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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Case Studies and Education in Data Science At Universities in Slovakia</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>L'ubomír Antoni</string-name>
          <email>lubomir.antoni@upjs.sk</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Erik Bruoth</string-name>
          <email>erik.bruoth@upjs.sk</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ján Guniš</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Peter Gurský</string-name>
          <email>peter.gursky@upjs.sk</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Stanislav Krajcˇi</string-name>
          <email>stanislav.krajci@upjs.sk</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ondrej Krídlo</string-name>
          <email>ondrej.kridlo@upjs.sk</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Radim Navrátil</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>L'ubomír Šnajder</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Gabriela Andrejková</string-name>
          <email>gabriela.andrejkova@upjs.sk</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Dušan Šveda</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Mathematics and Statistics, Faculty of Science, Masaryk University in Brno</institution>
          ,
          <country country="CZ">Czech Republic</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Institute of Computer Science, Faculty of Science, Pavol Jozef Šafárik University in Košice</institution>
          ,
          <addr-line>Jesenná 5, 040 01 Košice</addr-line>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Institute of Mathematics, Faculty of Science, Pavol Jozef Šafárik University in Košice</institution>
          ,
          <addr-line>Jesenná 5, 040 01 Košice</addr-line>
        </aff>
      </contrib-group>
      <abstract>
        <p>Data analysis solutions are already being used in many areas of technical, natural, humanitarian and economic sciences. The information hidden within data can help to solve the many pending issues within community, enterprise or science. Turning of data into knowledge and wisdom is beneficial and necessary. Moreover, students with knowledge of Data Science have the potential to be highly desirable in the labor market. We present the selected case studies in Data Science Area. We bring a review of Data Science subjects that are introduced and innovated at universities in Slovakia within the IT Academy Project.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1 Introduction</title>
      <p>
        The term "science" implies knowledge gained through
systematic study. In one definition, it is a systematic
enterprise that builds and organizes knowledge in the form of
testable explanations and predictions. Data science might
therefore imply a focus involving data and, by extension,
statistics, or the systematic study of the organization,
properties, and analysis of data and its role in inference,
including our confidence in the inference [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ].
      </p>
      <p>
        The huge amount of data and the need for
decisionmaking imply the demand for data analysis and
professionals for data processing. This issue is highly relevant,
data analysis solutions are already being used in many
areas of technical, natural, humanitarian and economic
science. Moreover, data analysis experts are already scarce,
and students with knowledge of Data Science have the
potential to be highly desirable in the labor market. In
developing and addressing this area, it is necessary to address
the amount of available data that is regularly generated by
many commercial devices and scientific instruments, and
the available methods of their analysis, which allow them
to discover new knowledge. The aim of is to extract new,
valid and potentially useful knowledge from available data
in various areas of academic and corporate life.
Completing objectives and knowledge itself leads to several phases
in which it is necessary to distinguish the phase of data
comprehension, data preparation, modeling, evaluation of
results and putting results into practice [
        <xref ref-type="bibr" rid="ref1 ref2 ref3 ref4">1, 2, 3, 4</xref>
        ].
      </p>
      <p>Section 2 describes classification tasks in general.
Section 3 provides a basic overview of university subjects at
the five partner universities of the IT Academy Project in
the area of Data Science, including classification tasks. In
Section 4, we present the analysis of the educational tasks
and objectives of five real teachers giving lessons in
computer science.
2</p>
    </sec>
    <sec id="sec-2">
      <title>Classification tasks</title>
      <p>
        Data Science is an interdisciplinary area that uses
scientific methods, processes, algorithms, and systems to
acquire knowledge and insights from data in various forms,
both structured and unstructured. It introduces the concept
of data unification, data analysis, machine learning and
related methods to analyze current data processes. Data
Science uses techniques and practices from the fields of
mathematics, statistics, or informatics [
        <xref ref-type="bibr" rid="ref1 ref2 ref3 ref4">1-4</xref>
        ].
      </p>
      <p>In the past, computers were used to process numerical
data. In recent decades, representation in the form of
relational data has also been promoted, because it allows the
relationship between the instances of objects to be
examined in a much wider dimension. Moreover, the
knowledges found in the data helps to solve many issues related
to science, business or society. Permanent modification
of input data into forms of knowledge and knowledge is
therefore beneficial and necessary. The data are obviously
in a tabular form, and we can obtain this form of data by
recording the results of doctor’s examinations, customer
behavior and consumer habits, or recording the results of
the students.</p>
      <p>
        Data classification is a two-step process, consisting of a
learning step (where a classification model is constructed)
and a classification step (where the model is used to predict
class labels for given data) [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ].
      </p>
      <p>In the first step, a model is created that describes a set
of data classes. The model is constructed based on the
analysis of input objects (called also examples, instances,
data points or samples) described by attributes. This is
the learning step (or training phase), where a classification
algorithm builds the classifier by analyzing or “learning
from” a training set made up of database tuples and their
associated class labels. A tuple, X , is represented by an
ndimensional attribute vector, X = (x1; x2; : : : ; xn),
depicting n measurements made on the tuple from n database
attributes, respectively, A1; A2; : : : ; An. Each tuple, X , is
assumed to belong to a predefined class as determined by
another database attribute called the class label attribute.</p>
      <p>
        Because the class label of each training tuple is
provided, this step is also known as supervised learning (i.e.,
the learning of the classifier is “supervised” in that it is
told to which class each training tuple belongs). It
contrasts with unsupervised learning (or clustering), in which
the class label of each training tuple is not known, and the
number or set of classes to be learned may not be known
in advance. The learned model can be represented in the
form of classification rules, decision trees, or a
mathematical formula. For example, for database of customer
credit information, classification rules can be used to
identify customers with excellent or fair credit ratings. In the
second step, the model is used for classification of the new
objects [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ].
      </p>
      <p>
        Data prediction can be viewed as the construction of a
model to assess the class of an unlabeled sample, or to
assess the value of a target attribute that a given object is
likely to have. In this view, classification and regression
are two major types of prediction problems, where
classification is used to predict discrete or nominal values, while
regression is used to predict continuous or ordered values.
In another view, data prediction differs from the
classification of data by the fact that the class label variable can
acquire continuous values [
        <xref ref-type="bibr" rid="ref1 ref2 ref3 ref4">1, 2, 3, 4</xref>
        ].
      </p>
      <p>
        Classification and prediction have numerous
applications including credit approval, performance prediction,
medical diagnosis, selective marketing, prediction of
water consumption in a given territory, prediction of user
rating of films, recommended systems [
        <xref ref-type="bibr" rid="ref1 ref2 ref3 ref4">1, 2, 3, 4</xref>
        ].
      </p>
    </sec>
    <sec id="sec-3">
      <title>3 Innovation of Data Science University</title>
    </sec>
    <sec id="sec-4">
      <title>Subjects</title>
      <p>As part of the IT Academy Project, the preparing of new
subjects and innovating of existing study materials are
aimed in the area of Data Science. In addition to the
presented tasks of classification, prediction and evaluation of
their accuracy, many of the other topics at the university
subjects are part of this attractive area. A basic overview
of these topics at the five partner universities of the IT
Academy Project is presented in the following.</p>
      <sec id="sec-4-1">
        <title>Case studies in data mining</title>
        <p>(Pavol Jozef Šafárik University in Košice)
The course is designed to deal with prepared case studies
using data mining methods, which is an interdisciplinary
topic and covers knowledge from a variety of disciplines,
such as mathematics, statistics, and various specific areas
of informatics. The course will introduce methods for
automated analysis of large volumes of data and extraction of
knowledge from these data. The course is aimed at
solving practical problems in the area of graphing using the
presented methods and using appropriate software tools.
R-project as a computing environment, Programming in R:
data structures, graphics, applied mathematics, data
analysis. Java libraries for data-mining, their use. Testing
data mining algorithms. Dissemination of data-mining
libraries. Solution of practical examples. Solutions for
application projects.</p>
      </sec>
      <sec id="sec-4-2">
        <title>Machine learning</title>
        <p>(Pavol Jozef Šafárik University in Košice)
The course is focused on modeling and algorithmization of
the learning processes of computer systems from data sets,
the result of learning being objects that take into account
input data sets. This modeling is based on the needs of
many areas of human activity (biomedical informatics,
expert systems creation, robot construction, speech and text
processing, predictions of some events, etc.). The basis for
this modeling is the knowledge of linear regression,
gradient methods of regression and classification, Bayesian
learning, clustering, decision trees, hidden Markov
models, but also the theoretical knowledge about probabilistic
approximation learning and the Vapnik-Cervonenkis
dimension. Data Pattern Search, Advanced Classification
Methods, and Prediction Methods.</p>
      </sec>
      <sec id="sec-4-3">
        <title>Large data processing technologies</title>
        <p>(Technical University in Košice)
Upon completion of the course the student will acquire
basic knowledge of large data processing, methods,
approaches and technologies used in this area. From a
theoretical point of view the student will gain knowledge about
grid and cloud computing concepts, distributed, NoSQL
and in-memory database systems, parallel and distributed
computing methods. The student will also acquire basic
skills for designing and implementing large data
processing applications.</p>
      </sec>
      <sec id="sec-4-4">
        <title>Knowledge discovery</title>
        <p>(Technical University in Košice)
Basic concepts of knowledge discovery and mining in
data. Knowledge Discovery Process, CRISP-DM
methodology, step-by-step description. Data Mining Methods
Predictive and Descriptive Mining in Data. Disclosure of
association rules, generalization, classification, prediction,
clustering. Data warehouses. Overview of selected
methods for discovering knowledge. Mining knowledge from
text document collections. Selected case studies from
research and development projects. Logical and physical
data warehouse model. Temporary and operational data
repositories. Searching patterns in data.</p>
      </sec>
      <sec id="sec-4-5">
        <title>Business Analyst</title>
        <p>(Technical University in Košice)
Business analyst extensively uses data and advanced
statistical methods to optimize individual areas and business
processes. The course focuses on knowledge, technology,
applications and methods for continuously exploring the
company’s historical performance with a view to deeper
understanding and management of business planning.
Rproject as a computing environment, programming in R:
data structures, graphics, applied mathematics, data
analysis. Practical examples.</p>
      </sec>
      <sec id="sec-4-6">
        <title>NoSQL databases</title>
        <p>(Pavol Jozef Šafárik University in Košice)
The course introduces different ways of storing and
working with large data. It compares the basic types of NoSQL
databases - DB type key-value, document DB, column DB
and graph DB as well as practical examples of work with
selected representatives of individual types. The different
types of data representations with which these databases
work are presented. The course focuses not only on the
use of NoSQL databases, but also on their architecture,
parallel, distributed and transactional processing.</p>
      </sec>
      <sec id="sec-4-7">
        <title>Programming, algorithms, complexity</title>
        <p>(Pavol Jozef Šafárik University in Košice)
The subject uses the more incoherent programming course
that is based on the "OO-first" approach (equally starting
with object-oriented programming). An important element
is the visualization and use of metaphors in conjunction
with the graphics implemented by the JPAZ2 framework.
In the second part of the semester, a systematic
interpretation with an emphasis on a good object design takes
place. The course is focused on the ability to implement
programs in the Java programming language, basic
knowledge about the principles of object-oriented programming.</p>
      </sec>
      <sec id="sec-4-8">
        <title>Basics of knowledge systems</title>
        <p>(Pavol Jozef Šafárik University in Košice)
The aim of the course is to apply advanced logic courses
to computer science, especially in database and knowledge
systems. The subject of the subject is procedural
semantics of logic programming, declarative semantics of logic
programming and its correctness, relationship of relational
database models and logic programming.</p>
      </sec>
      <sec id="sec-4-9">
        <title>Data mining</title>
        <p>(Constantine the Philosopher University in Nitra)
The aim of the course is to acquaint students with
computer data analysis and possibilities of application of
selected analytical methods in IT. Through examples and
case studies, students will get acquainted with selected
data analysis methods and their applications to address
specific issues. Case studies are focused on the
evaluation of information technologies and information systems,
specifically mediating the methodology of evaluation of
user interfaces, systems and processes. Logical and
physical data warehouse model. Temporary and operational
data repositories. Data warehouses.</p>
      </sec>
      <sec id="sec-4-10">
        <title>Educational data mining</title>
        <p>(Constantine the Philosopher University in Nitra)
The aim of the course is to acquaint students with
computer data analysis and possibilities of application of
selected analytical methods in IT. Through examples and
case studies, students will get acquainted with selected
data analysis methods and their applications to address
specific issues. Case studies are focused on the
evaluation of information technologies and information systems,
specifically mediating the methodology of evaluation of
user interfaces, systems and processes. Logical and
physical data warehouse model. Temporary and operational
data repositories. Data Warehouses. Educational Data
Mining (EDM) can be characterized as a research area
that develops new techniques and methods, testing new
approaches to learning, looking for user behavior patterns
of unstructured and structured data that have been created
by interaction between different types of users in a
particular virtual learning environment, educational software,
an intelligent or adaptive learning system, or a specialized
software for testing. Learning Analytics (LA) is a related
research area that aims to support decision-making
processes at the various levels of management of an
educational organization. The objective of the course in terms
of learning outcomes and competences. The aim of the
subject is to introduce the students to the above mentioned
problems, to familiarize them with the current trends in
the field of EDM and learning analytics research and to
present in practical examples the data mining methods in
the area of management of the educational organization.
Searching patterns in data. Solution of practical examples.</p>
      </sec>
      <sec id="sec-4-11">
        <title>Web content mining</title>
        <p>(Constantine the Philosopher University in Nitra)
The aim of the course is to acquaint students with
computer data analysis and possibilities of application of
selected analytical methods in IT. Through examples and
case studies, students will get acquainted with selected
data analysis methods and their applications to address
specific issues. Case studies are focused on the
evaluation of information technologies and information systems,
specifically mediating the methodology of evaluation of
user interfaces, systems and processes. Logical and
physical data warehouse model. Temporary and operational
data repositories. Data Warehouses. The aim of the course
is also to familiarize students with the process of
discovering knowledge from the content of the web.
Emphasis is placed not only on text mining but also on
acquiring knowledge from multimedia, searching information
in document content and extracting information from text
documents. Topics related to machine translation,
natural language processing and morphological analysis of the
language will be included.</p>
      </sec>
      <sec id="sec-4-12">
        <title>Neural Networks</title>
        <p>(Constantine the Philosopher University in Nitra)
Neural networks represent a bio-inspired approach to
intelligent information processing computational
algorithms. Recognition of knowledge in memory,
interpretation of input data, knowledge relations, generalization,
decision making, etc. spontaneously appear as a result of
the massive parallel interaction of a large number of
relatively simple calculation elements. From a content point
of view, the subject deals with topics such as: introduction
to neural networks, Binary perceptron, Backpropagation,
Reinforcement learning, Recurrent neural networks, their
training and application, Self-organization.</p>
      </sec>
      <sec id="sec-4-13">
        <title>Algorithms of numerical mathematics and optimization</title>
        <p>(Constantine the Philosopher University in Nitra)
The course provides an introduction to the basic methods
of numerical mathematics and optimization. It is based on
four aspects: mathematical basics of numerical analysis
and optimization, algorithmization, programming of
algorithms in MATLAB and algorithm visualization. From a
content point of view, the subject is focused on numerical
methods of algebra, numerical methods of mathematical
analysis and optimization methods, singleparametric
optimization methods, multiparametric optimization without
borders, least squares, and multiparametric optimization
with boundaries.</p>
      </sec>
      <sec id="sec-4-14">
        <title>Programming in Java</title>
        <p>(Matej Bel University in Banská Bystrica)
Program paradigms. Java programming language. JVM.
Encapsulation. Class declaration. Instances of classes
objects. Constructor. Access rights and scope in class.
Static attributes and methods. Heredity. Exceptions.
Abstract classes. Polymorphism. Interface. Modularisation,
abstraction, bonding, cohesion. Choice from JavaAPI.
Dynamic data structures. Streams of data. Solution of
practical tasks.</p>
      </sec>
      <sec id="sec-4-15">
        <title>Business Intelligence</title>
        <p>(Matej Bel University in Banská Bystrica)
Business Intelligence (BI) and BI type projects - focus,
reason, goal. Repetition of necessary knowledge and skills
from database systems, software systems and modeling of
data structures. OLTP vs. OLAP. Data warehouses, data
warehouse development, OLAP analysis, data mining
(architecture, metadata, implementation, ETL, OLAP, MDX,
reports). Waterfall model working on BI project. Agile
methods of working on BI project. Processing of input
information from the customer. Forms of offers (customer
response) for the customer. Project manager role in the
BI project. The activity of the project architect, his
competence and the relevant documentation. Data Architect
and its activity in the project. ETL developer work. Types
of inputs provided to customers. Work Report developer.
Participation in the project of individual actors as a
function of time. Output forms for the customer. Active work
with the customer. Logical and physical data warehouse
model. Temporary and operational data repositories. Data
warehouses. Searching patterns in data. Solution of
practical examples.</p>
      </sec>
      <sec id="sec-4-16">
        <title>Algorithms and Data Structures</title>
        <p>(University of Žilina)
Students will acquire basic knowledge of the theory of
data structures and will learn how to implement them
effectively. Upon completion of the course, the student is
familiar with the basic data structures and is able to use
them in solving practical problems, controls the process of
effective implementation of basic data structures.</p>
      </sec>
      <sec id="sec-4-17">
        <title>Statistics for practice Advanced statistical methods</title>
      </sec>
      <sec id="sec-4-18">
        <title>Fundamentals of numerical methods</title>
        <p>(Pavol Jozef Šafárik University in Košice)
The aim is to provide students with the theoretical
knowledge and practical skills needed to process real data and
create their mathematical models using multipurpose
computer algebra systems, respectively. Dedicated software
for addressing specific category issues.
4</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>Educational tasks analysis</title>
      <p>
        The study of structures and mappings which allow to
analyze the data in various forms is a challenging task.
In this way, the first attempts to interpret the lattice
theory as concretely as possible and to promote the better
communication between lattice theorists and potential
users of lattice theory represent the inception for data
analysis taking into account the binary relations on the
objects and attributes sets. Since the concept hierarchies
play an important role here, the term of formal concept
analysis has been adopted for this reasoning. Briefly,
formal concept analysis scrutinizes an object-attribute
block of relational data in bivalent form [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]. Formal
concept analysis allows us to explore the meaningful
groupings of educational tasks (referred to objects) with
respect to common objectives (referred to attributes) and
it provides the visualization capabilities. The conceptual
difficulties in mathematics education [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ], or the
integrated care pathways [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] are analyzed by formal concept
analysis, as well. An extensive overview of the various
application domains that include software mining, web
analytics, medicine, biology and chemistry data is given
by [
        <xref ref-type="bibr" rid="ref8 ref9">8, 9</xref>
        ]. The statements that people use to communicate
facts about the world are usually not bivalent. The truth
of such statements is a matter of degree, rather than being
only true or false. Fuzzy logic and fuzzy set theory are
frameworks which extend formal concept analysis in
various independent ways. In [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ], our aim was to provide
the system of objectives and tasks that is expected to fill
in the gap of the National Education Program in Slovak
Republic. In general, the National Education Program is
formulated concisely and we put emphasis on a long term
to particularize other supplementary curricular documents
and express the educational objectives more explicit in
various areas. Therefore, we have focused on an
algorithmic thinking area and chosen an array data structure
as an educational content in which we have fruitfully
applied formal concept analysis. Simultaneously in this
area, we focus on algorithms including searching, sorting
or text processing. Particularly, we have investigated
the educational tasks and objectives of five real teachers
giving lessons in computer science. We aim at specifying
the particular and relatively precise objectives of an array
data structure education in the algorithmic thinking area.
Regarding our long-term cooperation with the teachers in
the field, we declare some input set of objectives of an
array data structure:
1) to specify an array as the structured homogeneous
data type with elements denoted by a single
identifier,
2) to appoint the real examples of one-dimensional array
data structure (e.g. rooms in a hotel, seats in a plane,
etc.),
3) to interpret the notions of an array index (an array
key) and an array element and to explain the
difference between them,
4) to distinguish an array index type and an array
element type,
5) to reason that an array index type is an ordinal type
(numbers, characters, other enumerations),
6) to declare a variable of array,
7) to read and to write out the array elements,
8) to manipulate the array elements, to assign the array
element to the other variables, to increment the array
elements,
9) to appoint the common errors related to an array data
structure (incorrect index type, overflow,
incompatibility of the types),
10) to apply an array data structure in the simple issues
(e.g. to store an array, to find the maximal value, to
modify the elements of array, etc.),
11a) to apply an array data structure in searching,
11b) to apply an array data structure in sorting,
11c) to multiply access to the array elements,
11d) to apply an array data structure in a text processing,
11e) to apply an array data structure in a simple game
programming,
12) to recognize the issues in which array data structure
can be applied effectively, to appoint the advantages
and disadvantages of an array in comparison with
other simple data structures (an access to elements,
a space complexity).
      </p>
      <p>The specified aims are enumerated by the revised
taxonomy of Bloom in order to classify statements of what
we expect or intend students to learn as a result of
education. The revised taxonomy focuses on four knowledge
dimensions including factual knowledge (basic elements),
conceptual knowledge (interrelationships among the basic
elements), procedural knowledge (how to do something)
and metacognitive knowledge (awareness and knowledge
of one’s own cognition). In general, an educational
process consists of a motivation phase, a phase of the first
acquisition, a fixation phase and a diagnostic phase. The
phase of a systematization, a propedeutics or an
application phase can be also involved.</p>
      <p>We submitted the previous list of aims to the teachers
in the secondary schools in Slovakia. The teachers were
instructed to appoint the tasks which they usually apply in
an educational process of an array data structure in
programming. Teachers were not limited by the number of
tasks and moreover, it was possible to add some additional
aims. Regarding five teachers data and one additional set
of 10 tasks proposed by two of the authors, we have
analyzed 102 tasks and 23 educational aims obtained in this
research. We have generated the summary concept lattice
and found the following observations:
45 tasks (the first row in the summary concept lattice)
are the representatives; i.e. every task includes the
unique set of aims and there is no task that introduces
the superset of these aims,
5 tasks (from 45 representatives) are such that
every task includes the unique set of aims and there is
no task that introduces neither superset nor subset of
these aims,
3 aims (the first row in the summary concept lattice)
are unique, i.e. the aim is introduced only by one
task. In effort to prepare the graduated sets of tasks,
we have explored the longest paths extracted from the
summary concept lattice with reduced labeling of all
102 tasks. The longest path is shown in Fig. 2. Every
path contains the graduated system of tasks
depending on the final task we want to achieve in conclusion.
The object label, for instance 3.5, corresponds to the
fifth task of third teacher. The set of tasks labeled 6.1
- 6.10 comes from the authors.</p>
      <p>The longest path illustrates that if a student has a
problem with Task6.5, we ask him/her to solve Task3.12.
Moreover, if we have found that a student has a problem
with Aim6 in Task6.5, we give him/her to fixation one task
(or more) from the node which contains the set of equal
tasks Task1.3, Task1.4, Task1.5, Task1.8. In contrary, if
a student has no problem with Task6.5, we suppose that
he/she will pass also the Task3.12. There is only one path
including seven task nodes, however paths with six nodes
appear in the summary concept lattice several times.</p>
      <p>Moreover, we present some interesting educational
tasks which appear in the summary concept lattice mostly
in the first row and one can advise them to apply in the
educational process related to an array data structure. The
formulations are shortened in comparison with the original
texts.</p>
      <p>Propose the way how to denote the parking places in
front of a hotel. How are the train carriages
enumerated? How would you denote the overall and final
results of six teams in the television knowledge
contest?
We have observed GPS data containing ten altitudes
on our tourist route. Write a program to print out the
altitudes on a reverse route.</p>
      <p>Imagine that you have received SMS from your
friend. Write a program to count the number of words
in your text message.</p>
      <p>A musical instrument, like a piano, can be simulated
by a computer program. Some of the keys will have
assigned a particular tone frequency. Write a program
to play a tone when the particular key is pressed.
Consider the starting sequence of children’s names
and the final shift of Ferris wheel as the input. Write a
program to make a list of the children names in the
sequence in which they will get out of the Ferris wheel.
Write a program to generate twelve random values
expressing the number of your website visits in a
particular month. Draw a histogram, highlight the
maximum and minimum and show an average value as a
horizontal line.</p>
      <p>We have fruitfully applied formal concept analysis as a
powerful tool in a simultaneous analysis that involves the
teaching of programming skills in an open-source web
application App Inventor 2. The tutorial website1 provides
materials in the form of learning cards for building the
basic applications, but one of the authors of this paper has
prepared the set of ten complex educational tasks which
in summary cover 129 elements (components and their
elements, event handlers, call, set instructions, get
instructions, data structures, etc.) available at the present time.
The added value includes the proposal of the introductory
set of complex tasks and its further modification in effort
to teach and learn the different target groups. The talented
lower secondary school’s pupils participate in our optional
university courses and the teachers of secondary schools
attend the didactic workshops at our university. Our
results are concerned with the inclusion of the programming
language elements (available at the App Inventor website
at present) in the complex educational tasks and the effort
to extract the appropriate tasks for the different types of an
educational process. The formal context contains 10 tasks
as the set objects and 129 App Inventor programming
elements as the set of attributes.</p>
      <p>Exploring own attributes, the resulting concept lattice
and its attribute labels give information about the elements
introduced uniquely by a particular task. As conclusion,
we recommend the following methodology:
a task with a high ratio of the own elements and the
low total number of elements is advised to use in a
first acquisition phase of education,
in a fixation phase, we recommend a task with a low
ratio of the own elements and the low total number of
elements,
a task with a low ratio of the own elements and the
high total number of elements is suggested in a
systematization or diagnostic educational phase,
a task with a high ratio of the own elements and the
high total number of elements is the least appropriate
for an educational process, because it brings many
new elements without their introduction in a more
simple task.
1http://www.appinventor.org/
Data can be viewed simply as the observations, entities
or values which are collected in effort to form
information. To ensure the readability, data used to be converted
into tables and graphs. Table data appear frequently and
they can be observed either directly from the medical test
results, the customer habits, the scores of students or by
the various transformations from the other forms, for
instance, from database tables or questionnaires. The
information hidden within data can help to solve the many
pending issues within community, enterprise or science.
Turning of data into knowledge and wisdom is beneficial
and necessary, considering either the simple computing
in the spreadsheet calculators or various methods of data
analysis which are more complex. Data collecting,
preprocessing, reduction, visualization, dependencies
exploration and providing the metadata are important parts of
the scientific research, as well.</p>
      <p>Our ability to generate and collect data has increased
rapidly in recent decades. This has prompted the need for
new techniques and automated tools to help transform a
large amount of data into useful information and
knowledge. In other words, for the present time it is
characteristic that we are rich in data, but poor in information.</p>
    </sec>
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