by Axel Rondon
Many schoolchildren and their parents are faced with the problem of the low quality of knowledge received at school. What a child manages to learn in school mathematics lessons is often not enough to confidently cope with most of the proposed tasks and exercises and get a good grade. Moreover, this often applies to fairly developed and intelligent children. Maths tutors in Coventry practice shows that studying at school does not always allow one to acquire knowledge at the level of individual abilities and capabilities - at their level, many children do not have the results that they could have. And even children with good academic performance often have parts in the material they have covered that they could know much better. This is what a tutor has to deal with in everyday practice.
2.
There is no mystery as to why this happens. Of course, it all depends on the specific teacher teaching your child at school - some cope with the task of teaching simply brilliantly. But still, more often the emphasis is placed more on the controlling and punitive function than on the transfer of knowledge. As a rule, the learning process at school is structured in such a way that it poorly takes into account both the individual and universal characteristics of the perception and assimilation of the material by each student. And these problems are especially acute when studying mathematics.
3.
Mathematics as a subject is “terrible” because it consists of a very large number of small skills and operations, the knowledge of which is absolutely necessary when solving various problems and examples. If you do not have even one of these skills, it may be impossible to correctly solve a huge number of tasks. Neither school teachers nor parents are often able to monitor their adequate assimilation. Moreover, in order for each of these skills to be firmly mastered, practice is needed; thorough training in a wide variety of tasks and situations. In addition, human memory is designed in such a way that each learned technique must be returned several times after certain periods of time - otherwise the information received will not turn into confident knowledge. There is one more feature. The human brain is able to perceive only information that is somehow related to something already known and familiar. For example, there is a rule that all good lecturers know: the amount of new content in the material should not exceed 20%, otherwise the audience’s attention will be lost. In practice, this is implemented in the well-known principle of learning “from simple to complex.” If a new topic, when presented, is overloaded with techniques unknown to the child, and if the complexity of the tasks is not gradually increased, the student is simply not able to understand and perceive it. Here it comes down to individual differences, which are very difficult to take into account in any group teaching.
4.
Our textbooks generally do not sufficiently implement these principles. The same applies to a large number of different teaching aids. The number of training tasks contained in them, as a rule, is sufficient for mastering the material only by the most intelligent children who quickly grasp everything. By giving a limited number of tasks when going through a new topic, which does not allow them to properly understand and practice the new material, to “immerse themselves” in it, such exercises are then, although repeated more than once, chaotically scattered throughout the textbook, only disorienting the children. As a result, each new technique that needs to be taught to schoolchildren is taught too superficially, vaguely and fragmentarily, leaving no solid knowledge in the head. It feels like all our textbooks and teaching aids are written for mathematically gifted students who can learn from a minimum of examples, or that their authors have never taught. Children, who are often no less talented, but “slower” in terms of the pace of perception, do not have time to understand, delve into the material being studied, and begin to accumulate misunderstood or not completely understood parts of the program. When there are too many such “gaps,” it immediately has a detrimental effect on knowledge and assessment.
5.
Individual teaching has undoubted advantages over school group teaching precisely because it takes into account all of the listed aspects of learning. Can there be guarantees of learning outcomes? Any competent tutor after one or two lessons can assess the prospects of a given student. And they depend, of course, not so much on the level of knowledge as on the “learnability” of the child. In mathematics, this implies, first of all, the ability to memorize the necessary techniques, the ability to reproduce them and use the acquired knowledge in practice. The category of students who are doing well with such abilities, but have problems with academic performance solely due to a lack of knowledge and problem-solving practice, are the most “grateful” in terms of “return” from classes. Existing gaps are quickly filled, and from any level, even if it is necessary to “raise” one or two previous years of study. In these cases, the teacher can confidently talk about the results of the classes. The situation is more complicated if such abilities exist, but are relatively blocked, that is, the reasons for problems with academic performance lie not so much in knowledge, but in character. For example, in a weak ability to concentrate, excessive slowness, insufficient motivation to acquire knowledge or other characterological characteristics. It is clear that not all of these problems can be corrected as a result of individual training, and it is more difficult to predict the result in such cases. But some of these problems are also quite successfully solved as a result of classes.
6.
Firstly, in the process of classes the child gains important experience in overcoming and resolving difficulties. If previously, in response to difficulties, it was impossible to get clarification either in the textbook or from the school teacher, then during individual lessons the child can get an answer to almost any question about what he did not understand, and gets the opportunity to figure it out. Therefore, in children who are unsure of themselves, the fear of the subject, the feeling of constraint and incompetence gradually disappears. This also happens because the tutor does not scold his student for mistakes, does not give bad grades, and the student can get to know the subject better in a comfortable and safe environment.
7.
Secondly, the tutor teaches the student to think correctly, showing an example of how to act when performing this or that type of task, and breaking down the solution into simple and understandable steps. This allows children to adopt and internalize a more successful model of thinking and behavior when solving examples and problems. For children with shortcomings in concentration (this problem is, unfortunately, very common), such regular practice gradually disciplines and organizes thinking.
8.
And, of course, the biggest role in the success of classes is played by the opportunity to practice solving each type of problem exactly to the extent that is necessary for high-quality understanding and memorization - which, unfortunately, school often cannot give a student. This is especially important when mastering geometry and when learning to solve word problems - from elementary school onwards. It is almost impossible to obtain high-quality knowledge without a sufficient amount of practice in these areas of mathematics.
9.
No special testing is carried out during the first lesson, since in general the entire work of a tutor is constant testing in order to identify what type of tasks the student cannot solve or does not fully understand, what operations he does not master - with subsequent explanations and work on these "spaces". This kind of work begins almost from the very first lesson. Naturally, training is carried out primarily on topics that the student is currently studying at school, and is focused on the school level of requirements. Moreover, when choosing the level of difficulty of tasks, the teacher flexibly adapts to the student’s capabilities, making sure that they are not too simple or too complex for him, gradually complicating the examples as his knowledge grows. Thus, you can achieve high-quality and solid knowledge in almost any section of mathematics, and at any level. And the only limitation here is the amount of effort and time that the student is willing to spend on this.
10.
As a rule, the task of a tutor is to provide adequate assistance and support to the student in all problems related to the study of mathematics. This includes help with homework, preparation for tests and independent work, and moving forward with the material. As a rule, children who have the ability need one or two lessons a week to show good results. Such children differ from those who did not study individually in that they have greater self-confidence, they are much more free to navigate the material, and their knowledge is more systematized and organized.
eleven.
Those children who grasp, understand, and memorize material more slowly may need significantly more time in order to have time to understand, delve into the material being studied, and remember it firmly and reliably. Therefore, in order to raise the level of knowledge of such children from a weak C to a good B, parents are highly recommended to organize the lesson schedule in such a way that for each section of the textbook studied by the child at school, there are at least several individual lessons - to thoroughly “work” each topic. Without such “practice,” the knowledge acquired by children is not consolidated in their heads. If such “slow” students, in addition to current problems with academic performance, also have serious gaps in previous topics and classes, in class they have to spend time both working with current material and catching up on lost time. The volume of material requiring study by the student increases significantly, and compliance with this rule (“several lessons for each section of the school course”) is especially critical for achieving results. After all, according to the laws of human memory, the information received leaves a trace in the head only if it is repeated several times. Such repetition requires a certain amount of time (as well as effort).
12.
According https://nicetutor.co.uk therefore, one of the main factors of success is persistence, will, and determination to achieve results. The main thing is not to be afraid of the new and not to give in to what seems difficult and incomprehensible. Don't be afraid to make mistakes, try, and believe in yourself. In the process of teaching, I always try to show my students that mathematics is not at all as complicated as it seems at first glance, and is very logical. Everything in it obeys fairly simple laws and analogies. The main thing is to learn to break down a seemingly very difficult task into a sequence of small and simple steps that the student can complete. I wish all schoolchildren excellent results in their studies, overcoming fears and self-doubt, and their parents - brilliant success in promoting this.
2.
There is no mystery as to why this happens. Of course, it all depends on the specific teacher teaching your child at school - some cope with the task of teaching simply brilliantly. But still, more often the emphasis is placed more on the controlling and punitive function than on the transfer of knowledge. As a rule, the learning process at school is structured in such a way that it poorly takes into account both the individual and universal characteristics of the perception and assimilation of the material by each student. And these problems are especially acute when studying mathematics.
3.
Mathematics as a subject is “terrible” because it consists of a very large number of small skills and operations, the knowledge of which is absolutely necessary when solving various problems and examples. If you do not have even one of these skills, it may be impossible to correctly solve a huge number of tasks. Neither school teachers nor parents are often able to monitor their adequate assimilation. Moreover, in order for each of these skills to be firmly mastered, practice is needed; thorough training in a wide variety of tasks and situations. In addition, human memory is designed in such a way that each learned technique must be returned several times after certain periods of time - otherwise the information received will not turn into confident knowledge. There is one more feature. The human brain is able to perceive only information that is somehow related to something already known and familiar. For example, there is a rule that all good lecturers know: the amount of new content in the material should not exceed 20%, otherwise the audience’s attention will be lost. In practice, this is implemented in the well-known principle of learning “from simple to complex.” If a new topic, when presented, is overloaded with techniques unknown to the child, and if the complexity of the tasks is not gradually increased, the student is simply not able to understand and perceive it. Here it comes down to individual differences, which are very difficult to take into account in any group teaching.
4.
Our textbooks generally do not sufficiently implement these principles. The same applies to a large number of different teaching aids. The number of training tasks contained in them, as a rule, is sufficient for mastering the material only by the most intelligent children who quickly grasp everything. By giving a limited number of tasks when going through a new topic, which does not allow them to properly understand and practice the new material, to “immerse themselves” in it, such exercises are then, although repeated more than once, chaotically scattered throughout the textbook, only disorienting the children. As a result, each new technique that needs to be taught to schoolchildren is taught too superficially, vaguely and fragmentarily, leaving no solid knowledge in the head. It feels like all our textbooks and teaching aids are written for mathematically gifted students who can learn from a minimum of examples, or that their authors have never taught. Children, who are often no less talented, but “slower” in terms of the pace of perception, do not have time to understand, delve into the material being studied, and begin to accumulate misunderstood or not completely understood parts of the program. When there are too many such “gaps,” it immediately has a detrimental effect on knowledge and assessment.
5.
Individual teaching has undoubted advantages over school group teaching precisely because it takes into account all of the listed aspects of learning. Can there be guarantees of learning outcomes? Any competent tutor after one or two lessons can assess the prospects of a given student. And they depend, of course, not so much on the level of knowledge as on the “learnability” of the child. In mathematics, this implies, first of all, the ability to memorize the necessary techniques, the ability to reproduce them and use the acquired knowledge in practice. The category of students who are doing well with such abilities, but have problems with academic performance solely due to a lack of knowledge and problem-solving practice, are the most “grateful” in terms of “return” from classes. Existing gaps are quickly filled, and from any level, even if it is necessary to “raise” one or two previous years of study. In these cases, the teacher can confidently talk about the results of the classes. The situation is more complicated if such abilities exist, but are relatively blocked, that is, the reasons for problems with academic performance lie not so much in knowledge, but in character. For example, in a weak ability to concentrate, excessive slowness, insufficient motivation to acquire knowledge or other characterological characteristics. It is clear that not all of these problems can be corrected as a result of individual training, and it is more difficult to predict the result in such cases. But some of these problems are also quite successfully solved as a result of classes.
6.
Firstly, in the process of classes the child gains important experience in overcoming and resolving difficulties. If previously, in response to difficulties, it was impossible to get clarification either in the textbook or from the school teacher, then during individual lessons the child can get an answer to almost any question about what he did not understand, and gets the opportunity to figure it out. Therefore, in children who are unsure of themselves, the fear of the subject, the feeling of constraint and incompetence gradually disappears. This also happens because the tutor does not scold his student for mistakes, does not give bad grades, and the student can get to know the subject better in a comfortable and safe environment.
7.
Secondly, the tutor teaches the student to think correctly, showing an example of how to act when performing this or that type of task, and breaking down the solution into simple and understandable steps. This allows children to adopt and internalize a more successful model of thinking and behavior when solving examples and problems. For children with shortcomings in concentration (this problem is, unfortunately, very common), such regular practice gradually disciplines and organizes thinking.
8.
And, of course, the biggest role in the success of classes is played by the opportunity to practice solving each type of problem exactly to the extent that is necessary for high-quality understanding and memorization - which, unfortunately, school often cannot give a student. This is especially important when mastering geometry and when learning to solve word problems - from elementary school onwards. It is almost impossible to obtain high-quality knowledge without a sufficient amount of practice in these areas of mathematics.
9.
No special testing is carried out during the first lesson, since in general the entire work of a tutor is constant testing in order to identify what type of tasks the student cannot solve or does not fully understand, what operations he does not master - with subsequent explanations and work on these "spaces". This kind of work begins almost from the very first lesson. Naturally, training is carried out primarily on topics that the student is currently studying at school, and is focused on the school level of requirements. Moreover, when choosing the level of difficulty of tasks, the teacher flexibly adapts to the student’s capabilities, making sure that they are not too simple or too complex for him, gradually complicating the examples as his knowledge grows. Thus, you can achieve high-quality and solid knowledge in almost any section of mathematics, and at any level. And the only limitation here is the amount of effort and time that the student is willing to spend on this.
10.
As a rule, the task of a tutor is to provide adequate assistance and support to the student in all problems related to the study of mathematics. This includes help with homework, preparation for tests and independent work, and moving forward with the material. As a rule, children who have the ability need one or two lessons a week to show good results. Such children differ from those who did not study individually in that they have greater self-confidence, they are much more free to navigate the material, and their knowledge is more systematized and organized.
eleven.
Those children who grasp, understand, and memorize material more slowly may need significantly more time in order to have time to understand, delve into the material being studied, and remember it firmly and reliably. Therefore, in order to raise the level of knowledge of such children from a weak C to a good B, parents are highly recommended to organize the lesson schedule in such a way that for each section of the textbook studied by the child at school, there are at least several individual lessons - to thoroughly “work” each topic. Without such “practice,” the knowledge acquired by children is not consolidated in their heads. If such “slow” students, in addition to current problems with academic performance, also have serious gaps in previous topics and classes, in class they have to spend time both working with current material and catching up on lost time. The volume of material requiring study by the student increases significantly, and compliance with this rule (“several lessons for each section of the school course”) is especially critical for achieving results. After all, according to the laws of human memory, the information received leaves a trace in the head only if it is repeated several times. Such repetition requires a certain amount of time (as well as effort).
12.
According https://nicetutor.co.uk therefore, one of the main factors of success is persistence, will, and determination to achieve results. The main thing is not to be afraid of the new and not to give in to what seems difficult and incomprehensible. Don't be afraid to make mistakes, try, and believe in yourself. In the process of teaching, I always try to show my students that mathematics is not at all as complicated as it seems at first glance, and is very logical. Everything in it obeys fairly simple laws and analogies. The main thing is to learn to break down a seemingly very difficult task into a sequence of small and simple steps that the student can complete. I wish all schoolchildren excellent results in their studies, overcoming fears and self-doubt, and their parents - brilliant success in promoting this.