The theory and practice of developing curricula knows two ways of constructing them: linear and concentric.
AT recent times intensively substantiates, in particular Ch. Kupisevich, the so-called spiral method of constructing school programs.
The essence of the linear method of constructing training programs is that the individual parts (steps, portions) educational material line up, as it were, along one line and form a continuous sequence of closely interconnected and interdependent links - steps academic work, usually only once. Moreover, the new is built on the basis of the already known and in close connection with it.
Such a construction of curricula carries both positive and negative phenomena in learning. The advantage of the linear method of arranging the content of the curriculum lies in its economy in time, since duplication of material is excluded. The disadvantage of the linear method is that due to age and psychological features students, especially at the lower level of education, schoolchildren are not able to comprehend the essence of the studied phenomena, which are complex in nature.
The concentric method of constructing curricula allows the same material (question) to be presented several times, but with elements of complication, with expansion, enrichment of the content of education with new components, with a deeper consideration of the links and dependencies between them.
The concentric arrangement of the material in the program provides for not a simple repetition, but the study of the same issues on an expanded basis with a deeper insight into the essence of the phenomena and processes under consideration. And although concentrism slows down the pace of schooling, requires a lot of study time to study educational material, sometimes gives students the illusion of knowing the issues that they repeatedly encounter, which naturally reduces their level of activity in learning, concentrism in schooling inevitable. This is especially evident in the process of learning language, mathematics, history and other subjects that are studied in elementary school and then in high school. A similar phenomenon is observed in the study of other subjects.
The negative aspects of the linear and concentric method of constructing curricula can be largely avoided when compiling curricula, resorting to a spiral arrangement of educational material in them, thanks to which it is possible to combine the sequence and cyclicity of its study. A characteristic feature of this method is that students, without losing sight of the original problem, gradually expand and deepen the circle of knowledge related to it. In contrast to the concentric structure, in which to original problem sometimes return even after several years, there are no breaks of this type in the spiral structure.
In addition, unlike the linear structure, learning with a spiral structure is not limited to a one-time presentation of individual topics (Kupisevich Ch. Fundamentals of general didactics, M., 1986, p. 96).
3. Didactic spiralLinear and concentric constructions of curricula
Content subjects and partly the methodology of their teaching is specified in the curricula, which are documents that establish the composition, the sequence of the material presented for study in each subject with its distribution by year of study, sections and topics. For each topic, the amount of knowledge, methods of activity are indicated. The program determines the learning outcomes, interdisciplinary connections, basic knowledge necessary to study a section or topic.
Historically, there have been two main systems for constructing curricula - linear and concentric.
The first one is more simple: it assumes consistent study of the material, as a rule, without returning to the studied topic. Such a construction is logical and economical, but does not adequately ensure the depth of study, especially in the lower grades. Linear programs are mainly used in small (in terms of concepts) and short (in time) courses that fit into one academic year.
In concentric programs, the course is implemented in the form of two or more concentres. Concentres, each of which is a relatively autonomous full course, are built for several age contingents of schoolchildren who consistently study a single system of concentric courses, gradually expanding their horizons in the studied subject area. In each concentration, the student returns to the basic concepts and basic patterns of this subject area.
As they grow up and develop, students move from concentration to concentration, accumulating both fundamental knowledge and practical experience in using them.
The system of concentres is associated with the expenditure of significantly more study time. At the same time, it opens up opportunities for deeper assimilation and more solid consolidation of knowledge.
Idea of the didactic spiral, examples
When there are two different systems, compromise ideas are often born that give rise to new system, combining the advantages and minimizing the disadvantages of both source systems. Thus, from the synthesis of linear and concentric systems, a system that is now widespread has arisen, called didactic spiral. Didactic spiral differs from the usual concentric system of planning educational material by the continuity of the transition between concentres. Therefore, the didactic spiral as a system for constructing curricula and organizing the educational process has found its place in large multi-year courses that form the basis continuing education. Such, for example, is mathematics. Primary school and central middle school (primary school), in terms of whole and rational numbers, constitute the first branch of the didactic spiral, in the upper grades (basic school), where real and complex numbers, concept of limit and elements mathematical analysis, mathematics rises to the next branch of the spiral, in graduate and profile mathematical classes (and further in high school) begins the next branch of the didactic spiral - differential and integral calculus.
Such is biology with its various subject components: after the initial course of natural science in the basic school, individual biological disciplines- botany, zoology, anatomy - in order to come to a single science at the profile level of education - biology - with a rich baggage of concepts and knowledge accumulated at the previous round of the didactic spiral.
Such is the story, in which the initial branch of the didactic spiral is built from a series of separate (however, meaningfully thought out and arranged in a methodological sequence) stories from the history of their homeland and native land discussed in lower grades. The next branch of the spiral consists of a series of courses tracing the chronological epochs of human civilization - from the Ancient World, through Greece and Rome, to the Middle Ages and modern history. Finally, graduation profile classes schoolchildren enter a new branch of the spiral, where they can navigate not only in recent history, but also in general social problems development of human society.
It is easy to see that the didactic spiral is directly linked to the structural division of any extended continuous educational course into three components - propaedeutic, basic and profile. Such a connection of the components - turns of the didactic spiral - is confirmed by the educational standard.
Didactic spiral of informatics courseIn a school course in informatics, all three listed turns of the didactic spiral are present or, in any case, should be present 8 . For this reason, it is necessary to realize that pedagogical tasks, arising on each branch of the spiral, differ from each other in almost all categories of the educational process - goals, content, forms, means and methodology.
It is known that the goals (the system of knowledge, abilities, skills, and competencies formed by the student) are different on three turns of the didactic spiral of informatics education.
These branches also differ in the content of training: command systems, algorithms, directly and programmatically controlled executors - on a propaedeutic turn, data structures and control structures in algorithmics and modular systems in information technologies - on the basic, language systems of procedural and object-oriented programming - on the profile.
Game forms that captivate younger students will make high school students bored who feel the need to schematize and abstract knowledge.
The means are also incomparable: the younger ones have software executors and robots, the older ones have multilingual high-level platforms.
As a result, methods differ greatly: often an experienced teacher working with high school students is embarrassed and embarrassed when he has to work with kids.
It is important to note that the transition from one turn to another is not only justified (for example, by the requirements developmental psychology), but also controllable. Thus, when discussing the continuous school course In computer science, there is no question of including programming elements in such a course and, in particular, acquaintance with programming language systems. At the same time, at the first turn of the spiral of continuous school informatics education - in the propaedeutic informatics course - there is no programming (although a number of experiments not only do not deny the possibility of studying and mastering the beginnings of programming by younger students, but also include programming lessons in languages). The absence of programming mechanisms in a well-thought-out propaedeutic course is not accidental (see “ Propaedeutic informatics course”): the concept of a variable, its name, type and values, which are the foundation of programming, as well as control structures and data structures, require the level of mental maturity that can be formed by the basic course - by the eighth or, at best, seventh grade. The first turn of the spiral methodically prepares schoolchildren for the introduction of such important concepts with the help of algorithms, their types and properties, with the help of executors and their command systems, with the help of information search skills and object detection in a set by a given attribute.
The basic concepts of computer science at the basic level can be learned using the language tools of instructional languages or structurally-procedural high-level languages (Rapier, KuMir, Pascal), but in order to move to the next level of information education - specialized - today it is already necessary software based on new concepts - object-oriented programming.
Didactic spiral of the topic in the courseAmong other school disciplines, computer science is attractive in that the didactic spiral is used in it not only in the organization of a continuous course, but even within its individual (rather voluminous) topics. Here characteristic example- the theme of text information editing. It starts at the propaedeutic level. For example, in the well-known software and methodological system Robotlandia, the adapted educational editor Mikron becomes the main tool of the topic. It's a simple monospace editor whose limited tools make a word processing specialist smile indulgently. But we should not forget that they came to Micron, which delights children, after getting acquainted with a line editor (in particular, with command entry fields in performers and simulators). And now they go to the wide expanse of the full screen! In fact, there are so many new forms of work here that children do not lose interest in the possibilities of Micron for a relatively long time. And it will take a new incentive for them to change their hobby. On a typical context replacement problem, which is often encountered in Everyday life, a difficulty arises (conceived by the developers of Micron): in this program there is a context search operation for an information object, but there is no replacement operation.
The text editing theme methodology is structured so that the teacher leads children to such a task at a time when the need for a better tool matures. MikroMir appears in the lessons - an educational-oriented text editor with multi-window processing capabilities, using block structures, with tables and the ability to process tabular data, with macros and ..., of course, with contextual replacement. A large number of fundamental concepts from the field of word processing and general techniques of information editing are mastered in MicroWorld. But later, when it becomes necessary to show the importance of a single interface in different technological systems, the transition to the next round of the topic is brewing, when schoolchildren get acquainted with the professional Word editor.
Pay attention to the location of three text editors - Mikron, MikroMir and Word - in the school computer science course: the first of them works on the propaedeutic coil of the didactic spiral of the continuous course, the second - on the next coil, in basic school, Word - begins at the transition from the second round to the third, at the beginning of the computer science profile course. This makes it possible to teach information technology to schoolchildren not as a recipe for push-button techniques, but as a discipline that forms a worldview. The topic "Editing text information" lays the foundation for the study of other technological tools and consolidates the foundation of the previously mastered skills of the operational style of thinking. Based on such a didactic assessment of text processing technology, it is useful for the teacher to think over the classification of concepts, mechanisms and operations of a new topic. (It is important to emphasize that the classification under discussion is useful not so much for specific methodological recommendations for the transfer of new educational information to students, but for the formation of a clear idea in the teacher about the invariants of text editing, in other words, about the place and methods of presenting the topic under study in the general methodology of information education.)
The first category includes the most general concepts and methodological techniques that are invariant, common for all editors of information, regardless of the type of its presentation. On the image information editing invariants are shown as the core of the topic of information editing studied in elementary school.
Invariants of information editors are used as a basis for analogies in the topic of editing graphic information immediately following Micron, and later in the topic of musical information.
The second category is formed by concepts and operations that take into account the peculiarities of the textual representation of information and are common to all text editors, regardless of their purpose and level of complexity. Here they are named basic text editing operations. Basic text editing operations will need to be addressed not only when studying Mikron, but also at subsequent stages of continuous informatic education when studying other text editing tools (both educational and professional).
Finally, the third category includes the specific features of the Micron text editor. It is in these features that the orientation of the software product to a specific subject area is reflected - the methodology of the course of early education in computer science.
Understanding the classification of text editing mechanisms, their division into information editing invariants, the basic operations of the editor in question as a typical representative of text processing tools, and, finally, the specific features of a particular editor, allows the teacher to correctly navigate the didactic spiral of the topic, as well as to use analogies when studying “parallel” themes - editing of graphic and musical information, processing of numerical information.
In the didactic spiral of a particular topic, incentives may be provided for moving on to the next round of the didactic spiral. Here is how, for example, the issue of such a transition was solved in the first domestic two-component program-methodical system “Schoolgirl”, which consisted of Robik, the language for controlling executing robots, and Rapier, a learning-oriented structural programming language. Pupils elementary school mastered the methods of direct and programmatic control of robots-executors in Robik until the tasks for robots began to calculate arithmetic expressions (a task well known to students from school lessons mathematics). And in this new situation, for calculations, a system of commands that grew out of Robik was proposed, where addition with assignment of the result was written as follows:
ADD VALUE IN CELL BY NAME BUT
WITH VALUE IN CELL BY NAME B And
PUT RESULT IN CELL BY NAME D
Such a command stunned the schoolboy (who did not yet imagine the possibility of compact notation in programming languages) with its cumbersomeness.
The importance of such a command is clearly visible, this is the beginning of mastering the concept of a variable. And although, working on the principle of collapsing syntactic constructions, you can gradually move to shorter forms of the same command:
FOLD BUT With B PUT IN D
Nevertheless, the real satisfaction of schoolchildren comes when the teacher offers to use a new tool - the Rapier language, where the computational formula is written in almost the same way as in a mathematics lesson:
A+ B–>D
8 In fact, the intra-subject, informatic standard provides for another, not so much scientific and didactic, but rather an organizational classification of the components of the education management structure - federal, regional and school. Within the framework of this second classification, many fundamental problems of education development - material resources, personnel training strategy, decision-making methods - are moved from the scientific level to the administrative level, which cannot but lead to painful collisions in the education system. For example, the question of course setting early learning Informatics (propaedeutic course) in a particular school is given to the responsibility of the school principal (and not to the sphere of scientific, didactic arguments for early education in informatics), which, in the context of per capita funding of schools, forces the principal of the school (especially a rural ungraded school) to accept opportunistic, and not scientifically based solutions.
Modular-block training in music lessons (or KTP in a new way).
For many years, in my music lessons, I have been using the technology of modular-block learning. This is most relevant now, when we began to work according to the Model Program of 2015. It is no secret that the program for music lessons is, to put it mildly, unfinished: the main problem is that educational and illustration materials and planned learning outcomes are not distributed over the years.
Teaching experience led me to the need to structure the material into enlarged didactic units (blocks)in accordance with the thematic lines and planned learning outcomes, and I built the entire course of music lessons according to the concentric principle. Or, to put it more simply, in the distribution of educational material, I use 2 principles:
Modular block learning
Concentric principle of material distribution
Concentrism - the principle of building school courses in the basics of science, characterized by the fact that part of the educational material is repeatedly, but with varying degrees of depth, studied at all levels of education.
Modular block - this is the target thematic node, which combines the educational content and the technology of mastering it.
For example, your calendar- I build a thematic plan using the following thematic lines (see Sample Program):
Music as an art form - 3h.
Form - 3h.
Genres - 3 hours.
Musical image - 7 hours.
Styles: – 15h.
Folk musical creativity;
Russian music from the Middle Ages to the turnXIX-XX centuries;
Foreign music from the Middle Ages to the turnXIX-XX centuries;
Russian musical cultureXXin.;
Foreign musical cultureXXin.;
Contemporary musical life
The value of music in human life - 4h.
TOTAL: 35 hours
An example of the distribution of content by class:
Music as an art formHow did the arts come about? Art opens the world. Classification of the arts. Art genres
What does music have in common with literature Writers and poets about music
What does music have in common with the visual arts. Portrait in music and fine arts.
Classification of the arts. Art genres. Categories of art
Impressionism in music and painting.
The arts are different, the theme is one
Classification of the arts. Art genres. artistic intent
Plots, themes, images of art.
Historical events, pictures of nature, various characters, portraits of people in various types art
Symbolism of sculpture, architecture, music
Polyphony in music and painting
Creative workshop of the composer, artist.
Form 2h.
What is a musical composition. Two-part and three-part in music.
Ways of development in music:repetition (variability, variance), contrast
Two-partness in music. Two tunes in M. Glinka's romance "Venetian Night"
Three parts in the "Night Serenade" by Pushkin-Glinka.
The multidimensionality of the image in the form of a rondo.
Variations
sonata form
Development of musical themes in symphonic dramaturgy.
What gives the teacher and students the concentric principle of teaching?
All classes are on the same topic, with different levels of complexity of the material. Therefore, it is easier for a music teacher who works in all classes to prepare for lessons. The students, knowing that the topics are repeated, are happy to demonstrate their previous knowledge and feel quite successful.
In one parallel, classes, as a rule, have different levels of training - classes "A" are stronger than classes "D". The principle of concentric construction of the material allows you to simplify or complicate the topic, return to the previously studied or go "ahead of the curve"
The most successful students can independently individual plan, master the whole block module.
What gives MBO:
ensures the unity and integrity of the perception of the entire educational section;
provides full and general activity in the lesson and contributes to the optimization of the educational process;
gives greater independence to the student;
allows you to work in different modes
So, the first session of each thematic module, I begin by providing a general block. For example:
"Music as an art form"
Music genres
3. Musical image and means for its implementation.
fear emotional experiences, divine, heroic, comic, joy, tragic, solemn, sadness, lyrical, patrioticINTONATION
Raising or lowering the tone of the voice reflects feelings in some element of the melody. It is an expressive transition from one sound to another.
Mocking, decisive, imperious, compassionate, demanding, ironic, etc.
DYNAMICS
Sound power, loudness
p - piano (piano) - quietly;
pp - pianissimo (pianissimo) - very quiet;
mp -- mezzo piano (mezzo piano) - not very quiet
f - forte (forte) - loudly; *
mf -- mezzo forte (mezzo forte) - not very loud
ff - fortissimo (fortissimo) - very loud.
PACE
Music performance speed
Slow pace - soon, fun, joyfully
I love using the Timeline. For example: "Genres of music from primitive times to the present day", "Musical styles", "History musical instruments". Moreover, children themselves tend to create such timelines on other topics.
Each item of these schemes and tables will be studied in more detail and sequentially. But it is the beginning of each topic from a common large block that gives a complete picture of the material being studied. Children learn to make stories according to tables and diagrams, and vice versa, to make diagrams and tables according to the text, they can fill in the missing fragments in tables, etc.
A more detailed use of diagrams, tables, reference notes and tasks for working with them in my next publication.
concentrism
(from Novolat. concent-rum - having a common center) in teaching, the principle of building a school. courses of the fundamentals of sciences, characterized by the fact that part of the account. material repeatedly, but with varying degrees of deepening is studied for several. levels of education. Yes, in primary school children learn to produce all four arithmetic. operations with integers. On Wed. steps, these actions are studied again, but more attention is paid to the laws of arithmetic. actions, on the relationship between these numbers and the results of actions on them. The issues of divisibility of numbers are studied in detail. Literature course uch. the plan is provided as thematic for the middle level, then it is studied as a general elementary, and in Art. classes cf. schools - as systematic. Schools are built on the same principle. courses and many others. items. From the concentric location of account material differs linear, with Krom each section uch. the course is studied with the degree of depth and detail that the tasks of teaching require, without returning to it on the trail, stages of learning.Some-paradise stepping in the construction of schools. courses is based on the objective laws of the assimilation of knowledge by children: the essence of complex concepts, laws is usually not assimilated by them immediately in all depth. Therefore, when assimilating complex concepts, it is necessary to return to the old, but on a new basis, in the light of new theoretical concepts. ideas (moving up "in a spiral"). Re-study of the material at Art. levels of education are carried out at more than high level, taking into account the increased postures. student opportunities. As a rule, beginning concentric stage. study account. the subject is characterized by a special meaning of feelings, perception of objects and phenomena, the accumulation of information and facts. Subsequently, training becomes more and more systematic. character, and on Art. steps cf. education is in the nature of serious theoretical. generalizations.
At the same time, the repeatability of material throughout the entire period of study of students in cf. school, characteristic of K., leads to a greater than with a linear arrangement of accounts. material, cost account. time, generates an overload of students, and often reduces their interest in the subject. These disadvantages of K. become especially significant if it is necessary to achieve a certain degree of completeness of education at each of its stages. So, before the introduction of universal compulsory 7-year (and later 8-year) education, graduates of the beginning. schools, many of which did not continue their studies, had to give a certain range of, to a certain extent, complete knowledge accessible to children of this age. This explained Means. richness of programs classes in Russian lang. and mathematics. Striving for a certain completeness of the incomplete cf. education led to the introduction of elementary courses of a number of accounts. subjects in an 8-year school, the content of which in Means. measure was repeated in Art. classes.
Further improvement of school. programs and teaching methods leads to Means. K.'s decrease in training. In existing general education programs. cf. schools combine linear and concentric. building account. material.
Law Russian Federation"On Education", the decision of the collegium of the Ministry of Education dated December 28, 1994 No. 24/1 "On the development strategy of historical and social science education in educational institutions" substantiate the need to form a new structure and content historical education which ensure the formation of a holistic and complete system of knowledge at all stages of schoolchildren's education (in primary, basic, full high school). In the basic and complete secondary schools (grades 5-9 and 10-11) a concentric system of studying subjects of the educational field "Social disciplines" has been introduced. AT transition period the problem of the structure of historical education became more acute due to the unpreparedness of the teacher to work in the new conditions. Under the structure understand the order, the sequence of teaching courses of world and national history.
In the Soviet school, the linear principle of building school history education prevailed. This principle underlay the school history course for 43 years.
The linear structure involves the study of successive stages of human history from ancient times throughout the entire school course - each stage once.
The transition to a concentric structure of school history education in the mid-1990s. perceived as new. However, at the turn of the 19th-20th centuries, methodological thought saw the merits of the concentric construction of historical education. So, at the beginning of the 20th century, an accessible propaedeutic course of Russian history was introduced in the first and second grades of gymnasiums, and in 1913 the same course ancient history in second grade.
In connection with the introduction of universal eight-year education in the USSR in 1959, the teaching of history was restructured on the basis of the principle of concentrism. Students, graduating from an eight-year school, had to have an idea about the history of their country and foreign countries from ancient times to the present. The program provided for the study of elementary courses in the history of the ancient world and the Middle Ages in grades 5-6; in grades 7-8 - an elementary course in the history of the USSR with the most important information from modern and recent history, as well as the Constitution of the USSR; in senior grades 9-11 - systematic courses in the history of the USSR, modern and recent history; in the final class - social studies. This structure eliminated the main shortcomings of the former linear construction. The overload of students has disappeared, the possibility of a wider use of active methods and organization has opened up. independent work students. At the same time, a sufficiently thoughtful selection of the content and appropriate methods of presenting the program material in each of the concentres was not carried out. History of the USSR XIX and XX centuries, new and recent history were set out in textbooks for senior grades more specifically than in the 8th grade. Both stages were unacceptably close, which created certain difficulties in learning. Systematic courses, even under the condition of a three-year term (grades 9-11), turned out to be heavily overloaded with factual material. The whole course of study was marked by haste and superficial study. As a result, on May 14, 1965, a resolution “On changing the order of teaching history in schools” was adopted. As already mentioned, we returned mainly to a linear structure.
The last attempt to move to a concentric structure of historical education was made in 1993 and differs significantly from the previous ones.
Consider the advantages of teaching, which is based on the concentric principle of building a school history course. The concentric structure suggests a return to the material being studied. The same question is considered several times in different classes, and its content is gradually expanded, enriched with new information, connections and dependencies. At the first stages of training, elementary ideas are given, which, as knowledge is accumulated and cognitive abilities grow, deepen and expand. In this case, a propaedeutic course (preliminary) is introduced into the teaching of history. The principle of concentricity is widespread in foreign schools and schools of post-Soviet states (Lithuania, Latvia, etc.). Such a structure makes it possible to study the history of mankind with the same depth. The use of concentrism has a number of advantages if, firstly, the volume, specificity of the content and form of presentation of historical material in each of the concentres is correctly determined in accordance with age characteristics. The content for the basic school is not a reduced copy of the systematic course of the secondary school. Each concentration has its own specific material selection. Secondly, there is a gap in time between the relevant sections (3-4 years), it is not advisable to introduce more than two concentres (except for propaedeutics). Thirdly, there are textbooks and even educational and methodical complexes which take into account the peculiarities of teaching history.
modern school based on the principle of concentricity. The main reason for the transition to a new structure was the Law of the Russian Federation "On Education", according to which an obligation is introduced. Such a structure allows, in addition to the listed advantages of a concentric structure, firstly, to intensify the process of studying history; secondly, to more clearly synchronize the courses of national and general history, as well as to create a single integrated course "Russia and the world"; thirdly, to take into account the possibility in the second concentre to systematize and generalize all historical material on the basis of formational, civilizational, cultural and other approaches; from the event-chronological principle of studying the past to the problematic, interdisciplinary, thematic; actively use a variety of methods historical research in working with authentic texts. Fourth, it becomes possible to introduce profile and modular education in the second center, focused on the interests and career guidance of students in grades 10-11.
Structure historical knowledge reflects the specifics of history as a science and a subject of study. Just as in the life of society all phenomena are in development and interconnected, so historical knowledge must be dynamic and interconnected. Each of structural elements occupies a special place in the system of knowledge, performs a special function in its formation and development. The basis of the historical knowledge of schoolchildren is facts that make it possible to reveal significant connections and relationships between them: continuity, cause-and-effect relationships, their comprehension in historical process according to the age of the students. Nikulina N.Yu. Methods of teaching history in secondary school: Tutorial/ Kaliningrad. un-t. - Kaliningrad, 2000. S. 18-29