=Paper=
{{Paper
|id=Vol-2104/paper_150
|storemode=property
|title=Cognitive Tasks Design by Applying Computer Modeling System for Forming
Competences in Mathematics
|pdfUrl=https://ceur-ws.org/Vol-2104/paper_150.pdf
|volume=Vol-2104
|authors=Svitlana Lytvynova
|dblpUrl=https://dblp.org/rec/conf/icteri/Lytvynova18
}}
==Cognitive Tasks Design by Applying Computer Modeling System for Forming
Competences in Mathematics==
https://ceur-ws.org/Vol-2104/paper_150.pdf
Cognitive Tasks Design by Applying Computer Modeling
System for Forming Competences in Mathematics
Svitlana Lytvynova [0000-0002-5450-6635]
Institute of Information Technologies and Learning Tools
of National Academy of Educational Sciences of Ukraine,
9 M. Berlyns’koho st., 04060, Kyiv, Ukraine
s.h.lytvynova@gmail.com
Abstract. The article defines the basic concepts of “cognition”, “cognitive ac-
tivity”, “cognitive task”, “cognitive competence”, “system of computer model-
ing”; types of computer models; it determines the components and structure of
pupils’ competence formation in mathematics on the basis of solving cognitive
tasks using computer simulation systems; specifies levels and types of cognitive
tasks; singles out features, basic components and levels of pupils’ cognitive ac-
tivity of general secondary education institutions. It was found out that different
types of cognitive tasks (emotional-figurative, evaluation-educational, practical-
educational, theoretically oriented, information-oriented) consistent with their
levels of complexity (learning-reproductive, analytical, theoretical, applied, re-
search, creative) form a system for the development of cognitive abilities of a
high school pupil. It is determined that assessment of cognitive abilities of pu-
pils can be carried out according to the following criteria: cognitive bases, cog-
nitive processes, cognitive activity and cognitive qualities. It is established that
the use of cognitive tasks using computer modeling systems will facilitate the
formation of pupils' competences in mathematics. It is substantiated that the use
of computer modeling systems will provide variability of tasks, complexity,
universal access, organization of individual and team work.
Keywords: Cognition; Cognitive Activity; Cognitive Task; Structure; Cogni-
tive Abilities; System of Development; Computer Modeling System, Services,
CMODS, Establishment of General Secondary Education (EGSE).
1 Introduction
Problem statement. Within the framework of implementing the New Ukrainian
School Concept, the modernization of the content of education, the intensive devel-
opment of information and communication technologies, unlimited access to infor-
mation resources, the child-centered approach still remains fundamental along with
the development of cognitive abilities and learning capacities, the formation of com-
pulsory pupils’ learning outcomes (in terms of competences) at establishments of
general secondary education.
Therefore, one of the key competences mentioned in the New Ukrainian School
Concept is the natural sciences competence, namely: scientific understanding of na-
ture, ability to utilize it in practice; apply scientific methods, observe, analyze, formu-
late hypotheses, collect data, conduct experiments, analyze results, and use modern
technologies [1, p.13].
Modernization of the curricula contents, in particular the course of mathematics,
prompts the teacher to widely apply new methods of training, based on: cooperation,
game and design technologies, solving cognitive and research tasks, organizing and
conducting educational experiments, team work, etc. These processes are the basis for
the formation of key competences of the XXI century pupils.
Such transformational educational processes require new approaches to using digi-
tal and organizational solutions to form pupils' competences in mathematics, natural
sciences and technologies, in particular, in the development of cognitive abilities and
cognitive activity of pupils.
At the same time, the process of information perception by the pupils, formed in
the conditions of traditional education, and the continuous, chaotic development of
the Internet, saturation with an infinite number of social objects (video materials,
photographs, texts, etc.) and electronic educational resources, makes it impossible to
quickly search and select data; this may be achieved in the process of pupils’ cogni-
tion and formation of mathematical competence.
Scientists and teachers of educational establishments state that the problem of us-
ing the latest information and communication technologies, computer modeling of
natural processes and phenomena, the development of new technologies and models
of education, development of a system of cognitive tasks that would ensure the con-
tinuous development of cognitive abilities of pupils and activation of their cognitive
activity requires additional research.
2 Literature Review
Analysis of latest research and publications. Peculiarities of the use of Internet tech-
nologies for the investigation of natural phenomena are broached by scientists
Yu. O. Zhuk, O. M. Sokoliuk, N. P. Dementievska, O. V. Slobodianyk. Scientists
have identified the peculiarities of the use of Internet-oriented pedagogical technolo-
gies in the school experiment, in particular, when studying the course of physics in
institutions of general secondary education.
The general aspects of the concepts formation and different methods of the pupils’
research work are revealed by: V. I. Andreyev, M. A. Akhmetov, B. A. Vikol,
A. G. Iodko, V. V. Uspenskyi, L. M. Fedoriak, I. V. Kharytonova, M. V. Shabanova,
T. A. Yarkov. The scientists’ research results determine the need to use research tasks
to improve the quality of assimilating material by pupils while studying school sub-
jects.
The foundations of the didactic system of the activity-based teaching method are
grounded in the works of L. G. Peterson, O. S. Anisimova and others. Educators-
practitioners generalize the experience of constructing pedagogical systems on the
basis of the system-activity approach, describe the system of didactic principles and
the technology of the active method of teaching pupils in the classroom.
The use of the system of competence tasks as a means of forming pupils' IC com-
petences is disclosed in the works of N. V. Morse, O. G. Kuzminska and others [21].
Unresolved aspects of the problem. The intensive development of Internet technol-
ogies and the expansion of educational mobility possibilities of both teachers and
pupils, actualizes the problem of improving the method of using cognitive tasks for
the development of cognitive abilities of pupils in general secondary education
(EGSE) and elaboration of computer models for experimental and empirical research.
Currently there are a large number of on-line virtual laboratories in physics, chem-
istry, biology (for example, http://www.virtulab.net). However, they are mostly used
for “classical” experiments (in compliance with the curriculum). Thus, the pupils’
interest is formed through experiments visualization, while the combination of inter-
esting tasks formulations with online tools would allow pupils to develop research
qualities, curiosity, decision-making skills, constructing hypotheses, and others.
The purpose of the article is to summarize the main provisions and substantiate the
theoretical foundations of designing cognitive tasks using computer modeling systems
for building competences in mathematics and the development of pupils’ cognitive
abilities in the establishments of general secondary education.
3 Research Methods
This study was carried out within the framework of the research work entitled “The
system of cognitive tasks computer modeling with the aim of developing pupils' com-
petences in natural and mathematical subjects”. Methods, used in the course of re-
search, are: the method of theoretical sources analysis, the study of the advanced ped-
agogical experience of foreign and domestic teachers on the problem of the cognitive
tasks formation and application for teaching pupils; synthesis, generalization and
conceptualization for the formulation of the main provisions of the study; design and
modeling of cognitive tasks and the formation of pupils’ competences in mathematics;
generalization and evaluation of the results.
4 Research Results
4.1 Theoretical Foundations
At the core of the child-centered approach lies not only the direction of the education-
al process on the development of the pupil's personality, inborn talents, but also
his/her cognitive activity, which is the fundamental factor in the development of
his/her cognitive abilities.
At the philosophical level, cognition is the reproduction in the mind (individual
and collective) of the characteristics of objective reality. As it is noted by V.V. Laz-
archuk, cognition is socially and culturally mediated, historical in nature and in most
cases involves awareness of means and methods of cognitive activity [9, p. 103]. A
cognitive interest is formed in the process of cognition that has a search character and
focuses an individual on objects and phenomena, which provide a holistic view of the
world.
Cognition does not exist in itself; this process is inextricably linked with the activi-
ty of the pupil, the development of his/her cognitive abilities, in particular, the for-
mation of mathematical competences on the basis of solving cognitive tasks (see
Fig. 1).
Thus, N.F. Talyzina points to the inextricable connection of the pupil’s psyche
with his/her activity. Activity is the process of subject’s interaction with the surround-
ing world, the process of solving vital tasks. Thus, in the activity approach, the psyche
is understood “as a form of life of the subject”, which provides solution for certain
problems in the process of interaction with the world. The subject acts as a source of
activity, not as a simple set of his/her mental characteristics [2, p.6].
According to S.L. Rubinstein, “person's activity is characterized by the following
main features:
− objectivity;
− sociality, that is, socio-historical nature;
− individuality, that is, an individual-evolutionary nature;
− indirectness;
− social motivation and individual orientation;
− productivity, creativity” [3, p.41-45].
In addition, activities are classified according to the relative role of other processes
in them, namely: sensory, visual, auditory, and others.
The system of pupil’s activity in the process of cognition can be presented in the
form of the following basic components:
− motivational (stimulating);
− informational (orientation);
− goal-generating (programming);
− resultative (productive);
− affirmative (emotionally sensual) [4, p.29].
The transformative, cognitive and communicative activities are distinguished in
the activity system, which underlies the formation of pupils’ competences.
Researchers approach the consideration of the essence of “cognitive activity” con-
cept from different perspectives. With all the multidimensional approaches, we single
out two points of view:
− cognitive activity as activity;
− cognitive activity as a personality trait.
We will consider cognitive activity as an activity of an individual aiming to acquire
the cognitive, substantive and key competences.
Fig. 1. The use and development of competence tasks system of as a means of form-
ing pupils' mathematics and ICT competence
Modern psychologists distinguish three levels of schoolchildren’s cognitive activity:
Reproductive-imitative level: activity as a way of mastering the experience of an-
other person (reproduction).
Search-executive level: an activity, in which it is necessary to get a task and to find
the way for its fulfillment (interpretation).
Level of creative activity: activity, in the process of which the task is set by the pu-
pils themselves and is solved in a new, original way [5, p. 102].
It should be noted, that pupils’ cognitive activity is developed in line with the fol-
lowing principles:
Activity – a pupil gets knowledge not in the ready-made form, but acquires it inde-
pendently, in the process of individual educational activity.
Succession – the logical structure of the sequence of learning at the level of tech-
nology, content and methodology.
Openness – universal access to data and educational information.
Variation – the formation of the ability to consider various options and to choose
the optimal solution to the problem.
Integrity – formation of the holistic worldview.
Therefore, one of the ways of boosting cognitive activity is the application in the
educational process of cognitive tasks, which require a pupil to perform certain ac-
tions, such as:
− independently transfer previously acquired knowledge and skills into a new situa-
tion;
− understand the structures and characteristics of objects;
− search for alternative solutions or ways of solving problem assignments;
− combine previously mastered methods of solving problem assignments into new
ones [5, p.102].
As scientists point out, the problem of pupils’ cognitive activity development as a
way of obtaining a new quality of the individual is not exhaustively developed, and
the holistic systematic vision of the cognitive abilities development process as of the
individual’s ability in the process of learning is not formed, either [7, p.10-17].
The development of pupils’ cognitive abilities is a long process. In addition, to de-
velop pupils’ cognitive abilities means to form motives for learning. Pupils must not
only learn how to solve cognitive tasks, they need to develop their desire to solve
these problems. At present, one of the main tasks of modern school is to foster pupils'
motives [8].
This approach will enable the pupil to form cognitive competence.
Cognitive competence is the pupil's ability to independently engage in activities
that include elements of logical, methodological, heuristic, general educational activi-
ty, correlated with real objects that are perceived by the pupil. This includes the
knowledge and skills of organization of goal-setting, planning, ideas generation, anal-
ysis, reflection, self-assessment of educational and cognitive activity [9, p.102]. In
relation to the objects under study, the pupil acquires the creative skills of productive
activity, namely: obtaining knowledge directly from the surrounding world, mastering
methods of action in non-standard situations and heuristic methods of solving prob-
lems. Within the framework of this competence, the requirements of the correspond-
ing functional literacy are determined: the ability to distinguish between facts and
second-guessing, ability to apply measuring skills, the use of probabilistic, statistical
and other methods of cognition [9, p.105].
Guided by the nature of the pupils’ cognitive activity in the process of mastering
the substantive content, we distinguish two levels of cognitive abilities:
The first level: mastering the ready experience and reproduction of knowledge in
the process of his/her activities
The second level: mastering the ready knowledge, deepening the acquired
knowledge, formulation of the conclusions by the pupil is carried out using a variety
of sources of information and the implementation of imaginary and practical actions.
According to these levels, we distinguish three interrelated groups of cognitive
competences:
− ability to search and select the necessary information;
− ability to work with selected information;
− ability to produce new (subjectively new, new for the learner) knowledge, using
available information [10].
In case when the task is solved in order to determine the required characteristics of
the object, the basic data, which the object bears, will be called informational tasks.
Among the informational tasks the most important place is occupied by the cognitive
one [11].
The notion of “cognitive task” is considered in the general theory of problems, as a
generalization of the same concept used in psychology, pedagogy, methodology of
science [6].
We will give the advantage in the development of cognitive tasks to those that are
implemented in class: a lesson, a home assignment, a practical task or a training pro-
ject.
Taking into account the peculiarities of the process of cognition, which is carried
out on the basis of solving cognitive tasks, we define it as a fundamental one in teach-
ing pupils.
It should be noted that in today's digital world the opportunity to access education-
al resources is increasing. There appear different types of computer simulation pro-
cesses, phenomena, objects of living and inanimate nature, which can be applied to
model various cognitive tasks.
4.2 Examples of Implementation
The main objective of special subject teacher’s work is the development of cognitive
abilities of pupils. The achievement of this objective allows completing the main tasks
of studying, that is, to provide the stable and conscious knowledge of teaching materi-
al; to prepare pupils to close involvement in productive activity; to form the ability to
enrich their knowledge independently [8].
In view of the above-mentioned, we can distinguish the main levels of cognitive
tasks according to pupil’s way of thinking:
− learning-reproductive, that is, solving a typical problem;
− analytic-theoretical, that is, drawing general logical conclusions to the content line
and practical part of a problem;
− applied, that is, solving an untypical task.
According to the level of complexity, cognitive tasks should also be classified into
easy, advanced and difficult.
According to the way of forming pupils’ cognitive abilities, cognitive tasks are
subdivided into the following types [12, p. 351]:
− emotionally-figurative, which allows creating the “image’ of solution to a problem,
thinking intuitively, applying mental images, “getting into” the object under investi-
gation;
− evaluation-educational – thinking critically, comparing and correlating different
points of view, evaluating, making predictions and formulating hypotheses, reflecting
on one’s activity;
− practical-educational – constructing, conducting trials and experiments, observing
and modeling.
− theoretically oriented – creating “new” knowledge, generating ideas, asking ques-
tions;
− information-oriented – generalizing, systematizing and modifying educational
information, “encoding and decoding teaching material”, interpreting information.
According to the main types of educational activity, we can distinguish the follow-
ing cognitive tasks: research, problem-solving and creative.
Research – organizing and conducting investigation of a problem on the basis of
education.
Problem-solving – solving an education problem (within one discipline, project ac-
tivity).
Creative: generalizing data and developing one’s models, solutions.
Let us specify certain aspects of creative tasks. Thus, A. V. Khutorskyi suggests
implementing the following classification of creative tasks: cognitive, creative, organ-
izational-activity [12, p. 356].
Cognitive tasks aim at forming and developing pupils’ cognitive abilities: the abil-
ity to ask questions, feel the world around, conduct trials and experiments, and find
reasons for the occurrence of phenomena.
Creative tasks provide forming creative personality traits: the ability to make pre-
dictions, notice contradictions, flexibility, imagination, the ability to create something
new.
Organizational-activity tasks form the ability to realize and formulate the aim of
one’s educational activity, ensure one’s growth in education, recognize the results of
one’s education, and make judgments [12, p. 368].
We can identify the following requirements for creative tasks:
– openness (the content of problem situation or contradiction);
– conformity between the statement and chosen creative methods;
– variability of solutions;
– monitoring the current level of development;
– considering pupils’ age peculiarities [13, p. 84].
Summarizing the aforesaid, we come to a conclusion that the role of cognitive
tasks in teaching mathematics is to serve as a basis for organization of pupils’ educa-
tion process in form of statements and search for solutions to education problems for
the purpose of cognitive ability development.
As O. Yu. Burov states, one should also bear in mind the fact that pupils’ cognitive
abilities depend not only on skills and motivation, but also objective external factors
that are usually not considered in the context of personality [14]. Organizational ef-
forts are required to compensate for a gap between pupil’s abilities and his/her condi-
tions of education.
Therefore, we can regard the following categories as the components of forming
pupils’ cognitive abilities on the basis of use of cognitive tasks in educational process:
− cognitive basis (curiosity, learning new things, making decisions);
− cognitive processes (understanding, analysis, evaluation; creating new knowledge);
− cognitive activity (discussing, generating hypotheses, making conclusions, plan-
ning);
− cognitive features (perception of information (by tactile, visual, auditory channels),
memorizing, reproduction, understanding).
The development of information and communication technologies has facilitated
an opportunity to design cognitive tasks using computer modeling.
Modeling as a cognitive method has a centuries-old history. By different means
(verbally, graphically, with the help of mathematic formulas, physical and technologi-
cal patterns), a human being was trying to describe the phenomena he/she was observ-
ing as well as the objects surrounding him/her.
As N. Daneshjo mentions, computer models fall into two types [20].
The first type. Computer models which enable analyzing objects or systems, check-
ing, observing and specifying their characteristics. Nowadays, a significant number of
computer models for natural processes and phenomena are available, which allows
conducting the process of objects’ analysis in a simpler, more educational, interesting
and profound way.
The second type. Computer models which emerge as a result of development and
design (e.g. a model of household plot). This activity is usually supported by comput-
er technologies. Thus, we are talking about methods of automatic designing that re-
quires special software.
We will denote the experimental procedure with a model as simulation. Experi-
ments in the sphere of modeling allow conducting a thorough analysis and defining
the characteristics of an object, searching for alternatives or solutions of the problems
formulated.
As computer modeling system (CMODS) we will define software, intended for vis-
ualization of phenomena and processes, conducting numerous calculations of any
level of difficulty, aimed at clarifying and solving problems of different types.
Two types of computer modeling systems are appropriate for teaching scientific
and mathematical disciplines to pupils when they are only exploring the world and
lack visual objects, or when natural processes show dangerous features.
Let’s consider the computer modeling of the first type (simulation of the first type)
on an example of models Phet (phet.colorado.edu) for conducting classes in mathe-
matics. Mathematics is considered one of the most complex subjects of the school
course. In algebra lessons, for example, more attention is paid to working out the
skills of solving various examples and tasks. There is practically no time left for con-
ducting cognitive workshops. So, when studying the topic “Quadratic function, its
graph and properties”, pupils of the 9th grade would be offered to independently de-
termine the properties of the parabola and the features of graphing.
To organize such a cognitive workshop, the pupils would only need to download the
Phet simulator (phet.colorado.edu) and analyze the properties of the parabola by spec-
ifying different values of the variables a, b, c (see Fig. 2).
Fig. 2. An example of the Phet computer modeling system application
In order to deepen knowledge, pupils are also encouraged to find the range of values,
the intervals of decline and growth, constant signs, the greatest and least value of the
function, to analyze the results and to formulate general conclusions.
An example of computer modeling of the second type (simulation of the second
type) can be the implementation of research cognitive tasks:
1) Realization of cognitive activity by the pupil:
- to find an image of the Cheshire cat on the Internet, to find out who he is;
- examine his smile;
2) Implementation of cognitive tasks on the basis of computer modeling:
- to project a smile of the Cheshire cat in the Phet computer simulation system
(phet.colorado.edu), using the computer model “Graphs” (Equation Grapher).
3) Development of cognitive abilities:
- to compare the projected smile with the image;
- to find out how the projected smile will change if the mood of the cat changes.
- to summarize the properties of the projected smile (parabola), etc.
4) Identification of the level of pupils’ competences formation (see Fig. 1).
To project the described sequence of mini-tasks in Desmos (desmos.com) environ-
ment (see Fig. 3).
Fig. 3. An example of projecting a cognitive task in Desmos
The work with pupils could be carried out in small groups using tablets or mobile
phones. Main results are recorded in the tables.
The purpose of this work is to independently acquire knowledge about the basic
properties of a parabola.
For pupils who work in cloud-based learning environments, the results of work are
saved in tables (Excel Online), which can be accessed by all members of the group.
Such work on data collection will be faster and the work results will be monitored
by all group members. Each pupil can write intermediate deductions in OneNote, and
then the group members can summarize the results using the Padlet service
(padlet.com) [15, 16, 17].
Let’s project the described task in accordance with Fig. 1, taking into account the
pupils' work in the cloud-oriented environment (see Table 1).
Table 1. Projecting a Cognitive Task Using Systems of Computer Modeling.
The The title of the The content of the stage Tools, services,
number stage organizational
of the components
stage
0 Preparatory stage A thematic online notebook OneNote
(performed by is created (в Office 365)
the teacher) Access to it is provided to all Administrative
class pupils by the appropri- component
ate link
The link to the novel “Alice Forming compo-
in Wonderland” by Lewis nent
Carroll is placed in the
notebook
The link to the computer Forming compo-
modeling system is placed nent
in the notebook or the com-
puter model is embedded as
an object
The dashboard for discus- Padlet.com
sions “Cheshire cat and pa-
rabola” is created
The questionnaire of forma- Forms
tive assessment is created (in Office 365)
1 Implementation To find the image of the One Note (in Of-
by the pupils of Cheshire cat in the novel fice 365)
cognitive activity
To study its smile (to note OneNote
down hypotheses) (в Office 365)
2 Completion by To project the smile of the phet.colorado.edu,
pupils of cogni- Cheshire cat in the system of computer model
tive tasks based computer modeling “Graphs” (Equa-
on computer tion Grapher)
modeling
The screen copies are placed Padlet.com
on the dashboard
3 Development of To compare the projected OneNote
pupils’ cognitive smile with the image, pre- (в Office 365)
abilities sented in the novel
Find out how the projected Padlet.com
smile will change if the cat's
mood changes (conclusions
are written on a shared
board)
Generalize the properties of OneNote
the projected smile (parabo- (in Office 365)
la)
4 Level of for- To implement the formative Forms
mation of pupils’ assessment of pupils (we (in Office 365)
competences in consider the service to be a
mathematics means of determining the
level of competences formed
by pupils)
Let's consider another option of the cognitive task that is implemented in the system
of computer modeling of the second type Desmos (desmos.com) while studying the
topic “Graphic solution of inequalities” (see Fig. 4).
Fig. 4. An example of a creative cognitive task of increased complexity (Desmos)
Task. The school announced a competition for the best design of windows in the cor-
ridors. The teacher of mathematics offered the pupils to think, develop a design of
stained glass and present their projects in the form of a system of inequalities. Let's
consider the accomplishment by the pupils of the creative cognitive task of increased
complexity in more detail.
1) Realization of cognitive activity by the pupil:
- to find the images of stained glass on the Internet, to find out what it is;
- to study types of stained glass.
2) Implementation of cognitive tasks on the basis of computer modeling:
- to project a color scheme of stained-glass window;
- to project the stained glass for the window in the mathematics study in the system
of computer modeling Desmos.
3) Development of cognitive abilities:
- to compare projected stained-glass windows;
- to find out how the projected stained-glass window will change if you change the
marginal values of inequalities;
- to summarize pupils' knowledge of the graphic solution of inequalities, etc.
4) Identification of the level of pupils’ competences formation (see Fig. 1).
The system of computer simulation Desmos uses not only the internal mathemati-
cal system of calculations, but also adds elements of color gamut. This aspect gives
the opportunity to diversify the results of pupils’ work, to provide the process of mas-
tering the mathematical foundations with a certain artistic design, to bring the tasks to
real life needs. For example: to project a fragment of a decorative design of a ceiling
or a floor, to project a design of a bag or a cover of a pupils’ notebook.
The main types of lessons are identified on the basis of the activity approach (ac-
cording to L. G. Peterson):
- the discovery of new knowledge: the formation of the ability to independently
build new concepts and methods of action;
- construction of a knowledge system: the formation of the ability to generalize and
structure knowledge;
- developing monitoring function: the formation of the ability to exercise monitoring
function;
- reflection (final lesson of the topic): the formation of the ability to spot their diffi-
culties in the activity, to identify their causes, to find ways to solve them [22, c. 141].
The computer modeling may be used both at the lessons and in thematic groups, in
the process of preparing the works for the competition of the Minor Academy of Sci-
ences, at elective course, during the summer expeditions and practical exercises.
5 Conclusions and Recommendations for Future Research
The development of pupils’ cognitive abilities is one of the priority directions of insti-
tutions of general secondary education advance. The use of the system of cognitive
tasks in the process of learning subjects of the natural and mathematical cycle will
contribute to a greater understanding of the content of the subject and the reflection of
the information received on the environment, which, in its turn, will help the pupils
form a holistic view of the world.
Teaching pupils based on the system of cognitive tasks should be aimed at the abil-
ity of pupils to transfer the existing abilities to other types of social activities, to
strengthen and develop both general and personal (innate) abilities, which makes
them more flexible to the conditions of the modern world.
Different types of cognitive tasks (emotional-figurative, evaluation-educational,
practical-educational, theoretically oriented, information-oriented), taking into ac-
count their complexity levels (educational-reproductive, analytical-theoretical, ap-
plied, research, creative), form the system of cognitive abilities development of a high
school pupil. Assessment of such a system will be carried out against the following
criteria: cognitive basis, cognitive processes, cognitive activity and cognitive quali-
ties.
Computer modeling of cognitive tasks will ensure their variability, level of com-
plexity, universal access for individual and group work.
The researchs of foreign colleagues (S. Sahin, B. S. Choi, E. Gennaro, T. De Jong,
W.R. Van Joolingen, W. M. Dwyer, V. E. Lopez) confirm too that computer simula-
tions are good supplementary tools for classroom instruction and science laboratories.
Multimedia supported, highly interactive, collaborative computer simulations appeal-
ing growing interest because of their potentials to supplement constructivist learning
[23-26].
The new thinking highlights the central role of learning and rich interactions with
the physical and social environment for the development of human psychological and
cognitive capacities [27].
Further research is needed to define the concepts and terms used, in particular,
such notions as “computer modeling”, “computer model”, projection of cognitive
tasks; generalization, selection and justification of the use of computer models in the
educational process and generalization of information about mathematical compe-
tence of pupils at establishments of general secondary education also need to be fur-
ther investigated.
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