself?
I didn’t have tutors, but I compensated for their absence by hard independent work. Additionally, he solved problems and repeated the proofs. There was such a period at the turn of the end of grade 7 - the beginning of grade 8, when I felt insecure in understanding geometry. What has been done? Every day, I either read the paragraphs that I went through or mentally drove through myself the evidence of the theorems along with the wording of the objects involved in them. He did it even while lying in bed. If something was forgotten, I could get up at 12 at night and in the dim light of the lamp (so that my parents would not notice) see the evidence. Realizing or remembering the proof, he went to bed with a feeling of satisfaction. And so for about six months. At some point, the evidence began to be remembered by itself, and I confidently passed the final oral exam in geometry in grade 9 perfectly.

Tutor for future mathematicians
1) Solve solve and solve problems yourself again.
2) Do not stop in development having achieved high results.
3) Do not drop the task if it does not work out for you. Come to her after some time or change the solution method.
4) Try to prove everything and everyone. All the theorems that you use that catch your eye.
5) Find a math tutor with knowledge of additional subject chapters. Ask him more questions.
6) Be observant. Many methods use features of the object that you can notice.
7) Study the results of your transformations and calculations. Theorems are nothing but observations of them.
8) Attend math competitions at different levels. They will be able to further interest you in the study of the subject.
9) Do not focus only on preparing for the exam. View the subject more broadly. Look for interesting tasks on the Internet and in print. Their decision will beneficially affect your development.

Kolpakov Alexander, tutor in mathematics, Moscow. Preparation for the exam.

Everything is written very simply, but because (not to say brilliant) very accurately. To a person who is deaf to knowledge, not a single tutor will help to become a good specialist, unless he will prepare to pass an exam. Tutor in Russian, Yakov Semenovich.

Where is the answer itself? So I wanted to become a mathematician, I began an understandable business with arithmetic, then algebra and geometry. But when you are already starting to approach differentials, integrals and matrices, questions actually arise, but why is this at all? That's why you need a matrix? Well, yes, solve systems of linear algebraic equations. And many more where. But the question is different, how do I myself get to understand the need for matrices? No one explains this. Usually, the teacher simply retells the work of others and without giving an objective description of the very essence of the method.

There are many applied problems of economic content in which linear algebra is used, in particular matrices. True, most of them have such a number of variables that goes beyond human patience :) and therefore computers are involved in the relevant decisions. The principles of algorithms are revealed in the course of higher mathematics using examples of small-dimensional matrices (3 × 3, 4 × 4 ...). Of course, in the process of teaching the fundamental base, even a very practice-oriented tutor in mathematics should not (and will not) be able to simultaneously explain complex applied points from a separate course, for example, a linear programming course (do not confuse with “ordinary computer” programming).

Math study

Everyone can master any science, including mathematics, independently, especially if knowledge from the school bench has remained in his memory. You can become a mathematician at 20, 30 and 40 years old, the main thing is to adhere to some rules:

  1. Properly make a plan. In a short time, it is impossible to perfectly understand mathematics. Having selected a specific topic, it is necessary to draw up a definite plan, according to which training will take place.
  2. To write notes. This method will help to better master the material and remember the main points.
  3. Do not refuse to consult with people who are well aware of math. This will help in working on your own mistakes.
  4. Study the material carefully, re-reading and repeating several times.

Mathematics is a rather complicated science, which not everyone can quickly master. Only if you want to actively study the subject can you acquire the appropriate skills and abilities, reach new heights.

Thus, in order to become a good mathematician, it is necessary to apply science in practice as often as possible, to learn to reason logically.

Necessary skills

In order to become a mathematician, you must have the appropriate skills. Everyone has the opportunity to improve their knowledge through hard work and perseverance.

How to become a mathematician yourself? You need to do it every day for several hours until the knowledge begins to be acquired. If necessary, you can seek help from experienced professionals. A teacher who is well versed in arithmetic will help a beginner at the initial stage of learning science. In addition, you must have a healthy attitude to mathematics. Some believe that having chosen this field of science, they do not have enough knowledge. But this is not so, because everyone has the opportunity to improve themselves.

Teaching methods

There are many methods for studying the features of higher mathematics that are necessary for those who study this science on their own. Many people thought about how to become a mathematician without help.

The main methods that help to study mathematics and other sciences are as follows:

  • be able to properly shape your thoughts,
  • have the necessary motivation
  • read useful information
  • Use thematic guides
  • to solve problems
  • find time to relax, do warm-ups.

A person who wants to become a mathematician needs to be in a constant thought process. You can find new ideas and solutions using videos, of which there are a large number on the Internet.

Self confidence

Despite the fact that most people have no experience in becoming a mathematician, it is precisely indecision that is most often the reason that impedes the development of science and the acquisition of appropriate skills. Practice shows that a person’s awareness of the level of his mental abilities positively affects the development of learning. This means that, first of all, you need to believe in yourself. You can learn absolutely everything if you choose the right motivation.

Do not worry about if you are not immediately able to master some theory in mathematics. There is confirmation that mental activity of a person is formed, even if he makes some specific mistakes in his work. There should also be no worries that there are people who know a lot more about this science. The problem is only in experience and level of intelligence.

Currently, there is a large selection of literature that tells about whether one can become a mathematician and what needs to be done for this.

Problem solving

Mathematics is considered a consistent science. Some people think that for this it is necessary to keep all the formulas and theorems in mind, however, this method is not productive. The basic material needs to be understood, not memorized. For effective training, you need to solve problems by recording the sequence of your actions. In case of difficulties, you need to postpone the process for a while and proceed with the solution later. You need to return to the task until you find the right answer. If you feel that the situation is hopeless, do not neglect the help of those people who are specialists and know many ways to become a mathematician.

When starting to solve a particular problem, you need to understand that severe overwork or stress can negatively affect its implementation. Therefore, you need to find time to relax, so that in the future you can fully concentrate on the task.

What you need to become a mathematician

In order to perfectly know mathematics, you must constantly achieve the best results. There are methods, having mastered which, you can become both a tutor in mathematics and a professional teacher.

Levels that a beginner needs to go through:

  1. Light. At this level, people can solve problems according to the model, and are able to tell the material as it was described in the book.
  2. Advanced. A person who studies mathematics at this level can, without the help of others, not only master and retell the theory, but also solve more complex problems.
  3. Creative. The level when a beginner mathematician does not need to remember all the axioms and rules by heart, since if necessary he can independently derive a particular formula, draw up an example or equation.

These levels will be effective only when combined with practice. In order to better understand the topics, you need to solve a large number of tasks, both simple and more complex. From how deeply a person will master the theory, it depends on whether he can become a mathematics teacher, like many famous teachers.

How to learn to think analytically?

Thanks to analytical thinking, a person is able to reason logically, to generalize information. The features of such a process are expressed in the fact that a person carefully examines each question, studies the situation, at the same time makes an analysis, considering all the advantages and disadvantages.

If a person wants to, but does not know how to become a smart mathematician, it is important to understand that for this it is not good to know only mathematics. In this situation, you need to be able to navigate in other areas, such as programming, economics. Only in this way can one learn to think analytically.

Thus, anyone who seeks to achieve success in life and have positive results in the professional sphere can be a good analyst.

How to become a math teacher?

In order to teach people such a wonderful science as mathematics, knowledge alone is not enough. First of all, you need to treat this subject with love, receive joy from the learning process of other people, and treat students with respect. And also to be more demanding of oneself, objective, to show restraint and patience. These properties are effective not only in mathematics, but also in every science.

The teacher is obliged not only to teach, but also to take a direct part in the training together with his students. For example, it is worth trying in front of the whole class to solve a problem with an unknown answer. This will only cause respect and appreciation from the students. It is necessary to understand that a professional mathematician is a person who is able to understand, and not give as an example, pre-learned rules and formulas.

Thus, in order to become a mathematics teacher, you need to work with maximum dedication, strive to ensure that the work brings joy, rather than being a means of subsistence.

Attitude to math

One of the reasons that people may have difficulty in learning mathematics is a frivolous attitude to science. Those who think that in the absence of mathematical knowledge there is nothing wrong are mistaken. Each person is able to solve problems if he will master the subject, and not ignore it. Knowledge of mathematics and its basic aspects can be useful in many areas of life. Before you begin to study this science, you must initially choose the right motivation. Practice is considered one of the most effective methods for improving their mathematical abilities with a view to their further application. The main thing is not to stop studying mathematics and, if necessary, seek help. Purposefulness, diligence and perseverance will help to achieve a high level of learning.

With the wrong attitude to science, there is a chance to know disappointment. If a person is not confident in himself and thinks that he will never be able to master this subject, at the first difficulties he, however, may encounter such a problem. Therefore, it is worth thinking positively, as a positive attitude towards mathematics helps maintain motivation and achieve the goal.