Innovative technologies for teaching mathematics in primary school
Innovative technologies for teaching mathematics in primary school
The intense changes currently taking place in our society, requiring a creatively developed, creatively thinking, competent, active personality, orient teachers to a new level of teaching and educating students.
The increase in mental load in mathematics lessons makes us think about how to maintain students’ interest in the material being studied and their activity throughout the lesson. The emergence of interest in mathematics depends to a large extent on the methodology of its teaching, on how skillfully the educational work will be structured. In this regard, a search is underway for new effective technologies and teaching methods that would activate the thoughts of schoolchildren and stimulate them to independently acquire knowledge. The teacher needs to think about how each student works actively and enthusiastically, and uses this as a starting point for the emergence and development of curiosity and cognitive interest. At primary school age, constant interests and inclinations towards one or another subject are formed; it is during this period that one should strive to reveal the attractive sides of mathematics.
A modern teacher increasingly asks himself the question: “How to use innovative technologies in the educational process?”
The teacher’s goal is to teach schoolchildren how to learn by using new pedagogical technologies. And as practice shows, new educational technologies can only be mastered in action.
“Innovation is not just innovation or some novelty, but the achievement of fundamentally new qualities with the introduction of system-forming elements that provide novelty to the system” (P.S. Lerner)
Innovative technologies include developmental education technology, project technology, research activities, a person-centered approach, ICT technologies, and monitoring.
Technologies of developmental education: problematic presentation of educational material; partially search activity; independent project research activities.
Relevance of the selected topic
is the need for the widespread use of productive innovative technologies in mathematics lessons, which make it possible to achieve the goals of mathematics education faster, more economically and with better quality.
Productive technology is the one that can be used to achieve higher results faster and at lower costs compared to previously used technology. The teacher’s task is to organize effective learning activities for students, to teach them to independently acquire additional knowledge for successful mastery of the subject.
The introduction of new technologies brings radical changes to the education system: previously, its center was the teacher, and now it is the student. This allows each student to learn at a pace that suits them and at a level that matches their abilities.
In my practice I use the following modern educational technologies or their elements:
-Information and communication technologies
- Technologies of level differentiation and individualization
-Interactive technologies (design method, including
problem-based learning and research activities)
-Game technology
-Personally-oriented learning technologies
-Test technologies
-Health saving technologies
Information and communication technologies
Today, information and communication technologies occupy an increasingly larger place in the educational process. The main advantage of these technologies is clarity, since a large proportion of information is absorbed using visual memory, and influencing it is very important in learning. Information technology helps make the learning process creative and learner-centered.
The use of ICT in mathematics lessons allows me to: make the learning process more interesting, vibrant, and exciting due to the wealth of multimedia capabilities; effectively solve the problem of teaching visibility; expand the possibilities of visualizing educational material, making it more understandable and accessible to students.
It has been noticed that students show great interest in the topic when presentations are used to explain new material. Even passive students get involved in the work with great desire. I use ICT at different stages of the lesson: mental calculation, when explaining new material; during reinforcement, repetition, at the control stage.
Lessons using computer technology not only enliven the learning process, but also increase learning motivation.
It is difficult to imagine a modern lesson without the use of information and computer technologies.
Information computer technologies can be used at any stage of the lesson:
1. To indicate the topic of the lesson.
2. At the beginning of the lesson, use questions on the topic being studied, creating a problematic situation.
3. As an accompaniment to the teacher’s explanation (presentations, formulas, diagrams, drawings, video clips, etc.)
4. To control knowledge
The main educational value of information technologies is that they make it possible to create a more vibrant interactive learning environment with unlimited possibilities at the disposal of both the teacher and the student.
The advantages of information and computer technologies compared to traditional ones are manifold. In addition to the possibility of a more illustrative, visual presentation of the material, effective testing of knowledge and everything else, these include the variety of organizational forms in the work of students, methodological techniques in the work of the teacher.
If a student has difficulties with a particular question, he can return to the theory at any time and study the material again.
It is still necessary to note that a bright picture on the screen is just a way of presenting the material. It's one way traffic. The most important thing in a lesson is the live interaction between teacher and student, the constant exchange of information between them. Therefore, an integral attribute of any classroom is a blackboard. A board is not just a piece of surface on which both an adult and a child can write, but a field of information exchange between teacher and student. Of course, it is impossible to say for sure that student results will improve thanks to working with an interactive whiteboard, but my observations showed that students became more interested in what was happening in the lesson. They actively discuss new topics, strive to take part in work, and remember the material faster. Thus, the use of an interactive whiteboard helps to ensure sustainable motivation for students to acquire knowledge and increase their cognitive activity. These observations apply to new computer technologies in general.
Thus, the use of information technology helps teachers increase children’s learning motivation for the subject and leads to a number of positive consequences:
psychologically facilitates the process of learning material by students;
arouses keen interest in the subject of knowledge;
broadens the general horizons of children;
the level of use of visual aids in the classroom increases;
there is a more complete assimilation of theoretical material;
students are mastering the ability to obtain information from a variety of sources and process it using computer technology;
the ability to briefly and clearly formulate one’s point of view is formed.
The productivity of teachers and students in the classroom increases.
It is undeniable that in a modern school a computer does not solve all problems; it remains just a multifunctional technical teaching tool. No less important are modern pedagogical technologies and innovations in the learning process, which make it possible not only to “invest” in each student a certain stock of knowledge, but, first of all, to create conditions for the manifestation of students’ cognitive activity. Information technologies, in combination with properly selected (or designed) teaching technologies, create the necessary level of quality, variability, differentiation and individualization of training and education.
Slide presentations are effective at various stages of the lesson. Visual perception of the objects being studied allows you to quickly and deeply perceive the material presented. There is an opportunity to present the material emotionally and figuratively.
When using information and communication technologies, it is very important to take into account the requirement of the Sanpin, which indicates the duration of computer use in the lesson.
Technology of level differentiation and individualization
Differentiation contributes to a stronger and deeper assimilation of knowledge, the development of individual abilities, and the development of independent creative thinking. Different level assignments make it easier to organize classes in the classroom and create conditions for students to advance in their studies in accordance with their capabilities. Working differentially with students, I see that their attention does not drop during the lesson, since everyone has a feasible task, “strong” students do not get bored, since they are always given a task that they need to think about. The guys are constantly busy with hard work. As a teacher, I have the opportunity to help the weak, pay attention to the strong, and the desire of strong students to advance faster and deeper in education is realized. Strong students are confirmed in their abilities, weak students get the opportunity to experience academic success, and the level of motivation increases.
When using the technology of level differentiation and individualization, a special pedagogical tact of the teacher is required so as not to humiliate the student in front of his peers by giving him an easier task, but to give him the opportunity, together with everyone else, to experience the joy of a correctly completed task, thereby
“inspire” him for further work on a more complex task
Gaming technologies
“The subject of mathematics is so serious that it is good to take every opportunity to make it more entertaining.”
Blaise Pascal
I believe that the use of gaming technologies in lessons ensures the achievement of unity of the emotional and rational in learning. Thus, the inclusion of game moments in the lesson makes the learning process more interesting, creates a good mood in students, and makes it easier to overcome learning difficulties. I use them at different stages of the lesson. So at the beginning of the lesson I include the game moment “Guess the topic of the lesson”, when consolidating the studied material - “Find the error”, coded exercises. I also develop quizzes and hours of entertaining mathematics. All this is aimed at broadening the horizons of students, developing their cognitive activity, developing certain skills and abilities necessary in practical activities, and developing general educational skills.
Personality-oriented learning technologies
“If pedagogy wants to educate a person in all respects, then it must first get to know him in all respects”
K. D. Ushinsky
Virtually all developed countries have realized the need for personality-oriented learning, where the student becomes the central figure.
Taking into account his inclinations, abilities, capabilities, using advanced pedagogical and information technologies. Such training contributes not only to mastering a certain amount of knowledge and skills, but also, what is much more important, to personal development.
Studying the student’s personality, determining his condition in the initial period of training and after the implementation of pedagogical influence is one of the central issues of productive technology. Back in 1867, K. D. Ushinsky wrote in his book “Man as a Subject of Education”: “If pedagogy wants to educate a person in all respects, then it must first get to know him in all respects.” Therefore, the inclusion of the object of influence – the student – with the structure of the technological process is of particular importance. When designing pedagogical technology, it is desirable to take into account the characteristics of each student - his individual prerequisites that provide “resistance” or, conversely, favor the influence of teaching influences.
Personally-oriented teaching technology helps to create a creative atmosphere in the classroom, and also creates the necessary conditions for the development of individual abilities of students.
Test technologies
Test-based assignments have become widespread in teaching practice. I use them at various stages of the lesson, during different types of classes, during individual, group and frontal work, in combination with other teaching tools and techniques. Today there are a variety of test options. In my opinion, tests created by the teacher himself make it possible to most effectively identify the quality of knowledge and individualize tasks, taking into account the characteristics of each student. I compose test tasks taking into account the objectives of the lesson, the specifics of the material being studied, cognitive capabilities, and the level of readiness of students. Therefore, I have compiled tests for each group aimed at developing the skills of students and consolidating knowledge. Test technology helps in monitoring students' knowledge. The test provides a subjective factor when checking the results, and also develops logical thinking and attentiveness in children. Test tasks vary in difficulty level and in the form of answer options.
- Each lesson begins with the psychological mood of the class. After a friendly greeting and approving remarks, I offer the children a “Mood Sheet.”
1.Brain attack. I do it in pairs or groups.
- Puzzle solving task.
2. “Basket” of ideas, concepts, names.
On the board I draw a basket where everything the children know about this issue is supposedly collected.
Technology: 1) I ask a question about what the children know about the problem posed; 2) Each student independently remembers and writes down in a notebook what he knows in this regard (1-2 min); 3) Exchange of information in pairs (groups); each pair names one piece of information or fact, without repeating what was said earlier. For example, the topic of the lesson: Problems ..Challenge, various versions are developed: how the problem can be solved.
I use this technique at the beginning of the lesson at the stage of working with the book; students “put” their thoughts about what will be studied in the lesson today into the “basket”. This technique allows me to develop students’ skills in putting forward research hypotheses and determining whether they are proven or disproven, which is very important for developing students’ research skills when working with literature.
Health-saving technologies
The concept of “health saving” refers to a qualitative characteristic of any educational technology, showing to what extent the implementation of this technology solves the problem of preserving the health of the main subjects of the educational process - students and teachers.
The use of these technologies makes it possible to distribute various types of tasks evenly during the lesson, alternate mental activity, determine the time of presentation of complex educational material, allocate time for independent and test work, and normatively apply TSR, which gives positive results in learning. When preparing and conducting a lesson, I take into account: the dosage of the educational load; building a lesson taking into account the dynamism of students and their performance; compliance with hygiene requirements (fresh air, good lighting, cleanliness); favorable emotional mood; stress prevention (work in pairs, groups, stimulation of students); healing moments and changes in activities in the lesson, helping to overcome fatigue, despondency, and unsatisfactoriness; I follow the organization of educational work (preparing the board, clear notes on the board, using ICT).
Confucius
The activity of analytical comprehension of educational material by younger schoolchildren quickly decreases if students are forced to analyze the same unit of educational material and perform the same type of mental operations over the course of several lessons. It is known that children quickly get bored of doing the same thing, their work becomes ineffective, and the development process slows down. In order for the material to contribute to the child’s development of the ability to independently comprehend the phenomena of the life around him and to think productively, I use problem-based learning in my practice. Its essence is that I pose a problem (learning task) to the students and consider it together with them. As a result of joint efforts, ways to solve it are outlined, an action plan is established, which is independently implemented by students with minimal help from the teacher. At the same time, the entire stock of knowledge and skills they have is updated, and those that are relevant to the subject of study are selected from it. Mathematics at school, in my opinion, does not begin with counting, not with learning concepts, which seems obvious, but with... a riddle, a problem. Problem-based learning ensures stronger knowledge acquisition; develops analytical thinking and helps make learning activities more attractive for students. We are engaged in educational research projects for junior schoolchildren. The main idea of the project method is the focus of students’ educational and cognitive activity on the result that is obtained by solving a practical and theoretical problem. Project activities of students are joint educational, cognitive, creative and gaming activities that have a common goal, agreed upon methods of activity aimed at achieving a common result.
Using elements of research activity in teaching allows us not so much to teach children as to teach them how to learn and to guide their cognitive activity. Students participate with great interest in a variety of types of research work. The project method allows you to organize truly research, creative, independent activity during the educational time allocated for studying the subject. It involves a departure from authoritarian teaching methods and provides a thoughtful and conceptually sound combination with the diversity of the bathroom on constant difficulties; it focuses on the integrated use of knowledge.
Group work in lessons is very attractive to younger students. However, as practice shows, the first experience of its organization may be unsuccessful (excessive noise, slow pace of work, their inability to act together, etc.), which discourages further use of this form of training. Meanwhile, group work is a full-fledged independent form of learning organization. The use of group work in lessons convinced me that this technology carries the features of innovative learning: independent acquisition of knowledge as a result of search activity, therefore:
– the depth of understanding of educational material, cognitive activity and creative independence of students increases; – the nature of relationships between children changes; – friendship in the class is strengthened, attitudes towards school change; – class cohesion increases sharply, children understand each other and themselves better; – self-criticism increases, they assess their capabilities more accurately, and control themselves better; – students acquire the skills necessary for life in society: frankness, tact, the ability to structure their behavior taking into account the position of other people.
At the end of group work, the solutions developed by each group are discussed by the whole class. Thus, not only the result of solving the problem is assessed, but also the work of the group. Primary school is an integral part of the entire system of continuous education. One of the main tasks is to lay the potential for enriched development of the child’s personality.
The use of modern educational technologies can transform the teaching of traditional academic subjects, rationalizing child labor, optimizing the processes of understanding and memorizing educational material, and most importantly, raising children's interest in learning to a consistently higher level. Teaching a child joyfully, without coercion, is possible if the teacher uses innovative technologies in his work.
“The higher and further each of us goes, the more clearly we see that there is no limit to the achievement of perfection. The point is not what height you will reach today, but the point is to move forward along with the eternal movement of life” (E.I. Roerich).
Having tested educational technologies, the teacher himself will not want to work in the old way, and his lessons will turn into creative communication with students and students among themselves.
Innovative work experience of mathematics teacher Vodyakova V.V. methodological development on the topic
Presentation of innovative teaching experience
Vodyakova Valentina Viktorovna,
mathematics teacher at the State Budgetary Educational Institution “Ruzaevsky Orphanage-School No. 1”.
I consider the goal of my teaching activity to be the effective construction of the educational learning process, so I try to organize it so that it provides favorable conditions for all schoolchildren to achieve a basic level of training.
In my teaching activities I solve the following tasks:
- develop and strengthen interest in the subject;
— use new pedagogical technologies;
— to reveal the abilities, intellectual, creative, moral potential of each student;
— prepare students for an informed choice of profession, develop independent work skills.
Having worked in schools for more than 30 years, I am convinced that the pedagogical problem
“Formation of a student’s personality based on a differentiated and individual approach to learning”
is the most relevant.
—-Relevance and prospects of experience.
Having worked with children in an orphanage-school for many years, you are convinced that an individual approach to learning is the basis on which the entire educational process is built.
The difficulties of working with students in our school are that children show increased attention to themselves, have a heightened reaction to the opinions of others, and have a high sense of self-esteem. They are ambitious, but not always persistent and consistent in achieving their goals. They react sharply to their own failures and successes. Therefore, all my activities are focused on the development of the child’s personality in existing conditions.
What is differentiated learning and an individual approach to learning?
Differentiated learning is a form of organizing educational activities for different groups of students.
An individual approach is an important psychological and pedagogical principle that takes into account the individual characteristics of each child.
Different students acquire knowledge, skills and abilities in different ways. These differences are due to the fact that each student, due to his specific developmental conditions, both external and internal, has individual characteristics.
I try to organize the educational process so that each student is optimally engaged in educational activities in the classroom, taking into account his mathematical abilities and intellectual development, in order to avoid gaps in the knowledge and skills of schoolchildren.
Such an organization of teaching mathematics is required by the current state of our society, when in a market economy a high level of professionalism and such business qualities as entrepreneurship, the ability to navigate a given situation, and make decisions quickly and accurately are required from each person.
At the moment I work in grades 5,6,8.
I work according to a program compiled on the basis of the federal component of state educational standards of secondary (complete) general education (basic and specialized levels). I teach according to the textbooks of N.Ya. Vilenkin (5 and 6 grades), Sh. A. Alimov (algebra 7-9 grades), L. S. Atanasyan (geometry 7-9 grades). I use additional literature in class and in extracurricular activities.
Conceptuality
A differentiated approach is necessary not only to improve the performance of weak students, but also to develop strong students. Differentiation of learning involves its use at various stages of studying mathematical material: preparing students to learn new things, applying them to solving problems, and the stage of monitoring the assimilation of material.
The content of the material being studied can be differentiated; It is possible to differentiate teaching methods in order to provide varying degrees of individual or group assistance to students when organizing independent work to learn new things, when solving problems, it is possible to differentiate the means and forms of teaching.
Optimality and efficiency.
In my activities I take into account the educational needs of children and their individual abilities. Each child is unique, one grasps the material on the fly and assimilates it for a long time, another needs constant help from the teacher, the third needs a hint to move on, the fourth has great difficulty in perceiving the educational material.
How can we teach everyone under such conditions?
By identifying the cognitive and intellectual level of each student and the class as a whole, I plan my activities in accordance with this, setting specific goals and objectives for each level of child development.
I differentiate according to the degree of independence of students when performing educational activities.
For myself, I divided this work into several stages.
1. Study of individual characteristics of students - physical, psychological, and personal.
2. Identification of separate groups of students that differ:
- different levels of assimilation of the material at the moment;
-level of performance and pace of work;
-features of perception, memory, thinking;
- balance of excitation and inhibition processes.
3. Selection of differentiated tasks that help students cope with the task independently.
4. Constant monitoring of student performance results.
Students in the class are divided into three groups.
These groups are not permanent; their composition may change.
Group 1 - students who require constant additional help. They need additional explanations and examples of completing tasks. These are the majority of students in the class.
Group 2 – students who can cope on their own, but sometimes they need help from a teacher.
Group 3 – students who are able to cope with the material in a short time with high quality and help others. There are few such students, but they exist in every class.
Leading pedagogical idea.
The main task that I set for each student is not just to go through the program, but to learn to understand what you are talking about yourself and what others are saying, to learn to think, to learn to master fundamental knowledge.
Therefore, I have to constantly look for new means and ways of showing interest in the mathematical and logical tasks that I offer in class and during extracurricular activities.
The children's interest in individual tasks and in mathematics serves as an incentive for their participation in olympiads, mathematics tournaments, mathematical quizzes, and the publication of mathematical newspapers.
Every year, students of our orphanage-school take part in city mathematical Olympiads and in the international mathematical competition-game “Kangaroo”.
In 2010, 5th grade student Sasha Gurenkov, scoring 68 points, took 18th place in the region, 259 in the region.
In 2011, Alexandra Svetkina, an 11th grade student, scored 69 points and took 4th place in the region, 180 in the region.
The effectiveness of the experience.
As a result of an individual approach to teaching mathematics, it is possible to:
- reveal the abilities of students;
- increase children’s interest and passion for the subject;
- teach students to be more self-confident;
— teach students to try to use the acquired knowledge in various situations.
An individual approach to learning helps students prepare for the Unified State Exam.
All ten graduates of 2010\2011 crossed the threshold of 24 points. The average score was 39.9.
The students (Natalia Volchikhina, Alexandra Svetkina) entered universities where mathematics is a major subject.
Graduates of 2011\2012 showed good results in the Unified State Examination. The average score was 56.
I am concerned about the development of children, the success in learning of each student, and therefore in my teaching activities I take an individual and differentiated approach to teaching students mathematics.
Innovative activities of mathematics teachers in modern conditions
Innovative activities of mathematics teachers in modern conditions.
1. What is “Innovation activity”?
Almost all teachers see two main components in this concept: it is something new compared to the previous one, and this new thing is aimed at improving the quality of education. In general, the essence of the definition is indicated quite correctly. In the modern understanding, innovation is “the manifestation of new forms or elements of something, as well as a newly formed form or element.” A synonym for innovation is the concept of “innovation”.
In pedagogy, the concept of “innovative activity” is considered somewhat deeper and has a wide semantic range. This is a purposeful pedagogical activity based on understanding one’s own pedagogical experience through comparison and study of the teaching and educational process in order to achieve better results, obtain new knowledge, introduce new teaching practice, this is a creative process for planning and implementing pedagogical innovations aimed at improving quality education. This is a socio-pedagogical phenomenon that reflects the creative potential of the teacher.
As a pedagogical category, this term is relatively young, and this is one of the reasons that there are different approaches to defining this concept. The modern dictionary of pedagogy interprets this term as follows: “Pedagogical innovation is an innovation in pedagogical activity, a change in the content and technology of teaching and upbringing, with the goal of increasing their effectiveness.”
M.V. Clarin, for example, puts the following meaning into the concept of “innovation”: “Innovation refers not only to the creation and dissemination of innovations, but also to transformations, changes in the way of activity, the style of thinking that is associated with these innovations.”
The authors of works on pedagogical innovation M.S. Burgin, V.I. Zagvyazinsky, S.D. Polyakov, V.M. Polonsky, M.M. Potashnik, N.R. Yusufbekova and others correlate the concept of “new in pedagogy” with such characteristics as useful, progressive, positive, modern, advanced.
Despite different interpretations of the concept, the main indicator of innovation is the progressive beginning in the development of educational institutions in comparison with established traditions and mass practice.
In modern society, the first wave of awareness of the needs for a new quality of education resulted in the idea of creating educational institutions of a new type: gymnasiums, lyceums, colleges, educational centers, educational complexes, etc.
The second wave of transformations led to the need for expanded, qualitatively new scientific support for educational and educational processes in educational institutions that are not capable of independent, conscious and purposeful transformations. In this regard, the task of creating diagnostic and development centers that are new in content and ideology, regional centers for managing the development of education, which could take on a number of the most important functions of the educational system that remain unrealized today, comes to the fore. This is seen today as an effective way to bring science and pedagogical practice closer together.
Scientific support for experimental work in teaching and upbringing, with all its diversity, presupposes a certain unification and accessibility for wide practical use. The standardization processes currently taking place at the federal and regional levels at all levels of education are aimed at this. This is the third wave of transformations in the modern education system.
Russia is entering the international market of educational services and brings the curricula and educational programs of schools, secondary specialized institutions and universities into compliance with generally accepted requirements throughout the world.
2. The main features of a teacher’s innovative activity.
Innovative activity and its process largely depend on the innovative potential of the teacher. Therefore, there is a need to consider this category.
The innovative potential of an individual is associated with the following main parameters:
- creative ability to generate and produce new ideas and ideas, and most importantly - to design and model them in practical forms;
- openness of the individual to something new, different from one’s ideas, which is based on the individual’s tolerance, flexibility and panoramic thinking;
— cultural and aesthetic development and education;
— readiness to improve one’s activities, the availability of internal means and methods that ensure this readiness;
— developed innovative consciousness (the value of innovative activities in comparison with traditional ones, innovative needs, motivation for innovative behavior).
The readiness of a teacher for innovative activity is usually understood as the formation of the personal (high performance, ability to withstand strong stimuli, high emotional status, readiness for creativity) and special qualities necessary for this activity (knowledge of new technologies, mastery of new teaching methods, ability to develop projects, ability to analyze and identify the causes of shortcomings).
The innovative activities of teachers have their own specifics. It presupposes the presence of a certain degree of freedom of action among the relevant subjects. Due to the specific nature of innovative, exploratory work, it is often carried out by touch, outside the boundaries of existing experience and can only partially be regulated and controlled by existing institutions. Therefore, society is forced to trust the researcher, the innovator, believing that in the process of freely searching for truth, new solutions and ways to implement the tasks facing society, he will not take actions that could further harm the interests of society. Consequently, freedom of creativity must be coupled with the highest personal responsibility of the subject of innovative search.
A necessary condition for the successful implementation of innovative activities of a teacher is the ability to make innovative decisions, take certain risks, successfully resolve conflict situations that arise during the implementation of innovations, and remove innovation barriers.
3. What circumstances in the modern education system determine the need for innovative activities of a teacher?
The need for innovative orientation of pedagogical activity in modern conditions of development of society, culture and education is determined by a number of circumstances:
— ongoing socio-economic transformations, which have necessitated a radical renewal of the education system, methods and technologies for organizing the educational process in educational institutions of various types. The innovative focus of teachers’ activities is a means of updating educational policy;
— strengthening the humanitarization of the content of education, continuous changes in the volume and composition of academic disciplines; the introduction of new educational subjects that require a constant search for new organizational forms and teaching technologies. In this situation, the role and authority of pedagogical knowledge in the teaching environment increases significantly, the tasks of growing the professional skills of teachers are updated;
— changing the nature of teachers’ attitudes towards the very fact of mastering and applying pedagogical innovations. Under the conditions of strict regulation of the content of the educational process, the teacher was limited not only in the independent choice of new programs and textbooks, but also in the use of new techniques and methods of teaching. Nowadays, innovative activities in education are acquiring a selective, research character. That is why an important direction in the activities of the heads of teaching staff and methodological services of educational institutions is the analysis and assessment of pedagogical innovations introduced by teachers, the creation of the necessary conditions for their successful development and application;
o — the entry of educational institutions into market relations, which form the real situation of their competitiveness
o The innovative potential of a teacher is a complex of various components .
o Technological component - teachers’ knowledge of technologies for complex activities for the creation, development, use and dissemination of innovations.
o Creative component - teachers have a creative approach to their professional activities;
o The motivational component allows us to understand what main motives drive teachers in innovative activities.
o The cognitive component implies the presence or absence of knowledge about the innovations that will be introduced in the organization and cognitive difficulties among the subjects of innovation implementation.
o The regulatory component is defined as the attitude of the subject of innovation to the initiators of innovation, to the methods of creating and disseminating innovations.
o Emotional component, emotions can facilitate or hinder the perception of innovation. The complexity of organizing innovative activity is aggravated by the fact that the structure of an individual’s emotional states and their dynamics are deep . individual and therefore very diverse.
Innovative approaches to teaching mathematics
Grigorieva Natalya Vyacheslavovna MBOU "Verkhnemedveditsa secondary school" Kursk district
For a small rural school with one parallel and a small number of students in classes where it is impossible to carry out external differentiation, but it is necessary to take into account the interests and capabilities of each child, elements of the technology of level differentiation, parallel study of topics, and block presentation of material are successfully used.
The essence of leveled mathematics teaching is that at all stages of the lesson, all students are presented with tasks of at least three levels of difficulty: minimally compulsory, compulsory and advanced.
The student has the right to choose the level of difficulty, the form of delivery of the completed task, while developing the skills of self-esteem, the relationship between the work invested and the grade, and the understanding that in order to achieve the goal it is necessary to invest some work.
Leveled education removes the complex in schoolchildren: “I’m not like everyone else, I can’t solve something.” The use of leveled training builds self-respect and independence: “I chose it myself, I did it myself.” The ability to make decisions and be responsible for its consequences is also developed. Presentation of multi-level tasks makes it possible for each student to choose feasible tasks. Thus, lesson time is used most effectively.
To organize students’ independent work, it is advisable to create as many variants of tasks as there are students in the class.
Multi-level assignments, designed taking into account the capabilities of students, create a favorable psychological climate in the classroom. The guys have a feeling of satisfaction after each task completed correctly. Success experienced as a result of overcoming difficulties gives a powerful impetus to increased cognitive activity.
Students, including weak ones, gain confidence in their abilities, they no longer feel afraid of new tasks, they risk trying their hand in an unfamiliar situation, and take on problems of a higher level of complexity.
All this contributes to the formation of students’ general educational skills and the creation of positive motivation for learning.
The use of leveled learning allows you to cope with the organization of student activities in the lesson, and to use lesson time effectively and efficiently. There is an opportunity to pay attention to each child, developing general educational skills in accordance with their real educational capabilities.
The use of elements of level technology is carried out at all stages of the lesson: when learning new material, when consolidating what has been learned, when developing practical skills, at the stage of generalizing and systematizing knowledge, as well as when testing, evaluating and correcting it.
Let’s take a closer look at the application stage of learning new material.
During this stage, it is necessary to ensure that students master the volume of material being studied that is mandatory for all. Also at this stage it is necessary to form a moral attitude towards oneself, work, and the Motherland.
Contents of the stage of acquiring new knowledge:
- organizing students' attention;
- organization by the teacher of the process of perception, comprehension of primary generalization and systematization of acquired knowledge;
- teaching children their own activities.
It is necessary to strive to ensure that the teacher is “not enough” in the lesson, to carry out the educational process based on situations where the student becomes the main worker.
One of the activities of students when studying new material is working with sources of information (tables, models, reference books, textbooks).
When working with the text of a textbook on new material, the following tasks may be offered:
Level I. Find new terms, new formulas, make a drawing, answer questions.
Level II. Find the meaning of terms in the text, carry out formal proofs, deduce a formula or prove a theorem, make additional constructions in the drawing, draw up questions based on the text.
Level III. Draw up logical chains in the proof, draw up a proof plan, justify each stage of the derivation of a formula or proof. If possible, suggest another way of proof.
For example, when studying the topic “Area. Formula for the area of a rectangle,” students can be offered the following tasks to work with in the textbook.
Level I. Answer the questions:
- Name the units for measuring areas.
- How to find the area of a rectangle?
- Write down the formula for the area of a rectangle.
- How to find the area of the entire figure if the areas of its parts are known?
- Define a square.
- Write down the formula for the area of a square.
Level II. Make up questions for the text of paragraph 18.
Level III. Write down a formula to find the length of a rectangle if its area and width are known. Write down a formula to find the width of a rectangle if its area and length are known.
When studying the topic “Square of the sum” in 7th grade. Squared difference" you can suggest the following questions and tasks:
In grade 5, when studying the topic “Equation”, the following level tasks can be offered:
It is necessary to draw students' attention to the fact that equations of level III include equations of levels II and I.
When studying the topic “Square root of powers, products and fractions” in 8th grade algebra, you can offer the following tasks and give examples of recording their solutions:
One of the forms of improving the quality of training and developing competency skills is the parallel study of topics. Its advantages are the comparative analysis of two mathematical objects. In my opinion, it is convenient to study the following topics in parallel: “Arithmetic and geometric progressions”, “Derivative and antiderivative”, “Exponential and logarithmic functions”, “Polyhedra and bodies of revolution”.
For example, when studying the topic “Progression” in the 9th grade, students are asked to divide the notebook page vertically into two equal parts, one of them entitled “Arithmetic Progression”, and the other “Geometric Progression”. The resulting table is filled in during the lesson. It contains definitions of arithmetic and geometric progressions, their examples, and corresponding formulas.
Studying all of the above topics in parallel helps students create clear and strong semantic codes.
One of the ways to improve the quality of teaching is to present the material in blocks.
Studying the topic “Quadrilaterals” in 8th grade can be organized in various ways. The most efficient use of study time is achieved when considering the material as a single block.
During two lessons you can study all the theoretical material on this topic. Moreover, it is convenient to present new material in the form of a lecture-conversation, with the teacher asking students questions prepared in advance. Students, in turn, ask questions that arise in their minds. At the same time, they consider not only the formulations of the theorems, but also the fundamental proofs. In subsequent lessons, logical chains of proofs of theorems and solving problems of various levels of complexity are worked out.
Students' attention is focused on the fact that a rhombus, a rectangle, and a square are parallelograms, therefore they have common properties, but most importantly, these figures have significant differences.
When generalizing and systematizing knowledge on the topic “Quadrilaterals,” it is convenient to use the following diagram, which allows you to form a clear idea of the general and distinctive properties of all quadrilaterals.
Innovative technologies in preparing and conducting mathematics lessons
Innovative technologies in preparation
and conducting mathematics lessons
The development of society requires innovative behavior from the teacher, that is, active and systematic creativity in teaching activities.
The development of pedagogical innovation is associated with a massive social and pedagogical movement, with the emergence of a contradiction between the existing need for the rapid development of the school and the inability of teachers to implement it. The widespread use of new technologies has increased. In this regard, the need for new knowledge, for understanding new concepts of “innovation”, “new”, “innovation”, “innovation process”, etc., has become more acute.
The word "innovation"
- is of Latin origin. Translated, it means renewal, change, introduction of something new, introduction of novelty.
The concept of "innovation"
(innovation) is defined both as an innovation and as the process of introducing this innovation into practice.
The search for answers not only to the questions “what to teach?”, “why teach?”, “how to teach?”, but also to the question “how to teach effectively?” led scientists and practitioners to an attempt to “technologize” the educational process and, in connection with this, a direction appeared in pedagogy - pedagogical technologies.
Pedagogical technology
there is a model of modern educational and pedagogical activities thought out in all details for the design, organization and conduct of the educational process with the unconditional provision of comfortable conditions for students and teachers. Pedagogical technology involves the implementation of the idea of complete controllability of the educational process.
Analyzing effective research in the field of educational technologies, V. Guzeev, Doctor of Pedagogical Sciences, identifies four main ideas:
around which they concentrate: 1) consolidation of didactic units, 2) planning of learning outcomes and differentiation of education, 3) psychologization of the educational process, 4) computerization.”
Traditional pedagogical technologies
All teaching technologies are “designed” for students’ ability to learn independently; but, just as traditional didactics did not set the task of teaching students and used elements of the activity approach to solve only partial learning problems, so teaching technology retains this shortcoming.
The currently existing general didactic technologies (about 50 according to G. Selevko’s calculations) differ from each other in principles, features of means and methods of organizing educational material and the educational process, as well as an emphasis on certain components of the methodological teaching system.
Basic, known today, pedagogical technologies for teaching mathematics
at the methodological level they solve the problem of designing a learning process aimed at achieving planned results. Let's note some of them.
The technology “Enlargement of didactic units - UDE” is an integration of such approaches to teaching as:
a) joint and simultaneous study of interrelated actions and operations (in particular, mutually inverse functions, theorems).
b) ensuring the unity of the processes for composing and solving problems;
c) consideration of definite and uncertain tasks in mutual transitions;
d) reversing the structure of the exercise;
e) identifying the complex nature of mathematical knowledge, achieving systematic knowledge;
f) additionality in the exercise system.
The key element of the technology is a triad exercise, the elements of which are discussed in one lesson: a) the original task, b) its generalization; At the same time, in working on a mathematical problem, four sequential and interconnected stages are distinguished: composing an exercise, performing an exercise, checking the answer (control), moving on to a related but more complex exercise.
Technology aimed at developing general approaches to organizing the assimilation of computational rules, definitions and theorems through the algorithmization of educational actions
students, implements
the theory of the gradual formation of mental actions.
At the same time, systems of mathematics teaching aids serve as the material basis for the algorithmization of actions for organizing the indicative basis of actions, and teaching is carried out in cycles that vary from class to class. So, the four-lesson cycle consists of:
1) an explanation lesson that provides an indicative basis for actions with new material,
2) problem solving lesson,
3) a communication lesson using various orientation options,
4) independent work.
Technology of teaching in mathematics based on problem solving
based on the following conceptual provisions:
- personal approach, pedagogy of success, pedagogy of cooperation;
- teach mathematics = teach problem solving;
3) teach problem solving = teach typing skills + ability to solve standard problems;
- individualization of education for “difficult” and “gifted”;
- organic connection of individual collective activity;
- managing communication between older and younger schoolchildren;
- a combination of scheduled and unschooled work.
In the system of training sessions, of particular importance are unconventionally structured lesson-lectures, lessons on solving “key problems” (calculating the minimum number of main problems on a topic, solving each problem using different methods, solving a system of problems, checking the solution of problems by fellow students, independently composing problems, participating in competitions and Olympiads), consultation lessons (students’ questions on pre-prepared cards, working with cards: analysis, generalization, addition of cards), test lessons (completing an individual task, oral report to a high school student, correction when working in pairs until complete understanding, giving three grades - for answering theory, for solving problems from cards, for keeping a notebook; motivation for grades).
based technology , effective lessons
solves problems: creating and maintaining a high level of cognitive interest and independent mental activity of students; economical and expedient use of lesson time; variety of teaching methods and means; formation and training of methods of mental activity of students; formation and development of self-governing personality mechanisms that promote learning; high positive level of interpersonal relationships between teacher and students; volume and strength of acquired knowledge, skills and abilities.
Classification of lessons:
1) lessons where students learn to recall material (learn to keep it in memory),
2) a lesson in finding rational solutions,
3) a lesson in checking results by comparing them with data,
4) one task lesson (the pleasure of what they think),
5) a lesson in independent work that requires a creative approach,
6) a lesson of independent work on the material that was explained,
7) a lesson in returning to what was previously studied from a different angle,
benefit lesson
9) laboratory work on geometric material,
10) lesson - oral test,
11) lesson-test (thematic and final).
In park technology
teaching mathematics, the study of each topic consists of four stages: 1) an introductory lecture, 2) launch in pairs and groups of different ages (for which the educational material is divided into appropriate modules), 3) mutual exchange of educational material in same-age variation pairs and small groups, 4 ) control lesson.
In the technology of knowledge construction workshops
in mathematics, knowledge is not given, but is built by the student himself (in a pair or group) based on his personal experience; the teacher only provides him with the necessary material in the form of tasks for reflection. Workshops are designed according to a specific algorithm: individual work (using personal life experience), work in pairs (exchange of information based on personal experience), work in groups (completing tasks), class conversation (groups present their work, correction (groups make corrections) , additions to your version of the task), teacher’s word (highlighting important points, findings, mistakes of groups), workshop discussion (awareness of what has been done, formulation of unsolved problems). For workshops, topics that are difficult, and at the same time basic for understanding the course, are selected.
The trend of an integrated approach to learning has given rise to the technology of mathematics integration
as a basic school subject with computer science, physics, history, literature, English, etc. The goals of integrated courses are the formation of a holistic and harmonious understanding and perception of the world. To achieve this goal, a comprehensive integrated course program is being created, for which both the selection of content and the principles of its design are very important. Then - designing integrated lessons, learning tasks and ways to assess the results of students' learning activities.
The traditional form of teaching mathematics, as well as other subjects, was and is a lesson, which is currently becoming more sophisticated and diverse. A lesson is the main link in the learning process. Traditional lessons included studying new material, consolidating what was learned, or testing knowledge.
During their studies, schoolchildren acquire new knowledge and skills. When students first become acquainted with a fact, phenomenon, or event, they learn it only in rough, first approximation, in more or less general terms, and they do not grasp it firmly. As a result, the student does not so much know the material as present it in one way or another. In a word, this is the primary assimilation of educational material, shallow and fragile.
This means that additional work on the material will definitely be required. This is the second didactic learning objective, usually called consolidation. Unfortunately, this name is unfortunate: you cannot fix something that, strictly speaking, does not yet exist. We should talk not about consolidation, but about the development of knowledge. But the term “development” is used in a different sense (development of the mind), and most importantly, historically established terms are difficult to change.
In pedagogy, the term “consolidation” has been preserved from those times when it seemed that knowledge was acquired immediately in its final form and all that remained was to consolidate it so as not to lose it. In fact, we are talking about the gradual comprehension of knowledge, about transferring it from short-term memory to long-term memory, about developing the ability to operate with acquired knowledge.
Finally, the learning process also includes a third didactic task - monitoring and evaluating the results of students' educational work.
The teacher faces the problem of how to structure the learning process in order to best solve all three didactic tasks: initial development of new material, consolidation and testing of progress. The most important question here is how to distribute this, that, and the third in time. Depending on his decision, certain types of lessons arise.
The types of lessons that emerged in Soviet schools can be basically reduced to two groups: a group of specialized lessons and a group of combined ones. A specialized lesson solves mainly one of three didactic tasks. Accordingly, this will be a lesson either studying new material, or consolidating knowledge, or testing it.
Now we should look in more detail at the various teaching methods used in teaching mathematics.
In the process of many years of school practice, teaching methods have been developed, which are ways of transmitting cognitive information to schoolchildren, which are closely related to the activities of the teacher himself. Such methods, inherent in traditional teaching of mathematics, but which have not lost their importance in modern teaching, include a conversation, a story or a lecture by the teacher, as well as independent work of students with a textbook, or independent practical work of a training nature.
Innovative pedagogical technologies.
Innovation lies in the gradual re-evaluation of meaningful learning goals. If earlier educational goals were put in the foreground, and development goals were set as accompanying them, now priority is given to development goals. In this regard, in the modern mathematics curriculum, as is known, there are 3 levels of task complexity:
- Meets mandatory software requirements. The knowledge of each student must meet these requirements and the required level of knowledge, skills and abilities must be achieved by each student in the allotted time.
- There are tasks of medium difficulty level.
- Tasks that are intended for students who show increased interest in mathematics, as well as for use in classes, schools, and gymnasiums with in-depth study of mathematics.
If earlier the teacher was focused mainly on the average student in his work and the implementation of a differentiated approach in mathematics lessons was, figuratively speaking, a matter of conscience for the teacher, then modern innovative approaches to teaching mathematics require a mandatory differentiated approach, a mandatory student-oriented approach, in accordance with with which each student, figuratively speaking, chooses his own learning path. The requirements for each student and specific work with him will be determined by the level of abilities, capabilities and interests of each student.
The mathematics program of secondary educational schools provides for the development, first of all, of the intellectual sphere of students, the development of schoolchildren’s thinking, the basis of which is the mental operations of analysis, synthesis, comparison, generalization, classification and the ability to make inferences.
Differentiated teaching in mathematics is associated, first of all, with improving the setting of goals for teaching mathematics.
From the point of view of the technological approach, the goals of teaching mathematics should be to teach students to perform certain actions (observable or presented in the form of standards), which together form their readiness for learning, and the goals of teaching should be to learn how to perform these actions, and from a developmental point of view For a student, he needs not a simple formal adoption of the image of each action, but a deep understanding of it.
Consequently, the system of goals
of educational activity in a given educational field can be presented in the form of a certain
system of student actions,
adequate to the system of components of readiness for educational activity, which he must learn to perform as a result of training and for its success, and this will mean a shift in emphasis from mathematical education for
education through mathematics.
Currently, a mathematics teacher has the opportunity to use modern teaching tools. Increasingly, interactive whiteboards, multimedia projectors, and personal computers are used in lessons.
All innovations that are being introduced in the secondary school education system are based on positive results, which are still producing high results.
Along with traditional methods, innovative methods are used in mathematics lessons. One of them is programmed learning technology (block learning)
.
The use of certain techniques in teaching mathematics using programmed learning technology has made it possible to increase students' cognitive interest in the subject, teach them the skills of independently acquiring knowledge, and qualitatively prepare students for state exams.
As a result of the implementation of this technology, students develop an interest in processing visual information, the desire and opportunity to analyze it, raising the question of unknown connections, and obtain the desired result.
Education, which ensures the development and self-development of the student’s personality, based on the identification of his individual characteristics, was a priority both in traditional methods of teaching mathematics and at the present time. This method is person-oriented technology
. It is based on the recognition of each student’s right to choose their own path of development through the creation of alternative forms of education.
Pedagogical technologies reflecting a student-centered approach include:
— LEARNING IN COOPERATION
— PROJECT METHOD
— MULTI-LEVEL TRAINING
— STUDENT'S PORTFOLIO
- INTERNET TECHNOLOGIES
DEVELOPMENTAL TRAINING
— “Developmental education is a type of education in which human development is not a by-product, but a direct and main goal. The main features of developmental education: the student turns into a subject of cognitive activity; develops on the formation of thinking mechanisms, and not on the exploitation of memory;
— the student’s cognitive activity is mastered in the unity of empirical and theoretical knowledge; the learning process is based on the priority of the deductive method of cognition; The basis of the learning process is the educational activity of students during the implementation of educational tasks."
PRINCIPLES OF COLLABORATIVE LEARNING
— groups of students are formed by the teacher. Moreover, in each group there should be a strong student, an average and a weak one (if the group consists of three students).
— the group is given one task, but when completing it, roles are distributed between group members
— the work of the entire group is evaluated (i.e., one rating is given to the entire group);
— the teacher himself chooses a student in the group who must report for the assignment.
PROJECT METHOD
- a set of techniques, actions of students in their specific sequence to achieve the task: - solving a specific problem that is significant for students and formalized in the form of a certain final product.
BASIC REQUIREMENTS FOR THE PROJECT METHOD
— The presence of a problem that is significant in research and creative terms.
— Practical, theoretical significance of the expected results.
— Independent (individual, pair, group) activities of students in class or outside of class time.
— Structuring the content of the project (indicating stage-by-stage results and distribution of roles).
— Use of research methods: identifying the problem, the research tasks arising from it, putting forward a hypothesis for their solution, discussing research methods, drawing up the final results, analyzing the data obtained, summing up, adjusting, conclusions (using the “brainstorming” method during joint research, “ round table", creative reports, project defense, etc.).
Project technology requires the presence of a problem requiring research. This is a search and research activity of students, individual or group, organized in a certain way, which students carry out over a certain period of time.
The project method is based on the development of students’ cognitive skills, the ability to independently construct their knowledge, the ability to navigate the information space, analyze the information received, independently put forward hypotheses, the ability to make decisions, the development of critical thinking, the ability to conduct research and creative activities.
This approach fits seamlessly with a group approach to learning. Collaborative learning is part of the project method.
The method of projects in collaboration makes it possible to ensure that each student in the group masters the educational material at a level accessible to him, and thus, with further joint work, all students can take an active part in project activities, receiving an independent piece of work.
The ability to use the project method and collaborative learning is an indicator of the teacher’s high qualifications and his progressive methods of teaching and developing students. The teacher must think through the entire course of work on the project. But neither the problem itself, nor the hypotheses, nor the methods for studying creative, exploratory activity should be given to students in a ready-made form. Students themselves must come to a conclusion about the validity of the hypotheses, problems or their fallacy, but at the same time they must support their point of view with arguments, evidence, and facts.
The implementation of the project method and collaboration methods are very promising in the study of mathematics; work in these forms arouses genuine interest among students and is more effective than in traditional lessons.
In the process of preparing and conducting such lessons, the teacher has the opportunity to develop in students:
- new educational skills for independent acquisition and comprehension of knowledge of a wide range,
- new personal qualities.
The project method can be used in the educational process to solve various small problem problems, and then mini-projects can be organized quite often, teaching students to creatively apply the acquired knowledge independently.
Examples of short-term projects:
- Correct pyramid.
— Distance from a point to a plane.
— The angle between a straight line and a plane.
— Point coordinates and vector coordinates.
This method is also used to solve large problems and issues that are difficult to understand. Then fairly large projects (macroprojects) are used, taking up several lessons and quite serious independent search and research activities outside of class hours.
Examples of medium-term projects:
— Solving equations of 2, 3, 4 degrees according to the formula.
— Continuity of function.
— One-sided limits.
Organization and implementation of macro-projects requires a well-founded and reasonable approach. Such projects and, accordingly, lessons cannot be carried out too often, turning into something everyday - they must represent a celebration of knowledge, certain milestones in the study of such an interesting and wonderful science as mathematics.
Examples of long-term projects:
— Möbius strip and its properties;
— The golden ratio and its application in the architecture of the native city;
— The Pythagorean theorem is outside the school curriculum.
MULTI-LEVEL TRAINING
By multi-level education we mean such an organization of the educational process in which each student has the opportunity to master educational material in individual academic subjects of the school curriculum at different levels (“A”, “B”, “C”), but not lower than basic, depending on his abilities and individual characteristics. At the same time, the criterion for assessing the student’s activity is his efforts to master this material and apply it creatively.
"STUDENT'S PORTFOLIO"
— A student’s portfolio is a tool for self-assessment of the student’s own cognitive, creative work, reflection of his own activities. This is a set of documents, independent work of the student.
PRINCIPLES OF TECHNOLOGY “STUDENT'S PORTFOLIO”
— Self-assessment of results (intermediate, final) — Systematic and regular self-monitoring
— Structuring of portfolio materials, logic and conciseness
all written explanations.
— Accuracy and aesthetics of portfolio design.
— Integrity, thematic completeness of the materials presented in the portfolio.
— Visibility and validity of the presentation of the student’s portfolio.
Use of computer and information technologies
in mathematics lessons.
The use of computer and information technologies in teaching mathematics is explained by the need to solve the problem of finding ways and means of activating the cognitive interest of students and developing their creative abilities. A feature of the educational process using computer tools is that the center of activity becomes the student, who, based on his individual abilities, builds the process of cognition. A “subject-subject” relationship develops between the teacher and the student.
In the system of such training, two types of activities are distinguished - teaching and educational.
The first is characterized by the interaction of students with a computer. The computer determines the task that is presented to the students, evaluates the correctness and provides the necessary assistance. The second type is characterized by the fact that the computer helps the teacher in managing the educational process, provides the results of students completing test tasks, the computer can compare the performance of different students in solving the same tasks, and can give recommendations on the application of specific educational influences to students. In teaching mathematics, a computer can be used at all stages of the lesson, when explaining new material, consolidating, repeating, and monitoring.
A computer in the classroom is a tool that allows students to better understand themselves, the individual characteristics of their learning, and contributes to the development of independence. The use of computer technologies in teaching mathematics makes it possible to differentiate educational activities in the classroom, activates the cognitive interest of students, develops their creative abilities, stimulates mental activity, and encourages research activities.
