=Paper=
{{Paper
|id=Vol-2643/paper10
|storemode=property
|title=The students' brainwork intensification via the computer visualization of study materials
|pdfUrl=https://ceur-ws.org/Vol-2643/paper10.pdf
|volume=Vol-2643
|authors=Halyna I. Ivanova,Olena O. Lavrentieva,Larysa F. Eivas,Iuliia O. Zenkovych,Aleksandr D. Uchitel
|dblpUrl=https://dblp.org/rec/conf/cte/IvanovaLEZU19
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==The students' brainwork intensification via the computer visualization of study materials==
https://ceur-ws.org/Vol-2643/paper10.pdf
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The students’ brainwork intensification via the computer
visualization of study materials
Halyna I. Ivanova1[0000-0001-6432-2154], Olena O. Lavrentieva1[0000-0002-0609-5894],
Larysa F. Eivas1[0000-0001-6718-8464], Iuliia O. Zenkovych1[0000-0002-0996-6384] and
Aleksandr D. Uchitel2[0000-0002-9969-0149]
1 Kryvyi Rih State Pedagogical University, 54 Gagarin Ave., Kryvyi Rih, 50086, Ukraine
galina.ivanova.2308@gmail.com
2 State University of Economics and Technology,
5 Stepana Tilhy Str., Kryvyi Rih, 50006, Ukraine
o.d.uchitel@i.ua
Abstract. The paper the approaches to the intensification of the students’
brainwork by means of computer visualization of study material have been
disclosed. In general, the content of students’ brainwork has been presented as a
type of activity providing the cognitive process, mastering the techniques and
ways of thinking, developing the capabilities and abilities of the individual, the
product of which is a certain form of information, as a result of the brainwork the
outlook of the subject of work is enriched. It is shown the visualization is the
process of presenting data in the form of an image with the aim of maximum ease
of understanding; the giving process of visual form to any mental object. In the
paper the content, techniques, methods and software for creating visualization
tools for study material has exposed. The essence and computer tools for creating
such types of visualization of educational material like mind maps, supporting
notes and infographics have been illustrated; they have been concretized from the
point of view of application in the course of studying the mathematical sciences.
It is proved the use of visualization tools for study materials helps to increase the
intensity and effectiveness of students’ brainwork. Based on the results of an
empirical study, it has been concluded the visualization of study materials
contributes to the formation of students’ key intellectual competencies and
forming their brainwork culture.
Keywords: brainwork, intensification, visualization of study materials,
computer visualization tools, mind map, infographics, supportive notes.
1 Introduction
The global informatization of society, transformation the Internet into a world
repository of any information has substantially influenced the content of the educational
process, methods and techniques of students’ brainwork.
Thanks to the free access to the massif knowledge, there is no need for the traditional
information accumulation because of its rapid aging and avalanching growth.
___________________
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0).
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Therefore, the content of higher education should gradually change its direction,
envisage measures to intensify the educational process, facilitate the formation of
students stable processing skills and the use of constantly changing information in
practice. Due to this fact, higher education should use special mechanisms that will
reduce the emotional load on the central nervous system of both students and lecturers,
and at the same time promote the intensification of students’ brainwork. All these needs
increasing the overall lecturers’ teaching skills, as well as professionalization of
education at the level of time’s requirements.
It is the intensive teaching methods combining modern advances in scientific and
technological progress in the form of automated systems and learning technologies that
can be attributed to attempts to search in this direction. The most promising areas in
this context are computerization and informatization [19], which provide increase the
students’ mental activities, and ultimately, the quality and continuity of higher
education, mobility and competitiveness of graduates.
The purpose of this research is discovering and investigate the mechanisms of the
students’ brainwork intensification in the course of teaching mathematical sciences;
studying the possibilities and check the effectiveness of the use of computer
visualization tools in this process.
2 Materials and methods
In this paper we use methods of analysis and systematization of pedagogical and
psychological literature, works of domestic authors, methodological materials in order
to determine the conceptual and categorical apparatus of the research.
In general, the various aspects of the students’ brainwork have been studied by
Dmitrii N. Bogoiavlenskii [8], Boris P. Esipov [18], Petr Ia. Galperin [20], Valentyna
M. Grineva [23], Yuliia S. Ibrahim [25], Nina V. Kuzmina [31], Nina F. Talyzina [59],
Simon L. Soloveychik [56] and others. Scientists’ investigations clarify the sense of
culture and hygiene of brainwork, offer valuable ideas and recommendations on how
to learn more quickly, how clearly comprehend and memorize of training material, how
to work through and learn it, how to check the quality of mastered one. Separate
attention scientists paired to those aspects of the researches revealing the
psychophysiology of brainwork, to an analysis of the mechanisms of forming the
mental activity’s techniques, a rational organization and management of students’
brainwork, and a reading culture, the methods of independent work with the educational
book, etc. [43].
The intensification of brainwork is defined as the phenomenon of increasing its
productivity in each unit of time. In view of this significant interest is the works of Iurii
K. Babanskii [2], Vladimir P. Bespalko [5], Aleksei K. Gastev [21], Boris S.
Gershunsky [22], Anatolii I. Kuzminskyi [32], Olena O. Lavrentieva [34], Oleksandr
V. Malykhin [37], Leonid V. Zankov [66], and others. Scientists have characterized the
following main directions of intensification and optimization of the educational
process, such as: enhancing students’ cognitive motivation, increasing the learning’s
content informative capacity, the use of active didactic methods and forms, scientific-
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based management by the mastering knowledge process, development of skills and
ability of brainwork with use the mnemotechnies, visualization, self-control, and self-
efficacy techniques.
It should be notes that among the technologies of processing a large amount of data
lately the technologies of visualization of educational material are actively used; they
created on the basis of the works of Tony Buzen [10], Vasilii V. Davydov [11], German
K. Selevko [52], Viktor F. Shatalov [55], Andrey A. Verbitsky [63] and others.
Scientists’ researches, including Alexei G. Baryshkin [3], Mark I. Bashmakov [4],
Natalia V. Brovka [9], Hsinchun Chen [69], Viktor A. Dalinger [49], Thurston Domina
[16], Nataliia A. Reznik [3], Joshua Saldana [16], Bin Zhu [69], and others, confirmed
the fact that in the modern dynamic world where the computer-driven and smart-
technologies are increasingly becoming a reality of our lives, the approaches to
visualizing of educational content are must changing. Natalia M. Biloshapka [7], Steve
Cunningham [70], Irina S. Dereza [12], Petro I. Dovbnia [17], Hennadiy M. Kravtsov
[29], Pavlo P. Nechypurenko [44], Tatyana A. Oleinik [30], Valery M. Rakuta [50],
Yurii S. Ramskyi [51], Olena V. Semenikhina [53], Andrii M. Striuk [57], Oleh O. Tsys
[35], Oleg P. Zelenyak [67], Myroslav I. Zhaldak [68], Walter Zimmermann [70] have
devoted their studies of the use of computer visualization tools in the educational
process. Scientists justified the feasibility and necessity of using modern computer
visualization tools, including computer mathematics systems and dynamic mathematics
programs, as powerful tools to refine abstract mathematical models and processes.
This work will be analyzed the content and classification of computer visualization
software offered by Jörg Müller, Daniel Polansky, Petr Novak, Christian Foltin and
Dimitry Polivaev [36], XMind Ltd [65], Corel Corporation [41]. The results of
empirical study of their effectiveness for intensification of students’ brainwork in the
teaching mathematical subjects’ process will also be presented.
3 Theoretical background
3.1 The student’s brainwork and leading approaches to its
intensification
In our previous works [26], we have found that the concept of “brainwork” in most
scientific studies is interpreted as a creative activity, which is accompanied by the
tension of the sensory apparatus, the emotional sphere of the person and at the same
time does not require however considerable physical effort [25, p. 16].
From a physiological viewpoint, brainwork requires less energy expenditure of the
body compared to physical work. However, this fact does not mean its ease and
simplicity. The main working body in the brainwork is the brain as such. Physiologists
say that in intensive brainwork, its energy requirement increases to about 15-20% of its
total volume in the human body. At mental load the oxygen is used as like 5 times as at
maximum physical activity [26, p. 122]. The physiology state during of intensive
brainwork is characterized by impaired balance of the processes of inhibition and
excitation, deviates from the norm of the tone of the vessels of the heart and brain,
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increases protein and carbohydrate metabolism, growths blood pressure and respiratory
rate, etc. [43, p. 72].
That is, the interpretation of brainwork as an antithesis to physical one is very
conventional. Moreover, these types of work make a mutual impact on each other.
According to Boris P. Esipov [18] and Nina V. Kuzmina [31], the brainwork is
characterized by strain of attention, memory, perception. In addition, a sedentary
lifestyle and a monotonous posture cause stagnation in the leg muscles and, in the end,
poor brain’s oxygen supply [43].
As Simon L. Soloveychik is considered, the phenomenon of brainwork is the most
complex type of human activity that goes unnoticed and inviolable [56]. Scientist states
the brainwork is more difficult than any physical work, after that the person gets tired
faster and recovers longer, besides the results of brainwork are not always visible and
generally elusive. For example, when performing any physical work, anybody always
sees changes in the labor object. However, somebody can work on solving a particular
math problem for a long time, and eventually he/she can’t find its solution. At the same
time, representatives of psychological scientific thought (Dmitrii N. Bogoiavlenskii [8],
Petr Ia. Galperin [20], Nina F. Talyzina [59], and others) argue the main difference
between brainwork and any other type of work is its result. Product of brainwork is not
only solution of a certain intellectual problem, but the enrichment of the outlook of the
subject of work, change his/her attitude to reality [25, pp. 18–19].
Therefore, brainwork is a type of activity that provides the cognitive process,
mastering the techniques and ways of thinking, developing the capabilities and abilities
of the individual; the product of such work is a certain form of information, as a result
of the brainwork the outlook of the subject of work is enriched.
When considering performance brainwork’s indicators, takes into account its
quality, productivity, as well as the optimal organization to achieve maximum results
in a short time. It is not accidental in this conceptual chain the intensification of mental
activity process has not last role.
The Latin term intensive (intensio) means tense, reinforced, doing increased
productivity. Derived from it the term intensification (from French, Intensification –
“the hard work”) implies the achievement of the desired results in the work due to
qualitative factors, it in the investigated by us context – due to the tension of the
individual’s mental capacity [32, p. 212]. In reference sources, intensification is defined
as the process of increasing tensions, productivity, as the use of more and more efficient
technologies, advanced methods of work, the achievements of science.
Nina F. Talyzina sees the intensification as a process decrease in the duration of
training while increasing its quality and rising the amount of information assimilated
[59, p. 59]. Similar definitions are typical of the works of Sergei I. Arkhangelskii [1],
Natalia V. Kovalenko [27]. In the view of Sergei I. Arkhangelskii the essence of
intensification of learning process lies simultaneously in the effectiveness of teaching,
the effectiveness of studies and the effectiveness of study material [1].
The fact that in the process of extensive training (in contrast to intensive one) brain
capacity is used only by 15-20% is indicated about necessity of the students’ brainwork
intensification. At the same time, intensive techniques require excessively high mental
energy costs. Thus, the discrepancy between the requirements of scientific-and-
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technological progress on improving the effectiveness of learning and lack of modern
methods of information mastering put forward a problem of developing certain tools
that ensure the efficiency and productivity of students’ brainwork.
For the successful students’ brainwork, and its intensification, it is advisable to
strengthen the visual-figurative component of the study material. It is necessitating the
use of knowledge imaging technologies, as well as providing compactness,
expressiveness and dynamic presentation of the study material’s content.
3.2 Visualization of study material as one of the ways of intensification
of the students’ brainwork
The term “visualization” (from Latin visuals – to perceive visual one) is defined as the
process of presenting data in the form of an image for the maximum convenience of
their understanding; it is visualizing any mental object [61]. At the same time, scientists
are cautioned against such a simplistic concept of visualization if it comes to a
didactical method or principle, and offer to separate visualization from a visibility.
As Andrey A. Verbitsky points out the process of visualization involves the
collapsing of mental meanings into a visual image which in the future can be actualized
in certain situations and serve as a support for mental and practical actions. For its part,
a visibility is only a demonstration of those objects or phenomena, the presentation of
the finished image, set from the outside. Thus, a visibility serves to support thought
processes by performing an illustrative function, whereas the visualization implies
active brainwork [63].
At the heart of the visualization method are important psychological processes.
Viktor F. Shatalov proved that for better memorization and understanding, the study
information must be formed into an image. Within the visualization process it is
normalized, systematized and curtailed. In the following, the student who has processed
study information via visualization will be able to reconstruct the ones content, to
establish connections between facts or phenomena, what’s more to give examples and
to formulate conclusions [55].
In the educational process, such leading forms of visualization of study materials as
supportive notes or schemas, intellect cards and infographics are widely used [7,
p. 167].
Supportive Notes or schemas, by definition of Viktor F. Shatalov, are a system of
reference signals that have a structural connection and a visual construction replacing
the system of senses, concepts, and ideas as interdependent elements. The supportive
note is built on the basis of a boundary one generalization, coding, “collapsing” of
knowledge by means of conventional signs, symbols, diagrams, graphs, tables, and
whatever [55].
Actually, not every laconic record can be the supportive notes. There are main theirs
features, namely: 1) conciseness and clarity while the completeness of the information
presentation are maintaining; 2) availability of keywords and nodal concepts; 3) the
presence of structure both visual and logical; 4) simplicity and clarity of structure;
5) the existence of meaningful accents made with the help of different ways of design
– colors, frames, fonts, graphics, schemes; 6) the use of abbreviations and conventional
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symbols [60]. In Fig. 1 is shown the example of supportive note that demonstrate main
ideas for designing such schemes.
Fig. 1. It’s example of supportive notes that devoted to main idea of such schemes (it prepared
by authors with use [60])
Working with the support notes eliminates automatic rewriting of the study material.
If, in normal note taking, a student either copy a text from a textbook or blackboard, as
a rule without much thought in its meaning, then when student is drawing up a support
notes this process involves pretreatment the information, isolating nodal elements and
connections between them, creates anchor points for memorization [60]. At the same
time, reprocessing the support notes, compared to reading the text, is considerably less
time-consuming.
Mind Maps is a visualization of information in which step-by-step detailing of the
art and graphic means of the studied concept or phenomenon is represented in a
convenient format with the arbitrary addition of drawings and other auxiliary elements
(arrows, lines, graphic symbols, etc.) [10]. With all their similarities to the supporting
notes, mind maps are a dynamic means of visualization, that is, they are created in a
certain period of time being required to process a certain part of the study material. The
mind maps can help those whose personal and professional tasks suppose planning,
organizing, and structuring.
Mind maps are a way of depicting the process of thinking through schematics usually
in the form of a tree displaying ideas, concepts, keywords related to branches that
extend from the central object of the map. Sometimes other translations of the term are
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used: “intelligent card”, “associative cards”, “memory cards”, “mental cards”, “smart
cards”, “maps of consciousness”, “maps of mind”, “maps of representations”,
“diagrams of communication”, etc. [45].
The advantage of using mind maps is follow. Firstly, they allow capturing everything
with one look, since these schematic diagrams show the most important in associative
comparisons and interactions. Secondly, mind maps are an example of a rational
correlation of verbal, symbolic information and visual images. These are contributes to
the development of students’ visual thinking, which in turn organizes images,
systematize, structures and makes them holistic. These things far and away make
students’ brainwork more purposeful, concentrated, and resulting.
Mind maps as an effective visualization tool was re-invented by well-known expert
in intellect field Tony Buzen. The scientist paid attention that human thinking is
nonlinear but has a kind of branch structure. Here each concept is connected with other
concepts, in turn; these other concepts are connected with third ones and so on.
Therefore, working with mind maps significantly intensifies the development of new
concepts, ways of thinking and the general students’ brainwork. Throughout a such
activity, students study to express thoughts briefly and clearly, to encode information,
to structure it, to restore causation, to do conclusions [10] (see Fig. 2).
Fig. 2. The Mind Maps by Tony Buzen concept (it prepared by authors on the analogy of [41])
Infographics (one combines the terms “information” and “graphics”) are representation
of interconnections between data sets (concepts, phenomena, etc.) in a convenient
visual form by art and graphical means. In contrast an image, infographic conveys
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meaning, content, or data with the help of drawing but not the text [13]. A sign of
infographic is the preservation of meaning in the image, from which mentally or
technically the text explanations are removed [33].
In the heart of infographic technology is the fact that images makes the data more
attractive to perceive by whomever, and increase his/her memory efficiency. It is well
known that to 90% of information is perceived by a person visually, an additionally
human brain processes visual information much faster than textual. In line with this
regularity it is advisable to use infographics when you need to present a large amount
of information in a compact and logical way [69].
The tutorials with infographics activates the process of perception and understanding
of information, increase students’ ability to think critically. The principal advantage of
infographic images is providing information saturation and clarity of study materials,
appeal to the existing user experience. Accordingly, information graphics is an
intermediary in the path of choosing the trajectory of perception and information
processing by student [64, p. 200] and so it is a significant tool in students’ brainwork
organizing. In general, Iryna B. Chebotarova [14] based by way of presentation and
type of information proposes to consider 5 types of infographics (Fig. 3 shows it).
Fig. 3. Types of infographics by way of presentation and type of information (it prepared by
authors on the analogy of [14])
These are such as:
─ The spatial infographic showing the appearance, internal structure, size, scale, lo-
cation of objects, path from one to another.
─ The timeline infographic illustrating either chronology or a sequence of actions.
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─ The abstract infographic transmitting the system’s logic (hierarchy, block diagram,
diagram of relations, mind maps, etc.).
─ The quantitative infographic reproducing arrays of numeric data or statistics.
─ The comprehensive infographics that can include any above-listed types [14, p. 10-
11].
These visualization tools are widely applied in textbooks and all kinds of reference
books containing summary information and commonly used knowledge.
In view of the above, infographics have a high potential that can be used as a useful
tool to intensify the students’ brainwork. Infographic objects stimulate the simultaneous
operation of the left and right hemispheres of students’ brains complementing the
imagery of an abstract model of the object, making the perception more comprehensive,
the thinking – deeper, the learning – more interest and intense [58].
The review of major visualization tools (mind maps, infographics, support notes)
made determines their essential importance for the fruitful students’ brainwork thanks
to the physiological and psychological mechanisms of its intensification that realized
in them.
4 Techniques of computer visualization the study
materials
4.1 An overview of leading ways to visualization
Different tools can be involved in the visualization including computer and non-
computer ones. The first way is based on use widely available computer software,
which developers provide opportunities for visual representation on the screen or in the
printed form of abstract objects, processes, their models, and whatever. In spite of all
the attractiveness of prepared computer visualizations, self-created diagrams, maps and
infographics have considerable advantages, in particular: it is the quickness and the
possibility to reproduce at any moment and wherever, better memorization and more
painstaking students’ thinking activity [70]. Consider the methods of their creation and
approaches to use in the mathematics learning process.
The technique of “supportive notes” was proposed by Viktor F. Shatalov. He
developed and put into practice the technology of study intensification that showing the
huge, not yet discovered reserves of the traditional class-and-lesson system [55]. We
mean the following aspects. The “support” is an indicative basis of actions, a way of
external organization of the student’s internal mental activity. The “support signal” is
an associative symbol (sign, word, diagram, pattern, etc.) replacing a certain semantic
meaning. In turn, the “supportive note” is a system of support signals in the form of a
short conditional synopsis. In it all basic concepts and methods are introduced and
explained, the illustrative examples, control questions for self-testing, and the solutions
of typical problems are given. The material is presented in the same sequence like in
the lectures but without evidence. Only definitions, formulations and explanations of
the material, its interpretation, as well as drawings, conclusions, rules are given. The
secondary issues are generally being omitted here.
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Pedagogical experience usually uses teacher-pre-prepared supportive note, for
example, to prove theorems, explain complex concepts, interrelations between
mathematical concepts, memorize patterns, and so on. The lecturer presents the students
with a supportive note, explains its structure. During the course of the explanation
students redraw the note, or, using a ready one, make explanations, notes or markings
in it. While working out this material at home, the student as if reproduces it according
to the supportive note’s logical structure. Individual students may be asked to write
supportive note independently [60].
The supportive notes on mathematics can be made in the form of frames, logical
circuits, part-whole schemes, radial circuits, clusters, Euler-Venn diagrams, Pyramid-
type circuits, tree structures, and whatever [70].
A mind map is a way to visualize the process of thinking by creating non-linear
schemes. This is a way of fixation the process of thinking, which most similar to how
thoughts and ideas are being born and developed in our brain.
The map has a so-called radial structure, remotely resembling a tree, or a spider, or
an octopus, or whatever that has a center and branches. The procedure for working on
the creation of mind maps implies the following sequence of actions. In the center of
the sheet the main image (generic concept, phenomenon, and problem) is being drawn.
From it the key branches of the first level to the images illustrating the specific concepts
that associated with central image is being led. It is recommended the branches reflect
top ideas revealing these associative links. Further the branches of the first level will
be digress from the branches of the second level, and so on until the whole issue is
clearly worked out or the task is not addressed. Blocks should not be placed tight
enough, as they can be supplemented, become surrounded by new connections,
branches, data, examples, etc. [10].
The geometric data (families of triangles and quadrilaterals and their properties,
shapes in space and plane) are conveniently to represent on mind maps. Algebraic mind
maps are also popular. They show methods of solving logarithmic, trigonometric,
quadratic, etc. equations, actions with numbers, and rule of differential and integral
calculus.
The infographic is one of the forms of graphic and communication design of study
material intended to present information quickly and clearly [62]. Not only infographics
organize large volumes of information, but it also more clearly shows the links between
objects and facts in time and space, as well as demonstrate trends. This visualization
tool is widely used in textbooks and all kinds of reference books for math containing
summary formulas and commonly used mathematical transformations, heuristics, and
other interesting things.
As researchers consider there are two approaches to infographic design [33]. One is
the explorative way elaborated by Edward Tafty [15]. This approach is characterized
by a minimalist format. Here everything irrelevant isn’t being indicated, and the
information is being conveyed as accurately as possible. Another direction is the
storyline or narrative approach based by Nigel Holmes, who created the explanation
graphics [24]. The specified direction of infographic is characterized by attractive
images, expressive design, illustrative [46]. In our opinion it is advisable to use a
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harmonious combination of both approaches for intensification the students’ training
as well as their brainwork.
Evidently, it’s not easy to create quality infographics. So as to work up a functional
infographic, one has to go through many variants of their presentation, has basic
knowledge about tools of information’s performance, and a high level of understanding
of this process. Infographic is atypical visualization. It has own peculiarities and
differences. As researches emphasize the infographic is an individual manual work for
a particular dataset [46].
The creation and use of paper non-computer visualization tools are quite painstaking
and ungrateful work. It’s no wonder that in nowadays the computer visualization is
haven a number precedence over non-computer one and being use more and more in
educational process.
Natalia M. Biloshapka interprets the concept of “computer visualization” as an app,
in which it’s possible to visually present on the computer screen abstract mathematical
objects and processes, their models in a compact form (if necessary in various
viewpoint), or vice versa, in detail – with the possibility of demonstrating the internal
interconnections between the components that are usually hidden in the real world [6].
When all’s said and done the impact of computer visualization on the intensification
of students’ brainwork should be resulted and generalized.
We suppose the visualization of study materials is:
─ contributes to the better assimilation its scientific structure by students;
─ enables to independently select the pace of mastering a new study material;
─ opens the possibility of manipulation of information for the purpose the efficiency
of the organization of independent work and repetition of previously studied
material;
─ presented the dynamic information activates the simultaneous operation of different
types of memory that in turn increases the degree of the information perception, and
in the end enlarges the efficiency of the student’s brainwork.
The aforementioned features allow students to integrate both traditional statistical
information and dynamic knowledge during the brainwork.
4.2 A survey of computer visualization software
Computer visualization tools designed to support the teaching of mathematical subjects
are divided into two types: general purpose software and specific mathematical one
[54].
General purpose software tools provide a presentation of study material in a
compact, logical, holistic form that makes it possible to intensify learning, effective of
learning activities and, in the end of the day, to shape the culture of students’ brainwork.
In the heart of general purpose tools is computer graphics allowing to create, edit,
and convert graphics for any goals. Appropriate software has been developed for
working with graphic information including viewers, graphic editors, photo editors, as
well as specific tools – a graphic tablet, a digitizer.
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There are various graphic editors and packages (Adobe Photoshop, CorelDraw, 3D
Studio MAX, AutoCad and others), multimedia product development and
demonstration programs, text editors, and desktop publishing apps, etc. They allow
adding arsenal of visualization tools of educational information. In particular, these are
enable to use elementary and complex geometric shapes; to correct and to draw fairly
complex lines of different thickness and texture, to adjust points of various sizes, to do
fill, repaint, exchange colors and their brightness and transparency, to work with fonts
and graphic templates, to experiment with scaling, proofs and layout of elements, with
shadows and whatever [70]. However, successful work with such software requires
lecturers and students specific art and graphic abilities and skills. The Figs. 1-4 are
shown the results of the creation of such tools for visualization of study materials. So,
further it will be look at computer visualization tools that can be mastered by any
average person at the competence’s level.
Fig. 4. The supportive notes prepared by one of authors in Adobe Photoshop environment
Researchers (for example, Olena V. Semenikhina and Natalia M. Biloshapka) include
to general purpose software set following: 1) office software packages with Smart-Art
objects; 2) apps for realization of mind mapping technology; 3) apps for creating
infographics; 4) apps for creating a scribing presentation [53].
Smart-Art objects are a new type of graphic objects allowing the data in a text
document are being structured or presented their in schematics. It makes possible to do
the mastering of a new study material visual and step-by-step (by algorithmic way).
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Mindmapping is a technology enabling to systematize and synthesize the knowledge
gained through the formation of mind maps [45].
Scribing – sketches or drawings – the latest presentation technique, in which speech
is illustrated with drawings. It creates a “parallel passage effect”. In result we hear and
see the same thing, but the graphic is fixed only the key points of audio series. In this
sense, scribing can be put on a par with infographics. Computer scribing presentation
can be made with the PowToon service and the VideoScribe software, as well as
modern smart-systems. It should emphasized the scribing presentation also requires
mastering a certain art and graphic skills [38].
Therefore, we would like analyze in more detail the software environments for
making the computer visualization of study material. Among the applications that allow
the creation of mind maps and infographics there are the standalone applications –
XMind, FreeMind, Mindjet MindManager 2019, as well as the cloud services –
MindMup 2 For Google Drive, Bubbl.us, Mindomo Basic, and a lot of others.
XMind is a software tool to make visualization means that is installed on different
operating systems. The program contains a large set of pre-made templates that can edit
and create author’s visual products. The software toolkit lets to do export documents to
Microsoft Word, Microsoft PowerPoint, PDF-editors, to choose image format (bmp,
jpg, gif, and png). The program has several versions: free proposal with cut-down
features and paid one with advanced functionality [65].
The main disadvantage of using the XMind free version is the inability to add
images, mathematical formulas, videos, audio and more things to the illustration. In a
word, such visualization tool can contain only text and character information.
Mind maps created in the XMind free version can be used in higher mathematics
practical classes at the stage of actualization students’ supporting knowledge. For
example, during students study the content of topic “Straight line on the plane” the
lecturer at the beginning of the practical training indicates by means of mind map (see
Fig. 5) names of the basic types of the equations and main simplest tasks about straight
lines on the plane. From one’s part students must supplement each name with the
corresponding mathematical description that they got to know within a lecture.
A such form of consolidated of study material contributes to the intensification of
students’ brainwork, because the completed mind maps can be used repeated, after
addition and processing. It causes the model of study information to be fixed in the
students’ imagination and fasten into long-term memory.
FreeMind is a free mind maps builder running on any Java-enabled platform. The
program has advanced export capabilities in png, jpeg, xml, html, xhtml,
OpenDocument Text formats; plugin for export to svg and pdf. Exporting xhtml allows
to create a mind map with links to external sources. In fact, the program has all the tools
and features that need to make high-quality vizualization tools [36].
Consider an example of a mind map created in the FreeMind software environment.
In course of the presentation study material “The derivative and its application” at the
lecture session the main topic’s directions could be advisable determined via the
structural and logical scheme (it shown on Fig. 6). Further this mind map can serve for
a guide mark at the stage of generalization and systematization of students’ knowledge
for establish gaps in the studied material.
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Fig. 5. Mind map created by one of authors into XMind
Fig. 6. The structural and logical scheme “The derivative and its application” created into the
FreeMind software environment
Mindjet MindManager 2019 is commercial software for managing visualization tools.
This app offers the different ways to create mind maps. It can be a blank map to which
one adds all the necessary data, or a template, or a part of an existing map as the basis
for a new one. MindManager cards can be exported to Microsoft Word, PowerPoint,
Visio, and Project, saved both web pages and PDF documents. It should be noted the
capabilities of MindManager in the stylistic design of different types of mind maps are
quite wide [41].
Let’s consider an example of using MindManager cards in course of studying the
topic “The Polyhedron”. The structure of mind map (see Fig. 7) is reflecting the
classification of polyhedron based on the properties polygons that are the faces of
polyhedron. Apparently, such maps help to develop the students’ abilities to generalize
and classify objects by generic, species and other characteristics; as well as they
contribute to the streamlining of knowledge and a deeper understanding of the semantic
199
structure of the topic. To general advantages of the mind map “Polyhedron” should be
add possibility to create a set of tasks with incomplete data. It can be cards with
polyhedron names but without corresponding images, and vice versa; as well as cards
with images but without formulas, and on the contrary.
Fig. 7. The mind map for studying the topic “The Polyhedron” prepared in MindManager
environment by one of authors
Let’s consider an example of using MindManager cards in course studying the topic
“Matrix” (see Fig. 8). Such mind map can be used as basis to task solution on highlight
key concepts of the topic. What’s more it can also be used as a basis for hands-on
exercises on to supplement the mind map with missing information, in particular: to
add a images of the matrices types, the scheme of actions over matrices, formulas of
properties of actions with matrices, schemes and formulas for calculating the
200
determinant of the matrix, and whatever.
Fig. 8. Mind map “Matrix” prepared in MindManager environment
Students are able to do it, either in MindManager app or in any other graphic editor or
by hand on the printed maps.
MindMup 2 For Google Drive is a local app that integrates with Google Drive users.
Mind map created in this online service saves automatically. However, the possibility
to export mind maps for the free version is limited only objects to 100kb in size. In
addition, Google Drive mind maps can only be stored for 6 months. A Custom Gold
package allows creating mind maps already to 100MB and store them on Google Drive.
The Corporate Gold package removes any restrictions for users [42].
Bubbl.us is a relatively free local software environment for creating simple mind
maps and exporting them in image format. The program can change the color and font
of the text, the color of the nodes, and the general color scheme of the intellect card
[40].
Thus, despite the various functional capabilities, the apps that were discussed above
are built on the basis of a united principle for creating visualization tools of study
material for any educational subjects.
4.3 The special mathematical visualization software
Special mathematical visualization software includes programs of dynamic
mathematics. They provide dynamic operation of various mathematical objects with
201
the possibility of interactive obtaining of information about their properties [6]. These
programs allow doing animation and manipulation with mathematics’ objects. One
such software environment is GeoGebra [28].
GeoGebra is a free math program including tables, graphs, statistics and arithmetic.
It benefits embrace a friendly interface and powerful features that allow creating
interactive study material [48].
Major resources of this system cover to: calculation of mathematical functions,
creation of Java applets for insertion into Web pages, integration with the system of
distance learning courses [17]. The GeoGebra can also use as a virtual lab for
developing interactive models of mathematical objects, as a scribing tool, as an
environment for creating illustrative material and developing interactive exercises.
Consider the functionality of the GeoGebra in course of study of the unit
“Derivatives and its application”. As our experience is shown the most effective and
expedient is the use of a dynamic mathematics system on such stages of studying a
topic, namely:
─ finding a derivative of function (students can perform a self-test by comparing their
results with the result of a program; it contributes to saving time);
─ finding the equation of tangent line to the graph of the function (students construct
the graph of function and find equation of tangent line analytically, and then on the
type of completed construction they determine whether the desired line is tangent
one);
─ using the derivative of function to solve applied tasks (exploring the models into
GeoGebra);
─ studying the monotonicity and extrema, convexity and inflection points of the
function (student checks the correctness of conclusions by plotting the graph of a
derivative function by means of GeoGebra) [12].
The tasks are being carried out into the GeoGebra software environment aren’t just
illustrations. While the working the app saves an algorithm with all the steps and raw
data that can be edited as needed. Any changes to the algorithm are immediately
reflected in the graph. This significantly reduces the time spent on correcting errors,
since it does not require repeated execution of the task from the first step [67].
One advantage of using the GeoGebra system is the possibility to manipulate of
mathematical objects that allows keeping track the changes in their geometric
interpretation. In Fig. 9 the intermediate and final results of modeling into the
GeoGebra environment while studying the topic “Sum and Difference of Complex
Numbers” is shown. In this model the complex numbers are given in algebraic form
then the results of actions on them in graphical form are represented. To change the
parameter values into the environment there are sliders located on the top right of the
screen.
The solving higher mathematics tasks in the GeoGebra software environment,
students should not be given a readymade dynamic model or a readymade
demonstration algorithm. Initial skills in working with GeoGebra should be given, and
then offer to students to create of graphic images of the studying subject.
202
Fig. 9. The results of work into the GeoGebra environment
It can be concluding that the use of the GeoGebra mathematical program allows submit
calculations in an easy-to-read form, to combine calculations and construction on united
worksheet, thus increasing the studying productivity. It taken into account that getting
outcome during changing the value of the parameters does not require additional
calculations, any notes or create consistent conclusions. The involvement of the
dynamic GeoGebra program leads to an intensification of the students’ brainwork as
the process takes place against the background of instant visualization [47].
The solving higher mathematics tasks in the GeoGebra software environment,
students should not be given a readymade dynamic model or a readymade
demonstration algorithm. Initial skills in working with GeoGebra should be given, and
then offer to students to create of graphic images of the studying subject. This kind of
activity contributes to the students’ brainwork intensification and the deeper learning
of the mathematic.
4.4 The investigation of effectiveness of usage the computer
visualization tools as a means of intensification the students’
brainwork
In order to test the effectiveness of the study material visualization for the purpose of
intensifying the students’ brainwork the experimental work has been organized. The
investigation has been conducted on the Technology and Preschool Teacher Faculty of
Kryvyi Rih State Pedagogical University throughout 2017-2018 years and covered 213
number of participated.
During the experimental work it has been developed and tested: a set of mind map,
infographics, supportive notes to the main units of the course “Higher Mathematics”;
methods of working with them both in the classroom and in the process of students’
independent study activity; a system of training tasks based on computer visualization
tools including mining and scribing presentation. Some aspects of the above are
203
disclosed in the previous text of this paper.
The intensification of students’ brainwork in the teaching of mathematical sciences
was ensured by the involvement of certain computer visualization tools to solve
competently oriented tasks, among them: creating of visual models to basic
mathematical concepts, laws and rules; working with the prepared visualization tools
manually and with use visualization software; compiling a task system via the computer
and ICT tools.
The effectiveness of the developed methodology the students’ brainwork
intensification via the computer visualization of study materials has been evaluated by
such indicators as: the degree of mastering the main concepts of the topic (diagnostic
control work); interest in the subject and in the study of visualization tools
(questionnaires and interviews with students and lecturers); time required for learning
mathematical concepts and laws (chronocards methods).
It has been fixated the students highly appreciated the opportunity not only to re-
duce the time for the preparation to the classes but also to acquire the professional skills
of the organization of brainwork by means of computer visualization tools. 63,2% of
the students give preference to use general-purpose tools of computer visualization to
develop their professional careers. At the same time 81,6% of students are inclined to
apply the special mathematical visualization software. 51% perceive would like be able
to obtain specialist knowledge in the management of the other people’s brainwork
(students, subordinates, project team members and whoever).
By virtue of the experiment results an increase in the degree and completeness of
mastering knowledge in mathematical sciences by students has been noted (see
Fig. 10).
35.7% 40.8%
30.6%
25.5%
25.5%
18.4%
18.4%
8.2%
Insufficient Average Sufficient High
Output Stage Final Stage
Fig. 10. Dynamics of the levels of students’ knowledge mastering in line with experimental
work’s results
In order to find out the degree of intensification the students’ brainwork a chronocards
method has been applied. They have been used to record the time spent on by students
to solve learning tasks via computer visualization tools. The degree of intensification
the students’ brainwork has been estimated by the coefficient of intensification. This is
204
a correlation between time that students spend on to execute the tasks with use the
computer visualization tools and non-computer ones (to take more details see Table 1).
Table 1. The coefficient of effectiveness the use of computer visualization tools in the process
of higher mathematics study
The coefficient
Types of tasks Output Final
Stage Stage
Definition of mathematical concepts 1,1 0,8
Terminological work 1,2 0,5
Graphic, computational and practical tasks 1,0 0,7
Educational projects 0,8 0,5
Mastering the mathematical concepts and laws 0,8 0,5
Concretization of knowledge 1,2 0,8
Systematization of knowledge 1,3 0,7
Search for interrelation between mathematical concepts 1,4 0,6
Building models of mathematical phenomena 0,9 0,5
Independent study work 1,1 0,6
Creation of schemes, technological cards, consolidated tables, 1,2 0,7
construction of charts and diagrams
Mindmapping 1,3 0,7
Self-monitoring, test-control 1,0 0,6
It should be noted that the obtained results confirmed the high efficiency of computer
visualization tools to intensify the students’ brainwork in the process studying of higher
mathematics. Meanwhile, it has been confirmed the introduction of computer
visualization tools should be integrated one and provides for a variety of visualization
forms, the methods of their creation and processing, and, last but not least, a necessity
development of a special series of tasks which directed on working with them.
5 Conclusion
The analysis of the research results on the intensification of students’ brainwork via the
computer visualization tools has made it possible to draw the following conclusions:
1. The brainwork is a leading aspect of students’ study and cognitive activity. This
phenomenon implies mastering the techniques and ways of thinking, developing the
individual’s capabilities and abilities. Therefore, the issue of improving the
efficiency of students’ brainwork in the terms of the introduction of student-centered
learning is an important pedagogical problem.
2. The intensification is defined as the process of increasing tensions, productivity, as
the use of more and more efficient technologies, advanced methods of work, the
achievements of science. The intensification of learning process lies simultaneously
in the effectiveness of teaching, the effectiveness of studies and the effectiveness of
study material. The computer visualization tools are such mechanisms. Thanks they
are being used the speed of perception of information flows by means of visual
205
images increases significantly, and as a consequence the student’s brainwork
becomes more intense and productive.
3. The term “visualization” is defined as the process of presenting data in the form of
an image for the maximum convenience of their understanding; it is visualizing any
mental object. This phenomenon does not boil down to illustrating and
demonstrating the study materials. In the educational process, such leading forms of
visualization of study materials as supportive notes or schemas, intellect cards, mind
maps and infographics are widely used. Different tools are involved in the
visualization including computer and non-computer ones.
4. Computer visualization is thought like an app, in which it is possible to visually
present on the computer screen abstract mathematical objects and processes, their
models in a compact form or vice versa, in detail. There is the computer visualization
tools designed to support the teaching of mathematical sciences. They are being
divided into two types: the general purpose software and specific mathematical one.
The intensification of students’ brainwork via computer visualization tools requires
the development of a special methodology to use it in the Higher Mathematics
course, and a system of training tasks based on so-called “minding” and “scribing”.
5. An empirical research confirmed the effectiveness of using the computer
visualization of study materials to intensify the students’ brainwork in the teaching
mathematical sciences’ process. It was recorded that students praised the opportunity
not only to reduce the time for preparing for classes, but also to acquire professional
skills in organizing brainwork by means of computer visualization. Last, but not
least, an increase in the degree and completeness of students’ assimilation of
knowledge in mathematical sciences is noted.
The presented study does not exhaust the problem of the students’ brainwork
intensification. On authors opinion it should expediently develop the content of special
courses aimed at forming the culture of students’ brainwork both with the help of
modern information technologies and traditional non-computer ones.
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