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3extracurricular independent work); 3) high level (student tries to improve the methods of acquiring knowledge).
To activate extracurricular IWS in the study of mathematical disciplines, a teacher should use the comprehensive approach in organization of the both curricular and extracurricular process; it is necessary to use all types of independent work and to control the quality of their implementation. Most creative and active students should be involved in research work and participation in scientific conferences.
Activation of IWS in the study of mathematical disciplines can be based on a positive attitude toward the study of the discipline, interest in the perception of the material. The aim of university education is to develop student's awareness of the need to study mathematics, interest in mathematics, understanding the importance of its place among other disciplines, self-assessment of knowledge. Student awareness of the fact that the results of his extracurricular work can be used in future training activities and work improves his attitude toward his work and its quality; and participation in scientific conferences will greatly enhance student's self-esteem.
REFERENCES
1. Erovenko V.A. Law in the era of triple understanding of humanitarian poluobrazovaniya. - Pedagogy, № 9, 2010g.-s.65-72.
2. Kupavtsev A.V. Theoretical bases and practice of intense activity studying. - Pedagogy, № 8, 2011g.-s.69-76.
3. Malenkov R.A. Specificity of independent work of students in the implementation of competence-based approach. - Alma mater. Bulletin of the higher school, № 4, 2011g.-s.66-68.
FAMILIARIZING PUPILS TO EXPERIENCE OF DIFFERENT TYPES OF LEARNING ACTIVITIES
WHILE LEARNING MATHEMATICS
ABSTRACT. THE AUTHOR DESCRIBES THE FOUR TYPES OF LEARNING ACTIVITY OF PUPILS, CONSISTENT IMPLEMENTATION OF WHICH ENABLES TO FAMILIARIZE PUPILS TO CREATIVE MATHEMATICAL ACTIVITY.
KEYWORDS: EDUCATIONAL MATHEMATICAL ACTIVITY, CREATIVE ACTIVITY, RESEARCHING ACTIVITY, DESIGNING ACTIVITY
PAVEL GOREV
pavel-gorev@mail.ru
PhD in Pedagogic, Associate Professor, Chair of Mathematical Analysis and Methods of Teaching Mathematics, Vyatka State Humanities University, Kirov
One of the most important aspects of the implementation of student-oriented learning is to create conditions for the development of students in the process of active learning and cognitive activity. In practice, the creation of such conditions, along with the lessons of mathematics can be accomplished by involving students in the system of additional mathematical education. [1]
Labor, play and study are the main activities of children and adolescents; and the studying activities are aimed at mastering the specific knowledge and skills. The purpose of the mathematical learning activity is a preparation for independent solvation of the certain circle of mathematical by school children. The main mean is the specially selected educational objectives, which content and methods of work developed in the course of historical development of science.
There are three types of training activities: material-practical, social and spiritual. V.A. Gusev [2] noted that in the process of teaching mathematics experimental activity (e.g. implementation of additional constructions for solving geometric problems) and universal-transforming activity (transformation of raw data to obtain the desired result; search new connections between objects; construction of new combinations of objects; different interpretations of built mathematical models) are formed, which are included in the material and practical activities of pupils. The communication activity is one of the components of the social activities, which skills can also be developed at the lessons of mathematics. Spiritual activity of pupils consists of cognitive activity, value-orienting activity, emotional and sensory activity, which skills are developed by means of upbringing and developmental aspects of the threefold purpose of teaching mathematics.
Based on the work of G.A. Shchukina [3], we can form the following features of educational activity:
1) the activity of a pupil is connected with the activities of other people, so it allows child to take
a closer look into the possibilities, to have better motivation of activity, to develop various forms of independent activities;
2) The development of activities in the educational process marks the progressive development of the individual: first - performing activities; then - active-performing activity; later - self-active activity; then - creative and independent activity;
3) Gradually introspection of a pupil creates faith in his own strength, changes the position of a student: participation in learning activities becomes organically adjoin to the activities of the teacher; a pupil shares the cares about the intensity of the training process, economical ways of teaching, successful results of operations with the teacher; a pupil put forward his own judgments, based on those ones, that he has seen and read, learned outside the lessons, and so on.
Taking in consideration the listed above, we select two parameters of pupils educational activity: its content and structure. Under the content of educational activity, we understand the system of knowledge and skills, which in the course of this activity should be reached by a student. The structure of educational activity is a set of actions, carried out by a pupil in order to achieve the positive results in the development of the content of this activity.
Combining the power of students freedom choice of content and structure of teaching, we distinguish four types of training activities: educational, researching, designing and creative types (see Table 1).
TABLE 1. TYPES OF LEARNING ACTIVITIES OF PUPILS DEPENDING ON FREEDOM CHOICE OF ITS CONTENT AND STRUCTURE
Type of educational activity Content of activity Structure of activity
Educational Is determined by curriculum Is determined by an algorithm
Researching Free choice of pupil Is determined by an algorithm
Designing Is determined by a topic Free choice of pupil
Creative Free choice of pupil Free choice of pupil
Let us briefly characterize each of these types of learning activities.
Educational type is undoubtedly the most important of the proposed types, and represents the activity of achieving the basic knowledge and skills by learners. Content of educational type is determined by the requirements of the program in mathematics, content of textbooks and teacher's methodological developments. Pupils do not have an opportunity to choose the content; the choice is limited by self-determination of the level of complexity of the tasks. The structure of activity is determined by the structure of the lesson, developed by the teacher, as well as be the variety of ready-made algorithms, methods, ideas and solving problems. Educational type is characterized by the organization of pupils' activities from outside: the teacher previously explains pupils the solution algorithm of this type of problems or the main idea and then offers them the problem and tasks.
As students master the material on the subject, it is necessary to switch them to the other types of activities, including researching and designing activity, in which students can be involved at the same time.
Researching type of learning activity is aimed at mastering the ability to fill the familiar structure of the activities by the new content, in particular, from another area of expertise. At first time, it is necessary to help pupils the main fields of applications of a particular algorithm or idea, leaving them the choice and providing them by the opportunity to pick tasks from this area. For example, you can offer students to use the idea of the method from the contrary, formulated as the Dirichlet principle, in solving problems in various branches of mathematics.
Designing type of learning activity involves the expansion of content by changing its structure to self-selection of students. This type can be carried out by making projects on a given topic. In our understanding the training project is a co-aggregate of various activities, aimed at the acquisition of knowledge and skills in the discipline, their organization and creation of a new product with the recommendations for its use in one of the prescribed forms: portfolio (documentation package), presentation, database, video, visual model, and so on.
Both the researching and designing types of training activities provide students the choice of one of the parameters. Students need to feel the given opportunity to select, and to embrace a sense of ownership and liability to their learning process.
ISSUE 3 2014
Creative type of training activity suggests that both the content and the structure of the activity is the choice of each student chooses. The content of the activity arises from the formulated by the pupil creative task, in which as the result of the pupils' work on the topic at the research level of activity, the structure is determined by the activity of the students of the various forms of his work at the project level.
At the organization of mathematical education at school, which includes interconnection of curricular and extracurricular activities, it is assumed the following scheme of implementation of the learning types: first comes the educational type,: after the successful acquisition of knowledge and skills the parallel shift to the researching and designing types comes; obtaining positive results in the implementation of which gives the opportunity to do the creative type of learning activity.
If the scheme, proposed by G.I. Shchukina, suggests that performing, actively-performing, self-active, and active and creative learning activities are carried out in the conventional technique in math class, we expect the change of activity types in accordance with the different scheme, taking into account the close relationship of curricular and extracurricular forms of learning mathematics.
It is necessary to provide pupils by the basic knowledge and skills (educational type). However, the intellectual development of students, formation of qualities, typical to mathematical activity, is impossible without researching and designing activities, basis of which surely must be instilled during the lessons of mathematics. Some especially active in this area students can (and should) go to implement the creative activity. But, in practice, such cases are rare. In order to expand the range of students, who have the potential for creative learning activity in the field of mathematics, students are engage in supplementary mathematical education. Creating such a system in a separate school involves the provision of more opportunities for the majority of students for the implementation of researching and designing types of learning activities, which can lead to the creative level. Supplementary system of mathematical education, in addition to special training in three areas [4], involves more time and opportunity to supply the greater autonomy of students in the classroom.
Thus, consistent work on the implementation of different types of learning activity allows engaging pupils in the creative process of the study of mathematics, which gives positive results at the Final State Certification and different stages of the All-Russian contests in mathematics.
REFERENCES
1. Gorev P.M. An introduction to mathematical creativity: the extra-mathematical education of: monograph. -Saarbrucken: LAP LAMBERT Academic Publishing, 2012. - 156 p.
2. Gusev V.A. Psycho-pedagogical foundations of mathematics teaching. - M .: Verbum-M Academy, 2003 -432 p.
3. Shchukin G.I. Role of activity in the learning process. - M .: Education, 1986.
4. Gorev P.M. The main forms of supplementary mathematics education in high school // concept. - 2013. -№ 05. - ART 13116. - URL: http://e-koncept.ru/2013/13116.htm.
