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Realization of pedagogical model of education of valuable orientations of the senior teenager (means of a subject of "Mathematician")

As a result of working out of pedagogical model of education of valuable orientations of the senior teenager by mathematics means as subject laws, principles, factors, conditions and preconditions of studied process have been formulated, and also its pedagogical model is made.

Realisation of pedagogical model has resulted in necessity of revealing of methods of education of valuable orientations of the person for educational space of school subject means.

In pedagogics there are various approaches to definition of concept "method". This concept open as a way of interaction of the teacher and pupils (M.I.Rozhkov, L.V.Bajborodova) as set of ways and receptions of educational work (G.M.Kodzhaspirova, I.F.Kharlamov) as a way of influence on the person of pupils (I.P.podlasyj) etc. Recognizing that education of valuable orientations the more effectively, than more pupil shows the subektnost in the course of training and education, we will stop on such definition: the education method is a way professional
interactions of the teacher and pupils for the purpose of the decision ­ obrazovatelnovospitatelnyh problems [135].

the Variety of ways of interaction of the teacher and pupils causes also variety of methods of education. To carry out a choice of the methods corresponding to the purposes of education and to existing circumstances it is necessary to address to their classification - the system built to a certain sign. «Classification helps to find out with methods the general and specific, essential and casual, theoretical and practical and by that promotes their realised choice, to the most effective, application» [124, with. 189].

In system of methods of education there is a set of the classifications allocated on the various bases. So on character of influence on the person of the pupil allocate belief, exercise, encouragement, punishment (with N.I.Boldyrev, N.K. Queens, F.F.Goncharov, etc.); on an influence source on the person of the pupil explanatory-reproductive, problemno-situational, a method of schooling and exercise, stimulation, braking, a management, self-education (I.S.Marenko) etc.

it is frequent enough in the pedagogical literature classification of methods of education of G.I.ShChukinoj or its various interpretations is stated. According to this classification, education methods share on methods of formation of consciousness (the story, an explanation, an explanation, lecture, ethical conversation, admonition, suggestion, instructing, debate, the report, an example); methods of the organisation of activity and behaviour formation (exercise, the commission which is bringing up situations) and methods of stimulation (competition, encouragement, punishment).

From our point of view, any of existing classifications has the right to existence as serves definite purposes. In the given case the choice of methods of education should lean against phenomenon structure «valuable orientation of the person», aksiologichesky subject potential
"Mathematics", and be logic continuation of the formulated pedagogical model.

the Analysis of the philosophical and psychological literature has allowed to establish, that the structure of valuable orientation of the person represents interrelation of three components: kognitivnogo, emotional and behavioural. With these components correlate the revealed pedagogical conditions of education of valuable orientations of the senior teenagers in educational activity: actualisation of a valuable component of the maintenance of a subject of "Mathematician"; emotional enrichment of process of studying of mathematics; pedagogical support of a reflexion by pupils of own system of values and its realisation in behaviour.

Thus, proceeding their three-componental structure of the valuable orientation created of pedagogical model and existing classifications of methods of education, in reformative experiment we used following groups of methods:

1) methods forming kognitivnyj a component of valuable orientation of the person: the story, an explanation, conversation, discussion, debate, the analysis of concrete situations, problem situations, practical work, brain storm;

2) methods developing an emotional component of valuable orientation of the person: an example, creative work, the analysis of works of art;

3) methods realising a behavioural component of valuable orientation of the person: the commission, competition, a method of projects.

In spite of the fact that in the typology resulted by us methods correspond to any one component of valuable orientation of the person, it is necessary to consider such division in certain degree conditional as all methods of education have cumulative influence on all intrinsic spheres of the person, that thus does not exclude their grouping from the point of view of dominating influence on this or that sphere.

the Story is one of the methods realising kognitivnyj a component of valuable orientation of the person and represents «small on volume a coherent statement (in narrative or in the descriptive form) the events containing an illustration or the analysis of those or other moral concepts and acts» [75, with. 231]. Following demands are made To the story as to an education method: logicality, dokazatelnost, sequence, figurativeness, an emotionality, conformity to age features of an audience. At mathematics lessons this method was applied at realisation of all directions of actualisation aksiologicheskogo mathematics potential. So disclosing of a role of mathematics as method of knowledge of the validity began with studying in 7 class of a theme «Expressions with variables» and proceeded throughout all experiment. The strong basis in understanding of a place of mathematics among sciences was pawned at theme studying «the Axiom of parallel straight lines». At studying of this theme we not only considered an axiom of parallel straight lines, but told as a whole about axioms of geometry and deductive construction of mathematics as sciences, in particular.

Tsennostno-semantic development of mathematical concepts has been realised by means of the parables used at a stage of motivation. We will result one of parables of V.N.Klepikova's article «Pritchevye miniatures at mathematics lessons», told by us at theme studying «Comparison of pieces».

Wisdom

Once the young man has spent a piece on the earth and has asked a wise man that that has reduced it, not cutting down and not concerning. The wise man has in parallel spent longer piece and by that the initial piece has been belittled. «So it is possible to concern the merits and demerits, - the wise man, - increasing advantages has noticed, we thereby belittle lacks». In turn the wise man has set to the young man the following problem. On a sheet of paper two various points are noted. How them to combine if to exclude possibility of connection of points a line? The young man, having thought, has combined a leaf and has combined points. «So often happens in a life, -
the young man has noticed. - when the problem does not dare in“ flat measurement ”she is easy for solving in“ multidimensional ”» [72].

Value of a science during reformative experiment opened not only the teacher, but also pupils by preparation of messages. Thus were realised not only support principles on the maintenance of a subject, scientific character and communication of training with a life, but also a principle of activization of processes of self-realisation and self-expression. Application of this method was accompanied by use of audiovisual means. During reformative activity by joint efforts with pupils the videoshop devoted to various directions of integration of mathematical knowledge has been collected.

In the event that it was necessary more clearly and to open accurately an essence or to prove correctness of any positions, the explanation method was applied. «For an explanation the demonstrative form of the statement based on use of logically connected conclusions, establishing the validity of the given judgement» [108 is characteristic, with. 332]. Big aksiologicheskim potential intersubject integration of mathematics with other sciences possesses, but mathematics application especially in natural sciences and the technician is frequent it is difficult enough for understanding for what we and resorted to this method. So disclosing of application of properties of a rectangular triangle in the device of an angular reflector (8 class) demanded an explanation of organic laws of geometrical optics and performance of certain mathematical calculations, application of direct proportionality (7 class) in the physicist of an explanation and an illustration of law Guka etc.

the Story and an explanation are included organically into a lesson outline as, as a rule, do not occupy a lot of time for preparation and realisation and besides are actively used as training methods. But during the story and an explanation the pupil acts in a passive role - in a role of the listener. For awakening of activity of the teenager at a lesson it was used question-answer an interaction method - conversation. The logic structure of conversation had the following appearance: 1) the teacher entered pupils into a theme of conversation and asked a question; 2) teenagers
expressed; 3) the teacher generalised all stated, underlined proofs of the main positions and helped pupils to draw convincing conclusions.

At conversation planning it was considered, that the system of questions directing pupils on perception and acceptance of values should be thought carefully over, and the conversation subjects - to be scooped from a life and to interest teenagers. So among teenagers often there was an opinion, that in studying of mathematics there is no necessity in this connection we offered pupils of conversation in which basis statements about advantage of studying of mathematics have been put, for example: to think consistently, to judge demonstratively, to deny wrong conclusions everyone should be able: the physicist and the poet, the tractor operator and the chemist (E.Kolman). Besides other conversations were used by us as natural continuation of the story or an explanation. So film viewing about gold section in art always came to the end with conversation about necessity of its application.

Other methods realising a principle of consciousness and activity, discussion and debate are. Efficiency of these methods is based on position that «the knowledge extracted during collision of opinions, the various points of view, always differs a high measure obobshchennosti, firmness and flexibility» [108, with. 225]. Both discussion, and debate assume presence of a situation of some informative dispute, and presence, at least, two opposite opinions on a discussed question is obligatory. The basic difference between these methods consists volume, that discussion means acceptance of the decision which have settled and made by scientific authorities, on debate the certain and definitive decisions are not required.

At the discussion and debate organisation the tactfulness, argumentirovannost, persuasiveness of judgements of all participants in this connection it is expedient to acquaint pupils with rules of conducting informative dispute in advance is important. As it is necessary to notice, that these forms of education as well as possible correspond to age features of teenagers as to this age are peculiar «requirement for self-expression, the desire of the person is opened
to declare itself, the intentions, desires, belief and feelings, actively to express them in behaviour and dialogue» [13, with. 63].

Discussions and the debates promoting formation of knowledge of the maintenance of universal values, were spent as generalisation or fastening of the studied material, after studying of the big block of the information. We organised tsennostno-orientatsionnye debates and discussions on following themes: «True and logic» (whether mastering by laws of correct thinking is obligatory, rules of logic for reception of true knowledge?); «mathematics of beauty» (whether Probably matematicheski to describe human representations about beauty?); «the nature: chaos or law?» (As far as possible also it is necessary to describe the natural phenomena matematicheski?); «the Mathematical statistics in human life» (whether the mathematical statistics Influences human life?).

Besides the message to pupils of knowledge of universal values, it is not less important to inform knowledge of the ways of their realisation accepted in a society for what it is expedient to address to the analysis of concrete situations. Ample opportunities for realisation of this method at mathematics lessons problems possess. We used problems about work, about a healthy way of life, about thrift, about communication of training with a life, about mathematics application in various sciences etc. we Will result as an example some problems which decision is capable to push pupils on reflexions about harm of smoking, other examples of problems applied during experiment are resulted in the Appendix 7.

1. It is counted up, that smoking children reduce to themselves a life approximately to 15 %. Define, what life expectancy of present smoking children, if average life expectancy in Russia 67 years?

2. At check of a state of health of group of pupils of the school consisting of 20 persons, with the experience of smoking of 3-5 years it is revealed, that 70 % from them have on 2 diseases (breath and digestion bodies), the others - on one disease. Define, how many pupils of this group have on 2 and how many on one disease?

3. Define, how many percent of the revenue the person smoking one pack a day if one pack of cigarettes costs 50 roubles spends for cigarettes, and the monthly salary makes 25 000 rbl.

Realizations of a principle of activity and consciousness in education and training promoted problem situations. The problem situation is understood «as a situation of performance of the practical or theoretical task at which before the acquired knowledge it appears insufficiently and there is a requirement for new knowledge» [24, with. 374].

Throughout all experiment we created such problem situations which would lead to comprehension of essence of universal values. For example, on one of lessons in 8 class following couplet Esi CHerikover was offered to pupils:

I know It and I remember perfectly:

Pi many signs to me lishni, are vain.

Then to eight-graders it was informed, that this couplet was composed once by the schoolgirl of one taking a great interest in mathematics of the Moscow schools then the question was asked: for what it has made it? In the course of joint search of the decision and search of set of variants children came to true surprising them: the number of letters of each word in it a couplet is a sign in number record pi (and #8776; 3,14159265358), and the schoolgirl simply wished to facilitate its storing. Thus pupils realised, that not only the mathematics is a key to understanding of the validity and poetry including, but sometimes and the poetry can become assistants in mathematics development. This knowledge opened together brought the contribution to comprehension by teenagers of essence of values "science" and "art".

One of geometry lessons in 7 class began with a problem question: why at the Greek words "axiom" and "aksiologija" (the doctrine and values) the same root? In the course of reflexions interesting hypotheses have been received some: axioms so are called, because were perceived by Greeks as something valuable; many moral values represent some kind of axioms (the fundamental statements which are not demanding the proof, and 117

accepted, that is called «on belief»). In this case we promoted expansion of representations of teenagers not only about value "science", but also about morals including.

the Major method of development not only mathematical knowledge, but also knowledge of values is practical work. Such kind of work we organised after studying of large sections, and thus not only generalised studied, but also showed its practical importance. Pupils spent practical works not only in a class, but also outside of school. For example, to pupils 8 classes as a creative homework were offered to measure by means of a mirror house height in which they live, being based on signs of similarity of triangles.

As the mathematical statistics is one of the most demanded for today of sections of mathematics, carrying out of sociological interrogations at school can be considered as one forms of practical work. Pupils of the seventh class were offered to spend interrogation among contemporaries on their interesting themes, and then to analyse data, applying statistical characteristics known for it. We will result some variants of such questions: «How many hours per day you play computer games?», «how many interlocutors at you in social networks?», «how many hours per day you spend behind TV viewing?», «Skolkih you consider people as the friend?» Etc. the Maintenance of the given questions reflects the problems, interesting the given age group. Such work helps teenagers to learn itself as the person and to learn about a life of contemporaries more, and also to see application of mathematical methods in psychology and sociology and other sciences.

For formation kognitivnogo a component of valuable orientations of the senior teenagers the method of brain storm was used. This method is applied for produtsirovanija new ideas at the decision of scientific and practical problems. The method essence consists in the organisation of collective cogitative activity on search of nonconventional ways of the decision of problems.
participants state various (even ridiculous) ideas to criticise which it is forbidden.

Within the limits of experimental work in the end of an academic year we spent brain storm «What for to study mathematics?». Method realisation included following stages: organizational (the message of a theme, work rules, formation of working groups, a choice in each group of the person fixing ideas); the basic (the statement and fixation of ideas); an estimation and selection of the best ideas; representation of results.

the Second condition of education of valuable orientations of the senior teenagers in educational activity formulates emotional enrichment of process of studying of mathematics. In this connection we will consider the methods realising an emotional component of valuable orientation of the person. One of such methods - an example. This method, consists in that, «that on concrete convincing samples to illustrate a personal ideal and to show the sample of the ready program of behaviour» [Kodzhaspirova G.M.Pedagogika, with. 233]. Among the examples possessing in inexhaustible educational potential, examples from a life of great and outstanding persons are especially allocated. « The following feature of the given kind of an example consists that inevitably there is an internal dialogue thanks to awakening of absolutely special feelings at those who gets acquainted with them »[13, with. 31]. The expediency of this method as it is caused by that materials about people,« whose results on self-creation fairly admire many generations of people », has any school subject, including mathematics.

At lessons we used fragments of biographies Evklida, Pifagora, M.V.Lobachevsky, S.V.Kovalevsky, P.L.Chebysheva and others. So, for example, in the mathematician as a symbol of courage and high working capacity L.Euler acts. It posesses outstanding results in all areas of mathematics existing during its time, and also in the mechanic, optics, hydrodynamics, astronomy and many other things knowledge areas. During lifetime of Euler L have been published 530 books and articles. 17 years prior to death Euler L has gone blind,
but, despite it its scientific efficiency only has increased: almost half of all its works is created last decade lives. Thanks to ability to make difficult calculations in mind and phenomenal memory Euler L could dictate the works to pupils. Euler L was engaged in calculations up to death.

Use of similar fragments always came to the end with the organisation of a reflexion of pupils. The teacher set following questions: what qualities of the given person cause in you liking? An antipathy? What qualities you would like, that were present at your character?

Formation of the positive emotional relation to universal values as is promoted by the analysis of works of art. Art realises bringing up function, influencing emotions of the person, and integration with art is assumed by the maintenance practically all school subjects. So many art forms, such as painting, architecture, music, poetry are based on mathematical ideas. For example, the prospect in the fine arts leans against geometrical laws, and construction of a composition of works of art often is based on principles of symmetry and gold section. The analysis of dependences between a mathematical component of works of art and a plan of the author allows to get into the world of its senses and experiences and to make their element of the experience.

On one of lessons in the seventh class we have suggested teenagers to analyse M.Eshera's engraving of "Reptile" (the appendix 8). This artist became known for use in the works of a wide range of mathematical ideas which scooped from scientific articles including. On an engraving of "Reptile" the table, with the drawing of the reptiles collected in the form of a mosaic located on it is represented. Reptiles revive, are pulled out from flat drawing, pass a circle and again come back in lifeless drawing. Besides a mosaic on a table subjects which as critics consider settle down, personify natural sciences (a large bottle, a notebook, a square, a plant, the book). Among
these subjects the metal dodecahedron which represents the highest point along the line reptiles is especially allocated. It is interesting, that according to Pythagorean philosophy, the Universe has the dodecahedron form. Variety of interpretations of senses which has enclosed in this work in M. Esher, has given an inexhaustible source of materials for aksiologicheskogo the analysis at mathematics lessons. So, having united in groups pupils discussed the point of view existing in art criticism circles that on an engraving the cycle of reincarnations live beings is represented and offered the versions.

to Pupils 8 classes the personal understanding of a picture of h.p. popovoj «the Portrait of the philosopher» (was offered to formulate during group work the appendix 8). At first the image represented about styles a cubism caused negative associations, sharp corners of the polygons making a figure, frightened. Then gradually pupils came to that it is not necessary to take the picture name literally: the artist wished to represent not the person of the philosopher, and its internal, inconsistent world for what used geometrical figures.

to Create an evident image, to cause the emotional response, to throw light on unevident communications the poetry helped. Rather effective there was use at lessons of poems, in which mathematical concepts are used as metaphors and epithets (the appendix 9), we will result one that was read by the pupil at a generalisation lesson has undressed "Triangles".

Geometry udach

At each of us a Straight line,

to be crossed by It only time is given.

And in them peresecheni we meet

The trouble, destiny, good luck, but...

At each of us a Circle,

not Passing circle of problems, cares, poterjannost, utrachennost, uselessness, And new to poteplenju turn.

At each of us the Triangle.

And, escaping from the passions,

We rush about, overtaken by a pain

And the happiness divided for three.

And as the century throws us and breaks!

But on lips so few kind words.

At each of us the Curve And the Broken line with set of Corners.

Dmitry Chelyshev

Comprehension and acceptance of values is made, including, and in the course of performance of creative works. It is known, that creative process proceeds at interaction of private world of the person and the validity therefore changes both the first, and the second. For this reason, in the course of creative activity pupils not only create something new, but also find "vision", the "personal" sense of values. Compositions, drawings, photos, verses were the works promoting comprehension and acceptance of values, problems etc. the Subjects of such works were very various. Creative works on the mathematician have been devoted outstanding persons from the mathematics world, to application of mathematical ideas in other areas, valuable interpretation of mathematical concepts and laws etc.

the Composition, being, on the one hand, one of kinds of independent educational exercise, is, on the other hand, the most powerful means of self-disclosing, self-expression of the author. As the writing of the composition demands from the pupil of accumulation of an actual material, its ordering, an arrangement, logic, a choice of words and figurative means, this kind of creative work represents not only a product of the saved up knowledge and abilities, but also the effective tool of transfer of the thoughts, feelings, intentions.

the Educational effect of the composition is in many respects defined by a choice of its theme. The composition theme should consider age features of schoolboys, to them to be clear and interesting. So 7 classes we suggested to write to pupils the composition on a theme «the Mathematician - gymnastics for mind», 8 classes - «I Would like to be the pupil of school Pifagora?». The offered themes demanded from pupils
not only possession of knowledge in areas of mathematics and its history, but also development of the personal relation to a material. Here that pupils wrote, answering this question.

«I would not wish to go to school Pifagora because it was necessary before to become its pupil to expect three years. Then, after receipt in school for five years the pupil became only the listener, and only then could become a high-grade member of school and choose to itself a speciality. On the one hand, the pupil of school to be very difficult and there there passes half of your life, but on the other hand to study at such school, probably, very interestingly though not each person can study up to the end» (Olja, 8 class)

«At Pifagora there was an own school which was simultaneously and political structure. At this school there were very strict rules. All members of the Pythagorean union should not use meat food, open the doctrine of the teacher, not have a personal property, always listen to the instructor. But pupils received huge luggage of knowledge, excellent formation, were typed wisdom and patience. I would like to become its schoolgirl, but all it demands the big work and patience, endurance and performance of strict rules.» (polina, 8 class)

Other kind of creative work closely connected with development of the person - graphic activity. The educational potential of this kind of creative works speaks that is art-creative activity of teenagers is directed as on reflexion of the impressions received in a life, and on expression of own relation to the represented. In the course of such activity experience not only is formed, but realised and worried. During experimental activity pupils 7 classes created the drawings based on principles of zloty of section, and eight-graders represented autumn in style a cubism.

Disclosing of communication of mathematics and the surrounding validity, education of value of mathematics as sciences were promoted by the organisation at school of mathematical photo-exhibitions. Such kind of creative work is closest
to the teenage age, characterised special attention to various technical innovations. Within several years of work together with pupils we organised photo-exhibitions on following themes: «Triangles in a life», «Parallel straight lines round us», «Symmetry in the nature».

the Natural consequence of comprehension and acceptance of values is their realisation in activity, therefore the third condition of education of valuable orientations of the senior teenagers in educational activity we believe pedagogical support of a reflexion by pupils of own system of values and its realisation in behaviour. Proceeding from it it was necessary to organise ability to live and behaviour of pupils, for the purpose of fastening and formation in experience of children of positive ways and behaviour forms.

Realization of valuable orientations in activity was promoted by a method of commissions. «The commission - transfer to the pupil of certain functions to performance of socially useful business and responsibility for it» [75, with. 234].

Execution of the commission by the pupil was accompanied by understanding of the public importance and value of the charged task. As at distribution of commissions propensities, interests and possibilities of the pupil were considered. At realisation of this method on a course of its performance to the pupil it was helped, and the result was supervised, estimated and disclosed. Besides for us it was important, that commission performance was accompanied by translation by pupils of significant values. For creation of conditions for similar self-expression we spent not only traditional lessons, but also annual lessons-conferences. Besides pupils prepared wall newspapers, entertaining five-minutes, photo-exhibitions, reports etc.

an education Method «by creation of conditions when its each participant aspires to show as much as possible the abilities and to achieve the best results in comparison with others» is competition [75, with. 241]. This method leans against natural propensities of the child to leadership, to
to rivalry as in the course of competition children aspire to prove and show as much as possible all knowledge available for them and abilities. Besides competition not only stimulates activity of the child, but also forms at it ability to self-actualisation as during competitions the child studies to realise itself in various kinds of activity. For realisation of this method following forms were used: a lesson - competition, competition, a quiz, an exhibition, the Olympic Games etc.

One of the innovative methods, representing independent research on the chosen theme, directed on the decision of this or that practically or theoretically significant problem for the pupil, the method of projects is. «From the pedagogical point of view the method of projects is a creative educational activity in which process pupils are accustomed to think and realise creatively the means acquired by them and modes of work» [104, with. 361].

the Basic advantage of this method consists that it can include many other things methods (discussion, debate, the story, creative activity, practical work, etc.), so to "work" on various components of valuable orientation of the person. Besides, the importance of a method of projects consists in enthusiasm and interest of pupils in work, stimulation of their initiative and growth of creative possibilities; communications with a real life; involving of pupils in active creative, informative process; development of intellectual abilities of critical thinking; ability to work in group and to correlate the purposes to problems of others [104].

the Orientation of research activity on valuable development of the validity it was defined by subjects of projects. We will result the list that of the projects executed by pupils during experiment: «Mathematics and Russian","Mathematics and health of the person","Receptions of the fast account», «Mathematics of music and music of mathematics","the Mathematician and sports», «Mathematical calculations in economy of planning of the family budget","Mathematical methods in the physicist","the Mathematical component of works M

Eshera "," Polyhedrons in architecture "," Mathematics and chess »etc. Results of researches were made out in the form of the abstract, the report or computer presentation. In the course of performance pupils kept a project diary.

Thus, during forming experiment the wide spectrum of methods was used. It is necessary to notice, that though the presented methods and are united in groups, it does not exclude use of a method from one group for formation of a component of valuable orientation corresponding to other group. For example, the story is capable to have strong emotional influence, and practical work - to promote fastening of moral values in behaviour. Efficiency of use of the described methods in many respects is defined by personal characteristics of the teacher: knowledge aksiologicheskogo potential of mathematics and possible ways of its actualisation, professional mastering by education methods, and also a humanistic orientation of pedagogical activity.

3.3.

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A source: SEROVETNIKOVA SVETLANA ANATOLEVNA. EDUCATION of VALUABLE ORIENTATIONS of the SENIOR TEENAGERS by SUBJECT MEANS. The dissertation on competition of a scientific degree of the candidate of pedagogical sciences. Petropavlovsk-Kamchatka - 2016. 2016

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