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Research and development in the field of new IT and their applications
УДК 519.87
DOI: 10.25559/SITITO.14.201804.931-937
THE DEVELOPMENT OF APPROACHES FOR OBTAINING AUTOMATED SOLUTION ON THE FORMATION OF THE CURRICULUM
Anna V. Zykina, Olga N. Kaneva, Viktoria V. Munko Omsk State Technical University, Omsk, Russia
РАЗРАБОТКА ПОДХОДА ДЛЯ ПОЛУЧЕНИЯ АВТОМАТИЗИРОВАННОГО РЕШЕНИЯ ФОРМИРОВАНИЯ УЧЕБНОГО ПЛАНА
А.В. Зыкина, О.Н. Канева, В.В. Мунько
Омский государственный технический университет, г. Омск, Россия
© Zykina A.V., Kaneva O.N., Munko V.V., 2018
Keywords Abstract
Competence; competence Modeling of training processes contributes to obtaining effective solutions of problems in the educational
approach; curriculum; multi- system. One of the most important tasks in the planning of the educational process is computer-aided cur-
criteria optimization. riculum design taking into account imposed limitations and the requirements set educational standards and
institutions in accordance with the competence-based approach. Despite the considerable amount of the problem research, a systematic formulation of its solution does not exist. The approach is designed to obtain such a decision involving the relationship between disciplines, competencies and teachers. Features of the approach are connected with the formalization and generalization of semi-structured data. Its processing is possible by using the basis of modern decision-making methods with initial uncertainty. Approaches to solving these problems are proposed. Based on the received set of education profile field competences the formation model of the curriculum is constructed. This problem can be considered as an multi-criteria optimization problem.
Ключевые слова Аннотация
Компетенции; Моделирование учебного процесса способствует эффективному управлению в образовательной си-
компетентностный подход; стеме. Одной из важнейших задач в планировании учебного процесса является автоматизированное учебный план; проектирование учебного плана с учетом накладываемых ограничений и требований, заданных об-
многокритериальная разовательным стандартом и вузом в соответствии с компетентностным подходом. Несмотря на
оптимизация. значительное количество исследований, посвященных решению этой проблемы, системная поста-
новка её решения отсутствует. Разработанный в статье подход к получению такого решения основан на взаимосвязи дисциплин, компетенций и преподавателей. Особенности подхода связаны с необходимостью формализации и обобщения слабоструктурированных данных, обработка которых возможна на основе современных методов принятия решений в условиях исходной неопределенности. Предложены подходы к решению этих проблем. На основе полученного набора компетенций профиля направления построена модель формирования учебного плана, являющаяся задачей многокритериальной оптимизации.
bout the authors:
Anna V. Zykina, Doctor of Physical and Mathematical Sciences, Professor, Head of the Department of Applied Mathematics and Fundamental Informatics,
Omsk State Technical University (11 Mira Av., Omsk 644050, Russia), ORCID: http://orcid.org/0000-0001-9697-8342, [email protected]
Olga N. Kaneva, Candidate of Physical and Mathematical Sciences, Associate Professor at the Department of Applied Mathematics and Fundamental
Informatics, Omsk State Technical University (11 Mira Av., Omsk 644050, Russia), ORCID: http://orcid.org/0000-0002-3623-1607, okaneva@yandex.
ru
Viktoria V. Munko, Postgraduate Student, Department of Applied Mathematics and Fundamental Informatics, Omsk State Technical University (11 Mira Av., Omsk 644050, Russia), ORCID: http://orcid.org/0000-0003-0569-2459, [email protected]
Modern Information Technologies and IT-Education
Introduction
The curriculum formation is a key problem of the educational process of the University. Most of the research on this problem use information technology in the curriculum formation without analyzing the requirements of Federal State Educational Standards [1-11]. At the same time, the curriculum formation is characterized by a significant influence of the higher education workers contingent and, as a result, it needs a serious restructuring. This is especially true in the context of increasing requirements for the quality of training [12, 13]. A primitive curriculum with a random distribution of disciplines by modules leads to a decrease in the quality of the basic educational program. In consequence of that, there is a decrease in the quality of professional skills of graduates [14-22]. The inclusion of optimization procedures in the construction of the curriculum [23] allows us to evaluate the choice of specific disciplines that fully provide competence.
The formation of the curriculum is implemented under the condition of the fulfillment of many requirements that defined in the regulatory documents. According to the mathematical modeling, they are fuzzy. Requirements, on the one hand, can be represented as restrictions that imposed on the curriculum formation, on the other hand, can be represented as the target functions, the value of which must be maximized (minimized). As a result, the task of the curriculum formation is reduced to a class of poorly formalized problems with indistinct restrictions, incomplete and fuzzy data. The feature of this problems is that it is impossible to find the only acceptable optimal solution. These disadvantages leads to a variety of curriculum formation models. Moreover, the choice of a particular solution depends on subjective factors and during their formalization depends on the models and algorithms adopted.
Domain analysis
Imagine the process of curriculum formation in the form of: UP={D,K,L} (1)
where D — is the discipline of curriculum, K - content requirements (competences) for the educational program for which the developed educational plan, L - persons, ensuring the learning and curriculum development.
Disciplines, in turn, are divided into the disciplines of the basic part, the variable, the profile (optional), practice, and GIA:
D={Db Dv Dp DpB Da}. (2)
The idea of the approach to developing the curriculum development
Select the main entity in the formation of the curriculum:
• disciplines;
• competences;
• teachers.
The main element in the curriculum is the disciplines. Consider the communication of disciplines competences and disciplines teachers. The organizational unit of teaching can be considered disciplines. This implies that directly it is impossible to determine which competencies are acquired as a result of studying a particular discipline. Let us formulate the following principle of formation of the curriculum with the requirements of the educational standard: the subjects of the curriculum are directly linked only with descriptors (knowledge, skills, proficiency) which, in turn, are associated with competencies. The study [25] introduces a formalized representation of competence through a tuple. It contains a set of descriptors and a set of terms. Based on this, each the curriculum entity can be represented in the descriptor space in the form of:
V= <SV, DV, TV>, (6)
where V is the designation of the selected entity, SV- formulation of the selected entity in natural language, DV - set of descriptors («knowledge», «skills»,...), TV — set of terms.
Figure 1 presents a diagram showing the relationship of competencies, disciplines, and descriptors.
Fig. 1. Relationship between disciplines and competencies Рис. 1. Взаимосвязь компетенций и дисциплин
The substantive requirements include competence, which, in turn, have 3 levels: universal, general professional, professional:
K ={*, K„ Kp}. (3)
The person providing the training process and curriculum development are divided into internal and external:
L={
LproP LprJ Las}.
(5)
Note: the feature of the new educational standards is the division of rights to the competencies formation. Specifically, universal and general professional competences are defined by the standard, and professional competences are established at the educational institutions. The paper [24] proposes an approach that determines the profile and professional competence of the basic educational program, that the most relevant for the labor market in a particular region.
We define the identifying the relationship between descriptors and competences as Ц.е[0,1] - close ratio of the i-th competence of the j-th discipline. After obtaining the ratio we form the set of disciplines included in the curriculum. The result is a wide variety of disciplines, each of which provides the closure of the i-th competence is not less than the a value. We build an optimization problem to obtain a set of disciplines that provide the maximum competence (section 4.1), by distributing the resulting set of disciplines in parts of the curriculum. Before proceeding to the connection of disciplines and teachers, it is necessary to decide the structure of the curriculum (determination of the studying disciplines order). In addition, at this stage there is a distribution of credits for each type of the study discipline. After that, we turn to the connection of competencies and teachers. The entity of discipline and teachers are also connected through knowledge, skills, proficiency of teachers and disciplines. And they can be represented in the descriptor space [25]. Figure 2 shows the connection between disciplines and teachers.
Современные информационные технологии и ИТ-образование
Research and deveio pment in the field of new IT and their applications
Fig. 2. Relationship between disciplines and teachers Рис. 2. Взаимосвязь преподавателей и дисциплин
Let hp е[0,1] the connection of the descriptors of disciplines and teachers. It is the ratio profilinp oi the p-td t eache r at the s-th type of academic work of the j-th discipline. After obtaining the coefficient of profiling we transfer to the formation of the teachers set who have the right to exercise the type of the training discipline. The result is the set of indices of teachers, the profiling which is the s-th type of academic work of the j-th disciplinenot less than p. At this stage, the second optimization problem of maximizing the profiling of teachers in each discipline with minimum cost is set is describe d.
Ja ~ - is the set of indices of the disciplines involved
in the clwsoce of universal competencies.
J°a = U^o/tO/7 - is the set of indices of the subjects participating in tUe da sure of General p rofessional competencies.
Ja = U is!Pjla\Jf - is the set of ind ices of the disciplines involved
in the Uosure ofprofessional competences.
к - tde number of the strucOural parts of the curriculum: fa Оhe b a se part of the curriculum; k = 2 - the variable part of curriculum; k = 3 - profile part; fa 4 - practice; к = 5 - GIA.
Jh-Г и Г и Га - is the set of indices of the disciplines involved in the formation of the basic part of the pack.
Mathematical model of the curriculum
Га-ГиГа - is the set of indices of the disciplines involved in the
The resulting mathematical model of the curriculum consists of two parts:
• connection of disciplines and competencies;
• connection of disciplines and teachers.
Connection of disciplines and competences
We introduce the following notation:___
i - is the number of competence, f=1, щ.
iu = и*, q......i^s - is tha set of indices of the universal compe-
tences.
1° = {i°, i%,..., im0} - is tha set — indiwesof General —'ofessional competences.
Ip = {i0, f2,..., irnp) - is the set of indices of professional compe-
ten ce.
j - numUer of disciplins, jn .
ku e lw,d] - close ratio of the i-th competence of the j-th discipline. jf = } - is the set oO indices of the fundamental dis-
ciplines (required included in pack).
Ja — O1J2. = m - is the set of indices of subjects,
each of which provides the closure of the i-th competence is not less than the value a.
formationofthe variable partof the CP.
H=I°aVjl - is the set of indices of the disciplines involved in the for mation of the relevant part of the pack.
Г - is the set of indices of the disciplines involved in the formation of the part of the practitioner pack.
Г - is the set of indices of the disciplines involved in the formation of part oi the GSk pack.
vk o tde lower bound credits the k-th part of the pack.
у - upper limit of credits k-th part of the pack.
v - limitation on total number of credits up.
Vj - the number of credits allocated to the j-th discipline.
(1, if j-th iscipline isincluded into в k-th part curriculum,
0, otherwise. (2)
The solution of the problem will be a matrix X of dimension 5*n. We introduce a limit on the number of credits for each structural part of the curriculum:
V'ZljejHVjXbjZ'-.kaTJ. (3)
We introduce a limit on the singleness of entrance of j-th in the curriculum:
EL< 1J‘= Ml. (4)
IMern Info rmati 0 n Technologies and IT-Education
It is necessary to maximize presence of each competence in the curriculum:
T.jejb'Ek^kijXkj -» max,i = P,m. Connection of disciplines and teachers
(5)
У
ps
=l1,
lo,
discipline,otherwise
(6)
It is demanded to maximize the profiling of teachers in each discipline:
(7)
hs^E^pdnpSj hpjypj
maX' j = 1,n.
EdEDs ^LcDdnp;0
• min, j = 1, n.
After analyzing the requirements of educational standards, we introduce a restriction on the share of scientific and pedagogical workers having the scientific degree:
,j
У7=1 ^sESJ EdEDs ^pepdnpsJn(pkn\jpdn) ^^sjVsp — Y-
(9)
We introduce the following notations: p - number of teacher, p = 1, l, d - the number of the qualification of the teacher: d=1 - professor; d=2 - associate professor; d=3 - senior teacher; d=4 - assistant, ___________________
Pd = {pi, pd.......Ptd}, d = 1,4 - is the set of indices of teachers
d-th of qualification,
Pdn = \j)dn, pdn,..., pfj^} - is the set of indices of teachers with a scientific degree Doctor' of Sciences.
PKn = {pfn, p!fn,..., pff^C - is the set of indices of te achers with a scientific degree of candidate ct Sciences, cd - cost: of one rate a teacherd-th qualificatinn s-type numtrier of training =ct:iv[ities on the discipline: s=1 - lectures; s=2 - practical lessons; s=3 - laboratory wcr1; s=4 - contact independent work; s=5 - fxam;
s=6 - consultation on exam; s=7 - test, s = 1c q.___
Sd = {sf , s- , . . ., s'.e, j = =,11 - is tlie; set of indices of the training activitie s, which are part of thee j-th d iscipline.
Vj - the number of credit's providet tor tlie s-th type of study j-th discipline. _____
Ds = [cO0 (.-,..., d^s}, S = 1, q - is the set of inticts of the qualifications allowed for' the implementation of the s-th type nf academic work.
hspj e [0,1] - coefi;icieei^t: of profiling ot the p-th teaclee] at the s-sh type o= academic wor'lk telae j-th discipline. If hpj = 1- then the p-th teadier is the leader for the j-th discipline. This ratio is dependent on tlie =ducation diplomas, teacher training courses, publications, personal rating, etc.
Pp* = 1,p^,...,p^}, jf = 1,7e,S = 1,( - is the set of indices oI teachers, profiling; of 'whicil^ is the s-th type of academic work the j-th discipline not less than (3.
Ps = UdeDs^d is the set of indices of teachers (eligible to exercise the s-th type ofacademic work..
- the rate provided to s-th type of training on the j-th discipline.
Let us introduce the conditions on the number of people fro m s cie n -tific and pedagogicalworkers, in every kind of work discipline:
Урер*УрХ = 1,5 = 1,; = 1,n. (10)
Crepes — 1,5 = -J = 1, гг. ( 1 1 )
Cep^s — 1,5 = з,у = 1, n. ( 1 2 )
Cepsyps — 1,5 = 4, j = 1, n. ( 1 3 )
1, iq p -th te acher leads s-th type о f acadsmi c work the i-th [t ]
The total value of the discipline in the cur jioulum should ire minimal. This requires to minimize the cost of each discipline::
d c^^i --™e- /-ТТ (8)
-‘pep1
The constraint (10) means that lectures may be read only by one teacher Constraints (11), (12), (13) indicate that laboratory and practical contact and independent work may be provided by more than 1 person.
Conclusion
The work result is the developed approach for automated decision design of the curriculum taking into account imposed limitations and the requirements set by educational standards and institutions in ac-de'dance with thn competence-bated approach. A mathematical model of th e curriculum, including co mmunicatiok of disciplines, competences ann teachers is offered. The sulrsystem designed automated solution of thn formation of the curriculum includes the discipline, requirements of the standard and the University, technology implemrntation of the curriculum experts who provide the educational process. The obtained results can be used to solve tasks for im-froving the eOficiency of crmpiling and verifying the compliancr of the curricula quality criteria.
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Совремпсные информационные технологии и l/IT-te есрг^;1С)1Е8.;^ние
Research and development in the field of new IT and their applications
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Submitted 12.07.2018; revised 10.10.2018; published online 10.12.2018.
Modern Information Technologies and IT-Education
Список использованных источников
[1] Gusyatnikov V.N., Bezrukov A.I., Sokolova T.N., Kayukova I.V. Information technology to assess the level of competence in the educational process // Proceedings of the 9th International Conference on Application of Information and Communication Technologies (AICT). Rostov on Don, 2015. Pp. 473-476. DOI: 10.1109/ICAICT.2015.7338604
[2] Viriansky Z.Y., Raychuk Y.A. Quality assurance in education at
the stage of curriculum development // Proceedings of the IV Forum Strategic Partnership of Universities and Enterprises of Hi-Tech Branches (Science. Education. Innovations). St. Petersburg, 2015. Pp. 86-87. DOI: 10.1109/IVFo-
rum.2015.7388262
[3] Rongrong R., Gang X., Linan G. A model for university counsel-
or's competence evaluation based on GIOWA operator // Proceedings of 2010 Chinese Control and Decision Conference. Xuzhou, 2010. Pp. 1845-1848. DOI: 10.1109/
CCDC.2010.5498651
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[7] Hrmo R., KriStofiakova L., Mistina J. Building a quality system of technical and vocational education in Slovakia towards a European labour market // Proceedings of 2015 International Conference on Interactive Collaborative Learning (ICL). Florence, 2015. Pp. 237-243. DOI: 10.1109/ICL.2015.7318032
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Поступила 12.07.2018; принята в печать 10.10.2018; опубликована онлайн 10.12.2018.
|об авторах:|
Зыкина Анна Владимировна, доктор физико-математических наук, профессор, заведующий кафедрой прикладной математики и фундаментальной информатики, Омский государственный технический университет (644050, Россия, г. Омск, пр. Мира, д. 11), ORCID: http://orcid. org/0000-0001-9697-8342, [email protected]
Канева Ольга Николаевна, кандидат физико-математических наук, доцент, кафедра прикладной математики и фундаментальной информатики, Омский государственный технический университет (644050, Россия, г. Омск, пр. Мира, д. 11), ORCID: http://orcid.org/0000-0002-3623-1607, [email protected]
Мунько Виктория Васильевна, аспирант, кафедра прикладной математики и фундаментальной информатики, Омский государственный технический университет (644050, Россия, г. Омск, пр. Мира, д. 11), ORCID: http://orcid.org/0000-0003-0569-2459, [email protected]
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