=Paper=
{{Paper
|id=Vol-2770/paper18
|storemode=property
|title=Constructing Domain Model based on Logical and Epistemological Analysis
|pdfUrl=https://ceur-ws.org/Vol-2770/paper18.pdf
|volume=Vol-2770
|authors=Julia Vainshtein,Roman Esin,Gennady Tsibulsky
}}
==Constructing Domain Model based on Logical and Epistemological Analysis==
https://ceur-ws.org/Vol-2770/paper18.pdf
Constructing Domain Model based on Logical and
Epistemological Analysis*
Julia Vainshtein1[0000-0002-8370-7970], Roman Esin1[0000-0002-9682-4690] and
Gennady Tsibulsky1[0000-0001-6661-5591]
1
Siberian Federal University, Svobodny, 79, 660041 Krasnoyarsk, Russia
yweinstein@sfu-kras.ru, resin@sfu-kras.ru,
gtsybulsky@sfu-kras.ru
Abstract. In modern conditions of active development of new pedagogical
technologies and innovative forms of organizing personalized learning in an
electronic environment, adaptive learning begins to take the main positions. The
development of the structure and content of adaptive e-learning courses, the de-
sign and implementation of educational strategies, teaching methods, approach-
es to assessing results are determined by the educational content model. The
purpose of the study is to develop an approach to building a model of educa-
tional content for an adaptive e-learning course that provides a formalized
presentation of educational material and building a logically grounded learning
strategy. The paper presents an approach to its construction based on the inte-
gration of logical and epistemological methods of the correlating between the
volume and content of concepts with the methods of graph theory. Adaptive e-
learning courses, implemented on the basis of the proposed approach, made it
possible to present educational content in the form of logically integral educa-
tional objects that allow adapting the educational environment to the personal
characteristics of students. The proposed approach has been tested in the educa-
tional process of students of the training direction "Information systems and
technologies" of the Siberian Federal University. In the future, the results of the
study can become the basis for the development of a personalized adaptive
learning ecosystem of a university in the context of digitalization of education.
Keywords: Educational content model, Domain model, Logical and epistemo-
logical analysis, Adaptive e-learning course, E-learning, Adaptive learning,
Personalization.
1 Introduction
In the last decade, the goal of specialists in the field of electronic educational technol-
ogies has become the development of innovative methods for e-learning and various
tools for analyzing the educational process. New pedagogical technologies and inno-
*
Supported by by the Russian Science Foundation, grant No.18-013-00654.
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0
International (CC BY 4.0).
Proceedings of the 4th International Conference on Informatization of Education and E-learning Methodology:
Digital Technologies in Education (IEELM-DTE 2020), Krasnoyarsk, Russia, October 6-9, 2020.
vative forms of organizing personalized learning in an electronic environment are
developing, for example, adaptive learning [1].
The analysis of educational practice in the field of adaptive learning testifies to the
diversity of its models and the active development of new approaches and modern
technologies for its implementation [2-8]. An adaptive e-learning course (AELC) is
an e-course that provides the formation of an individual educational path and provides
the student with a personal educational space. Such a space is filled with educational
content, the form and content of which is adjusted to the individual characteristics of
students and provides them with the necessary information [9]. The design of AELC,
the definition and application of approaches to assessing learning outcomes is deter-
mined by the structure of knowledge embedded in the domain model - the model of
educational content, which is the basis of any AELC [10].
In recent years, the presentation of the educational content of e-learning courses is
carried out in accordance with the principles of microlearning, which is teaching a
small amount of material in a short period of time [11]. However, despite the inten-
sive use of microlearning, existing educational practices are mainly focused on divid-
ing educational content into fragments. In this case, the key factor is the division of a
length of time devoted to its study. This approach often does not include the pro-
cessing of the content of the educational material and entails the fragmentation and
lack of logical coherence of the developed adaptive e-learning courses. At the same
time, it should be emphasized that modern requirements for micro-proportions of
educational material are that they should be independent fragments of educational
content and meet the criteria of logical integrity, independence, logical completeness
and verifiability [12, 13].
In these conditions, it seems relevant to develop an approach to building a model
of educational content of an adaptive e-learning course that provides a formalized
presentation of the educational content of the discipline and the construction of a logi-
cal strategy for its study.
2 Domain model
Structuring domain model for AELC discipline serves to perform based on methods
of logical and epistemological analysis of concepts [14-16]. The structure of domain
model of the discipline, in this case, can be represented in the form of a tree, where
the vertices correspond to the concepts of the subject area of the discipline, and the
relations between them are the relations of the hierarchy: "genus-species relations"
and "part-whole relations" [17, 18]. Two types of models characterize any concept
C : phenomenological and structural model. The phenomenological model of a con-
cept has the form:
C f x1 , x2 ,..., xn ,
where x1 , x2 ,..., xn are essential features of a concept, the minimum set of which is
sufficient to identify the concept being described from all concepts in a given subject
area, regardless of the current learning goals – external heterogeneity of the concept.
The structural model of the concept has the form:
Cs A, R ,
where A is the set of sub-concepts of the described concept, R is the set of essential
features of the sub-concepts of A , which form the phenomenological models of the
sub-concepts – the internal heterogeneity of the concept. External and internal hetero-
geneity of the concept represent two main characteristics of the concept – qualitative
and quantitative.
The concept of domain model is characterized by its volume and content. The de-
notation (extensional, degree of generality) is a set of its sub-concepts and is a set of
classes of objects included in the concept. The content of concept (intension) is a
finite minimum set of essential features. The intension of a concept can be represent-
ed by a class standard, which has averaged values of features within its scope and an
acceptable range of values of features. Any concept can be defined by specifying its
intension or extension.
Typically, when constructing a tree domain concepts, three types of concepts are
distinguished: differentially general concepts, integrally general concepts and collec-
tively general concepts transitional between them [15]. These concepts differ from
each other in their logical and epistemological properties and functions. Differentially
general concepts represent concepts in which objects in selected essential features are
identified in a single class, and other indications are discarded and are not included in
the meaning (essence) of this concept. The content of integrally general concepts
includes information about all special cases of a feature (information about the sub-
classes of a given class of objects), which are deduced from them by imposing re-
strictions or a meaningful classification reflecting the entire historical path of devel-
opment of the concept.
Differential general concepts obey the formal-logical law of the inverse relation-
ship between the content and denotation of a concept, which means that the larger the
content of the concept, the less its denotation. Integrally general concepts characterize
both direct (epistemological) and reverse (logical) relations of their content and deno-
tation. These relations correspond to subordinate and genus-species relations included
in this concept.
When constructing a domain model in the tree concepts rupture can occur when
you can not establish a relationship between certain concepts. This semantic gap do-
main violates its unity. This demonstrates the heterogeneity of domain model, and it
should be presented as a set of concept trees, and the training materials of the disci-
pline as a separate module for each tree. In this case, each module will have the disci-
pline content integrity. The emergence of a semantic gap in domain model necessi-
tates the use of a training project in the educational process that ensures the intercon-
nection of the course modules.
The concept tree is used as a basis for identifying the minimum portions of theoret-
ical material, which we will call terms. The term can be defined as a sequence of se-
mantic facts and procedural rules having the semantic completeness. Each term repre-
sents some fragment of the discipline's concept tree. In this case, the tree of terms is a
hypergraph of concepts (tree hypergraph), in which subsets of concepts included in
the term are connected by an edge.
The study of terms is carried out sequentially: from general to specific, which al-
lows us to correlate the concepts of a term with their place in the general structure of
the course and contributes to the formation of a holistic perception of the discipline.
The presentation of domain model in the form of a tree allows you to structure the
discipline at the level of basic concepts and lay the foundation for basic educational
activities. These activities in the course can be considered the assimilation of concepts
in the field of their definition, identifying the main features and properties of the stud-
ied objects and identifying structural and logical relationships within the framework
of the studied theory [16].
From a didactic perspective, an important component of the educational process in
an adaptive e-learning course is the formation of students' competencies in accordance
with federal educational standards and an educational program. This can be done
through the decomposition of competencies into indicators of their achievement,
which are knowledge, skills and labor actions. Further, the indicators are decomposed
into a set of verifiable descriptors in the discipline's evaluation tools. Knowledge in
work is understood as mastered specialized information in the form of concepts, their
main features and connections. Skills are the ability to perform operations on the stud-
ied concepts of the subject area of the discipline [9] and, regardless of the subject
area, rely on the classically distinguished types of operations on concepts: generaliza-
tion, restriction, embedding, intersection, union and complement.
The content of each formed term can be expanded by operations on the concepts
that are included in the term. This allows the design of a set of command and measur-
ing materials to ensure control of the assimilation of each term and the formation of a
coherent micro-proportion of educational content. The construction of command and
measuring materials is based on an a priori assignment of a tree of operations or their
combination.
The domain model includes two kinds of concepts: operators and operands. The
concept-operands are the concepts of the domain model and the concept-operators
describe the actions performed on the concept-operands (operations on the concepts
that are presented above). During the construction of a tree of operations on concepts,
a situation is possible when the combination of one concept-operand with different
concept-operators is carried out to form different resulting concepts. An increase in
the level of abstraction of operands and operators in the tree of operations increases
the complexity of the skills formed in the student. The low-level operand is the basis
for constructing various higher-level operands.
As a result, the formation of a skill at each step of training is to form the trainee's
ability to independently combine operands and operators of the same level of general-
ity (abstraction) and obtain a new operand (result of the operation) of a higher (lower)
level of abstraction. The process of forming abilities carried out at each step in the
study of learning next domain concepts.
It should be noted that each step of training is divided into three phases: assimila-
tion of the current concept of the domain model (knowledge component), formation
of ability (ability formation operate with the received knowledge), formation of the
required skill (the ability to perform an operation on the acquired knowledge at an
expertly specified time).
At the same time, skill is considered as a way of performing operations on con-
cepts, brought to automatism and ensuring high productivity in performing profes-
sional tasks. After each phase, appropriate measurements are carried out, and the
phase is implemented until the learner reaches the normative levels of knowledge –
K st , ability – Ast , and skills – S st , Fig. 1.
Fig. 1. Step of learning in AELC
3 Conclusion
As a result, the domain model is built from concepts to a tree or a set of trees of disci-
pline terms and operations. The next step is the transition to the formation of the
course content corresponding to the developed domain model. At the same time, the
terms of educational content are independent fragments, bricks of knowledge, in other
words, educational objects [9]. The selection of "educational objects" (structuring the
educational material of the AELC) and, accordingly, the formation of a minimum
portion of the educational material can be carried out through the indication of the
intension or extension of the concepts included in it. Knowledge about the external
and internal heterogeneity of concepts, the phenomenological and structural models of
the studied concepts, respectively, is a necessary and sufficient content of the essence
of the educational object.
The approach proposed by the authors has been tested and has shown its effective-
ness in the educational process of students in the areas of training in the field of com-
puter technologies at the Siberian Federal University. Adaptive e-learning courses,
built on the basis of the approach proposed by the authors, allow structuring the sub-
ject area of the discipline: moving from concepts to terms - logically integral micro-
proportions of educational content. The peculiarity of the proposed approach to the
construction of a model representation of the educational content is a formalized rep-
resentation of educational material and the possibility of constructing a logically rea-
sonable sequence of its study.
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