The advanced training of a mathematics teacher largely depends on the degree of proficiency in the ability to analyze one's own activities and the activities of one's colleagues. The analysis and introspection of the lesson should be aimed at comparing the put forward educational, educational and developmental goals with the achieved result. The lesson is a living cell of the educational process, everything that is most important and most important for the student takes place in the classroom. Is each lesson a step in the knowledge and development of the student, a new contribution to the formation of his mental and moral culture? Not every. Why didn't the lesson work? We ask ourselves and come to the necessity of its introspection. Pedagogical work is basically close to scientific work. The scientific nature of pedagogical work lies, first of all, in the analysis of facts and the need to foresee them. Schemes, algorithms for analysis and introspection of the lesson are now offered in the methodological literature quite a lot, but basically they are compiled along the path of least resistance - the presentation of facts. The most difficult thing is to interpret the fact! The problem of the analysis of the lesson was dealt with by the scientist-didact of the world scale Yuri Anatolyevich Konarzhevsky.

Slide 3 from the presentation "Introspection of the lesson as a means of improving the effectiveness of the teacher's work"

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"Degree with a negative indicator" - Perform actions. Compute: Solve the equation. Degree with a negative exponent. Solve the problem. Simplify the expression:

"Properties of the degree" - Application of knowledge to solve problems of various complexity. Development of perseverance, mental activity and creative activity. Computational pause. Task. Test. Check yourself! Properties of a degree with a natural exponent. Generalization of knowledge and skills in applying the properties of a degree with a natural indicator.

"Degrees of comparison of adverbs" - What words are involved in the formation of a complex comparative degree of an adjective and an adverb? Differences between the degrees of comparison of adjectives and the degrees of comparison of adverbs. Question: The superlative degree for adverbs ... For an adverb in Russian, only a complex form of a superlative degree is possible. 2. What category of adjectives has degrees of comparison?

"Degrees of two" - List of materials used. 1011011101 = 2 + 2 + 2 + 2 + 2 + 2 + 2 = = 512 +128 + 64 + 16 + 8 + 4 + 1 = 733. Convert the number 1998 from decimal to binary. Rules for transferring from one number system to another. 3. Add the decimal values. Now let's convert to decimal notation 1011011101.

"Degree with a natural indicator" - Exponentiation of a fraction. If a?0, then a0=1. N zeros. Properties of a degree with a natural exponent. A+a+a+a+a= a+a+a+a+a+a+a+a+a+a= a+a+…+a=. Division of powers with the same base. The mass of the Earth is 5.976 × 1024 kg The mass of the electron is 9.11 × 10-31 kg. Determination of the degree with a natural indicator. How to write shorter

In modern heating systems, plate heat exchangers have firmly taken a leading position, which is a clear proof of their high efficiency in the operation of hot water and heating systems. And not only in residential areas, but also on manufacturing enterprises. But they need periodic flushing. The frequency of washing the heat exchangers depends on many factors, such as the degree of contamination, the quality of the source water, the time spent by the water heater. But it should be noted that modern heat exchangers have the ability to self-flush with a certain frequency due to the creation of turbulence in the fluid flow. In addition, the heat exchanger plates are made of a special material, which makes them much less susceptible to deposits.

However, this does not mean that the heat exchangers do not need to be flushed at all. Naturally, during their operation, a huge amount of lime deposits accumulate on the walls of the heat exchanger, which reduce the performance of water heating equipment. This is largely due to the unsatisfactory quality of the source water. There is a good opportunity to reduce the frequency of flushing of heat exchangers by installing cleaning filters upstream of the inlet. But if there are no filters, then mandatory flushing is needed, the frequency of which depends on the degree of contamination.

The reasons why heat exchangers need regular flushing are reduced performance, energy consumption to maintain the required temperature, etc. All this is a consequence of the accumulation of hard-to-remove lime deposits, which over time become so coked that it is not always possible to remove them by ordinary flushing - complete or at least partial disassembly is required. By the way, the frequency of flushing the heat exchangers also depends to some extent on this - it is undesirable to allow the deposits to harden. The thermal conductivity of lime deposits is much less than that of metal plates of heat exchangers, therefore, in order to maintain the required temperature regime, it will be necessary to significantly increase energy consumption.

You should not take it to extremes and wait until the amount of deposits reaches a critical point, when ordinary flushing does not help and you have to disassemble the boiler and clean the heat exchanger mechanically. During such cleaning of the boiler, it is possible to accidentally damage some elements of the device, and besides, it is necessary to change the sealing rings, since the old ones become unusable and let the liquid through. In addition, it will cost much more than timely preventive washing with a certain frequency, and it will help to avoid accidents in the future.

It must also be said that the frequency of flushing heat exchangers is determined by the manufacturers of heating equipment themselves. Many of them recommend doing this once a year. However, an important point should be taken into account - these recommendations were developed taking into account the use of clean water. Well, as for the water that flows in domestic water supply systems, it is far from ideal. Therefore, the frequency of flushing of heat exchangers should be reviewed - as a rule, they need to be cleaned two to three times a year.

In the event that the frequency of flushing the heat exchangers is strictly observed, and all actions are carried out by qualified specialists, the procedure can be performed without dismantling the heat exchanger, due to the circulation of the flushing solution in a closed circuit of the system. As a rule, such a procedure does not take much time and is not too expensive.

By the way, experts warn that the use of any acid for flushing is strictly prohibited. The result of such ill-considered actions may be the failure of the heat exchanger, since the action of the acid extends not only to scale in the heat exchanger (and it is not at all necessary that it will completely remove it), but also to the material itself from which the plates are made.

When it comes to happiness, there are several questions that need to be asked at once. What is happiness? Is it real or is it an illusion? What does happiness depend on? Is it achievable? Does it exist in this world or only in another life? Even before our era, philosophers tried to comprehend these questions. There have been many different approaches to happiness. The pinnacle of these reflections were the works of Aristotle, whose ideas of happiness remained unsurpassed for a very long time. Nothing more serious after Aristotle did not appear for a long time.

Aristotle gave this definition: "Happiness is the activity of the soul in the fullness of virtue." He believed that understanding happiness depends on who we ask. To find out what happiness is, we must ask wise people because different people will give different answers. Therefore, the first main idea is that everyone has their own happiness. It may vary from person to person. The dictionary definition of happiness is: "Happiness is the highest good available to man." But there is disagreement as to what this good consists of. Aristotle and many of his contemporaries tried to determine what exactly a person needs for happiness, what properties and virtues a person must possess in order to be happy.

Experimental research on happiness

But there is another approach, according to which a happy person is one who feels himself to be happy. In this case, happiness is understood as some emotional state, the most positive experience available to a person, which is sometimes described as an optimal experience. In the last 30–40 years, experimental psychological studies of happiness have been developed, taking into account mass surveys around the world. Since then, a lot of new things have appeared in the study of problems of happiness. The researchers write that over the past 30 years we have learned more about happiness than in the previous 2000 years after Aristotle.

Experimental research began with psychologists bringing together all the circumstantial evidence and common sense stereotypes and developing assessment techniques. Studies have shown that about half of what was considered obvious was confirmed, and half was not. For example, young people were thought to be happier than older people. It turned out that happiness is not related to age. Young people have more intense positive emotions, but also more intense negative emotions. And the overall balance of positive and negative emotions has nothing to do with age. The same was true for the floor. Women are both happier and unhappier at the same time. They have more positive emotions than men, and more negative ones. But in general, everything in nature is balanced. Since the time of Ecclesiastes, the “woe from wit” stereotype has been known, according to which the smarter a person is, the less likely he is to be happy. When psychologists began to study this hypothesis, it turned out that this was not the case, there was no logical connection.

The level of happiness largely depends on the general warehouse of the individual - temperament and character. Some scientists have written that happiness is 50% due to genetic factors, that is, the psychological characteristics of our biological parents. But the data shows that this is not entirely true. Epigenetic studies, that is, studies on the relationship of genetic factors and causes with environmental factors, suggest that the influence of these factors can vary in the range from 10 to 40%. At the same time, there is no one or two main genes that affect subjective well-being. Eat whole line different genes, each of which makes a small, albeit statistically significant, contribution. In total, taking into account the interaction with the environment, they make a fairly weighty contribution.

Subjective view of happiness

Happiness is largely a subjective matter. There have been studies examining how happy people are in the most unfavorable social groups, i.e. people with severe incurable diseases, the disabled, the homeless, the unemployed, those from the lower social strata. Scientists interviewed people who live in extremely unfavorable natural conditions: Greenlandic Eskimos, Maasai in the jungles of Kenya, street prostitutes in India. They were expected to have low scores on their life satisfaction. But it turned out that the vast majority had a positive balance and people who feel unhappy, even in these groups, were a minority.

German psychologist Ursula Staudinger talks about the "paradox of subjective well-being": people can be happy regardless of the obvious reasons for this. American psychologists Sonya Lubomirsky and Ken Sheldon summarized the results of various studies and formulated a model known as the “pie model”. The pie is divided into three unequal parts, representing three groups of factors that determine individual differences in how people evaluate their own subjective well-being or happiness.

First group - external factors that do not depend on us, the conditions in which we are lucky or unlucky to be born and live.

Second group - factors associated with a stable personality warehouse. There are people who are happy in their nature. Nothing can take them out of a positive state. But there are unfortunate people, like the donkey Eeyore. Nothing can make them happy.

Third group - this is what we ourselves build with our own hands. These are our goals that we set and achieve, the relationships that we build with other people.

It turned out that the weight distribution of these groups of factors is very different from what stereotypes suggest. External factors related to geography, social conditions, wealth, education, explain 10-12% of individual differences in the level of happiness. They depend on less than it might seem.

The dependence of happiness on material well-being

Since the 1990s, mass surveys of thousands of samples have been conducted in different countries with periodic repetitions to reveal the dynamics of changes in happiness in different countries and what it depends on. On the surface lies the question: is happiness in money? To what extent does happiness depend on the level of income, gross domestic product per capita, and so on? It was found that the dependence curve is divided into two parts.

In the first, lower part of the curve, where we are dealing with the poorest countries, this straight line goes up as the level of well-being at the nation level rises, there is a sharp increase in estimates of subjective well-being. This pattern is very clear and manifests itself not only at the level of nations, but also at the level of individuals. When basic needs are not met, a person does not eat very well and he does not have confidence in his own safety, there is no roof over his head, housing, and so on, then he has many reasons for negative emotions. Frustration arises in life, which prevents him from being prosperous.

Satisfaction of basic needs roughly corresponds to what in our time is denoted by the concept of " middle class". This is the level of well-being at which people have the opportunity to eat well, to healthy lifestyle life, have medical service, a roof over your head, education for yourself and your children. These are quite specific needs that have saturation limits.

Further, it turns out that the dependence of happiness on material well-being is changing. The curve breaks sharply. She becomes much more flattering. There have been discussions over the past 5-8 years whether well-being stops growing after the tipping point, or continues to grow, but much more slowly, or, on the contrary, starts to go down a little.

The most recent data that has been published on this topic suggests that further increases in material well-being are positively associated with happiness, but this association is mediated by what exactly you spend your money on. It has to do with the art of spending the money you have on meeting your really deep personal psychological needs, and not just on some primitive consumerism. And it turns out that it’s not so much the wealth itself that matters, but the importance you attach to money. People who attach more importance to money are less happy than people for whom money is not the most important thing in life.

Happiness is not a destination, but a path

Russian philosophers of the Silver Age criticized the idea of ​​happiness and the pursuit of happiness as the main principle of human behavior. Nikolai Berdyaev, in particular, noted that in a state of happiness a person stops and he does not need anything else. All motivation is nullified. Happiness is a state of complete merging of the desired with the actual. And in this sense, striving for happiness means striving for a stopped moment. It is no coincidence that they often say about the state of happiness that at this moment one can or even wants to die, because nothing else is needed. But happiness cannot last for a number of reasons. We are always doomed to move in the direction of what we want. Only for a very short time can we fully achieve this fusion, and then we again live at some distance from what we want. And this distance creates the tension that leads to the fact that at certain moments of life we ​​experience a state of happiness, and the rest of the time we try to find this state anew.

The doctor of the Russian national team Eduard Bezuglov told how the football player does not lose shape during the winter holidays, noted the foods that are best avoided on vacation, gave recommendations for recovery. The specialist also told how many FNL players underwent rehabilitation in his Moscow clinicSmart Recovery and noted the good physical condition of Kirill Pogrebnyak.

The winter break in the FNL is longer than the break in the Premier League and much longer than the break in the leading European championships. In this regard, are there any special recommendations for keeping a football player in shape: training, nutrition?

Indeed, a longer pause leaves a certain imprint. If it’s too “good” to rest for a long time, then it will be very difficult to get into a working rhythm and have time to lay a functional base at the training camp. Detraining occurs after three weeks of inactivity. And detraining, combined with excess weight and weakened muscle tone, is already a mixture that is dangerous for health.

At the same time, the guys who spend the off-season competently get an advantage from the first training camp, which only grows over time. Therefore, I would recommend passively resting for no more than 2 weeks, and then systematically preparing for the training camp: laying down an aerobic base and working on weak points. For this, 4-5 workouts per week for 60-90 minutes are enough. Moreover, they are very well tolerated and can be carried out anywhere in the world.

- Are there any activities and products that you need to refrain from on vacation?

It is clear that in the offseason, the athlete's diet becomes more diverse and you can afford some liberties. The main thing is not to gain more than 2-3 kg of excess weight. Subsequently, forced weight loss can adversely affect the muscles and tendons.

Minimum of refractory fats;

Minimum sugary carbonated drinks;

Minimum alcohol;

A minimum of semi-finished products (sausages, sausages);

A minimum of snacks and simple sugars.

Most FNL clubs have only the simplest means of recovery. Can an athlete show the maximum, having a minimum of funds for recovery? How can he compensate for the lack of these funds?

Believe me, if there is a desire, any football player in any of the leagues can recover on his own. high level: it primarily depends on the level of consciousness of the athlete and to a much lesser extent on material capabilities.

Five main ways to recover as quickly as possible after the end of the load:

Reception of protein (20-30 g) and carbohydrates (70-80 g) in the first half hour.

Compression stockings to be worn during flights as well.

Replenishment of water and electrolyte balance. Within 3 hours we drink 1.5 times more liquid than we lost in weight: we lost 1 kg during the game, which means we drink 1.5 liters.

Cold baths. The simplest ice maker produces 15-20 kg of ice per day. An inflatable pool costs only a few thousand rubles. 5-7 minutes to the waist, and do not be afraid for the aggravation of urological problems (laughs).

Sleep is the most important thing in recovery! At least 8-9 hours of sleep every day and, believe me, you will have much more strength.

It is also important to monitor the intake of carbohydrates. FIFA recommends 6-7 grams of carbohydrates per kilogram of body weight on the pre-game day. To get carbohydrates, it is good to use spaghetti, baked potatoes, buckwheat, brown rice, special bars, carbohydrate gels. To replenish the depot of glycogen in the muscles and liver, I would recommend such doses of carbohydrates in the first two days after the game.

As you can see, there is nothing complicated! And do not believe in fairy tales about magic droppers and some kind of nanotechnology - in 99% of cases these are fairy tales.

You cited RFPL statistics, according to which the players of each team get 40-50 injuries per season, 18-20 of which are muscular. There are periods in the FNL when teams of three rounds play on cold fields or on low-quality synthetics three days later for the fourth. At the same time, the spread of cities in the first league is greater than in the Premier League. Do you have injury statistics in the FNL?

I don't have injury statistics for FNL. This requires systematic work over many years. So far, I have not seen such a desire on the part of colleagues. But the constant transition from one surface to another, flights, games every three days increase the risk of injury - this is a proven fact.

Reducing the level of injuries largely depends on the level of self-awareness of the player himself. If you get enough sleep, eat right, are not overweight, and do regular injury prevention workouts, then there will definitely be fewer problems.

FIFA has long developed the "11+" program and in the teams that have implemented it on an ongoing basis, injuries have decreased by 2-3 times.

- What is worse for a football player's joints: old synthetics or a frozen lawn?

Both options are bad, and their combination is just disgusting.

In such conditions, and this, unfortunately, is our reality, the recommendations listed above to reduce injuries play an even greater role.

- Most FNL players are poor people. Are you sure that they will pull services in your clinic?

The clinic is often visited by football players from FNL clubs and often they come after clinics where prices are much higher. At the same time, we try to treat the guys taking into account their profession, and not as ordinary people, and, believe me, these are often different things.

So, the financial factor, in our case, definitely should not stop.

- How many FNL players are undergoing or have undergone rehabilitation in your clinic?

Depending on what you call a severe injury. There are injuries that can threaten health in general. There are injuries that can threaten a later career.

The second group includes all ruptures of the crosses, ruptures of the tendons of large muscles, fractures of long tubular bones, as in Kirill Pogrebnyak. Unfortunately, there are many such injuries, but now, with adequate rehabilitation, the guys can be helped.

The first group primarily includes injuries to the head and spine, so I will name the injuries of Andrey Lunev in the game with Spain and Vasily Berezutsky in the game with Austria. It's good that everything worked out and the guys quickly returned to duty.

Interviewed by: Artur Fedorkov