extracted_text:
UDC
A474
FUNCTIONS
AND TYPES OF VISUAL MODELS IN THE PROCESS OF TEACHING MATHEMATICS

L. E.
Alekseevskaya,
(5th year
student of the Faculty of Mathematics and Computer Science)
(scientific
supervisor – N. P. Shatalova, candidate of physical and mathematical sciences,
associate professor)

Annotation. The
article is devoted to defining the functions and types of visual models. It is
shown that the use of visual models simplifies the perception of the proposed
material. The author gives recommendations for enhancing the use of visual
models by students in mathematics lessons.
Keywords:visualization,
visual model, types of visual models, types of visual models, mathematics.

There
is a serious need to build the learning process from the point of view of
balanced work of both the left and right hemispheres of the brain, that is, on
a rational combination of logical and visual-figurative thinking. One of the
key provisions of this approach is the extensive and targeted use of the
cognitive function of clarity. It is important to note that it is necessary to
ensure the implementation of a set of learning conditions in which students’
visual thinking reserves are most used.
Visual
models act as an intermediate link between the educational material and the
learning result, as a kind of cognitive-evaluative mechanism that allows you to
“compact” the cognition process, weed out minor details and thereby optimize.
Visual models provide a synthesis of knowledge, allowing for an indirect and
visual representation of the phenomena being studied in those areas in which
direct visual perception is difficult or even impossible. [Shatalova N.
P, 2010].
By
applying visual models to the educational process, the issues of training
students are resolved in order to develop their readiness to effectively solve
problems of professional content, condensation and visualization of the
knowledge provided, including using multimedia, with the ability to effectively
present educational material with the condition of its systematic assimilation.
None of the acquired knowledge can claim scientific status without clear visual
models. One of the main components of the process of presenting information to
students should be the methodology of visibility [Shatalova N.P., 2000].
Psychologists
have found that visual models are necessary to provide a number of didactic
functions: students’ acceptance of a learning task, motivating it, “tuning” the
student to the learning process, and providing the student with general
orientation for his future activities.
In
the methodology of teaching mathematics, there are four functions of visual
models listed below.
1. Cognitive
function. The main goal of implementing the cognitive function
is the development of a cognitive visual image of the object being studied. The
formation of development with the help of this function proceeds from simple to
complex, provided that the comprehension of the material takes place along a
simpler and more rational path to achieve the goal.
2.
The function of managing the student’s activities.In order to
implement this function, use the following steps:
a)
orientation towards the construction of a drawing corresponding to the
condition under consideration, or the introduction of additional elements into
the presented drawing;
b)
control aimed at finding errors when analyzing a drawing made by students,
placed in teaching aids, or in identifying the properties that an object should
retain during certain transformations;
c)
communication, responsible for the stages of implementation of the function of
managing the student’s activities, which corresponds to the analysis of the
results obtained by him; by performing these actions, students through
experience can explain to others or to themselves the essence of the phenomenon
or fact being studied according to the constructed visual model.
3.
Interpretive function. The essence of the interpretative
function is represented by the fact that the same object can be expressed using
different signs and visual models, for example, a circle can be defined using a
pair (center and radius), an equation relative to the coordinate axes, using a
picture or drawing.
4.
Aesthetic function. Aesthetics implies
beauty. Aesthetics is comprehended through the senses, that is, formal beauty,
and intellectual beauty, accessible only to the mind. In a mathematical proof,
the logical and visual parts must be proportionate. Thus, thanks to a simple
visual model, the essence of the proof becomes clear, and logic clarifies only
some details of the proof.
Various
drawings, drawings, diagrams, tables are aesthetic objects. They reflect the
logic of processes, therefore they deepen knowledge and help reveal the inner
beauty of mathematics.
5. TO methodological
functions of visual models One can also include the function of
ensuring the student’s focused attention, the function of memorizing when
students repeat educational material, the function of using applied
orientation, etc.
6. In his
works, A. N. Leontiev also highlights psychological function included
in the learning process using visual models. It consists in the fact that the
material presented in the form of a visual aid serves as an external support
for the internal actions that the student performs under the guidance of a
teacher in the process of mastering knowledge.
How
the teacher understands the role and significance of each function of visual
models depends on the construction of the learning process and the development
of its optimal methodology. In accordance with the functions of visual models,
the principles of their classification are also considered. Let's consider the
classification of visual models according to the gradation of activity
techniques that reflect various ways of modeling individual mathematical
knowledge or an organized set of knowledge [Alekseevskaya
L. E., 2017. P. 178-183].
Operational
visual models – these are models
that are based on supporting external actions. Operational visual models
include demonstration educational models (the use of drawings, diagrams,
tables, posters, graphs, models); the use of operational visual models when
solving problems of professional content expands the number of channels for
transmitting and receiving information, accelerating and deepening the
perception of the material being studied.
Formalized
visual models - these are models
that are based on structural external actions that develop “external”
structures, structures of notation, highlighting or placing text on the board
or in a teaching aid. This type of visual models includes: using italics,
frames, paragraphs when writing, highlighting individual formulas in a line,
underlining important words and sentences, indicating the significance of the
text in the margins with various signs, indicating the beginning and end of the
proof, using color to highlight important formulas and elements .
Structural and visual models – these
are models that develop educational models in the learning process, based on
structural external actions in the process of developing the “internal
structure”. Structural visual models include identifying the main material from
the total mass, presenting and constructing a visual model based on stable
associations, which is characterized by a complete presentation of basic
concepts, methods, theorems, and working with the material until it is
recognized in any task.
Background
visual patterns – the process of
modeling the specific features of a given organized set of knowledge, which has
a motivational end-to-end nature, ensuring better perception and assimilation.
Background visual models are characterized by duration, non-one-dimensionality,
support of associative-reflexive functions of perception, and “unobtrusiveness”
of side effects. An example of the use of this type of visual models can be the
techniques of creating a background of mood, creating a reduced background of
intensity around supporting information, attracting historical material, and
using various mnemonic effects.
Distributive
visual models characterized by
structural external actions when studying the formed educational model in the
process of educational activities. This type includes the structure of the
placement of material, the identification of basic definitions, portions of
material, and the classification of methods of proof. The use of this type of
visual models allows you to place emphasis on the material being studied, makes
it accessible for perception and assimilation, teaches you to think logically,
analyze, highlight the main thing and establish connections between the
concepts being studied, be able to navigate a large amount of information,
fosters a critical attitude, and teaches you to be collected.
Visual
models of continuity characterized by
the support of associative connections within the section, subject and
intersubject. This includes the structure of relationships, methods of
presentation, propaedeutics, supporting motivational historical tasks, cycles
of research tasks.
In
general terms, we can say that the most productive use of visual models in
practice will be carried out only if the teacher clearly knows all the
functions and types of visual models and applies them according to need.

Literature
Alekseevskaya L. E., Shatalova N. P. Using visual models in teaching mathematics // All-Russian Scientific and Practical Conference:
electronic scientific publication. 2017. pp. 178-183.
Shatalova
N. P.
The path to creativity: research,
essays, experiments // scientific and
practical methodological collection of Municipal Educational Institution
Secondary School No. 3 of Barabinsk and Scientific Research Laboratory of the
KF State Educational Institution of Higher Professional Education
"NGPU" / Ministry of Education and Science of the Russian Federation,
Kuibyshev Phil. GOU VPO "Novosibirsk State Pedagogical University",
Municipal educational institution of secondary school. No. 3, Barabinsk,
Novosibirsk region. ; [ed. N.P. Shatalova]. Krasnoyarsk, 2010.
Shatalova
N. P.
Current problems in the theory and
methodology of studying functions in the educational system
"school-university" // Collection of
materials of the mathematical thematic conference in the educational system
"SCHOOL-University" / 2000. Volume Issue 1

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