DEVELOPING SKILLS IN USING VISUAL MODELS WHEN SOLVING PROBLEMS OF PROFESSIONAL CONTENT IN MATHEMATICS CLASSES

L. E. Alekseevskaya,

Novosibirsk State Pedagogical University (Kuibyshev branch), Kuibyshev
scientific supervisor Shatalova N.P.,
Professor of the Department of Mathematics, Computer Science and Teaching Methods, Novosibirsk State Pedagogical University (Kuibyshev Branch), Kuibyshev

USING VISUAL MODELS IN THE PROCESS OF TEACHING MATHEMATICS

Annotation. This article reveals the concept of visual models in the process of teaching mathematics and, in particular, their use in the process of solving problems of professional content.

Key words: visual models, tasks of professional content, modeling of mathematical models.

Summary. This article reveals the concept of visual models in the process of teaching mathematics and, in particular, their use in the process of solving problems of professional content.

Key-words: visual models, professional content problems, modeling of mathematical models.

There is no doubt that when helping students find a solution to a problem, it is necessary to make a schematic drawing or drawing of the problem for a better perception of the problem conditions, and when explaining each calculation method, accompany it with explanations of the actions with objects and the corresponding notes. For this, it is important to use visual aids with maximum visualization in a timely manner. The manuals should illustrate the very essence of the explanation, which will attract students to work with the manual, which would illustrate the whole essence of the explanation, attracting the students themselves to work with the manual and the explanation. Revealing methods of calculation, measurement, problem solving, etc. need to be very clear movement (add-add, subtract-remove, move) [Dahlinger, 1996, p. thirty].

An example would be the arrangement of drawings and notes in notebooks, short notation using known and unknown variables, etc. When introducing new material and consolidating knowledge and skills, it is necessary to organize work with a visual model in such a way that students themselves operate with them and accompany the actions with appropriate explanations. Thanks to visual models, the quality of material assimilation in most cases increases significantly, since various analyzers are included in the work (visual, motor, speech, auditory). In this process, students master not only mathematical knowledge, but also acquire new skills to independently use visual models in the process of solving problems. The teacher, for his part, must encourage students in every possible way to work using visual models in independent work. The most important condition for effectiveness is the use of visual models. The use of a sufficient and necessary number of visual aids in lessons contributes to the development of abstract thinking of students.

Visual models can play not only a positive role, but also a negative one, for example, if they are used where there is no need for it, they can lead students’ thinking away from the task at hand. If used inappropriately, visual models not only do not help, but can also harm the development of problem solving skills, that is, choosing actions on the numbers given in the condition.

There is no doubt that one of the main points in the methodology of teaching problem solving is the question of how best to teach children to solve problems of professional content. In the process of observing the work of students during teaching practice, it turned out that many of them not only do not want to solve problems of professional content, but also do not know how.

In the learning process in a modern school, there are a large number of techniques that will contribute to the development of skills in solving problems of professional content, but there are very few tasks in which the construction of visual models is involved. Most textbooks offer models in the form of a brief note and an image of the problem as a drawing; much fewer models are presented in the form of a drawing and, accordingly, there are few tasks for comparing them.

Scientists (V.A. Dahlinger, E.S. Kanin, G.I. Sarantsev, etc.) believe that in order to reveal the essence of visual models, it is necessary to consider the very concept of a model. All types of means that are used for construction, all models can be divided into schematic and symbolic [Sarantsev, 2003, p. 130].

In turn, schematized models are divided into real (subject-based) and graphic, depending on what action they provide. But we can include a brief recording of a text problem and a table among iconic models that are made in natural language. The iconic models of professional tasks that are written in mathematical language are: formula, expression, equation, system of equations, recording the solution to a problem using actions.

In our opinion, tasks of professional content that are visualized include the use of all types of models in order to find the value of the desired quantities that are included in the task, as well as to establish connections between them. The very methodology of teaching modeling tasks of professional content includes the following stages: the preparatory stage of work for modeling tasks of professional content; the stage of learning to compile models for problems of professional content; the stage of consolidating the skills of constructing models in the process of solving problems of professional content.

The preparatory stage of work should be aimed at performing any substantive actions. Students display the necessary actions graphically in the form of a picture. Next, the drawing should be presented in the form of a model. Consequently, the next action will be for students to transition to a symbolic form of notation: equalities, formulas, equations, etc. Before presenting a problem of professional content in the form of a visual mathematical model, you must become familiar with its content. When solving such problems, the biggest problem is “translation” from Russian into mathematical language and vice versa [Kanin, 2006, p. 130].

In such cases, it is necessary to determine the “mathematical core” of the problem under consideration. A necessary condition for this is the identification of quantities and relationships between them, which, as students say, are contained in “key” words and numbers (letters).” In order to facilitate this process, you can discuss with students how we will distinguish them from other words. We always highlight the issue of professional content tasks in particular, since it is the goal of our subsequent actions. Along with schematic modeling, symbolic modeling is also used - this is a short recording of the problem.

Let's take a closer look at the short record. The short record records quantities, numbers - data and what is being sought, as well as some words that show what is said in the task: “was”, “put”, “became”, etc. A short record of a task of professional content can be done in a table and without her.

When using tables, it is necessary to highlight and name the value. The arrangement of numerical data should be determined in such a way as to help establish relationships between quantities: on the same line, one below the other. The required number is indicated by a question mark [Friedman, 1983, p. 133].

In order to consolidate the skills of drawing up visual models for professional tasks, creative exercises can be used. Such exercises include: drawing up models for problems of increased complexity, problems with insufficient and redundant data, also exercises in composing and transforming problems using these models.

Literature

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