UDC513
A474
L. E. Alekseevskaya,
student at the Faculty of Mathematics and Informatics,
Kuibyshev branch of Novosibirsk State Pedagogical University, Kuibyshev, Russia
Scientific supervisor – N. P. Shatalova, candidate of physics and mathematics. Sciences, Associate Professor.
DEVELOPING SKILLS IN USING VISUAL MODELS WHEN SOLVING PROBLEMS OF PROFESSIONAL CONTENT IN MATHEMATICS CLASSES
Annotation.The article presents key forms of organizing activities aimed at developing skills in using visual models when solving problems of professional content in mathematics classes; methodological recommendations are given on the use of visualization tools for the development of the following types of visual models: background, formal, operational, systemic, in mathematics lessons. Examples of lesson notes show the addition of the educational process with a more active use of visual models in the process of solving problems of professional content.
The relevance of the problem we have posed lies in its practical application in the process of teaching mathematics.
Keywords:visual models, professional tasks, mathematics, skills, visualization.
The problem of purposeful teaching to find solutions to mathematical problems of professional content has always attracted the attention of leading mathematicians, methodologists, and high school mathematics teachers. Works that have become classics are devoted to this problem, which primarily include the books of the world-famous methodologist and mathematician D. Polya. Among domestic researchers, much attention was paid to this problem by such well-known authors as S. I. Tumanov, M. B. Balk, G. D. Balk, L. M. Fridman, E. N. Turetsky, E. F. Danilova, A. B. Vasilevsky, A. K. Artyomov and others, in different years, who published books for mathematics teachers and secondary school students.
Figure 1 – Components and criteria of the studied qualities and objects
Criteria of the studied qualities
To determine the level of skills in using visual models when teaching ninth-graders to solve mathematical problems of professional content in the process of teaching, the following criteria for the types of visual models and types of mathematical problems were identified (see Figure 1).
There are three levels of development of skills in using visual models when teaching ninth-graders to solve professional mathematical problems:
● high level – this includes students who independently know how to create visual models and use them in the process of solving problems;
● average level – include students who find it difficult to construct a model, but know how to apply them when solving problems;
● low level – include students who find it difficult to build a model and find it difficult to use it.
To develop skills in using visual models in the process of solving problems of professional content, we will highlight the types and types of lessons that most effectively solve problems in improving the qualities being studied.
Table 1 – classification of basic types of lessons for developing the use of visual models in the process of learning to solve problems of professional content
|
№ |
Lesson Types |
Types of lesson |
|
-1- |
-2- |
|
|
1 |
A lesson in discovering new knowledge |
|
|
2 |
Reflection lesson |
|
|
3 |
Lesson of general methodological orientation |
|
|
4 |
Developmental Control Lesson |
|
In order to competently organize the learning process in order to increase the use of visual models in the learning process and in particular tasks of professional content. To do this, the teacher must select a specific form of activity for each stage of the lesson. To develop skills in working with visual models. As an example, the key forms of organizing educational activities are presented in Table 2.
Table 2 – forms of organizing educational activities
|
№ |
Types of lessons |
Forms of organizing educational activities |
Components and criteria for developing skills in using visual models in the process of solving professional problems |
|
|
lesson - travel (Lesson of discovering new knowledge, acquiring new skills and abilities) |
|
|
|
2 |
lesson - abstract (Lesson of discovering new knowledge, acquiring new skills) |
|
Operating |
|
3 |
lesson - multimedia(A lesson in discovering new knowledge, acquiring new skills and abilities) |
|
Background |
|
4 |
Lesson - creativity (Lesson of discovering new knowledge, acquiring new skills and abilities) |
|
Formal |
|
5 |
lessons - competition (Lesson of discovering new knowledge, acquiring new skills) |
|
Structural |
The above lesson structure is recommended for use in the polyhedra section in 9th grade. According to the following thematic planning
Table 3 – thematic planning for the section polyhedra (according to the textbook)
|
№ |
Lesson topic |
Time (ac.hour) |
Type of lesson according to Federal State Educational Standards
|
|
54 |
Subject of stereometry. Geometric bodies and surfaces. |
1 |
A lesson in discovering new knowledge, acquiring new skills and abilities |
|
55 |
Polyhedra: prism, parallelepiped, pyramid. |
1 |
A lesson in discovering new knowledge, acquiring new skills and abilities |
|
56 |
Formulas for calculating the volumes of polyhedra |
1 |
A lesson in discovering new knowledge, acquiring new skills and abilities |
|
57 |
Bodies and surfaces of revolution: cylinder, cone, sphere, ball. |
1 |
A lesson in discovering new knowledge, acquiring new skills and abilities |
|
58 |
Formulas for calculating their surface areas and volumes. |
1 |
A lesson in discovering new knowledge, acquiring new skills and abilities |
To develop lesson notes, we recommend the following database to help the mathematics teacher
Table 4 – database of digital educational resources from the Internet
|
№ |
Lesson topic |
Name of digital resource |
Address
|
|
Presentations |
|||
|
1 |
polyhedra |
nsportal.ru |
https://nsportal.ru/shkola/geometriya/library/2013/05/29/mnogogranniki |
|
2 |
polyhedra |
info lesson |
https://infourok.ru/prezentaciya-po-matematike-na-temu-mnogogranniki-klass-915473.html |
|
Video material |
|||
|
3 |
Geometry 9th grade |
Youtube teacher channel |
https://www.youtube.com/channel/UCnooVihOGi-BLP20XdW_vBw |
|
4 |
Mathematics |
Youtube teacher channel |
https://www.youtube.com/channel/UC6NEvbUaBx_1GR7IGesCGEQ |
|
5 |
Introduction to Sterometry |
INFROUROK |
https://www.youtube.com/watch?v=-VWz0tkLJ7c |
|
Online tests |
|||
|
6 |
Polyhedra |
Online Test Pad
|
https://onlinetestpad.com/ru/tests/geometry |
|
7 |
Polyhedra |
GDZ excellent |
https://otlgdz.com/testy/test-po-geometrii-dlya-9-klassa.html |
|
Miscellaneous |
|||
|
8 |
Material on various topics |
Learningapps |
https://learningapps.org/index.php?category=2&s= |
Thus, visualization of a problem of professional content is the use of models (visual model tools) to find the values of quantities included in the problem, data and required numbers, as well as to establish connections between them. The methodology for teaching modeling tasks of professional content includes the following stages:
− preparatory work for modeling a task of professional content;
− training in modeling tasks of professional content;
− consolidation of the ability to solve problems of professional content using modeling.
Скачано с www.znanio.ru
UDC513 A474
The problem of purposeful teaching to find solutions to mathematical problems of professional content has always attracted the attention of leading mathematicians, methodologists, and high…
Criteria of the studied qualities
KVN; creativity. 3Lesson of general methodological orientationstudy; role-playing and business games; competition; drafting
Conversation with the teacher "decoder" game
Student report (with presentation)
The above lesson structure is recommended for use in the polyhedra section in 9th grade
Bodies and surfaces of revolution: cylinder, cone, sphere, ball
Mathematics Youtube teacher channel https://www
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