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Week 5 Homework

After reviewing the case study this week by Krizanic (2020), answer the following questions in essay format.

  1. What is the definition of data mining that the author mentions?  How is this different from our current understanding of data mining?
  2. What is the premise of the use case and findings?
  3. What type of tools are used in the data mining aspect of the use case and how are they used?
  4. Were the tools used appropriately for the use case?  Why or why not?

In an APA7 formatted essay answer all questions above.  There should be headings to each of the questions above as well.  Ensure there are at least two-peer reviewed sources to support your work. The paper should be at least two pages of content (this does not include the cover page or reference page). 

Technology in Education – Research Article

Educational data mining using cluster
analysis and decision tree technique:
A case study

Snježana Križanić

Data mining refers to the application of data analysis techniques with the aim of extracting hidden knowledge from data by
performing the tasks of pattern recognition and predictive modeling. This article describes the application of

data mining

techniques on educational data of a higher education institution in Croatia. Data used for the analysis are event logs
downloaded from an e-learning environment of a real e-course. Data mining techniques applied for the research are
cluster analysis and decision tree. The cluster analysis was performed by organizing collections of patterns into groups
based on student behavior similarity in using course materials. Decision tree was the method of interest for generating a
representation of decision-making that allowed defining classes of objects for the purpose of deeper analysis about how
students learned.

Educational data mining, cluster analysis, decision trees, case study, log file

Date received: 30 September 2019; accepted: 18 January 2020


Data mining is a widely spread approach for analyzing

large data repositories to extract necessary or useful infor-

mation. The goal of data mining application is to extract

hidden data patterns and to detect relationships between

parameters in a vast amount of data. The exploration of

data in education using data mining techniques is com-

monly known as educational data mining.

Different edu-

cational data are stored in large databases. This is

especially true for online programs, for the support of

teaching processes and in which student learning behaviors

can be recorded and stored. The most common type of such

information systems is learning management system.

Many educational institutions evaluate the performance

of their students based on final grades which depend on a

course structure assessment and learning objectives to

achieve an effective and consistent learning process.

In this article, cluster analysis and decision tree tech-

nique are used to analyze student behavior for a real

e-course during one semester. The data used for analysis

are event logs downloaded from an e-learning system for

one e-course at a higher education institution in Croatia for

a student generation in 2017/2018. The file in which infor-

mation system records are stored is called a log file and the

data in it are called event


Cluster analysis is a technique for creating organized

collections of patterns into groups based on their similarity

of some property or action.

Because of the fact that cluster

analysis is used for different purposes in educational data

mining, one of the most interesting areas of its application

is for grouping the students to identify typical patterns of


1 Faculty of Organization and Informatics, University of Zagreb, Varaždin,


Corresponding author:

Snježana Križanić, Faculty of Organization and Informatics, University of

Zagreb, Varaždin 42000, Croatia.


International Journal of Engineering
Business Management

Volume 12: 1–9
ª The Author(s) 2020

DOI: 10.1177/1847979020908675

Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License

( which permits any use, reproduction and distribution of the work without further

permission provided the original work is attributed as specified on the SAGE and Open Access pages (



The purpose of decision trees is to identify specific

object classes. Decision trees use different object attributes

to classify different object subsets and do not use just one

attribute or a fixed set of attributes.

The attractiveness of

decision trees is in their easiness for understandability and


The aim of this article is to investigate which recorded

elements of student behavior in the e-learning system could

contribute to successful passing of exams in the observed e-

course. The research questions this article is trying to

answer are as


1. Which student information can be extracted from

event logs of an e-learning system?

2. Which variable values have a significant influence

on grouping students with regard to their behavior in

the e-learning system?

The motivation for writing this article comes from

finding a course that is interesting to analyze due to its

variety of student activities based on which advanced data

mining techniques can be applied to improve content

management in that course. The quality of e-course exe-

cution at higher education institutions in Croatia reflects

the quality of teaching according to which higher educa-

tion institutions are ranked.

In the literature review, an analysis of the existing lit-

erature is conducted. In this chapter, educational data min-

ing, application of logs, cluster analysis, and decision tree

technique are researched. Further on, research methodol-

ogy of this article is presented with the aim of introduction

on research data and research technique. Methodology is

followed by a description of the results obtained by cluster

analysis and decision tree technique. Article ends with

final discussion remarks on perceived knowledge and

future work.

Literature review

Logs could contain a wide range of information about pro-

cess executions.

Data mining shares some characteristics

with automatic process discovery techniques, and in data

mining, “meaningful information is extracted from fine-

granular data, so that these techniques of automatic process

discovery are subsumed to the research area of process


Data mining is the process of extracting useful informa-

tion and knowledge from a large set of data warehouses. It

involves the application of data analytics tools to detect

unknown patterns and relationships in large data sets.

“Data mining is a multidisciplinary area in which several

computing paradigms converge: decision tree construction,

rule induction, artificial neural networks, instance-based

learning, Bayesian learning, logic programming, statistical

algorithms, etc.”

In addition, some of the most useful data

mining tasks and methods are statistics, visualization,

clustering, classification, and association rule mining.

These methods reveal new, interesting, and useful knowl-

edge based on the available information.

The application of data mining techniques on educa-

tional data is called educational data mining.

The primary

goal of using data mining techniques in the field of educa-

tion is to develop models by which we can predict the

overall performance of students in selected courses.

The steps to improve the level of education are as


� Creating data sources of predictive


� Identification of different characteristics or factors

that influence student learning performance during

academic life.

� Construction of a predictive model using classifica-
tion data mining techniques based on predictive


� Validation of a model that was developed according
to students’ performance while learning.


As there are many databases containing students’ infor-

mation, it is possible to operate with large repositories of

data reflecting how students learn.

Folino et al. were

investigating the usage of external-memory decision tree

induction approach to deal efficiently with large logs.


mining techniques economically provide adjustable educa-

tion, effectively improve the system, and reduce the costs

of an educational process.

Higher education institutions

are concerned about the quality of education and use a

variety of ways to analyze and advance understanding of

student achievements.

In the context of teaching and learn-

ing, student data can be used to create and construct pre-

dictive models through which student performance can be


“By extracting information from data, it is pos-

sible to generate process models representing various pro-

cess scenarios in education.”

Asif et al. state that the aim

of forecasting in educational data mining is to predict stu-

dents’ educational outcomes.

Examples of data mining

techniques usage in the e-learning process are assessing

student learning performance, ensuring course adjustment,

and generating learning recommendations based on student

behavior while learning, evaluating teaching materials and

educational courses, providing feedback to teachers and

students, and discovering atypical student behavior while


Márquez-Vera et al. present a method for predicting

student success, which consists of the following commonly

used steps in educational data mining:

1. Data collection. Refers to collecting all available

student information. Users create data files starting

with e-learning databases.

2. Data preprocessing. At this stage, a data set is pre-

pared for the application of data mining techniques.

To successfully complete this stage, data

2 International Journal of Engineering Business Management

preprocessing methods such as data cleansing,

variable transformation, and data partitioning must

be used.

3. Data mining. Data mining algorithms, such as clas-

sification and clustering, are applied to predict

student success.

4. Interpretation. At this stage, the models are ana-

lyzed to predict student suc


Various data mining techniques such as classification

and clustering are applied to reveal hidden knowledge

from educational data.

Clustering is used by pattern anal-

ysis, decision-making, and machine learning, which

includes data mining, document retrieval, image segmen-

tation, and pattern classification.

Various pieces of infor-

mation stored for each event can be used for clustering,

correlating, and finding causal relationships in the event


Using cluster analysis, we separate students into

groups, so that students in the same group share the same

progression within the group.

Data clustering used with

k-means algorithm enables teachers to predict student

performance and associate learning styles of different

learner types and their behavior with the aim of collec-

tively improving institutional performance.


is the most popular and the simplest partitional algori-

thm used for clustering.

“Measuring the similarity of

two objects is done by calculating a distance measure

such as the Euclidean Distance attributes having numer-

ical values.”

Several methods have been developed to solve classifi-

cation problems. Among all these methods, decision tree is

recognized as suitable, because it is considered to be one of

the most commonly used methods in the supervised learn-

ing approach.

Decision tree is a classification algorithm that is dis-

played in the form of a tree in which two different types of

nodes are connected by branches.

The induction of the

decision tree is done through a supervised knowledge dis-

covery process in which prior class knowledge was used to

channel new knowledge.

The tree consists of internal

nodes that match the logical attribute test and the connect-

ing branches which represent the test outcomes.

The deci-

sion tree classifies instances by sorting them down the tree

from the root to the leaf nodes.

The decision tree is con-

sidered to be a procedure that decides whether a particular

value will be accepted or rejected, uses IF-THEN rule, and

ensures that the current state is mapped to a future state to

make a different decision.

IF-THEN rule is one of the

most popular forms of knowledge representation because

it is easy to understand and interpret by nonexpert users

and can be directly applied in the decision-making pro-


The nodes and the branches form a consecutive

path through the decision tree that reaches the leaves, and

it represents a specific mark. All the nodes in the tree

correspond to a subset of data. Ideally, the leaf is clean,

which means that all elements in the leaf have an equal

chance of being a target variable or a class.

In the context

of learning through the decision tree, the target variables

refer to attributes. Each attribute node splits a set of

instances into two or more subsets. The root of the tree

corresponds to all instances.

Decision trees are easy to understand and well adapted

to the classification problems. They suffer from a sensi-

tivity of the data used in their construction and they are a

less natural model for regression. The advantage of deci-

sion trees is that there is a large number of efficient algo-

rithms, which can find approximately optimal tree


In addition, decision trees are able to

break down the complex problem of decision-making into

several simpler ones.

The steps in decision tree building are as follows:

1. Suppose C is a set of objects to be classified by

starting from the current node. If all members within

a set C are of the same class or C is empty, we

determine that the current node is a node of the leaf,

label it according to its class, and complete the pro-

cedure. Otherwise, we move on to step 2.

2. Suppose Ai is the attribute selected for the current

node. The attribute Ai has possible values in Vi ¼
fAi1, Ai2, . . . , Aivg.

3. We use attribute values to divide the set of objects C

into mutually exclusive and exhaustive subsets fCi1,
Ci2, . . . , Civg. Each subset of Cij contains objects in
C which have the value Aij for the attribute Ai.

4. We create a child node in the tree for each attribute

of the Aij value and the corresponding subset of Cij.

Then we label the arc from the current node to the

child node with the attribute value Aij.

5. For each child node, we recursively call the pro-

cedure over the subset Cij with the set of available

attributes fA � Aig.7

Decision nodes are usually represented as squares and

child nodes are drawn to the right of their parents.


decision tree can be used to predict and classify new stu-

dents depending on their activities and decisions made,

because the attributes and values, which are used for clas-

sification, are also represented in the form of a tree.

According to knowledge from the data associated with the

execution of numerous traces, the aim is to build a decision

tree model for use to predict membership into the clusters

for forthcoming enactments.

In comparison with other

data-driven approaches, decision trees are easy to under-

stand and their application does not include complex com-

puter knowledge.


In this paragraph, research methodology used for conduct-

ing the analysis will be presented. First, the proposed model

for educational data mining using cluster analysis and

Križanić 3

decision tree technique is presented. Then, the data source

and the data type are described.

Educational data mining model

According to the literature researched in the previous stage,

the activities shown in Figure 1 are recognized as some of

the most important ones in educational data mining using

cluster analysis and decision tree technique.

First, the analyst needs to select a data set to analyze,

that is, to select the targeted e-course. After selecting an e-

course, log files from an e-learning environment need to be

downloaded. On the basis of the downloaded event logs,

the next phase of the educational data mining process can

be provided. When the data are downloaded and stored,

data cleaning activity can be launched. In this activity, the

data analyst performs unnecessary data cleaning and data

separation of information that are not relevant for the anal-

ysis. After data cleaning activity, data partitioning is per-

formed. This means that the relevant data are extracted and

combined for further analysis. This activity depends on

data mining techniques and the outcome of the analysis.

Once there are manageable data, the application of cluster

analysis can be performed to create groups of students

similar within the group and different to another group.

According to these groups, it is possible to apply another

data mining technique over the obtained data, for example,

decision tree technique. In other words, after having the

obtained data from cluster analysis, the same could be

exported and prepared for decision tree technique

implementation. When there is a model resulted from the

previous activities, the model validation can be performed.

The analyst should be informed in a way of controlling the

correctness of the resulting model. After confirming the

model validation, the obtained model can be interpreted

according to the results.

Data description

The data used for the analysis are event logs downloaded

from an e-learning system for one e-course of a higher

education institution in Croatia for a student generation in

the 2017/2018 academic year. The time span in which the

data were observed was from February 2018 to June 2018.

Originally, there were 62,985 records, and after data clean-

ing and removing around 3000 records about course admin-

istrations and teachers, 59,605 records remained for

analysis. These records represented the raw data which

consisted of access date and time, student names, context

(e.g. lecture materials), component (e.g. “record”), activity

description, source (e.g. “web”), and the IP address of the

student who accessed the e-course.

The data cleaning included removing information about

the activity of system administrators and teachers because

only students’ behavior in the e-learning system was inter-

esting for this analysis. In addition, due to the sensibility of

the data and privacy, only a subset of anonymized data was

extracted for further analysis. In total, there were 185 stu-

dents participating in the e-course during the semester.

There were two mid-term exams which were performed

Figure 1. Educational data mining process using cluster analysis and decision tree technique.

4 International Journal of Engineering Business Management

in April 2018 and in June the same year. Each mid-term

exam had 40 points at maximum, and there was no thresh-

old for the required minimum points. The results of the

mid-term exams were assigned for each student individu-

ally in the e-learning system.

As stated in previous research,

the following variables

were recognized as significant for cluster formation:

1. “Context” from the event logs that provides infor-

mation about the e-content type.

2. A description of the activity that relates the activity

with the unique student identification label.

Previous research aimed to find groups of students

according to their behavior in the e-learning system but

another generation. By applying the same variables on

another data set (the generation 2017/2018 in this case), the

usefulness of the context variables is tested. To further ana-

lyze and understand student behavior, this study takes a

deeper approach and applies additional decision tree tech-

nique on data.

The values of the variable “Context” were as follows:

access to lecture materials, access to auditory materials,

access to laboratory materials, and access to forums. Lec-

ture materials were available to students each week when

the teaching topic was processed. Before or after the

lectures, students were able to download the teaching mate-

rials from the e-learning system. Before auditory exercises

(AEs), students were able to download and print teaching

materials so they could easily follow the class. On average,

it took about five clicks to download each material. Labora-

tory exercises (LEs) were held in laboratory classes at a

higher education institution where students were asked to

show independency in solving the assignments. During the

class, students were required to download e-learning mate-

rials, which also required approximately five clicks. The

forums consisted of a Discussion Forum, where students

were able to ask questions about the e-course and commu-

nicate mutually, and a News Forum that contained news

related to the e-course and teacher consultations, which

were addressed by the teachers themselves.

After data cleaning, a pivot table was created, contain-

ing information about frequency of access for each student

according to his or her recorded identification label. Fre-

quency of access to the e-content shows the popularity of

the content, and the “popularity” can be measured by how

many times requests are made for the e-content during the


By the frequency of access to the e-content in

the e-course, it is possible to determine which e-content

students recognized as relevant for passing the mid-term

exams and whether the frequencies of the access influenced

the final outcome of the



So, the pivot table con-

tained student identification labels in a form of numbers

and numerical frequencies of access to materials from lec-

tures, AEs, LEs, and forums for each student. This table

was imported into RapidMiner

tool that has been used for

performing the next data mining techniques: cluster analy-

sis and decision tree. These data mining techniques were

selected because, according to the literature,

data mining

uses a more direct approach, such as the percentage usage

of well-classified data, while statistical techniques are usu-

ally used as a quality criterion for the veracity of the data

given model. Besides, data mining techniques work well

with very large amounts of data, while the statistics does

not work well in large databases with high dimensionality.

The tool settings for the cluster analysis were the applied

algorithm was k-means, the number of groups was 3

(according to testing, it was considered to be the best value

with promising results), the grouping variable was stu-

dent’s ID, the method chosen for normalization was

Z-transformation, measure types for grouping were

numerical measures, and chosen numerical measure was

Euclidean distance. Finally, the selected influential vari-

ables on grouping were frequencies of access to materials

from lectures, AEs and LEs, and forums.

The tool settings for the performance of decision tree

technique were respectively: the target variable whose out-

come was intended to be predicted is the number of stu-

dents’ points achieved in two mid-term exams where both

mid-term exams amounted to 80 points in total. Student’s

points are the variable that yields the highest information

gain. Further on, the method chosen for normalization was

Z-transformation, the criterion by which the decision trees

were created was the least square, maximal depth of the

trees was 10, minimal leaf size was 2, minimal size for split

was 4, and a number of prepruning alternatives was 3.

These settings were applied to all decision trees which

resulted from this research. The difference was in the size

of the minimal gain, and it was as follows:

� For the decision tree of the cluster number 0: 0.105.
� For the decision tree of the cluster number 1: 0.081.
� For the decision tree of the cluster number 2: 0.08.

These values were chosen considering the best resulted

branching of the trees and the acceptability of the results for

interpretation according to previously obtained clustering



The educational data mining analysis, conducted in this

research, resulted with one model by cluster analysis show-

ing groups of students according to their behavior in the e-

learning system and three models of decision tree made

according to previously conducted cluster analysis. The

following section describes the results of the grouping anal-

ysis and decision tree. In addition, a box plot diagram made

by points of the students from the mid-term exams is pre-

sented to show the verification of gained models by stu-

dent’s success.

Križanić 5

Interpretation of the grouping results

The aim of grouping the students was to find groups of

students who were similar to each other within the group

and different in respect to the other groups. The similarity

depends on the behavior of the students in an e-learning

system during the semester. Behavioral intention is an

important predictor of student behavior that varies between

different behavioral, control, and normative beliefs on the

desired behavior.

The application of the k-means method

over the data which contained information about 185 stu-

dents in one e-course, at a higher education institution,

resulted with the following three groups:

� Group 0 contained 84 students.
� Group 1 contained 82 students.
� Group 2 contained 19 students.

Figure 2 represents the groups of the students in a form

of a tree, while Figure 3 represents the plot with the move-

ments of the value of the variable “Context” according to

the range of the centroid values.

Figure 2 shows the groups of students in a form of a tree.

According to Table 1, which is a centroid table, group 0

contains the students who had the lowest access to the

content in the e-course. This group shows weekly down-

loading activity of materials from LEs and lectures. Group

1 contains students who had a medium frequency of access

to e-content. They mostly accessed materials from LEs and

lectures. The least accessed set of materials for this group is

related to forums. In group 2, there are 19 students who had

a high frequency of access to materials from AEs, lectures,

and LEs. Figure 3 represents a plot diagram showing the

movement of groups by the value of the variable “Context”

and the range of the centroid values. According to this

analysis, group 0 contains the students with the lowest

frequency of access to the content in the e-course, and

group 2 contains the students with the highest frequency

of access to materials from the e-learning system.

Interpretation of the results obtained by
the decision tree technique

After conducting a cluster analysis, which resulted with one

model showing three groups of students, three decision

trees were created based on these groups. Each decision

tree model represents the behavior of one group of the

students. Figure 4 represents the decision tree demonstrat-

ing the behavior of the students from group 0, Figure 5

represents the behavior of the students from group 1, and

finally, Figure 6 represents the decision tree showing the

behavior of the students from group 2. The variable that

gives the highest information gain is the student’s points

from the mid-term exams. The nodes represent the contents

of the e-course or the value of the variable “Context,” and

the values on the arcs represent the frequencies of access to

the e-contents.

Figure 4 represents the decision tree model for group 0

from the grouping method. The model shows that there

were only a few students for whom the highest frequency

of access to materials from lectures meant the highest fre-

quency of access to other e-contents. Many students in this

group had low frequency of access to lecture materials.

However, those students who attended the lecture materials

mostly accessed the forums. Frequent access to forums did

not mean frequent access to other e-contents. Low access to

forums also led to low access to materials from AEs. Low

access to materials from AEs also led to low access to

materials from LEs. Students with greater points in mid-

term exams combined frequent access to materials from

lectures with frequent access to materials from LEs.

The model from Figure 5 represents the decision tree for

group 1 by cluster analysis. The more often students

accessed materials from lectures, the more they accessed

forums. Low frequency of access to lecture materials

resulted with poor results in the mid-term exams. There

were many students in this group who mostly applied the

combination of accessing lecture materials and materials

from AEs. Students in this group with the highest number

of points in mid-term exams seemed to recognize the

importance of accessing the combination of materials from

lectures, AEs, and LEs. The more often they accessed lec-

ture materials and materials from AEs, the more likely they

were to score better points in the mid-term exams. Unlike

group 0, group 1 consisted mostly of students who had

medium frequency of access to all e-contents.

Finally, the third decision tree model in Figure 6 repre-

sents the behavior of the students from group 2. This group

was the smallest and contained 19 students who had the

highest frequency of access to the contents from the e-

learning system. According to Figure 6, low frequency of

access to materials from AEs and LEs indicated lower score

on the mid-term exams. Higher frequency of access to

Figure 2. Groups of students.

6 International Journal of Engineering Business Management

materials from LEs and AEs, as well as more frequent

retrieval of lecture materials, provided better points at the

mid-term exams. Many students in this group combined all

of these three elements and they achieved very good results

at the mid-term exams.

This analysis indicates that, from the teacher perspec-

tive, content management in the form of focusing on the

quality of theory-oriented materials is crucial due to the

fact that, without a well-presented theoretical background,

students cannot successfully complete the course.

Analysis of students’ achievement through
mid-term exams

There were two mid-term exams in the e-course through

which the students could pass the exam. Each mid-term

exam contained a maximum of 40 points. The mid-term

exams included two types of questions: theory oriented

(mainly from lecture materials) and practical assignments

(mainly from materials from AEs and LEs).

No minimum

number of points from the first mid-term exam was

required to access the second mid-term exam. Figure 7

represents the points from both exams in total for all the

students in the e-course. Cluster 0 represents the points of

those students who by cluster analysis on Figure 2 in this

article belong to group 0. Cluster 1 contains the points from

the exams of those students who by cluster analysis on

Figure 2 belong to group 1. Finally, cluster 2 demonstrates

the points from those students who by cluster analysis

belong to group 2. As can be seen from Figure 7, cluster

0 contains the points of the students whose behavior can be

described as the one with the least attention to downloading

learning materials continuously from the e-learning system.

Besides, the students in this group gained the lowest points

at the mid-term exams. Cluster 1 contains the points of the

students who had medium frequency of access to e-learning

materials, and their points vary. Some students achieved

low points (e.g. less than 10 of 80), and some achieved a

high number of points (e.g. more than 70). Cluster 2 con-

tains the points of the students who had the highest fre-

quency of access to the e-learning materials. These points

are globally the highest points in the e-course. According to

the data on created groups and the most accessed contents

by these groups, the content-related variable of behavior

that makes the difference between the points achieved by

the students is found in the behavior of accessing the lec-

ture materials. Students who accessed materials from the

lectures more often achieved better results at the mid-term



In this article, educational data mining field was explored.

This field became very popular in recent years due to the

Figure 3. Movements of the groups according to “Context.”

Table 1. Centroid table.

The value of the
variable “Context” Group 0 Group 1 Group 2

Lectures materials �0.723 0.385 1.536
Auditory exercises �0.675 0.223 2.020
Laboratory exercises �0.784 0.451 1.522
Forums �0.440 0.115 1.449

Križanić 7

emergence of big data stored in databases containing

records about students’ behavior in e-courses of higher

education institutions. The quality of study programs is

very important due to the competition between the higher

education institutions and because of the knowledge stu-

dents bring with them to the job market after graduation.

Educational data mining is a part of data mining field and

therefore cluster analysis and decision tree technique have

been applied in the research conducted in this article. The

cluster analysis resulted with groups of students according

to the frequencies of access to the e-contents, confirming

author’s previous research. The decision tree technique was

applied to the grouping results to enable a deeper analysis

Figure 4. Decision tree for group 0 from the cluster analysis.

Figure 5. Decision tree for group 1 from the cluster analysis.

Figure 6. Decision tree for group 2 from the cluster analysis.

Figure 7. The points of the students from the mid-term exams by
the groups they belong.

8 International Journal of Engineering Business Management

of student behavior in teaching and learning processes.

Based on the knowledge acquired by educational data min-

ing, course teachers can identify the content of the e-course

that is worth putting more attention to emphasize its impor-

tance and select more suitable motivating techniques to

encourage students to use that content while preparing for

the exams. The following research could focus on collect-

ing data from other generations and conducting similar

analysis on other courses with similar process scenarios for

the purpose of revealing differences between the behaviors

of students’ generations or differences that are related to

course management.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with

respect to the research, authorship, and/or publication of this



The author(s) received no financial support for the research,

authorship, and/or publication of this article.


Snježana Križanić


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Križanić 9

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