BACKBONE COMPONENTS OF TECHNOLOGY IN THREE-DIMENSIONAL
METHODOLOGICAL SYSTEM OF LEARNING
ZHAUMBAY KARAYEV
First Deputy Chairman of the Board
JSC “NCPD “Orleu”,
Doctor of pedagogical sciences,
Professor
Kazakhstan
Annotation
The article gives definitions of: didactic matrix, three-dimensional methodological system of
learning. It reveals the essence of three dimensional methodological system of learning technology.
Logical-structural model of the technology in question is substantiated. The role of three dimensional
methodological system of learning technology in the implementation of the constructive learning
model based on the competence approach.
Keywords: didactic matrix, three-dimensional methodological system of learning, three dimensional
methodological system of learning technology.
This article reveals the essence of two backbone components of technology in three-dimensional
methodological system of learning, because three-dimensional methodological system as well as the
didactic matrix are not only the basis for the development of modern pedagogical technologies, but
also the modern theory of learning, the core of new paradigm for the development of learning in
general.
The relevance of the input of these two concepts in the modern didactics is necessitated by the
diagnostic position of setting learning objectives in the context of implementation of personal-activity
approach.
V.P. Bespalko believed that diagnostic methodology of goal formation is the starting point for
the development of pedagogical technologies, proving that there are still no diagnostic objectives in
modern school and pedagogy (1). “Paradoxically, today, the educational process is carried out without
a clear statement of purpose and objective, without regard to its results. Passing a description of the
purpose, the teachers immediately rush to the design of course plans, programmes, textbooks and other
teaching tools. It loosens the conceptual framework of education, making it amorphous…” – says V.P.
Bespalko (1).
As it is known, diagnostic position of setting learning objectives is characterized by learning
outcomes, expressed in the actions of students, that be can identified accurately and measured. The
phrase “learning outcomes expressed in the students’ actions” implies the following: a) learning should
be organized on the basis of independent cognitive activity of students; b) learning outcomes form
hierarchically dependent structure, as students’ activity is characterized hierarchy: by reproductive,
constructive and productive actions (2).
Proceeding from the hierarchy of types of activities, scientists identified relevant hierarchies of
learning outcomes. For instance, academician V.P. Bespalko identified the following levels
(hierarchies) of mastering learning material: pupillary, algorithmic, heuristic and creative levels of
mastering (1).
While projecting pedagogical system based on technological approach, V.P. Bespalko suggests
implementing consequent mastering of learning material, i.e. consequent transition of student’s
cognitive activity from reproductive level into constructive one, and then further to productive level
(2).
Hierarchical structure of learning outcomes (mastering levels) involves the construction of the
relevant objectives of the system, which highlighted their category and successive levels. The purpose
and the result should be presented, measured, characterized and described in the same terms and in
same settings (4).
The most famous system of objectives having such properties is the Bloom’s taxonomy of
learning objectives.
American scientist B.Bloom substantiated a hierarchical structure of learning objectives
(Bloom's taxonomy), i.e. vertical hierarchy of one of the elements of a complete methodological
system of learning. It should be noted that Bloom's taxonomy of learning objectives developed in the
middle of the last century, has played a progressive role in the development of learning theory, in
general, didactics. In world practice Bloom's taxonomy is the basis of planning education and objective
evaluation of educational achievements of students. Abroad, based on Bloom's conceptual ideas "a
theory of complete mastery" and learning technology was developed, implementing this result-oriented
theory. However, foreign scientists have not investigated hierarchical essence of other elements of a
coherent methodical system of learning (content, methods, forms and means of learning), as well as the
hierarchical nature of learning motives, levels of teaching material mastery by learners and other
components of educational process in connection with diagnostically intended learning objectives.
Our research has shown that not only the objectives, but also all components of methodological
system of learning (objective, content, methods, forms and teaching aids) form a hierarchy and are in a
tiered relationship with levels of mastering, motive, activity, skill and quality of knowledge (2,3). Let
us note that the structure of two elements (objective, content) of methodological system form a strict
hierarchy, and hierarchical structure of the rest of elements is called “tertiary” from them. Hierarchical
essence of education content is scientifically proved in works of I.Y. Lerner and H. Taba (2). H.Taba
identified three successive, hierarchically organized stages of thinking formation and thus three types
of learning activities: 1) formation of concepts; 2) interpretation of the data; 3) application of rules and
principles. She also proves that each of these types of learning and cognitive activity has its own
learning strategy. It is easy to notice that the theory of I.Y. Lerner about four-element basis of
education content is confirmed by conceptual conclusions of H. Taba. In Figure 1 there is no fourth
element - a system of norms emotionally valuable relation that defines the content of the educational
function. The requirements of this element will be taken into account when designing the content of
level of educational tasks. It should be noted that the hierarchical essence of the content emphasizes
not only its structural and substantive basis, but procedural and educational aspects, which in the
conditions of “knowledgeable” content are not visible and barely functioning.
Methodological system of learning, elements of which form hierarchically arranged multilevel
structure, which we call three-dimensional methodological system of education. “Threedimensionality” means presence of multiple levels of hierarchy, i.e. vertical line (height) with respect
to each of the components of methodological system of learning: objectives, content, methods, forms
and means of instruction. Traditional “knowledgeable” content corresponded with the
“knowledgeable” learning, which was realized by components of first-level three-dimensional
methodological system of learning. “Wrapped” around the first level of a three dimensional
methodological system of “knowledgeable” methodological system “would not let” the educational
process in the zone of proximal development of the student, educational success of children were
assessed mainly on the level of “knowledge and understanding”. For this level of mastery students
received "good" and "excellent" grades, which led to the mass production of students not confirming
their level to receive Altyn belgi award. Learning, designed for memorizing, contributed to the fact
that each year on average 20-25% of school leavers were unable to cross the threshold level of UNT.
Only three-dimensional methodological system adequately meets the requirements of
developing education and student-centered approach, as on the basis of independent cognitive activity,
gradually doing leveled tasks, ranging from the level of “knowledge” and finishing with the level
“creation”, the student acquires the research skills, and application of skills and knowledge, and it
allows him to create his functional literacy. Note that the formation of the subject specific competences
in students occurs when the level of mastery is not below the level of “application”. The
implementation of developing learning is realized with the help of consequent solution of threedimensional content leveled assignments by students. Our research has shown that the transition from
the knowledgeable content to three-dimensional requires modernization of the existing theories of
curriculum content, theory of textbooks and theories of learning (2.3).
The revision requires traditional principles and selection criteria of educational content, which
corresponded with requirements of “knowledgeable” model of learning. Three-dimensional
(hierarchical) content attains all functions to itself: Three-dimensional (hierarchical) content becomes
all the functions of the dialog-substantive, procedural, educational, activity, and through the
implementation of the 4th element (I.Y. Lerner) – developing aspects of the modern content, designed
on the basis of personal-activity approach. New textbook theory must be based on a new educational
content theory. It should be noted that in this case the development of "worksheets" becomes relevant
on the basis of three-dimensional learning content. Textbooks with encyclopedic text content will
actually be replaced by developing textbooks, textbook-interlocutors, consisting of three-dimensional
content of tasks.
After combining the whole spectrum of levels of objectives, contents, methods, forms and
means of learning, three-dimensional methodological system of learning becomes developing part of
constructive model of learning.
Our research has shown that the structure of motive levels, skills, quality of knowledge and
mastering has a science-based hierarchy. Table of their relationships with three-dimensional
methodological system of learning, the components of which are connected with each other vertically
and horizontally, we called it a didactic matrix (see Figure 1.).
Since the techniques of mental activity (analysis, synthesis, comparison, selection of main
thing, generalization, etc.) are used in all levels of mastering (knowledge, comprehension,
application, etc.) in varying degrees of complexity, we included in didactic matrix a revised version of
the B. Bloom’s taxonomy of objectives, developed by L. Anderson and D. Crotwell, combining the
processes of synthesis, assessment and creation. As it is known, the creation (creativity) is not included
in the earlier taxonomy, is the highest level in the new version. In order to perform creative tasks
students generate, plan and produce (create).
In our view, only such a taxonomy of objectives (knowledge, comprehension, application and
creation) is adequate to meet the level of the hierarchy of mastering (learning outcomes).
We argue that only by organizing didactic process that aimed at the implementation of tiered
relationship of didactic matrix we can organize a truly developmental, productive and ensuring
learning outcome.
Didactic matrix allows us to visualize not only the three-dimensional methodological educational
system, but also the entire educational process, which is described by the formula of V.P.Bespalko
Didactic process = Motivation + Cognitive activity + Skills [1]. "Entrance" in the process begins with
diagnostically intended objectives of learning, "exit" - is characterized by levels of mastery.
It [4] was proved that quality of learning is described as the ratio of objective and result, as an
achievement measure of objectives, so in that, objectives (results) are given only diagnostically and
predicted in the zone of proximal development of the learner. Didactic matrix allows, on the basis of
this, clearly and hierarchically arrange the quality of a learner’s knowledge [2].
At the same time, an appropriate level of motivation contributes to the gradual ascent on the
“ladder” of didactic matrix. Wherein, we rely on the concept of Maslow hierarchy of needs, which is
the basis of a “process of motive”, which provides a gradual movement of the student to the top of the
didactic matrix from the level of “knowledge” to “creation”. Also, an enabling approach of students’
educational achievements assessment plays an important role here (2.3).
Group and independent cognitive activity of the student is defined in the implementation of the
strategy of all phases of research and sequential completion of level-based assignments. Management
component consists of self-monitoring of research activities and solving level-based problems, as well
as the implementation of the necessary corrective actions.
Thus, the didactic matrix is a synthesis of all the components hierarchically representing the
didactic process and methodical system of training. At the same time it allows us to represent them in a
relationship, over time, covering motivational, meaningful and methodical, evaluation, remedial and
developmental aspects.
Moreover, the didactic matrix allows us to visualize and imagine the dynamics of the gradual
displacement of the quality of the subject from the “zone of proximal development” (ZPD) of the
student to “his zone of actual development” (ZAD) (6). In the context of the application of technology
of three-dimensional methodological system of learning, which is projected on the basis of the didactic
matrix, this movement of ZPD occurs systemically.
Since we assume that the learning vector is directed from the lowest rung to the highest didactic
matrix, this process of moving can be described as a gradual "absorption" ZAD ZPD. In the context of
the application of technology of three-dimensional methodical system of learning, which is projected
on the basis of didactic matrix, this movement of ZPD occurs systemically.
If we consider the process of learning development of new teaching material, then ZAD is the
level of “knowledge” and ZPD is with other levels of the process of cognition. The conceptual idea of
Vygotsky states that the child firstly collaborates with the teacher, then is able to perform tasks on his
own.
Thus, training leads to development. The boundary between ZAD, ie the level of “knowledge”,
and the zone of proximal development, is a difficult task, which the child is not able to do on their
own, and needs the help of an adult.
The technology of three-dimensional methodological system of learning (TTMSL) is a project of the
educational system, developed with the support on the didactic matrix and integrates didactic
possibility of two major trends in the system of educational technology:
1) implementation of learning, presented in the form of the research process (constructivism,
critical thinking technology) in synectic part;
2) implementation of result-oriented learning in its second part (2).
Thus, the technology of three-dimensional methodological system of learning incorporates the
innovative potential of two types: technology, which is oriented on research and result-oriented
technology. In synectic part of TTMSL, interactive teaching methods are applied. Our experience has
also shown the effectiveness of the application of critical thinking, technology, synectic part of
TTMSL, consisting of three stages: challenge, comprehension and reflection (2). The transition from
one stage to another is more systematical, relying on three-dimensional components of methodological
system of learning, as well as procedural and didactic educational potentials of the matrix. Stages of
implementation of critical thinking technology form a hierarchy. This hierarchy is corresponded to the
hierarchy of the taxonomy of objectives and levels of learning material mastering.
The three-dimensional content in this case is characterized by the tasks presented in the form of
"thin" and "thick" issues at the stage of understanding, as well as in the form of tasks in the process of
reading, "lecture with a stop" or during the heuristic conversation. At every stage of research process,
the relevant techniques and methods are used, ie and in this case, the methods of individual search and
cognitive actions form a hierarchy. Setting of objectives and their implementation is carried out within
the framework of set subject learning objectives. Moreover, the generated search and research skills of
students allow them to operate at the level of heuristic and creative learning.
The main purpose of integration of two educational technology trends is not only defined in the
educational process of their united innovation potential, but at the same time in avoiding some of their
disadvantages.
Effective application of critical thinking technology in primary school is difficult, since children
have not yet formed the ability to use methods of mental activity [2]. To accomplish this in pre-school
education, educational games should be used, and in elementary school it requires the active
implementation of educational tasks aimed at the formation and application of methods of mental
activity. Therefore, we offer elementary school teachers to use technology in synectic part of a variety
of interactive teaching methods.
Practice also shows that in the conditions of application of active learning methods in synectic
parts (including critical thinking technology), because of the group nature of learning, it is difficult for
a teacher to apply criteria-based assessment system, therefore, to accurately assess the academic
progress of each student and to hold timely corrective work [7].
The critical thinking technology even quite successfully implemented, does not guarantee that all
students (except for the leaders of small groups) will learn and apply the techniques of interpretation
and reflection.
These disadvantages of critical thinking technology, i.e. synectic part TTMSL, are balanced in its
second result-oriented part. Sequential multi-level performance of tasks by each student individually,
gradually forms their conversation skills, appropriate levels of "knowledge", "understanding",
"application", "estimate" and "creation".
Many researchers believe that the use of result-oriented technology to achieve the planned
results, сonstrains creativity, self-employment of the teacher as well as of the students, planning their
actions within the framework of the selected algorithm. However, our research showed the problems of
such a judgment, as a reasoned decision of leveled assignments requires the use of methods of mental
activity, which, in turn, contribute to the formation of skills of search and research activities. The main
disadvantages of result-oriented technology are dominant personalization, priority independence,
poorly articulated group work and spontaneous discussion learning environment.
Thus, the need for diagnostic staging of subject learning objectives, the transition from
informative content to activity, developing content of learning, the introduction of objective teaching
quality control, including a criteria-based assessment system, the formation of functional literacy of
students require the implementation of the result-oriented TTMSL.
The common ground of both parts of TTMSL is the didactic matrix (see. Figure 2).
Figure 2.The relationship of the two parts TTMSL
In synectic part of TTMSL, students, working in a group and using interactive teaching
techniques and strategies for all stages of critical thinking, climb the “ladder” of the didactic matrix.
Stages of critical thinking: challenge - comprehension - reflection conform hierarchy (levels) of
thinking: reproductive, productive (creative) and hierarchy of didactic matrix levels.
In result-oriented part, students, independently solving leveled assignments, individually “climb
the stairs” of the didactic matrix and at the same time reinforce generated substantive competence in
synectic part. Note that the formation of functional literacy of students requires learning organization
covering levels “application”, “generalization, assessment and creation” of TTMSL didactic matrix.
Thus, two parts of TTMSL, complementing each other, increase the effectiveness of a lesson,
strengthen the innovative potential of the integrated technology, i.e. TTMSL.
Since the student-activity approach is selected as conceptual framework of learning, the contents
of each level of three-dimensional methodological system is formed as multi-leveled tasks. They are
developed on the basis of:
1) characteristics of the taxonomy of learning objectives;
2) essential characteristics of the basic qualities of the appropriate level of knowledge;
3) requirements of V.P. Bespalko to mastering levels.
4) requirements of I.Y. Lerner and H. Taba to the determination of the education content.
Note that in the implementation TTMSL, the outcome of learning at each successive stage of the
hierarchy is narrowed at the top, so the logical-structural model of TTMSL takes the form of a pyramid
(see. Figure 3).
Figure 3. Logical – structural model of TTMSL
Thus, the logical-structural model of TTMSL is represented as a pyramid consisting of B.
Bloom’s taxonomy of objectives, hierarchy of critical thinking stages and activities, the backbone core
of which is a didactic matrix. Pyramid of TTMSL becomes a project of pedagogical system, upgraded
on the basis of personal-activity approach, i.e. algorithm of design of constructive learning card (2).
With this individual learning trajectory of student’s development is characterized by a gradual
transition of student activities from low reproductive levels to higher productive ones. In synectic part
of TTMSL student “climbs” the “ladder” of the didactic matrix as a member of a small group.
In the application of this technology, objectives of the first and second levels (knowledge,
comprehension) are implemented by 100% (2). This performance is guaranteed by a strict sequence of
leveled tasks complexity (knowledge, comprehension, application, synthesis, assessment and creation),
high motivation and engagement of students, as well as stimulating assessment approach (2, 3).
This is a distinctive feature and advantage of the technology of three-dimensional
methodological system of learning.
At the same time, we take into account that the independent informative activity of the student
is carried out based on methods of mental activity (analysis, synthesis, main ideas identification,
generalization, etc.), which are used at higher levels of subject content mastering in greater depth and
awareness.
References:
1. Bespalko V.P. The terms of pedagogical technology. - Moscow: Education, 1989. –p. 192.
2. Karaev Z.A., Kobdikova Z.U. Actual problems of modernization of the educational system on
the basis of the technological approach. - Almaty Zerde, 2014, p. 311.
3. Karaev Z.A. Activation of cognitive activity of students in the conditions of the application of
computer technology learning. // Abstract of Doctor. disser-., Almaty, 1994, p. 36.
4. Potashnik M.M. et al. Management of education quality. - Moscow: Pedagogical Society of
Russia, 2000 –p. 448.
5. Maslow A. Motivation and personality. 3rd ed. - SPb: St. Petersburg, 2011.-p. 352.
6. Vygotsky L.S. Thinking and speech. – “Labyrinth”, Moscow, 1999. –p. 352.
7. Zair-Bek S., Mushtavinskaya I.V. The development of critical thinking in the classroom. - M .:
Prosveshenie, 2004. -. P. 174.