=Paper=
{{Paper
|id=Vol-2254/10000229
|storemode=property
|title=A
genetic-algorithm approach for forming individual educational
trajectories for listeners of online courses
|pdfUrl=https://ceur-ws.org/Vol-2254/10000229.pdf
|volume=Vol-2254
|authors=Denis Parfenov,Veronika Zaporozhko,Irina Bolodurina
}}
==A
genetic-algorithm approach for forming individual educational
trajectories for listeners of online courses==
https://ceur-ws.org/Vol-2254/10000229.pdf
A genetic-algorithm approach for forming individual
educational trajectories for listeners of online courses
Veronika V. Zaporozhko Irina P. Bolodurina
Department of Informatics Department of Applied Mathematics
Orenburg State University Orenburg State University
Orenburg 460018, Russia Orenburg 460018, Russia
zaporozhko vv@mail.osu.ru prmat@mail.osu.ru
Denis I. Parfenov
Faculty of Distance Learning Technologies
Orenburg State University
Orenburg 460018, Russia
parfenovdi@mail.ru
Abstract
One of the main directions for further improvement of the online courses
is to provide complex personalization. The need for personalization of
learning is a reflection of the natural for mankind desire for an indi-
vidual approach to personal needs, preferences, and opportunities. A
serious disadvantage of the online courses is the lack of an individual
and differentiated approach to each student due to a pre-determined
learning route in typical courses. In the present work, a genetic algo-
rithm is proposed that allows you to form an optimal learning route,
designed to meet the personal educational needs and individual capa-
bilities of each listener of the massive open online courses. The results
of a computational experiment and examples of individual trajectories
formed on the basis of the proposed algorithm are presented.
1 Introduction
The individual educational trajectory in massive open online courses (MOOC) is a realization way of individual
educational needs and abilities of students, their right to choose their personal development and self-improvement
path [Sun15]. We define an individual educational trajectory as a personal path to realize the personal potential
of each MOOC listener [Par18, Zap17]. There are several ways to realize an individual educational trajectory.
For example, through the use of various educational technologies (tertiary differential education, problem-based
learning, game-based learning, portfolio and others) or personalization technologies in MOOC (inquiry-based
learning, personal recommender system, and others) [You15, Han18]. Another way is to form an individual
learning route, which is a sequence of elements of the training activity of a particular student at some fixed stage
of the study on the online course.
Copyright c by the paper’s authors. Copying permitted for private and academic purposes.
In: Marco Schaerf, Massimo Mecella, Drozdova Viktoria Igorevna, Kalmykov Igor Anatolievich (eds.): Proceedings of REMS 2018
– Russian Federation & Europe Multidisciplinary Symposium on Computer Science and ICT, Stavropol – Dombay, Russia, 15–20
October 2018, published at http://ceur-ws.org
Purposefully designed an individual learning program is a technological tool for the implementation of an
individual learning route. Individual learning routes for MOOC listeners differ not only in terms of volume but
also in the variability of the forms of presentation of the electronic learning content. This is due to the individual
learning styles of students and, accordingly, their activities used in the study of the same learning object. In
our opinion, it is impossible to design an individual learning route in advance, as it must reflect the dynamics of
learning, revealing it in movement and change. Such an approach will allow timely making necessary adjustments
to the educational process implemented on the basis of MOOC. For example, to fill certain gaps in the knowledge
and skills of the course listeners, or vice versa, to speed up the learning process or deepen the learning program.
The task of our research is to construct an optimal individual educational trajectory based on a genetic
algorithm that is as close to the real possibilities and features of each listener of the course as well as corrected,
if necessary, in real time. The remainder of this paper is organized as follows. In section 2, we present the
results of a literature review devoted to the consideration of various approaches to the formation of an individual
educational trajectory based on genetic algorithms. In section 3, we disclose the problem of the formation and
implementation of an individual educational trajectory based on genetic algorithms. A mathematical model of
the form of the optimal educational trajectory in the massive open online courses. Section 4 deals with the
description of the practical implementation of the proposed model and the evaluation of the results obtained.
2 Related work
At present, the amount of research devoted to the problem of development an individual educational trajectory
in the implementation of the concept of the digital educational environment is permanently growing. Here are
presented various approaches to the generation of individual learning route.
Researchers from the National Taiwan Normal University [Hon05] suggested using adaptive computer testing
to identify problems in mastering individual blocks in the online course learning process. The database stores
information about courses with given coefficients of difficulty. Based on the results of testing, the selection
of appropriate courses with the lowest coefficient of labor input is carried out. Using the obtained data, the
automated system generates an optimal individual training program for each student, using a genetic algorithm.
A group of researchers from Pondicherry University proposed to generate an adaptive learning scheme. The
proposed approach allows to take into account the context-dependent content of learning. Depending on the
educational goals and intentions of the learner, the most appropriate content is selected, which can be represented
by three different types: Media, Presentation, Content. To select a particular type of content, researchers
suggested using a genetic algorithm. On the basis of the data obtained, a learning path is drawn up, which best
corresponds to the learner’s intentions [Bha10].
A group of Taiwan scientists in their study suggested solving the problem of identifying the ability to learn
and the difficulty level of the recommended curriculums to each other. This problem is key when generate
an individual learning route. To collect data within the framework of the study, the scientists conducted the
assessment of students after mastering each block of educational content. The evaluation was carried out through
computerized adaptive testing. The test results were then used to form the optimal route for each student. The
approach proposed in the study is based on the hybrid use of the genetic algorithm and the case-based reasoning
[Hua07].
Samia Azough et al. (Morocco) used a genetic algorithm to generate pedagogical paths which are adapted
to the learner profile and to the current formation pedagogical objective. In their study they developed the
description of an adaptive e-learning system. The system proposed by the authors allows the learner to study
courses adapted to his profile. To implement adaptive learning, researchers applied two-step work of the genetic
algorithm. At the first stage, the proposed mechanism is used to form optimal trajectories for the search for
learning goals, taking into account data from the student’s profile. At the second stage, the results obtained
were adapted using data obtained from social networks [Azo10].
A team of researchers from the University of Alcala (Spain) investigated how to perform dynamic selection of
learning objects based on the genetic algorithm for constructing a course structure depending on the input set
of competencies (formed in the learner) and the output (planned learning outcomes) [Mar11].
Thus, the conducted review of researches has shown the urgency of development optimal individual learning
routes and their correct in real time. At the same time, the heuristic algorithms are the main tool that allows
the most effective management of individual educational trajectories.
3 Problem formulation and implementation
As part of our study, MOOC has a modular structure consisting of a certain number of units. Within each
unit, there are learning objects (LOs) of different types (Table 1), which are the structural components of the
course electronic learning content [Zap17]. A certain set of LOs provides the formation of one or more relevant
competencies.
It is known that each learner of the course has its own learning style [Zap06]. Researchers distinguish the
following 4 types of students, differing in the dominant style of learning: Visual learners (”V”), Aural learners
(”A”), Read-write learners (”R”), Kinesthetic learners (”K”). To what type each of the MOOC listeners belongs,
we identify at the beginning of the learning process, using the VARK methodology [Fle95]. So, in our work,
each listener of the course (as an object under study) is characterized by the following input parameters (a set
of attributes characterizing the state of the given object), which are presented in Table 2.
We distinguish four generalized groups of content types depending on the dominant learning style (Table
1). For example, the first group consists of the types of content most suitable for students with the dominant
modality ”Visual”. It is established that students can also have mixed modalities. Therefore, we propose to
form a course with different types of content, but at the same time taking into account the revealed dominant
modality as much as possible.
Table 1: Composition of four generalized groups of different types of content
The The Relative
Type of electronic Dominating
designation attribute attribute
learning Learning
of the content value weight
content Styles
type coefficient (b)
Group 1. Types of content most suitable for students
with the dominant modality ”Visual” (G1)
Presentations (slides) V LO1
µ1 1
Infographics, illustrations V LO2
Webinars V LO3
Video lessons V LO4
Group 2. Types of content most suitable for students
with the dominant modality ”Aural/Auditory” (G2)
Audio conferencing A LO5
Audio notes A LO6
µ2 1
Audio lessons A LO7
Workbooks audio A LO8
Group 3. Types of content most suitable for students
with the dominant modality ”Read/write” (G3)
Glossaries R LO9
µ3 2
Reading R LO10
Quizzes (or tests) R LO11
Assignments R LO12
Group 4. Types of content most suitable for students
with the dominant modality ”Kinesthetic” (G4)
Video and educational games K LO13
Virtual laboratories K LO14 µ4 2
Interactive learning K LO15
Workshops K LO16
Thus, a number of LO from the list of each group must be present in each unit. Accordingly, for each listener,
a unit must be dynamically formed, consisting of LO, mainly corresponding to its learning style.
To establish a representative correlation of different types of content (learning objects) of a particular unit,
depending on learning style, 15,457 respondents were surveyed. The use of the VARK methodology allowed an
analysis of the real situation.
Based on the results of the survey, we will determine the ratio of different types of content in a specific online
course for each type of student (Table 3). Then the sum of the content types ratio of the different groups for
Table 2: Characteristics and values of attributes for a set of students
Possible The attribute Relative
Attribute Attribute
Attribute value attribute
Name (parameter)
Values coefficient weight (ν)
Female a1,1
a1 Gender 1
Male a1,2
under 18 a2,1
19-25 a2,2
26-34 a2,3
a2 Age group 2
35-44 a2,4
45-54 a2,5
55+ a2,6
Visual learners a3,1
Learning Aural
a3 a3,2 3
Style learners
Read-write
a3,3
learners
Kinesthetic
a3,4
learners
each type of learner should be equal to one µ1 + µ2 + µ3 + µ4 = 1. Varying the ratio of µ1 , µ2 , µ3 , µ4 in the
overall content structure gives different sets of LOs in the individual learning route.
Table 3: The ratio of different types of content in each unit
The weight of each type of content
Types of students in the course structure
(by VARK) G1 G2 G3 G4
µ1 µ2 µ3 µ4
Visual learners 0.31 0.21 0.26 0.22
Aural learners 0.25 0.31 0.22 0.22
Read-write learners 0.24 0.18 0.34 0.24
Kinesthetic learners 0.22 0.23 0.24 0.31
Completion of the study of each unit is accompanied by the performance of a summative test, the results of
which allow one to draw a conclusion about the success of learning process or the prevalence of difficulties in the
course student.
Thus, the individual learning route in MOOC is a varied set of learning objects of different types for each of
the units. Their list is formed and adjusted in real time mode when the listener moves from stage to stage (from
one unit to the other).
3.1 Mathematical model of the problem
We created a model for the formation of the individual educational trajectory in the online course. Let us
presented the initial data for solving the claimed problem with the help of the mathematical tools of the genetic
algorithm [McC05].
Having analyzed the subject area of the task, we have identified the following tuple, characterizing the for-
mation process of the individual educational trajectory (IET).
IET = (S, C, P ), (1)
where S = (sk ) the set of students learning a particular MOOC, k number of students, K ∈ N ; C = U nitx
MOOC, located in a cloud-based learning environment and consisting of units, x number of units in a particular
course, x ∈ N .
Each unit of the MOOC contains a specific set of content groups. Then let G = g1 , . . . , gn the set of generalized
content type groups, when n number of these groups, n=4. Each group contains a certain set of learning objects
gi = LOi,j , where LOi,j the set of LOs in each unit, belonging to the selected generalized group gi (Table 1).
U nitx = G1 , . . . , G4 .
Then P = P1 , . . . , Pn is a valid set of individual routes for each student. Each individual learning route
should consist of a specific set of LOi,j different types (according to the Table 1). Each learning object LOi,j
can take part in the formation of an individual learning route with its mandatory entry into a generalized group
gi . For the purposes of formalization, we introduce the Boolean variables 0 or 1, which describe alternatives to
the selection of learning objects, i.e. LOi,j = {0, 1}.
Each object of the sets G and S can be represented as a set of attributes that numerically characterize these
objects. Attributes are defined on a limited set of positive values. The definition of characteristics and values
of attributes (parameters) for the identified sets is presented in Tables 1 and 2, respectively. The task of
determining the value of the attribute coefficient and the relative weight of the attribute is solved using empirical
data, obtained as a result of the questionnaire, and expert estimates. To identify the relative weights of these
attributes, experts were asked who ranked attributes values in order of increasing importance.
The weight of each unit in the course is determined by the following formula:
D
Y
WU nitx = (µh,sk )bh , (2)
h=1
where µh,sk - attribute coefficient value µh for unit x depending on the particular type of student sk , bh
relative weight of attribute gh for unit (Table 1).
To select an individual learning route in MOOC, you also need to find the weight of the student. The weight
of each student is determined by the following formula:
Z
Y
WSk = (ay,sk )νh , (3)
y=1
where ay,sk - attribute coefficient value a y for student sk , νh - relative weight of attribute ay (Table 2)
In the process of optimization under consideration, the parameter space under study is sufficiently large. The
task does not require a strict global optimum, so it is sufficient to find an acceptable, most suitable (effective)
solution in a short time. To find an acceptable (optimal) individual learning route P in a cloud-based learning
environment (depending on parameters (a1 , . . . , a3 , ν1 , . . . , ν4 ), we use the genetic algorithm.
3.2 Individual educational trajectory generation based on genetic algorithm
We consider a genetic algorithm that works with a population (a finite set of individuals). The set of optimized
parameters is represented in the form of genes that form a chromosomal filament. In the chromosome of each
individual, a possible solution of the problem is encoded. This algorithm consists of the following steps:
Step 1. Initialization (formation) of the initial population from P chromosomes. The population is a collection
of several vectors P. The size of the population is set before the genetic algorithm begins work. The individual
is one element of the vector P. The gene is an element of LOi,j from the vector P. In our model, the chromosome
consists of LO genes, in which the alleles of each of the genes are the values of {0, 1}.
Step 2. Calculate the fitness function of the chromosome in the population F(P).
The objective function numerically characterizes the result of selecting an individual educational trajectory
in MOOC by the following formula:
x
X
F (P ) = F (P )max − (WU nitx · Wsk · Tx (Sk ) · Z(Px )), (4)
1
where P vector of selection of individual learning route; WU nitx the weight of each unit in the course; Wsk
the weight of each student; Tx (Sk student test score in each unit; F (P )max maximum value of the objective
function; Z(Px ) function of formation a set of LOs.
Step 3. Selection of the best individuals from the current population (two parent chromosomes) for further
crossbreeding using one of the selection methods. Selection: the fittest individuals have the best chance of
reproducing.
iindividual LO1 LO2 LO3 LO4 LO5 ... LO16
Chromosomes1 Crossover Chromosomes16
jindividual LO1 LO2 LO3 LO4 LO5 ... LO16
Figure 1: Crossover operator in a genetic algorithm.
Step 4. The use of the genetic operator crossover. Crossover: exchange genetic material between two
individuals (see Fig. 1). Creation of a new population of descendants on the basis of the original one using a
crossover.
Step 5. The use of the genetic operator mutation. Mutation: randomly change part of the genetic material
(see Fig. 2). Creation of a new population of descendants on the basis of the original with the help of a mutation
of individuals (descendants) with a certain probability.
iindividual LO1 LO2 LO3 LO4 LO5 ... LO16
Mutation
jindividual
LO1 LO2 LO3 LO4 LO5 ... LO16
Figure 2: Mutation operator in a genetic algorithm.
Step 6. Repeat steps 3-5 until a new generation of the population containing n chromosomes is generated.
Step 7. Repeat steps 2-6 until the end-of-process criterion is reached - the ”best” chromosome (the optimal
solution of the problem is found).
The criteria for termination of the genetic algorithm are as follows: obtaining a solution of the required quality;
the solution falls into a deep local optimum of the objective function; search time expired.
4 Experimental results
In this section the results of a simulation study are presented. Using the built-in functions of MATLAB, we
implemented a genetic algorithm with the following experimental parameters. The size of the population, we
have established 50 individuals. Each chromosome is represented as a binary code. The probability of a mutation
is 0.05. The probability of crossing-over is 0.8. The Table 4 illustrates individual learning routes, which are
obtained from the results of the experiment. The experimental realization of our algorithm was carried out for
Information Technology MOOCs for technical specialties at the university.
The LO value is ”0” if this learning object is not included in the individual learning route. The LO value is
”1” if this learning object is present in the individual learning route.
5 Conclusion
In this article, we introduced a new algorithm that allows forming individual educational trajectories of MOOC
listeners. This algorithm is proposed for the cloud educational platform, which implements the concept of
personalized learning. The mathematical tools of the genetic algorithm are used in this proposed solution. The
created algorithm is able to find the optimal set of course learning objects that constitute an individual learning
route. The results of the computational experiment show that the proposed algorithm is able to find solutions
that are very close to optimal solutions and in most cases are identical to them.
6 Acknowledgements
The research was conducted with the support of the Russian Foundation for Basic Research (project no. 18-37-
00400).
Table 4: Examples of individual learning routes for one unit formed on the basis of the genetic algorithm
Age Dominating Individual
Listener of MOOC Gender
group learning style learning route
0011101110010001
Student 1 Female 19-25 Aural
LO3 LO4 LO5 LO7 LO8 LO9 LO12 LO16
0101110100111000
Student 2 Male 19-25 Aural
LO2 LO4 LO5 LO6 LO8 LO11 LO12 LO13
0010000110011010
Student 3 Female 19-25 Read-write
LO3 LO8 LO9 LO12 LO13 LO15
0001100010011110
Student 4 Female 19-25 Kinesthetic
LO4 LO5 LO9 LO12 LO13 LO14 LO15
1110010111001000
Student 5 Female 19-25 Visual
LO1 LO2 LO3 LO6 LO8 LO9 LO10 LO13
0010001101101100
Student 6 Male 19-25 Kinesthetic
LO3 LO7 LO8 LO10 LO11 LO13 LO14
0001010001101010
Student 7 Female 19-25 Read-write
LO4 LO6 LO10 LO11 LO13 LO15
0101001001100100
Student 8 Male 19-25 Visual
LO2 LO4 LO7 LO10 LO11 LO14
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