=Paper=
{{Paper
|id=Vol-2433/paper22
|storemode=property
|title=Cloud-based complex of computer transdisciplinary models in the context of holistic educational approach
|pdfUrl=https://ceur-ws.org/Vol-2433/paper22.pdf
|volume=Vol-2433
|authors=Liudmyla I. Bilousova,Liudmyla E. Gryzun,Daria H. Sherstiuk,Ekaterina O. Shmeltser
}}
==Cloud-based complex of computer transdisciplinary models in the context of holistic educational approach==
https://ceur-ws.org/Vol-2433/paper22.pdf
336
Cloud-based complex of computer transdisciplinary
models in the context of holistic educational approach
Liudmyla I. Bilousova1[0000-0002-2364-1885], Liudmyla E. Gryzun1[0000-0002-5274-5624],
Daria H. Sherstiuk1[0000-0002-5330-2905] and Ekaterina O. Shmeltser2
1 H. S. Skovoroda Kharkiv National Pedagogical University,
29, Alchevskyh Str., Kharkiv, 61002, Ukraine
{Lib215, Lgr2007, DSerstuk}@ukr.net
2 Kryvyi Rih Metallurgical Institute of the National Metallurgical Academy of Ukraine,
5, Stepana Tilhy Str., Kryvyi Rih, 50006, Ukraine
Abstract. The paper represents the authors’ cloud-based complex of computer
dynamic models and their transdisciplinary facilities. Proper theoretical
background for the complex design is elaborated and the process of the computer
models development is covered. The models in the complex are grouped in the
sections according to the curriculum subjects (Physics, Algebra, Geometry,
Biology, Geography, and Informatics). Each of the sections includes proper
models along with their description and transdisciplinary didactic support. The
paper also presents recommendations as for using of the complex to provide
holistic learning of Mathematics, Science and Informatics at secondary school.
The prospects of further research are outlined.
Keywords: holistic education, cloud-based learning environment, computer
dynamic model, transdisciplinary tasks, didactic support of holistic learning.
1 Introduction
Contemporary education at all of its levels is currently experiencing the period of
necessary transformations. It is connected with complicated social processes,
tendencies to globalization, integration of science branches, and incredible growth of
new knowledge amount. As a result, it causes challenges to education and training at
schools and universities. Mainstream educational paradigm (considered today to be
static and split up [9]) tends to be transformed with holistic educational approach which
tries to build dynamic, harmonized, and interconnected pedagogy.
This approach aims to form students’ concentrated conceptual knowledge and the
complex of transdisciplinary skills. It will allow to establish in the trainees’ memory
greater amount of strong links between concepts and notions, and as a result, to
encourage students to investigate and apply what they know and can do to other subject
areas. In order to provide such an approach we need to elaborate special teaching
strategies and arm teachers with effective aids appropriate for different students and
learning situations.
___________________
Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0).
337
Thus, it is really urgent today to develop and implement special learning tools in
order to facilitate implementation of holistic educational approach.
Analysing recent research papers on the theory of holistic education, we could
distinguish main characteristics and peculiarities of the approach. According to some
authors, holistic education should be considered as a paradigm (not as a technique,
strategy or method) that provides educators with a system of principles which can be
used in various ways [9; 14; 15].
The core idea of holistic education is the cohesive development of the whole person
both at the intellectual and emotional levels [22]. At the same time this cohesive
development should base on strong links between personal experience and real life
problems.
Among basic principles of holistic education the studies (in particular, [9; 13]) point
out several pillars which seem to be really important and significant in the context of
contemporary requirements to the education. The first pillar expects students’ freedom
and autonomy. So, within the holistic paradigm any trainee is considered to be really
active participant of the learning process who is ready to interact with reality via his
own cognitive activity, via his own ups and downs.
Next important facet of the holistic approach is necessity to establish connections
and relationships between the object of learning and existing knowledge. The more
links trainees have, the stronger memories are formed in their minds and better
understanding of the whole they obtain.
Similar to the establishing links is the principle of transdiciplinarity which focuses
teaching and learning on ruining boundaries between subject fields themselves as well
as between subject areas and reality.
Researchers also point out that holism helps both the connection facet and
transdiciplinarity, because it seems to be fruitful to learn separate things which in fact
are not separate. However, at the same time it is necessary to understand how they work
together.
The analysis of the holistic education basis reveals a need to apply efficient learning
tools enabled to provide holistic approach to nowadays teaching and learning.
One of such tool seems to be computer dynamic models (CDM). The learning of
recent studies on their didactic facilities testifies that CDM have quite powerful
potential as for revealing transdisciplinary connections and facilitating their
understanding by schoolchildren. In particular, researchers point out that CDM are
typically based on the mathematical model of a concept (process, phenomenon, etc.),
and enable to visualize its essence at real time operation, learn dynamic changes, and
investigate the concept or process via active cognition. In such a way CDM help to
form and develop students’ techniques of mental activity including transdisciplinary
ones [1; 18].
Characterizing advantages and facilities of CDM using in the context of holistic
education, it is important to emphasize that they encourage students to learn objects
independently and actively. In addition, they reveal and demonstrate in action the
wholeness of the learnt concepts (phenomenon).
The special attention must be paid to the cloud-based complex of CDM as a potential
mean of holistic approach realization. According to recent studies, cloud-based learning
338
environment for teaching STEM disciplines opens wide horizons for holistic education
due to its important features. Among them researchers call support for various
processes of learning and research activities; great level of learning resources
flexibility; integration of variety of educational components based on innovative
technologies [10; 12; 19; 20; 21].
On balance, cloud-based complex of CDM (as an integral part of the learning
environment) with transdisciplinary didactic support is able to enhance the advantages
of CDM usage and to facilitate implementation of main pillars of holistic education.
The purpose of the article is to describe the authors’ cloud-based complex of
computer dynamic models and their transdisciplinary facilities. The paper also presents
recommendations as for using of the complex to provide holistic learning of
Mathematics, Science and Informatics at secondary school.
2 Theoretical framework
During the research, the set of theoretical, empirical, and modelling methods were
applied. Theoretical background for the cloud-based CDM complex elaboration made
deep and comprehensive analysis of the proper subject areas, held by the authors
beforehand. In order to meet the main pillars of holistic approach (covered earlier) it is
necessary to reveal key objects of learning in the subject areas, establish connections
between them, and build chains of proper transdisciplinary links.
Researchers distinguish different types of transdisciplinary connections. However,
scientists (in particular, [2; 5; 11]) recommend to base the connections classification
upon the set of three main grounds: information content of the subject, structure of
learning activity, and organization of educational process. As a result, considering the
transdisciplinary connections from the standpoints of holistic education, we have to
reveal key concepts of subjects, detect their place in the current curriculum, consider
peculiarities of their mastering and proper cognitive activity.
These procedures were done through the learning main content threads of the said
curriculum subjects [16; 17], author’s didactic analysis of each subject (covered in [6;
7]) and detailed analysis of the subject areas.
Main content threads of Mathematics, Science subjects (Physics, Chemistry,
Biology) and Informatics enabled us to reveal some transdisciplinary chains. We would
like to point out a paramount role of penetrating content threads in revealing
transdisciplinary concepts and links between them. According to the Concept of the
New Ukrainian School, there are four penetrating content threads - “Ecology security
and sustainable development”, “Civil responsibility”, “Health and security”, “Financial
literacy” – which are seen as a mean of key competences integration of all curriculum
subjects. The penetrating threads are considered to be socially important super themes
that focus teaching and learning on the trainees’ holistic understanding of the world.
They are recommended to be regarded during the learning environment creation [8].
Analysis of subjects’ content threads in the terms of four penetrating threads enabled
us to build the following set of connection chains between curriculum subjects:
Algebra – Geometry – Informatics;
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Algebra – Physics – Geometry;
Physics – Algebra – Geometry – Biology;
Chemistry – Biology – Informatics;
Physics – Biology – Geography.
Subsequent detailed analysis of the subjects standards [16; 17], textbooks, and subject
areas resulted in establishing of transdisciplinary links between learning elements (LE),
representing concepts and phenomena which are co-explored by several subjects. In
particular, the effective semantic analysis was held with the help of specialized
software, such as: TextAnalyst 2.0, Text Miner 12.1 (its Text Parsing Node), Trope 8.4.
Such a “smart” analysis of the subject areas enabled to distinguish the weightiest LEs
of the specific subject along with their conceptual links.
Basing on the depicted analysis, for the revealed weightiest LEs of a subject it was
built a graph, representing their transdisciplinary links with exact learning elements
(LE1...LEn) of other subjects, according to the chains of connections mentioned earlier.
The general scheme of the graph and the example of the graph for selected physics LEs,
representing the transdisciplinary links for the chain: Physics – Algebra – Geometry –
Biology, are given on the Figures 1, 2. Graphs also contain information about the school
grades (from the 5th to 9th) in which the LEs are studied according to current curriculum
standards.
Fig. 1. The common scheme of the graph, representing their transdisciplinary links with exact
learning elements (LE1...LEn) of other subjects and grades numbers
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Fig. 2. The example of the graph for selected physics LEs, representing the transdisciplinary
links for the chain: Physics-Algebra-Geometry-Biology (Section “Physics”. Model “Lens”)
3 Results and discussion
The results of theoretical framework were used at the design of cloud-based complex
of computer transdisciplinary models.
The process of the models elaboration embraces some phases. At the first phase
mathematical model of the future computer model is built. At this point it is done: (1)
revealing and learning of the transdisciplinary essence of the proper concept (See
theoretical framework); (2) defining of the mathematical dependencies which can
illustrate and investigate the concept; (3) determination of the fixed model parameters
and changeable ones along with the range and step of their changes; (4) picking up
proper graphic elements which are able to illustrate dynamic changes; (5) revealing of
transdisciplinary tasks and real-life problems which might be solved by the model.
At the second phase the mathematical model is built by the means of GeoGebra. In
particular, the set of standard GeoGebra tools are used (Points, Lines, Special Lines,
Polygon, Circle and Arc, Measurement, Transformations) as well as the CAS
components (Calculations and Analysis Tools). For realization of dynamic
transformations, the Action Object Tools and Movement Tools are used [18].
341
In order to make the use of the complex more flexible and available to a wide
community of students and teachers, we organized it in the form of GeoGebra Book.
GeoGebra Book is a cloud service which enables to gather GeoGebra resources, to
enhance them didactically, and to share them easily. Due to this fact, our complex of
models is oriented to be a component of a cloud-based learning environment.
The third phase is devoted to the testing, debugging and improving of the model.
The models in the complex are grouped in the sections according to the curriculum
subjects (Physics, Algebra, Geometry, Biology, Geography, and Informatics). Each of
the sections presents proper models along with their description and transdisciplinary
didactic support. Main page of the complex and some of its sections are shown on the
Figures 3-5.
Fig. 3. Main page of the complex of computer transdisciplinary models
Fig. 4. Computer models of the Physics section
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Fig. 5. Episode of work with Algebra section of the complex
Each of the models is presented in the complex according to the general scheme.
It includes (see examples below):
─ model title;
─ chain of the transdisciplinary links which are illustrated by the model;
─ model description which explains concept (phenomenon) that is a prototype of the
model;
─ dynamic model itself with a proper functionality;
─ procedure of cognitive activity on the realizing the essence of the concept
(phenomenon);
─ didactic support as a set of transdisciplinary tasks and real-life problems for forming
holistic image of the said concept (phenomenon);
─ graph of the revealed transdisciplinary links for the visualization and remembering
this holistic representation.
As it was mentioned above, holistic education expects students’ personal cognitive
activity. In order to facilitate it we elaborated procedure of cognitive activity which
includes some tips on changing the parameters of the dynamic model, monitoring the
results, investigating, making conclusions etc. Such a procedure is aimed to streamline
understanding the essence of the concept (phenomenon).
Our didactic support for each model is developed to involve students into the solving
special problems and real-life tasks which encourage them to obtain holistic
understanding of the basic concepts via special cognitive activity based on work with
dynamic models. All of the tasks focus students on the revealing and realizing
transdisciplinary links.
Some of the models with their description and functionality are included into more
than one subject section. However, didactic support as a set of transdisciplinary tasks
343
for each model is specific in each section and focuses on the subject essence of every
concept and different transdisciplinary connections.
Below we demonstrate fragmentary some of the models from various sections of the
complex (according to general scheme of model presentation depicted above) and offer
recommendations as for their using to provide holistic learning of Mathematics, Science
and Informatics at school.
Example 1. Section “Physics”. Model “Lens”
Chain of the transdisciplinary links: Physics – Algebra – Geometry – Biology.
Model description: The model illustrates principle of operation of a lens as a simplest
optical device that focuses or disperses a light beam. A lens consists of a single piece
of transparent material (e.g. glass or plastic). A lens can focus light to form an image
which differs it from prism (See Section “Physics”. Model “Optical dispersion”). A
lens has its optical axis, two focuses, main optical center and plane (you can find their
definitions in your textbook). Lenses are classified by the curvature of the two optical
surfaces. The model demonstrates the operation of exactly biconvex lens.
Procedure of cognitive activity with the model (selected tasks):
1. Operate the model. Change curvature with the slider. Monitor the focuses positions
and image positions. Find and formulate dependences.
2. Fix the lens curvature and change the object position relative to the focus. What is
happening with the image of the object?
3. Fix the object at the distances: d = 2F, d > 2F, d < 2F. Analyze changes and make
conclusions.
4. Analyze changes of the image’s size and position when the object is between 2F and
F, between F and lens center.
Fragment of didactic support as a set of transdisciplinary tasks and real-life problems
for forming holistic understanding of the optical device (might be offered trainees
during both Physics, Algebra (Geometry), and Biology lessons):
1. Operate the model. What is mathematical dependence between object distance to the
lens and focus distance? How is it called? Write the formula of the dependence.
2. What geometrical figures describe the object, its image, light beams and the
phenomena of light penetration through the lens?
3. What geometrical facts and properties are revealed by the device operation?
4. Which angles are equal at any values of the model parameters? Why? Which rays
are parallel? Why?
5. Working with the model, detect the parameters of the model which provide the
highest optical power of the lens.
6. Operating the model and using the scheme of the optical system of a human eye
(Figure 6), answer the questions: (1) what are the components of the eye optical
system? (2) what is the difference between real and virtual image? (3) what are the
basics of a human eye functioning from the standpoint of physics? (4) can you
explain eye-sight disorders (short sight, long sight, etc.) via physical concepts and
phenomena? (5) compare the principles of human eye operation and work of a digital
camera.
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Fig. 6. Scheme of the optical system of a human eye
Episodes of transdisciplinary tasks doing and the model operating are shown on the
Figure 7.
Fig. 7. Episodes of transdisciplinary tasks doing and the model “Lens” operating
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Graph of the revealed transdisciplinary links for the visualization and remembering
this holistic representation (presented on Figure 2 above).
Example 2. Section “Geometry”. Model “Clock”
Chain of the transdisciplinary links: Geometry – Algebra – Physics.
Fragment of didactic support as a set of transdisciplinary tasks and real-life
problems.
1. Operate the model, turn the clock hands, set the time (See Figure 8) and detect degree
measure of the angles made by the hands.
Fig. 8. Various moments of time to measure the angles between clock hands with the help of
the model
2. Use the model with different parameters and calculate degree measure of: (1) the
angel which makes tree fifth of the right angle, (2) the angle five sixth of which make
a right angle, (3) the angle which makes 30% of a flat angle etc.
3. Operate the model to express the given values of speed in the measure of m/c:
7,2 km/h; 3600 cm/min; 6 m/min; 36 dm/h etc.
4. You know that clock is a device which measures time that is really precious thing
for real life. Try to solve the real-life task like this one: Vira and Lara decided to
send messages to his friend Igor to greet him with his birthday. Vira can text 24
words per 4 min, whereas Lara - 35 words per 7 min. Who is quicker, and whose
greeting will Igor receive earlier if Vira sent a message of 30 warm words, and Lara
texted 20 ones?
Episodes of transdisciplinary tasks doing and the model operating are shown on the
Figure 9.
Presented transdisciplinary tasks done with the model, focus on forming holistic
understanding of (1) a clock as a physical and geometrical device, (2) time as a physical
concept and social phenomenon, (3) geometrical, algebraic and “clock” sense of degree
measure of an angle.
Graph of the revealed transdisciplinary links (Figure 10).
Examples of transdisciplinary tasks doing with the different models operating are
shown on the Figures 11, 12.
Our monitoring trainees’ cognitive activity testified that they often do offered
transdisciplinary tasks, applying two or three dynamic models together. It helps
students to visualize cognitive connections and makes the investigation process more
attractive and motivating for them [3]. The results of trainees’ exploring with the
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models “Binary tree” (Section “Informatics”) and the model “Similarity” (Section
“Geomentry”) are given on the Fig. 13.
Fig. 9. Episodes of transdisciplinary tasks doing and the model “Clock” operating
Fig. 10. Graph for selected Geomety LEs, representing the transdisciplinary links for the chain:
Geometry-Algebra-Physics (Section “Geometry”. Model “Clock”)
Characterizing our didactic support to the models it is important to emphasize that it
offers the transdisciplinary tasks of various types. In particular, there are tasks on
establishing connections between concepts from different subjects. The aim of these
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tasks is to specify and generalize mentioned connections; to form the system of the
notions of different level of generalization and subordination; to illustrate casual
relations of phenomena. This type tasks and problems are directed on the forming of
the set of transdisciplinary skills: to understand the links between the notions of
different subjects and to formulate them verbally; to explain processes and phenomena
of one science branch with the help of concepts of other branch; to make outlook
conclusions based on common concepts, and others.
Fig. 11. Episodes of transdisciplinary tasks doing and the model “Number systems” operating.
Connections chain: Informatics-Algebra
Besides, our didactic support proposes students transdisciplinary tasks on the
determination of community of the facts from different subject areas. They help to
specify learning material, to form new concepts and explain them from the standpoints
of other branches of science, to use some facts to illustrate other ones. Such tasks are
aimed at the forming students’ skill of facts’ analysis, generalization and explanation
from the standpoint of general scientific ideas; skill to integrate generalized facts into
the existing knowledge system; skill to apply generalized knowledge into practice.
In addition, into the didactic support there are included the tasks on the establishing
connections between theoretical knowledge and methods, and their practical use.
Mostly they are real-life problems which focus on the ruining boundaries between
subject fields and reality. They might help to form the students’ skill to see scientific
subtext in pure practical tasks, to attract generalized knowledge from surrounding areas,
and to apply them to resolving the problem.
Designing learning activity with the complex of models, we would recommend
offering described transdisciplinary tasks of the didactic support after students’ learning
the model description and procedure of their cognitive activity with the model. It will
also promote wholeness of the learning elements understanding.
Thus, the cloud-based complex of computer transdisciplinary models as for their
functionality provides main principles of the holistic education, such as connections
establishing, personal cognitive activity, focus on the ruining boundaries between
subject fields and reality. It seems to be relevant to predict positive influence of the
complex application on the forming of trainees’ holistic system of knowledge and
skills. Elaboration of proper methodology of its diagnosing [4] and estimation is a
prospect of our further research.
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Fig. 12. Episodes of transdisciplinary tasks doing and the model “Cannon” operating.
Connections chain: Algebra-Physics-Geometry-History
4 Conclusions
In accordance with its goal, the paper represents the authors’ cloud-based complex of
computer dynamic models and their transdisciplinary facilities. Proper theoretical
background for the complex design is elaborated and the process of the computer
349
models development is covered. The models in the complex are grouped in the sections
according to the curriculum subjects (Physics, Algebra, Geometry, Biology,
Geography, and Informatics). Each of the sections includes proper models along with
their description and transdisciplinary didactic support. The paper also presents
recommendations as for using of the complex to provide holistic learning of
Mathematics, Science and Informatics at secondary school. The prospects of further
research are outlined.
Fig. 13. Results of trainees’ exploring with the models “Binary tree” (Section “Informatics”)
and the model “”Similarity” (Section “Geomentry”)
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