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Appendix to Protocol №4

Speaker: Vardasheva T.N.

Work on the liquidation of gaps in students' knowledge.

One of the main problems that our school teachers have to solve - work with poorly speaking students. Weakly need to be considered students who have weak mental abilities and weak learning skills and skills, low memory or those who have no effective exercise motives. It is no secret that such students in schools exist. So that this category of students has not passed into the category of poor, systematized work with poorly speaking students is necessary. I would like to stay at work with lagging spelling in the Russian language.
In big i. an important problem Combating the abominability of students and improving the quality of knowledge I see the two sides: the problem of preventing the impressability and the problem of liquidation of gaps in knowledge of students.
The abominability of students is generated by numerous and diverse reasons depending both from the teacher himself (its experience, preparation, its techniques) and the student itself. To eliminate the reasons, the consequence of the abominability of students, the efforts of all teachers should be sent. The prevention of failure is carried out by formulation of classes in general.
Working with lagging students implies a mandatory individual approach to students, as well as individual tasks with separate students. These tasks should be considered as additional to what is given to the whole class.
Looming has to do a larger amount of work than a haunted learner. Therefore, these tasks should be small. For example, a small card from the didactic material.
In each class, as you know, students have learned, having serious gaps in knowledge and skills. These students experience great difficulties in working on educational material and need constant attention to themselves from the teacher and in the lesson, and out of occupation. Only under this condition, such students may eliminate gaps in knowledge and rise to the level of the whole class.
The first thing that the individual work begins is the study of students, gaps in their knowledge and the causes of these gaps, psychological characteristics, etc.
Carefully studying your students, I see that some unstable attention, it is difficult for them to focus on educational material, others tend to mechanically memorize rules and conclusions, others are addicted to work.
One student has a more developed visual memory, others have a hearing, third-party. In any class there are students who do not speak the discipline of mental labor. This is also manifested during presentation or repetition of the material and even more in the process of independent work. The task of the teacher is to study the individual features of students and provide them with timely help, facilitate their work on educational material. By organizing individual work with students, it is important to cause their interest in the classes and the desire to eliminate gaps in knowledge, and for this it is necessary to impose faith in them in their forces. It is necessary to open the reasons for their lag before students and indicate ways to eliminate spaces, it is necessary to carefully follow the students, help them in class and at home, celebrate their slightest successes. The desire to learn is formed in the process of successful work on the material, so it is important to organize individual assistance in such a way that the student constantly felt his promotion. As experience shows, often even a minor promotion turns ahead of students, excites them more intensively and increases interest in classes, and this ensures them successful mastering the material. Some believe that individual assistance to students is only working with them outside the lesson. This, of course, is incorrect. Individual work with students is, above all, constant attention to each of them during the lesson: during the survey of students, in the process of presentation and consolidation of the material, as well as when explaining homework.
Group additional classes Organize only in the most exceptional cases.
Such groups must be small in the number of students engaged in them. This is mainly those students who missed classes for any reason or the one who is incomprehensible to anyone.
How do I organize individual work with students?
First of all, I try to identify the weak and strengths of each student, keeping accounting, what students are behind, what rule make mistakes.
When performing written exercises, when checking homework, paying special attention to the lagging: I give them individual tasks, I work with each student on the mistakes allowed. When parsing errors, the main attention is paid to typical errors that are found in many students in control dictations. These errors are dealt in the class.
The main thing is individual work with each lagging. To account for errors in the Russian language, I will buy a special notebook in which the page is given, where the subject of the lesson is fixed (which children are difficult and put + or - near every surname). Installing which errors one or another student allows, I give a task on a textbook or Card at this rule. After each test dictation, the words on those rules that students are already learned, in his card are drained, and new words, in the spelling of which errors are made in the dictation, are entered into a card. Valuable in this form of organization of individual homework students in the Russian language is that it does not require bulky accounting. Preparation for this work is also not a time-consuming for the teacher. In my work, I apply individual cards. Individual additional work of students gives a big effect. But it requires hard work as a student and teacher, since additional work should be fulfilled by the student, and the teacher is to check.
Very good acceptance of work on errors is, in my opinion, this method. I discharge mistakes from 2 - 3 control dictations with their explanation. After the children intertwically digeantly, the rule and learn the words in which they made mistakes, a self-task is given: Write creative dictation or an essay using words and suggestions with errors.
Examination in the footsteps of their errors is very useful. Forms and methods of individual work in the lessons of the Russian language are diverse. When preparing for the lesson, I plan to give some of the students during the survey to prepare more time, and to whom is smaller who ask the table, at the board, who will give a card.
When surveyed 1, I make focus on the practical part of the material, to apply the rule to the ability, from another requires an explanation of the meaning of the rule, from 3 to achieve a clear, consistent recovery according to plan. As additional material 1 - analysis of the composition, 2 - explanation of spelling words, 3 - declination or losing words.
Individual work with students during the explanation of the material plays a big role. It can take a variety of forms: I appeal to one student with questions, another I propose to give examples, thirdly attract illustrations. It activates educational process, involves all students to work and helps to learn the material. The question of who from students what task is to offer, solve, too, taking into account their individual characteristics.
If the student is distinguished by instability, i.e., the inattentive, I appeal to him, I attract it to the analysis of examples, I propose to repeat the appropriate position, students who remember the material mechanically, I propose to choose your examples, explain the spells or punctuation signs, retell the rule in your own words.
As a didactic material during the presentation, I use examples in which students made mistakes in written works.
The assimilation of spelling is a complex process. Ways of mastering spelling are diverse. They follow not only from the specifics of the educational material, but also from the psychological characteristics of children. The teacher must take these features and, above all, all types of students' memory.
Almost this means that in the process of explanation, the teacher must combine the word with visibility, the story with the elements of the conversation, the analysis of examples recorded on the board, with the analysis of examples chosen by students, since children in children are different: visual, auditory, motor. The fixation of spelling material is one of the most responsible stages of the lesson.
One of the common drawbacks in the teaching of the Russian language is the underestimation of hearing problems, especially when consolidating. Performing cool or homeworkStudents usually perceive the orfirogram of visually, reinforcing its visual image only by motor perception. Sound image in this process, as a rule, is not involved. Not surprisingly, therefore, that even students have time to make mistakes in hearing dictates for this rule. It is simply explained: in the process of working on material, students were focused on visual and motor perception of spelling, and during dictation - to the auditory, that is, at that kind of memory, which did not participate in the work on the material. From here it is seen: working on the spell, the teacher must combine the tasks so that all types of students participated in the assimilation of it. To this end, I practice pre-pronounce separate words (words with non-promotable consonants, unverified vowels, etc.) I spend warning, explanatory dictations.
An individual approach to students and in preparation for test work. Preparation for dictation I start a few days before it. In front of the dictation, I inform you to repeat specifically. I give to memorize the words that are difficult and can meet in dictation, I spend training in the formulation of punctuation marks, we deal with words in composition. When dictates are written, the students check them. Check are carried out purposefully, under my leadership. For example, I propose to first find and check the writing of all, nouns, then find adjectives and verbs. After such an inspection, the text is read again and note the notebooks. Sometimes, when the work is handed over, I ask what it seemed the most difficult. Then I write down difficult orphograms on the board. For fresh tracks, the correct writing is better fixed in the memory of students.
To individual work with students, I proceed from the very beginning school year. And after lessons, I spend only when the student missed a lot or did not understand the material. If the student has undertaken to fulfill the task, from such a demand secondary execution, sometimes leave after lessons. In other cases, I spend the work individually with each lagging students. Practicing notebooks for additional work. Depending on the nature of the errors, I invest in the notebook of the student with a task. You should not give several cards at once - so as not to burden the student work. Students willingly work on their mistakes with cards - tasks. Each independent work to correct errors is checked by the teacher and the journal necessarily exhibits evaluations on a par with estimates for testing.

Rules for the Teacher when working with "Larous Summer Pupils

1. Believe in the ability of the "weak-sleeping" student and try to give him this faith.
2. Remember that the time for the "delicious" need to understand the material passed. It is impossible to rush it.
3. Each lesson is the continuation of the previous one. The multiple repetition of the main material is one of the techniques of work with "delicate" students.
4. Installing children Hope in what they will remember, will understand the material, more often give them the same type of tasks (with the teacher, with the class, independently).
5. Working with "weakly speaking" children is a huge work and patience. The gradual development of memory, logic, thinking, interest in teaching.
6. Do not chase for a lot of new information. Choose from the material being studied the main thing, repeated repeated and fix it.
7. Head to arrange such children to yourself. Communication is the main component of any technique. Only then receives the result of training.
8. Learn to manage the class. Lessons must be diverse, then the attention of students will be riveted to the material studied.
9. Starting purposefully work with "weakly speaking" children, remember: after some time, their group will again break up - on capable, average and ... "weakly speaking."
10. Learn to attract stronger children to teaching "weakly speaking" children. The material was outlined, interviewed the strong - put them to "weak", and let the study continue.

1. When a "slack-free" survey, students need to give an answer algorithm; Allow the use of the plan drawn up when preparing homework; give more time to prepare for the answer at the board; Allow taking presets, enjoy visual benefits.
2. If possible, ask the students leading questions that will help them consistently set out the material.
3. Systematically checking the learning material on the topics of lessons on which the student was absent for one reason or another.
4. During the survey and when analyzing its results, create an atmosphere of goodwill.
5. In the process of studying a new material, the attention of the "weak-sleeping" students appeals to the most complex sections of the topic studied. It is necessary to address them more often with questions that find out the understanding of the educational material, to stimulate the questions of students in difficulty in the assimilation of the new material.
6. In the course of independent work, at the lesson, weakly needed students are encouraged to exercise aimed at eliminating errors allowed by them with oral responses or in written works.
7. It is necessary to note the positive points in their work, difficulties and indicate how to eliminate them, assist with the simultaneous development of independence in the teaching.

JavaScript,

Reactjs

Website development

• Transfer

Yesterday I talked with a friend who is looking for a developer to open vacation. He expressed some disappointment that I also experience lately:

I have problems finding a frontend developer, mainly by WP, FOUNDATION, CSS, JS, to a low-level position. I can not understand what's the matter. No one from the candidates no "basic knowledge" is nothing of the listed. But they can do sites on React or other JS frameworks, or on the basis of WP templates. But if I say that you need to make simple changes in CSS, look empty eyes ... or some trifle on pure JS, nothing.

There is no shortage of training camps, courses, fully resources for studying frontend development. But I interviewed a bunch of guys from these training camps and I think that there is seriously underestimate the importance of CSS and the basics of JavaScript.

Of course, there are restrictions on how much you can assimilate in 12 weeks of training. But a huge part of the problem is that our industry admires new, is obsessed with the most last and beautiful SPA-frameworks, at the same time devalued CSS and "old" implementations.

Admiration new

Our industry admires new approaches to the development. What else can you explain the continuous desire to throw away all the developments and "remake from scratch" every time a new, best and more complex framework appears? Every time we argue that this will lead to a cleaner, simple, ideally abstracted architecture, and each time everything ends with the invention of bicycles, recreating the bugs and the discovery of all border situations that again lead to the same ugly code.

It does not mean that never needs to rewrite or that new is never the best. We just fell victims of a cult of free thing and ideas of perfect abstraction. Each new architecture is ideal until it faces the hardest conditions of the real world. Unfortunately, people are pretty chaotic creatures, and all our software is created to solve human problems. Therefore, each program in real world Ends up holey abstractions, clumsy border situations and new compromises.

This race on endless alteration and concentration only in the last and best often leads to the abandonment of the previous solutions of those problems that eventually appear again. It also leads to the fact that we apply new tools in completely unsuitable areas, simply because they are new.

Obsession with the latest and beautiful SPA frameworks

Publishing a list of sending on Frontund Development, I see this problem every day during the current SPA boom. I read a huge set of articles where the authors write about different technologies, and believe me, almost everything in the world JavaScript write about one or another of these frameworks as if it is absolutely new and unique innovation. Although these are excellent tools, but each of them is created to solve a particular problem. They are based on a similar basis and make a different choice depending on the tasks for which optimized.

You can take a REACT for example, because it is so moving so much in the past few years ...

Do not get me wrong, I love React. This is a phenomenally powerful tool. It does not only possible, but also simple creation of interfaces that seemed unreal when I started web development. However, newcomers in the industry come and see all this noise around REACT and suggest that this is the only truth, as you should write on JavaScript. Make a new web application? Use React! Non-standard blog template? REACT! Redo the old site? Go to REACT!

This is a catastrophic approach to using technology! And do not listen to me, listen to one of the most prominent developers in the REACT community, Dan Abramova! When Corey House asked for the deficiencies of React, Dan gave the most detailed description:

ITS PERFORMANCE IS WORSE THAN TEMPLATES IF MANY THINGS UPDATE EXTREMELY FAST AT THE SAME TIME. For example Stock Trading Apps.

Dan Abramov (@dan_abramov) September 16, 2017

"Its performance is worse than templates, if many things are quickly updated at the same time. For example, applications for stock trading "

IT Trades Memory Pressure for Expressiveness. React Apps Typically Do More Short-Lived Allocations Under Heavy Load.

Dan Abramov (@dan_abramov) September 16, 2017

"For the sake of expressive language abilities, the memory is sacrificed. React applications usually make more short-term accommodation in memory under heavy loads »

It's Mostly Driven by The Needs of Facebook. So If Your Apps Are Very Different from What FB is Building, May Not Satisfy Your Use Case.

Dan Abramov (@dan_abramov) September 16, 2017

"It is mainly designed based on Facebook. So if your applications are very different from what Facebook does, then REACT may not come for your needs.

This is only a part, but Dan's openness pushed the measles to the answer:

Gotta Say, I "M Floored That The Best Input I" VE Gotten on Why "Not * to Use React Is From You Dan. Really Admit SUCH CANDOR AND NUANCE.

Cory House (@Housecor) SEPTEMBER 17, 2017

"I must say, I am amazed that the best list of reasons not Use React came from you, Dan. Really admire such a frank and detailed answer "

Obviously, Dan has no illusions that REACT is ideal for everything; He is well acquainted with compromises to which the developers went! But such a large part of the community hurries to switch to SPA frameworks for everything in a row and completely ignore the fact that these tools solve specific areas of tasks. Yes, it is phenomenal tools and great pleasure to work with them ... But often they are absolutely not suitable for solving problems in other areas.

Exalting frameworks over all the rest, we do not notice solutions that are much more suitable for these areas.

Depreciation CSS.

The industry has a tendency to humiliate HTML and CSS as "not real development" and something low. I think it comes from the fact that the logic has become overclocked over graphic / spatial thinking ... CSS and HTML embody hierarchical, graphic and spatial relationships, while JavaScript focuses primarily on logic.

But a wonderful feature of logical languages \u200b\u200b/ expressions is that they can often include Other types of relationships ... What allows you to express spatial relationships in a logical language. However, in the industry often incorrectly interpreting such a large latitude of a possible expression as the fact that the expression in this language is strictly superb.

This is not true!

In fact, if you look at examples from mathematics and physics, then often the opposite! In these areas, if you start with a logical model, then often desperately trying to find a spatial or graphic model that can be applied here.

The reason is that these spatial models often reveal much more intuitive or concise ways to present problems - and they lead to important insights and conclusions that we are then painstakingly try to translate back to a logical form.

CSS represents an incredibly powerful framework for expressing graphic and spatial relations, sometimes solely difficult!

Preservation of complexity

This leads me to my key thesis on the development of software preservation of complexity.

In any problem, there is a certain inherent level of complexity, and this complexity must be taken into account somewhere.

This emerges in many cases, but in this example we are about the complexity of expressing graphic and spatial relations. Various items on the page are spatially interconnected with each other. incredible A difficult way at different levels, especially taking into account the manipulations and movements of these elements. This complexity should be somewhere taken into account, and in the case of CSS browser makes almost all the work for you!

There is * incredibly a lot of JavaScript code, written simply because the developer does not know enough CSS well enough.

Truth. I WORKED ON PROJECT THAT HAD 2000 LINES OF JS TO DO WHAT POSITION: Absolute Already Does Because The Didn "T Understand IT

Sarah Drasner (@Sarah_edo) September 16, 2017

"It's true. I worked on the project, where 2000 Lines js did what was already implemented in Position: Absolute, simply because the developers did not understand this "

What to do?

I am not trying to say that we should not use or teach people the newest and best tools. SPA frameworks like React, Angular, Vue and Ember allow you to create in the web an incredibly powerful interfaces that were simply impossible only a few years ago. These tools really changed the idea of \u200b\u200bwhat is possible to do online.

But I believe that the elitism of the SPA should be eradicated and re-emphasize the importance of basic knowledge and choosing the right toolkit.

The creators of these frameworks rarely declare that they are good for everything in a row, but in the industry they are so elevated that newcomers completely missed the study of the basic basics and suggest that only this complex toolkit is the only "correct" way to solve their problems.

If all new developers will look at CSS with contempt, we will come to the fact that 2000 JavaScript lines will try to re-implement Position: Absolute; .

If all new developers decide that the new HTML code and JavaScript can only be written through SPA, then we will come to exclusively redesigned, buggy and brake blogs, marketing sites and the rest, which is now well implemented on old technologies.

We should seriously talk about what skills we expect from developers in our industry and what we teach them. It is quite normal to start learning a novice in some training camp, but there is a serious gap between modern graduates of these camps and the fact that the industry requires. It may be unrealistic to expect compliance with these requirements after 8-12 weeks of study, but you need to directly send them to the right path.

To the curriculum of the basics

I did not make a textbook of the basics of web development, but several things would definitely include there. They are listed below with reference to free and paid resources for a deeper study, but what would you include on the list? Write in the comments.

CSS.

1. Basic block model in CSS (Box Model). This is the main of the foundations that you must understand. As a free resource, you can recommend Neck Hou from His free Course Learn to Code HTML & CSS. From a paid side, especially if you easier perceive audiovisual content, my friend James Stone has a good video course on a block model in CSS.
2. CSS specificity. This is one more important basiswhich you need to understand if you are going to do web development. Without a solid understanding of the specificity, you will continually try to force your CSS code to work as needed. SMASHING MAGAZINE There is a great overview for a start.
3. Flexbox.. The FlexBox specification produced a revolution in the layer methods, and you will certainly need to take advantage of this technology. The best resource on FlexBox, which I saw - this directory from CSS Tricks. If you are looking for a FlexBox video course, see

"Detection and elimination of gaps in knowledge, skills and students' skills - one of the main conditions for improving the quality of education"

Mathematics it appears before the teacher in various sides.

Mathematics - deductive science, axiomatic method and some reference standards.

Mathematics - Method of knowledge of the world and tool for practical activities in this world.

Mathematics - This is a specific technique, a set of techniques and methods for solving a variety of tasks. The ability to constantly train and improve this technique.

Mathematical education should with sufficient completeness to reflect all sides of mathematical science. And reflect not only on paper: in programs, textbooks, but also in practical work Teacher. Mathematical education should expand due to historical information, due to the enormality and practical significance of the tasks being solved. In addition, it is necessary to bring up respect for science - the hard work of the human mind.

Nowadays, in the context of the development of a market economy, when there is an unprecedented increase in information, from each person is required high level Professionalism and such business qualities as enterprise, the ability to navigate, make decisions, and it is impossible without the ability to work creatively.

Education in general and mathematical in particular, I understand, first of all, as management, as a leadership development. I believe that there is no emphasis on knowledge and skills in itself, how important is the impact on the development of the child. I teach my students to think logically, think, appreciate the opinion of others and defend your own.

Work on identifying and eliminating gaps in knowledge of students is an integral part of the activities of each teacher. The timeliness and thoroughness of this work is the key to high learning results.

The teacher-practitioner knows how painstaking and important this work. If you do not pay a given question of serious attention, then very soon even the capable students are marked in errors. It is impossible to diminish the roles and let this work on samonek, which is called, from the case to occasion. It is necessary to conduct activities to identify and eliminate gaps in knowledge systematically and systematic.

It is difficult to identify this species pedagogical activity From the holistic process - the learning process in which everything is interconnected.

Systematic work on identifying and eliminating shortcomings and gaps in students' knowledge is one of the main conditions for improving the quality of education. The teacher should use generally accepted forms and to invent, implement its control tools, skillful possession of which warns the lag, provides active work Each student.

Objectives:

formation of durable knowledge;

training of self-control techniques;

formation of the need for self-control;

raising responsibility for the work done;

development of individual creative abilities Pupils.

Tasks solved during work

Controlling . Identifying the state of knowledge and skills of students, their level mental Development, studying the degree of assimilation of the techniques of cognitive activity, rational learning skills. Comparison of the planned result with valid, the establishment of the effectiveness of the methods used, forms and learning tools.

Tutorial. Improving knowledge and skills, their generalization and systematization. Schoolchildren learn to allocate the main thing, the main thing in the material studied. Checked knowledge and skills become clearer and accurate.

Diagnostic. Obtaining information about errors and gaps in knowledge and skills and generating their causes. The results of diagnostic checks help choose a more intensive learning methodology, as well as clarify the direction of further improvement of methods and learning tools.

Prognostic. Obtaining advanced information: whether it is enough for specific knowledge, skills and skills to assimilate the following portion of the educational material. The forecast results are used to create a model for further behavior of the student who makes this type of error today or having certain gaps in the system of intake of cognitive activity.

Developing. Stimulating the cognitive activity of students. The development of their speech, memory, attention, imagination, will, thinking.

Orientative . Receiving information about the degree of achievement of the goal of learning a separate student and class as a whole. Focus oriented in their difficulties and achievements. Opening the gaps, errors and shortcomings, indicate the directions of the application forces to improve knowledge and skills.

Raising. Education from students responsible attitudes towards learning, discipline, honesty, perseverance, habits for regular labor, self-control needs.

The organization of work on identifying and eliminating gaps in knowledge is divided into steps: identifying errors; Fixing errors; Analysis of assisted errors; planning work to eliminate spaces; Elimination of Zun gaps; Prevention measures.

From the 5th grade, I start with students with common notebooks (96 sheets) for algorithms that are conducted to grade 11 (Appendix 1).

From the 5th grade, I start with students with general notebooks (96 sheets) for additional work on eliminating gaps in Zun, which are underway to grade 11 (Appendix 2).

Stage I. Detection of errors

It is carried out during the verification of written works, oral answers, self-control and mutual control.

Written works I spend regularly. Strictly followed the independence of execution. The most effective (to identify errors) I believe in written works:

at the beginning, over half and at the end of the school year - test work followed by the preparation of a table with results in a special notebook, in which the errors of each individual and the class as a whole are clearly visible;

individual independent work on the analysis of errors;

during the school year - traditional control and preceding verification and independent work, written survey of theoretical material;

to assimage the control of the "narrow" topic: Mathematical dictations ("Finish the phrase", "Fill the Pass", "formulate a question", "Calculated orally and write the answer"), "chains" (to verify the learning of knowledge with numbers and polynomials), mini tests ("I agree with the statement - put" + ", otherwise" - "). The tasks of this type allow you to quickly and, most importantly, to promptly detect gaps in knowledge on the topic under study, which is useful and to the teacher, and the disciple.

Oral check Zong is aimed at identifying typical errors of a particular theme and general scientists and skills. It is effective if aimed at identifying the meaningfulness of the perception of knowledge and the awareness of their use, if it stimulates the independence and creative activity of students. Quality of questions is determined by the nature of mental actions that are performed by students when answering the question. Therefore, among the verification tasks, we allocate questions that activate the memory (to reproduce the studied), thinking (on comparison, proof, generalization), speech. Great importance Have problematic issues that make the knowledge gained in practical activity. The quality of verification depends on the selection of questions and the sequence of their formulation. Each question should be logically completed, extremely compressed and accurate. Allow two conditions for high-quality knowledge detection:

- nobody interferes with the student (the answer commented later);

- it is possible to interrupt the student only if it does not answer the question, but evades.

Oral checking intakes using at various stages of the lesson.

Practice students of skills and skillsselfontrol Not only allows them to find their own mistakes, but also a beneficial, psychological and pedagogical point of view. Forms: "Find and explain the mistake" (your admitted by a classmate planned by the teacher), "Check the answer and understand the error", "Raising your answer."

Interconnected Quality and efficiency learning activities Schoolchildren helps the teacher to verify the knowledge of students and promotes the development of such qualities of personality as honesty and justice, collectivism. "Ask a question", "Find a hole in the decision (as in the Mathematical Boy) and ask a question" (To help the responsible to find a mistake), "Give a review of the answer", "Explain the decision of a comrade", the mutual test of domestic and verification work, Rules, formulas, theorems, definitions, not all forms of the interconnection. Positively also the fact that the mutual test can be carried out in after-school time. The mutual test of knowledge activates the activities of students, increases interest in knowledge and like them. In the course of mutual control, individual features of students are revealed, interest in knowledge increases. The guys like the process itself, their relationships are strengthened with comrades.

At this stage, the correctness of perception and understanding of the educational material is analyzed, weaknesses are revealed in knowledge, shortcomings, gaps, errors in the works and responses of students are revealed. This allows the teacher in time to schedule measures to overcome and eliminate them.

Stage II. Fixing errors

Fixing errors occurs in parallel to their identification, but not every student is able to assimilate the material and develop strong skills and skills even after the classic chain: the teacher showed - the student himself pester - the teacher pointed to errors - the student performed work on errors. Getting Study new topic, Schoolboy often forgets a lot from the previous material. Only by repeated, long, periodic repetition by each student of their "problem" topics, returning to the "weak" link in the knowledge chain, you can achieve results in mathematics training. It is necessary to maintain strict accounting of errors in the form of a list, to work regularly with it: make changes to keep an error on control to that time until there is a solid confidence as a learning. This occupation is not of the lungs, it requires patience and time. But the goal justifies funds. And one who will pass this path will be rewarded by the academic achievements of their students. Rational forms of fixing errors, in my opinion, are the following:

Error accounting note contains a list of class and monitoring of "certificates" with all written works. Information about specific errors is entered into this notebook, knowledge learned is carried out. Visually can be seen who has any problems who did not pass.

In the course of the lesson, when doing homework, I strongly recommend students if something could not immediately understand, put the mark on the fields (like "?") To then think or use the help of the teacher, classmate. Fart the students saying not to leave "incomprehensible" sites without attention.

III stage. Analysis of admitted errors

Analysis of the mistakes made after each type of work orally or writing, a teacher or student - depending on the kind of activity. A quantitative and qualitative analysis is carried out. A carefully conducted analysis allows to deeply examine the gaps and the achievements of individual students, to highlight typical errors and the main difficulties of students, study the reasons for their appearance and outline their removal paths.

IV stage. Planning work to eliminate gaps in knowledge

This work is based on the analysis, the results of which are brought to students.

The teacher outlines when, who, for what purpose, ask and what to use the funds for this.

Working on errors is carried out after each written work, re-offline, after unsatisfactory mark.

Strict control is carried out for each student to fulfill all control and credit work (even missed).

V stage.

Elimination of gaps in knowledge

Analysis of work in the class.

Finding out the view of the class about the results obtained.

Work on errors, individual and frontal, with mandatory follow-up written check (before receiving a positive mark).

Tasks for repetition during the front survey and individually (before receiving a positive mark).

VI stage. Prevention measures

It is difficult to treat the disease, it is better to prevent it. Errors - also a kind of illness. The following preventive measures contribute to minimization.

Texts of written tasks must be convenient for perception: competently formulated well readable.

Active oral testing of the main zone, regular analysis of typical errors.

With the explanation of the new material to predict the error and choose a system of tasks to work out the correct assimilation. Compatient attention on each element of the formula, the performance of differentty tasks will allow the minimity to minimize.

Selection of tasks causing interest forming sustainable attention.

A durable absorption (which means that there is no mistakes) contribute to the rules that are convenient for memorization, clear algorithms, following which will know the target.

Systematic teaching to self-control allows to achieve noticeable results. At the same time, the general mathematical culture of schoolchildren, their work and answers become more competent.

Attachment 1

Algorithm

find the coefficient.

Signed numeric factors ahead of the expression.

They recorded alphabetic multipliers at the end of the expression.

Found a product of numerical factors.

Simplified alphabetic multipliers, using a multiplicative and the combination property of multiplication (alphabetic multipliers can be several).

Numeric factor (one) - coefficient.

Example: a)= -24 m.

b) = - 96 m.

Algorithm

solving problems for direct

and inverse proportional dependencies.

An unknown number is indicated by the letter x.

The condition is recorded in the form of a table.

This establishes the type of dependence between values.

Straight proportional addiction It is indicated by the same directional arrows, and inversely proportional dependence - oppositely directional arrows.

The proportion is recorded.

Her unknown member is.

Appendix 2.

The notebook of learning to learn topics.

F.I.

student

The topic according to the program designed for 8 hours

Lesson number 1

PR№1

DZ #1.

Lesson number 2.

PR№2.

DZ№2.

RO №1

Lesson number 3.

MD №1

DZ№3.

RO №2.

Lesson number 4.

OSR No. 1.

DZ№4.

RO number 3.

Lesson number 5.

CP №1.

DZ№5.

RO No. 4.

Lesson number 6.

CP №2.

Kr

Analysis of the Kyrgyz Republic, Ro

All homework is carefully checked in the class.

1. The following on the topic has passed (after test work on the topic) are eliminated in notebooks on the liquidation of spaces.

2. Foundations are selected by didactic material (Gives a week).

3. The student writes repeated test, The mark is put in magazine (test work analysis).

Appendix 3.

Independent work on levels ::

Solve the system of equations:

Graphically.

Method of substitution.

Way of addition.

Block A block in

There are gaps in knowledge.
They could appear for a variety of reasons, sometimes completely independent of children.
Someone fell ill and missed the lessons at school. This is the most common cause of spaces. After all, some topics are presented in the textbooks at all in the best way.
And someone flees the teacher. And when I went to work, it was forced to catch time: in the hourly program, the teacher's lesson is not laid.
This year the lessons were canceled due to the flu epidemic. This means that all teachers will try to catch up with a missed time.
Someone from the guys misunderstood something in the lesson. Does the child have the right to not misunderstand something wrong?
Believe me, transferring reasons can be continued to infinity. But it is better to talk not about the reasons, but about the consequences.

1. Sloves in knowledge - trouble, but trouble is corrected

Therefore, encountered with a space in the knowledge of the child, do not be discouraged, and rejoice. It is very good that you have discovered the gap. Why?
Slobs in knowledge as an incomplete wound. They are bothering a person, bring inconvenience, limit freedom. In school life, they can turn into unpleasant surprises in the form of bad marks. It turns out that gaps in knowledge are a source of constant stress that the child is depleted, undermine the faith in itself and interfere with living. Often, the guys cannot determine what they have gaps. The child knows that he does not know something. And that's it. Why a mistake in the analysis? Does not know why. The child is not able to realize that when he had an angina three years ago, the school was explained new Materialwhich is not in the textbook. About angina is so, only for example, the reasons, as we defined, can be different.

2. Useful assumption

Be sure to make an assumption: maybe my child has other gaps in knowledge. Believe rarely, when such an assumption is not confirmed. Why? Because the language is a system, and not a random set of random items. If a child knows one element, he does not know the connections of this element with others. So, properties, signs, functions, the nature of entire classes of phenomena for him is incomprehensible.
In order to figure out that the child knows, and what does not know, and if he knows, he understands whether to the end, there are on this site

• section of forces,
• rubric Trial of forces. Total test In each chapter of the theoretical section, Russian grammar. Directory on theory for 5 - 11 classes.

Any child can undergo diagnosis and find out which gaps in knowledge he has.

3. If there are mistakes in the notebooks, we assume thoughtfully

Errors in writing are one thing, and in the instructions - another.
Many mistakes are symptomatic. Often, different errors have one reason. Understand it - it means to find the right path. Since the language is a system, then errors can be systemic.
Imagine yourself by a doctor. On the one hand, one disease has different symptoms. And on the other, the individual symptoms of different diseases may coincide. For successful treatment, the correct diagnosis is needed.
The same situation with errors. Errors - this is not the disease itself, but the symptoms of unfavorable. In order for such symptoms to assemble and deal with them, determine their reasons, we offer to undergo testing on the site as regularly, like trainings.

4. If the child has a lack of knowledge, then the question is naturally the question: where to take them, from which source you draw?

Take the textbook of your child. This is also a source of knowledge, more precisely, one of the sources.
Read paragraphs. In sequence. Thoughtfully. Spend on this occupation hour of your time. Then appreciate what you learned. Is it a lot or a little? Remember, the child has no experience with information. This means that it will be even smaller with the volume of learned material, and the number of time spent even more.
Even if you are satisfied with the content of the paragraphs of the school textbook, think about the fact that this source of knowledge is not always at the child at hand. What if the topic was studied last year? Two, three years ago? In our school there is a long tradition to issue books by the guys at the beginning of the school year and take them at the end. Not all parents can buy all school textbooks. It is expensive, I assure you. And where to store them? Most of our families live in very constrained conditions. And how to know what books to buy? Which of them are more necessary?
This site is also a source of information. Strengthen the study sections one hour. Compare the feed efficiency here and in the school textbook.

5. Knowledge comes through understanding, awareness

Never force the child to learn the rules on the textbook without understanding. It is not useless - it is harmful. Nothing but disgust for the subject you will not achieve.
If you are a supporter of traditional technologies, then first disperse in everything yourself. Think out overall logic, as well as all the details and trivia. Then give the child the essence itself. Explain simply, accessible as small. Then be sure to check how the child understood you.