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.

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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