Our home is our fortress! information and analytical portal of independent parents! How to help a student overcome knowledge gaps.
PERFORMANCE
at the pedagogical council
Working with underachievers, closing gaps, increasing interest in learning as a way to improve the quality of education
mathematics teacher: Gataullina F.Kh.
The problem of academic failure worries everyone: both adults and children. Obviously, there is not a single mentally healthy child in the world who would like to study poorly. When dreams of successful school years are dashed by the first “f”, the child first loses the desire to study, and then he simply skips classes or becomes a “difficult” student, which most often leads to new negative manifestations in behavior. Underachieving students begin to look for people around whom they will not feel insignificant. So they end up in yard companies, joining the army of hooligans and drug addicts.
A student may lag behind in learning for various reasons that are dependent and independent of him:
u absenteeism due to illness;
u poor general physical development, presence of chronic diseases;
u mental retardation. Often children with a diagnosis are taught in general education classes due to the lack of correctional classes or the reluctance of parents to transfer the child to a specialized class or school;
u pedagogical neglect: the child’s lack of developed general educational skills and abilities over the previous years of study: low reading technique, writing technique, counting, lack of independence skills in work, etc.;
u dysfunctional family;
u the problem of the “street”;
u absenteeism.
We, subject teachers, must know why a student does not master the curriculum, and how he can be helped in this matter. School specialists (doctor, psychologist, speech therapist, social pedagogue) should help the teacher and class teacher to establish specifically the reasons for underachievement. the student's parents, himself and his classmates.
Goals:
Closing student learning gaps;
Creating conditions for successful individual development of the student.
What is the first thing you need to do when working with low-achieving students?
Create a favorable atmosphere in the classroom;
Provide timely assistance in additional classes and organize the work of consultants;
Change the forms and methods of educational work in the classroom in order to overcome the passivity of students and turn them into an active subject of activity. Use educational games for this;
Free schoolchildren from the fear of mistakes, creating a situation of free choice and success;
Orient children towards values: man, family, fatherland, work, knowledge, culture, world, which cover the most important aspects of activity;
Cultivate physical development and a healthy lifestyle.
Plan for working with low-performing students
| Events | |
| 1. Conducting a test of the knowledge of class students in the main sections of educational material from previous years of study. Target: a) Determination of the actual level of knowledge of children. b) Identification of gaps in students’ knowledge that require rapid elimination. | September |
| 2. Establishing the reasons for the lag of low-performing students through conversations with school specialists: the class teacher, doctor, speech therapist, meetings with individual parents and, of course, during a conversation with the child himself. | September |
| 3. Eliminate gaps in knowledge identified during the tests, and then conduct a repeated knowledge test. | During the school year. |
| 4. Using a differentiated approach when organizing independent work in the lesson, include feasible individual tasks for low-performing students, and record this in the lesson plan | During the school year. |
| 5.Use various types of questioning in lessons (oral, written, individual, etc.) for objectivity of the result. | During the school year. |
| 6. Regularly and systematically survey, assigning grades in a timely manner, avoiding the accumulation of grades at the end of the quarter, when the student no longer has the opportunity to correct them. | During the school year. |
| 7.Notify the class teacher or directly the student’s parents about low performance if there is an accumulation of unsatisfactory grades. | During the school year. |
| 8. Keep a mandatory thematic record of the knowledge of low-performing students in the class, and, if possible, keep a thematic record of the knowledge in the subject of children of the entire class. | During the school year. |
| 9. Conduct additional (individual) classes for low-performing students. Teach children independent work skills. | During the school year. |
How to encourage students to be active and intensive during the lesson?
Among the various areas of new pedagogical technologies, the most acceptable from my point of view is group technology :
Firstly, because in a classroom-lesson system this type of lesson fits most easily into the educational process.
Secondly, group technology ensures not only the successful learning of the material by all students, but also the intellectual and moral development of students, their independence, goodwill towards each other, sociability, and desire to help others.
I will highlight the advantages of group training over traditional:
introduction to important life skills: effective communication, the ability to listen, the ability to take another’s point of view, the ability to resolve conflicts, the ability to work together to achieve a common goal;
improving academic performance;
education of self-esteem;
strengthening friendship in the class, changing attitudes towards school;
lack of competition in educational activities;
Convincing students of the value of mutual assistance.
To increase the effectiveness and real result of the lesson, to enhance the cognitive activity of students in mathematics lessons, I use a system of key tasks. Its use allows, on the one hand, to include each student in the work, and on the other hand, develops systematic, logical thinking of students. For motivated children, there is an opportunity to analyze and evaluate the material in full, compare different solution methods, and determine the limits of applicability for further use of the acquired knowledge when solving more complex problems.
How can we ensure that the lesson not only equips students with knowledge and skills, the significance of which cannot be disputed, but that everything that happens in the lesson arouses sincere interest in children, genuine passion, and shapes their creative consciousness? For effective educational activities of all students, differentiate them according to their level of preparation, encourage students who are good at mathematics, and support those who have difficulties. That is why I use elements of the “Differentiated Learning” technology in my work.
The formation and development of cognitive interests is part of the broad problem of raising a comprehensively developed personality. The principle of the child’s activity in the learning process has been and remains one of the main principles in didactics.
This concept means a quality that is characterized by a high level of motivation in the acquisition of knowledge and skills. This kind of activity in itself occurs infrequently; it is a consequence of targeted managerial pedagogical influences and the organization of the pedagogical environment, i.e. technology used. One of these technologies is gaming. Game technology ensures the unity of the emotional and rational in learning.
At the present stage of development, it is difficult to imagine a society without computers, therefore one of the main tasks of education is to introduce people into the information space. With the help of a computer, you can significantly increase the visibility of learning, ensure its differentiation, and facilitate the testing of students’ knowledge, abilities, skills.
At school, we sat together in the back desks, but thousands of questions about the universe still remained. How to fill in the gaps?
For unknown reasons, at school we were bored reading textbooks on various “extra” subjects: “I’m a future economist, why do I need this?” In part, you will be right that you really don’t need this for the Unified State Exam, but, you must admit, it’s better to know than not to know.
As adults, we eagerly absorb books about the Universe, microbes, animals, anatomy, etc., because we have grown up and the questions remain. The sooner we start filling in the gaps, the better – all the accumulated knowledge will always be needed. For example, who knew that calligraphy lessons would lead Steve Jobs to worldwide fame? It's never too late to start. Start now.
We tried to convince you that it’s worth catching up on lost knowledge, and now we offer a couple of books that are simply a must read.
livelib.ru
1. Brief history of time. Stephen Hawking
Without further ado, it is worth saying that this book is simply brilliant! After reading this book, you will want to book a ticket on a rocket and fly away. Doesn't string theory, black holes, space-time context, and much more sound tempting? After reading the book, you can go watch “Interstellar” and competently comment on every moment. This book is not even about space, but about the magic and magic that happens above our heads.
vladtime.ru
2. Look what's inside you. Rob Knight
Did you know that the number of microbial cells exceeds human cells by 10 times? Gastritis, depression, allergies - all this is the result of the work of your microbes. It's stupid not to know anything about them, right? When you read this book, you feel like a small child who constantly opens his mouth in surprise and mutters: “It can’t be...”. Did you know that diabetes, arthritis and depression are very often caused by the fact that... you had little contact with animals as a child and that, most likely, there was no summer at grandma's, where most children plant flowers, eat cherries from the tree and run barefoot around village. These and other secrets of our roommates can be found in this book.
superomsk.ru
Yes, it doesn’t look like a book, but it is a resource for an artistic extravaganza. You can visit any museum in an hour! Right now I'm walking through the Guggenheim Museum. And now I’m in Portugal admiring the local street art.
wm-painting.ru
4. Bridge over the abyss. Paola Volkova
An excursion into history and art. There are 6 books in total in this series, each telling about a different time period. Some criticize Ms. Volkova for the fact that the narration is a little chaotic (this is clear: Paola Volkova is a born lecturer who talks about everything in an exciting way), but it is impossible to accuse her of boring presentation. For those who found the MHC course superficial and too fast.
I'm deteriorating. I'm in tenth grade. I finished the ninth year with almost an excellent certificate; it wasn’t too difficult for me to study. But this school year something changed in me. Now I have become interested in science and plan to choose a profession related to physics, but I understand that this requires high intelligence. I became insanely lazy, began to “get sick” (diseases are real, but I make mountains out of molehills, something terrible out of a common cold) for two or three weeks. At this time, I can read, study the subjects I need, and do at least simple homework. But I adopted a cat’s lifestyle: I lie on the couch, eat, sleep, and constantly surf the Internet. Yesterday, some kind of willpower finally appeared in me and I forced myself to start doing algebra. I make simple expressions, but my body wants to lie down, wild laziness plays in me again and I have no desire to sit at the table with a notebook, I just want to throw it somewhere far away. Some will say that it’s a lack of interest in the subject, but no, I always liked algebra! And okay, some written lessons, you can still do them by forcing yourself, but learning something is simply unrealistic. But I have a lot to study, the Unified State Exam is in a year and a half. I started looking for different methods of concentration, tried to meditate, but nothing helped. My classmates say that the teachers have already forgotten what I look like. The feeling of anxiety about my studies and my future is growing. I still don’t know how to pull myself together and get to the previous state when it wasn’t so hard for me to do anything.
1 answer
14 years old. Mom constantly screams, this is not so, then that. In general, it leads to a terrible state when you just want to run away and hide from everyone. Sit alone and cry. I begin to be afraid of her, this fear leads to the fact that my studies become worse. This is also why he screams. Constantly reproaches him for something. I try not to pay attention, work hard, but still nothing leads to good results... I’m already fed up with everything, what should I do?
2 answers
I am 16 years old. I live in abundance and I can’t say that my parents didn’t give me anything. But there are eternal problems that make me very sad. Mom always makes scandals because I always spend time on the phone and don’t devote time to them. She always reproaches me for not studying well enough, and although she understands perfectly well that I am trying to do everything to study well, I am not an excellent student, I am a good student (one 4). When she is not in the mood, these scandals turn into arguments with her father, which really annoys me. I have practically no relatives whom I could trust, because these people betrayed me, accusing me of everything they could. Sometimes I just don’t understand why it’s not fair? I don’t go for walks practically at all; I do, but rarely. Because school, tutors, various consultations, because I am a future translator who must achieve goals, as my mother says. We make peace, but all this is still killing me, I’m tired of fighting, my hands just give up on their own, and I don’t know what to do about it...
2 answers
Have you taken the Unified State Exam? It so happened that I take the worst subjects - specialized mathematics and physics. If I can still cope with mathematics (at least), then with physics everything is completely bad... I can’t even get the minimum. I read the assignment and don’t understand what needs to be done. The entire 10th grade was preparing for completely different subjects. I had goals and dreams, but now it doesn't matter anymore. And now there are a couple of months left before the exams, and I still have not moved forward in my knowledge of physics.
1 answer
I started studying in college and came across a strange supervisor. She is a woman and behaves rather strangely towards me. I go to college regularly, I have no debts and everything is fine with the other teachers. But from the very beginning she simply ignored me, for example, she asked the group who wanted to go to the conference and get an autograph from the famous author of the book, no one raised their hand and she began to list, asked everyone except me, she also teaches us some subjects and At one of them she gave a task, she listened to everyone, and when it was my turn and I started reading, she immediately changed the subject and did not let me answer. There was another case, I quickly walked by and dropped a couple of papers that were lying on the edge, I began to pick them up, to which I heard: “you can wipe them all over the floor,” I put the papers down, and didn’t answer anything, sat down at my place. There was also the following situation: the commission was sitting, we were writing the exam, I did everything, started handing in the sheet and the woman from the commission said that I should give it a five, and my supervisor said: “no, I’ll give it a four,” and how do I understand this? He personally didn’t do anything bad to her, didn’t skip her class, didn’t cause any problems. Now I’m already on another course and now she constantly asks me in classes and just shows all sorts of attention to me, now I don’t even know how to react. All enthusiasm disappeared in the first year.
1 answer
Learn English. I taught at school, at university, with a teacher, and now I teach with another teacher. But I'm marking time. It feels like I'm throwing away money. It seems like there is motivation. I went to work for an international company, they needed good English, and at the very least I passed the interview, having memorized everything in advance. Business trips are coming soon, but I can’t put two words together right away, my mouth is a mess. When I read in class, I start to get angry that it comes out terrible and I don’t know the words, I give up and don’t want to do anything! It's just annoying! For a month I studied for an hour on the road in one direction, an hour in the other + sometimes I could do something at home. Nothing changes. I just can’t speak, that’s all. I start watching the video, nothing is clear and I sit in rage. The young man is trying to help, he even taught with me. As a result, I just start crying that I’m stupid and everyone corrects me, but I can’t do anything.
Does anyone have any current advice? My job is the only thing that is preventing me from quitting learning English at the moment out of rage and powerlessness.
4 answers
Hello. I'm just tired of everything. I'm tired of going to school and learning things that in 5 years I won't even remember. I don’t know where to go, I have a lot of different hobbies, I don’t have enough time for them. I have always been an excellent student, but now I realized that there is no point in chasing grades. I have health problems, most likely due to the fact that I constantly worry about my grades. And now I decided for myself that I don’t need it. Studying for another 2 years. I don't know how to endure this.
2 answers
I’m tired, no matter how trite it may sound. Sometimes it seems that no one needs it (of course, not counting the parents), there is no one to talk to. Over a certain amount of time, so much has accumulated... I had to take exams soon, which ones I decided to take back in the summer, but my mother came and said that she had signed up for a group where they were preparing for the English exam. Fine. I've come to terms with it. But doubts were present. But now, I firmly decided that I don’t want to take this subject. I ask my mother to transfer me to a regular group, but in the end it all leads to quarrels. I don’t know how to explain all this to her. Doesn't want to understand me. And inside there is a feeling of some emptiness.
2 answers
Hello, I'm 13 years old. I am in 8th grade. At the very beginning of the school year, I set the goal of finishing this semester well. I have 2 problems:
1). I started learning the language with which I want to connect my life and future. If I don't do this, I'll just rot in this country. I started taking courses. And then it began. Everyone understands everything, everyone is a nerd, etc. They are asked - they answer in a second, even when the topic is new. And I. I'm sitting here dumbfounded. I can’t answer, etc. I don’t attach much importance to this, but when I come home, I understand that the assignment was assigned for this lesson. I need to learn a lot of words, etc. I keep putting it off until later. In the end, nothing comes of it at all. I know and understand that I need to sit down and do this for my dreams, but I just can’t. I'm lazy. I have motivation and patience. etc., but laziness... It’s hard for me to just get up and go do something. I do not know what to do.
2). As I said, I'm in 8th grade. I have 9 lessons a day and I study every day. I have health problems, or rather scoliosis. I go to physical education every day and arrive at the gym only at 12. There are already 5 lessons. I have to borrow notebooks from my classmates and copy homework. I can copy, but mostly I skip mathematics, chemistry, Ukrainian language and Ukrainian literature. Almost all of this will need to be taken for the ZNO/USE. I can’t catch up and understand myself. It's hard for me to get it. I can’t go up to the teacher and ask - the breaks are too short. Relatives don't mess around. My classmates are stupid and don't care about grades. And as I said, I need it for the future. I don’t understand how they explain it on the Internet. Because of this, my laziness now lies in this. I can't even write it off. I'm lazy. In my mind, it’s still not clear why I should write it off. I realize that it is not right and I can and need to. But again, laziness... If I had time, I would do it even through force. But when I come home from school and classes at 5, I just don’t want anything. So this is not the end of the problem. I really like to surf the Internet and watch something. And, as they say, I am degrading. I’m sitting watching something, the episode ends and I say: “I’ll watch two more and that’s it.” In the end, I watched the entire season and did nothing. It's hard for me to tear myself away. And if I break away, then in the middle of lessons or something I remember and simply can’t do anything anymore. I am independent and can easily delete social media. networks or something else, but again my laziness is killing me. Even motivation doesn't help. I can spend hours thinking about the future and still not doing anything. What to do? You need something very strong.
1 answer
I live with my mother and grandmother. We don’t live poorly, but my mother naturally works a lot. I study at the university, I entered on a budget, I study with excellent marks. My family constantly told me that I was sitting on my neck and that I was not doing anything; this put a lot of pressure on me. I tried to get a job, but I still couldn’t. I have the ability, but the schedule was difficult. At the same time, I wasn’t allowed to go to extramural classes, and extramural classes aren’t much fun. In short, I finally built my schedule so that I have several free days on which I started giving lessons (tutor). Things got going. But now, on the contrary, they yell at me because I don’t go to extra classes on my free days. They say you need to educate yourself. And I can’t even just develop anymore. I'm trying to make money, take on as much work as possible. I can’t afford to just hang out with someone, go to dances, for example, just read, read as quickly as possible (although literature is one of the elements of my education). In short, I have developed some kind of freeloader complex. I know that many successful people started working and supported themselves from an early age. I'm 20, and I've only recently started working on my independence. I had the idea of leaving home, living the way I wanted, even if I worked all day, but at least for an hour I could come home and breathe calmly. But I’m scared to break ties with my family, to make them worry, this is a sin, in my opinion. I don't even know what to do. I would like to blame the state, which pays such scholarships that a student who studies and works is forced to feel like a hangover. By the way, I am still studying excellently, because this provides me with a slightly higher scholarship. I lost interest in science...
Work plan
to close knowledge gaps
in geometry in 8th grade
Plan developed
math teacher
Bazakina A.V.
Lambir-2016
annotation
The main purpose of a science and mathematics teacher’s activity is to create a situation of success for each student. Success in learning is the only source of a teenager’s internal strength, generating energy to overcome difficulties in studying such a difficult subject as mathematics. Even a one-time experience of success can radically change the psychological well-being of a student. The success of a student can be created by a teacher who himself experiences the joy of success. The teacher can help a low-performing student prepare a feasible task with which he must speak in front of the group.
A student may lag behind in learning for various reasons dependent and independent of him:
absences due to illness; poor general physical development, presence of chronic diseases; impaired mental function; pedagogical neglect: the teenager’s lack of acquired general educational skills and abilities over the previous years of study: low reading technique, writing technique, counting, lack of independence skills in work, etc.;
dysfunctional family; "street" problem; absenteeism;
We, subject teachers, must know why a student does not master the curriculum, and how he can be helped in this matter. The teacher and class teacher should be helped by narrow specialists (doctor, psychologist, social worker), the student’s parents, the student himself and his classmates to determine the specific reasons for underachievement.
Goals:
- closing gaps in students’ learning in mathematics;
-creating conditions for successful individual development of the student.
What is the first thing you need to do when working with low-achieving students?
- create a favorable atmosphere in the classroom;
- provide timely assistance in additional classes and organize the work of consultants;
- change the forms and methods of educational work in mathematics lessons in order to overcome the passivity of students and turn them into an active subject of activity. Use educational games for this;
- free teenagers from the fear of mistakes, creating a situation of free choice and success;
- orient children towards values: man, family, fatherland, work, knowledge, culture, world, which cover the most important aspects of activity;
- cultivate physical development and a healthy lifestyle.
Organization of work to fill gaps
Work to identify and eliminate gaps in students' knowledge is an integral part of the work of every teacher. The timeliness and thoroughness of this work is the key to high learning results.
A practicing teacher knows how painstaking and important this work is. If you do not pay serious attention to this issue, then very soon even capable students will become mired in mistakes. You cannot downplay the role and let this work take its course, as they say, from case to case. It is necessary to carry out activities to identify and eliminate knowledge gaps systematically and systematically.
It is difficult to isolate this type of pedagogical activity from a holistic process - a learning process in which everything is interconnected.
Systematic work to identify and eliminate deficiencies and gaps in students’ knowledge is one of the main conditions for improving the quality of education. The teacher must use generally accepted forms and invent and implement his own means of control, the skillful use of which prevents lag and ensures the active work of each student.
Objectives:
formation of solid knowledge;
training in self-control techniques;
formation of the need for self-control;
instilling responsibility for the work performed;
development of individual creative abilities of students.
Problems solved during the work
Controlling. Identifying the state of knowledge and skills of students, the level of their mental development, studying the degree of mastery of methods of cognitive activity, skills of rational educational work. Comparing the planned result with the actual one, establishing the effectiveness of the methods, forms and means of training used.
Educational. Improving knowledge and skills, their generalization and systematization. Schoolchildren learn to identify the most important and fundamental aspects of the material being studied. The knowledge and skills being tested become clearer and more accurate.
Diagnostic. Obtaining information about errors and gaps in knowledge and skills and their causes. The results of diagnostic checks help to choose a more intensive teaching methodology, as well as clarify the direction for further improvement of teaching methods and tools.
Prognostic. Obtaining advanced information: whether specific knowledge, skills and abilities are sufficiently formed to master the next portion of educational material. The results of the forecast are used to create a model of the future behavior of a student who today makes errors of this type or has certain gaps in the system of methods of cognitive activity.
Developmental. Stimulating cognitive activity of students. Development of their speech, memory, attention, imagination, will, thinking.
Orienting. Obtaining information about the degree to which the learning goal is achieved by an individual student and the class as a whole. Guiding students in their difficulties and achievements. Revealing gaps, errors and shortcomings, indicate directions for applying efforts to improve knowledge and skills.
Educating. Fostering in students a responsible attitude to learning, discipline, honesty, perseverance, habits of regular work, and the need for self-control.
I divide the organization of work to identify and eliminate knowledge gaps into stages: identifying errors; fixing errors; analysis of mistakes made; planning work to fill gaps; eliminating the gaps of the knowledge base; preventive measures.
Stage I. Troubleshooting
It is carried out during checking written work, oral answers, self- and mutual control.
Written works I do it regularly. I strictly monitor my ability to perform independently. I consider the most effective (for identifying errors) forms of written work:
at the beginning and end of the school year - testing followed by drawing up a table in which the mistakes of each individual and the class as a whole are clearly visible;
during the academic year - traditional tests and independent work preceding them, a written survey of theoretical material;
to master the control of a “narrow” topic: mathematical dictations (“Complete the phrase”, “Fill in the blanks”, “Formulate a question”, “Calculate orally and write down the answer”), “Chains”, mini-tests. Tasks of this type allow you to quickly and, most importantly, promptly identify gaps in knowledge on the topic being studied, which is useful for both the teacher and the student.
Oral test ZUN is aimed at identifying typical errors of a specific topic and general educational skills. It is effective if it is aimed at identifying the meaningfulness of the perception of knowledge and awareness of its use, if it stimulates the independence and creative activity of students. The quality of questions is determined by the nature of the mental actions that students perform when answering the question. Therefore, among the test tasks, I highlight questions that activate memory (to reproduce what has been learned), thinking (to compare, prove, generalize), and speech. Problematic issues that force the application of acquired knowledge in practical activities are of great importance. The quality of an oral test depends on the selection of questions and the sequence of their presentation. Each question must be logically complete, extremely concise and accurate. I will highlight two conditions for qualitative identification of knowledge:
No one bothers the student (the answer is commented on later);
You can interrupt a student only if he does not answer the question, but deviates to the side.
I use oral testing techniques at various stages of the lesson.
Instilling skills and abilities in students self-control not only allows them to find their own mistakes, but is also beneficial from an educational, psychological and pedagogical point of view. Forms: “Find and explain the mistake” (your own, made by a classmate, planned by the teacher), “Check the answer and understand the mistake,” “Evaluate your answer.”
Mutual control the quality and effectiveness of schoolchildren’s educational activities helps the teacher test students’ knowledge and contributes to the development of such personality qualities as honesty and fairness, collectivism. “Ask a question”, “Find a hole in the solution and ask a question” (to help the answerer find the error himself), “Give a review of the answer”, “Explain the solution to a friend”, mutual checking of homework and test work, rules, formulas, theorems, definitions - here not all forms of mutual control. It is also positive that mutual verification can be carried out outside of school hours. Mutual testing of knowledge activates students’ activities, increases interest in knowledge and makes them like it. During mutual control, the individual characteristics of students are revealed and interest in knowledge increases. The guys enjoy the process itself, and their relationships with their friends are strengthened.
At this stage, the correctness of perception and understanding of educational material is analyzed, weaknesses in knowledge are revealed, shortcomings, gaps, and errors in students’ work and answers are discovered. This allows the teacher to timely outline measures to overcome and eliminate them.
Stage II. Fixing errors
Fixing errors occurs in parallel with their identification, but not every student is able to master the material and develop strong skills even after the classic chain: the teacher showed - the student solved it himself - the teacher pointed out the errors - the student worked on the errors. When starting to study a new topic, a student often forgets much of the previous material. Only through repeated, long-term, periodic repetition by each student of his “problematic” topics, returning to the “weak” link in the chain of knowledge, can results in teaching mathematics be achieved. It is necessary to keep a strict record of errors in the form of a list, work with it regularly: make changes, keep the error under control until there is firm confidence in the quality of assimilation. This is not an easy task, it requires patience and time. But the end justifies the means. And the one who follows this path will be rewarded with the educational achievements of his students. Rational forms of error recording, in my opinion, are the following:
A table in which the results of the test are entered. It allows you to see the picture of “handling” for the class as a whole and for each student individually (Table 1).
The error notebook (it can be done electronically) contains a class list and monitoring of “handling” of all written work. A separate page (or part of it) is created for each student, where information about specific errors is entered, and a record of knowledge acquisition is kept. It is clearly visible who has what problems, who did not pass what (Table 2).
During the lesson, when doing homework, I strongly recommend that students, if they could not immediately understand something, make notes in the margins (such as “?”) so that they can think later or use the help of a teacher or classmate. I encourage students not to leave “incomprehensible” areas unattended.
Stage III. Analysis of mistakes made
An analysis of mistakes made is carried out after each type of work, orally or in writing, by a teacher or student - depending on the type of activity. Quantitative and qualitative analysis is carried out. A carefully conducted analysis allows us to deeply study the gaps and achievements of individual students, highlight typical mistakes and the main difficulties of students, study the reasons for their occurrence and outline ways to eliminate them.
Stage IV. Planning to address knowledge gaps
This work is based on analysis, the results of which are communicated to students.
The teacher outlines when, whom, for what purpose to ask and what means to use for this.
Work on errors is carried out after each written work, re-testing after an unsatisfactory mark.
Strict control is exercised to ensure that each student completes all tests and tests (even if he missed them).
V stage.
Closing knowledge gaps
Analysis of classroom work.
Finding out the class's opinion on the results obtained.
Work on errors, individual and frontal, with mandatory subsequent written verification (until receiving a positive mark).
Repetition tasks during a frontal survey and individually (until a positive mark is received).
Stage VI. Prevention measures
It is difficult to treat a disease; it is better to prevent it. Mistakes are also a kind of illness. The following preventive measures can help reduce them to a minimum.
The texts of written assignments should be easy to understand: well-formulated, easy to read.
Active oral practice of basic learning skills, regular analysis of typical mistakes.
When explaining new material, predict the mistake and select a system of tasks to practice the correct assimilation of the concept. Focusing on each element of the formula and performing different types of tasks will help reduce errors to a minimum.
Selection of tasks that arouse interest and form sustainable attention.
Strong assimilation (and therefore the absence of errors) is facilitated by rules that are easy to remember, clear algorithms, following which you will certainly arrive at the intended goal.
Systematic training in self-control allows you to achieve noticeable results. At the same time, the general mathematical culture of schoolchildren is growing, their work and answers become more literate.
Work plan to close the knowledge gap in geometry
GAPS IN EDUCATION
Let's talk about modern school education, more precisely, about its main principles. Of course, there are different schools: special schools with a focus on certain subjects, experimental schools, etc., but we will talk about principles work of simple secondary schools. 
The principle by which training takes place in such schools is systematic forward movement. First one topic is mastered, then another, etc. Students are expected to repeat the material covered and take what they are taught very seriously. Topics move from year to year, are supplemented, become more complex, and are considered at a new level. Here you go cyclicality, which is extremely necessary. In terms of volume and coverage of material, and in depth of elaboration, our program surpasses many Western ones. In theory, everything looks very cool.
The problem is that the programs are designed to " ideal", diligent, student. But not such a large percentage of children have natural inclinations to learning. Some have a hidden talent for trading, some just like to work with their hands. But there is only one educational program; it is designed for an active type of student, the best and most diligent, with a penchant for learning.
What about the rest? In this case, the role of the teacher is extremely important. He should be able to reorganize material in a way that everyone can understand.
Unfortunately, in practice everything turns out a little differently. Having gone through one topic, and then several more, most students forget what they went through a month ago. As a result, after completing the annual course of study, they do not study anything seriously.
The reason for this is that they are too big intervals between classes, too frequent switching attention associated with a large number of subjects that have to be studied. Schoolchildren lose integrity perception. And a superficial study of the subject does not make it possible to see completeness and harmony. If the information is not closes, is transformed into something whole, into some kind of complete picture, then memory very quickly removes its support, freeing itself from “ insignificant» information. Relevance is determined by repetition. 
Memory works like car, she does not understand declarations like: “My name is Vasya, and I really, really, really need English. He is very important to me." Whatever Vasya wants, if his actions do not correspond to what is proclaimed, then Vasya’s memory will not understand. She will mercilessly erase incomplete information, despite all his statements. The importance for her is determined only by the cyclical repetition, that is, by the specific rhythm of the work itself, and not by intentions alone.
Remember when we looked at this principle of memory? Once again: if information is not repeated a certain number of times in a certain period of time, then it is simply erased. Alas, this is our memory, do not expect understanding and compassion from it.
