DEVELOPMENT OF SPATIAL PERCEPTIONS IN PRESCHOOL AGE THROUGH GEOMETRIC TRANSFORMATIONS IN THE APPLICATION OF A COMPETENCE APPROACH

During preschool age a number of notions are formed related to the development of the child’s personality. Orienteering within space is part of the mathematical preparation of children in kindergarten. This section is one of the most difficult to master. A specific feature of childhood is the concrete-image thinking. To perceive the world around them, children need many examples. Preschoolers handle objects – they rotate, move, but do not analyze their actions. This paper describes the need and role of setting appropriate cognitive tasks to promote the development of spatial orientation of preschool children. The main part of the cognitive tasks related to the formation of spatial perceptions is intended to be mastered through the mathematical educations. Insufficient provision of materials and difficulty in perception by children do not motivate teachers to prefer to work in time for additional activities. It is this fact that provokes us to show that many resources can be created that are interesting for children and at the same time have great cognitive value. Practical developments about the topic are presented, which are realized in the education of students – future pedagogues. Various options are proposed, related to translation or transfer of an object, construction of objects and counting of geometric figures. The presented practical results are part of a study of the possibilities for applying a competency approach in kindergarten. In order to achieve a change in the educational system, it is necessary the University to prepare young educators for a new way of pedagogical interaction.

DEVELOPMENT OF PRINCIPLES AND MEANS OF DIAGNOSTICS OF COMPETENCIES FORMED WHEN STUDYING DISCIPLINES OF THE MATHEMATICAL PROFILE IN STUDENTS OF TECHNICAL SPECIALTIES

The state of solving the problem of formation of mathematical competencies in the study of mathematical disciplines in technical students is clarified. Approaches to the diagnosis of mathematical training of students in the process of teaching mathematical disciplines at the university, which provide continuous, objective and timely information about the current level of mathematical training of students, as well as gaps and shortcomings in the formation of mathematical competence. The goals of diagnostics are formulated, which should reflect the structure and content of mathematical competence as a result of mathematical training. In the structure of mathematical competence, in accordance with the content of mathematical activity, it is appropriate to consider: possession of heuristic methods of finding solutions to problems; possession of methods for solving problems; knowledge of methods of mathematical modeling, application of mathematics in other areas. The analysis of prospects of application of automation of process of estimation of knowledge of students on the basis of computer testing is carried out that gives the chance to receive the full information on process and results of mathematical preparation of students, increase of motivation of their cognitive activity, development of reflection and skills of self-diagnostics. The advantages and disadvantages of using automated knowledge control systems are considered. With the help of such systems the differentiation of educational material is carried out, the interrogation providing objectivity of diagnostics of knowledge is carried out, results of training of students are fixed. Automated systems are focused on in-depth assimilation of information individually by each student.

Diagnosis of the reading and interpretation of statistical graphs by undergraduate students from economic-administrative sciences programs at the University of Guadalajara

Recently, statistical reasoning has been of vital importance not only in quantitative analysis but also in the interpretation of graphs at all educational levels. There are students that can make calculations almost immediately but are not able to interpret or present their ideas graphically. In this way, the present study seeks to conduct a diagnostic of the problems that economic-administrative students have when reading and interpreting graphs in their statistics courses. For this, a Spanish version of the test Comprehensive Assessment of Outcomes in Statistics (CAOS) was administered. This instrument allows for the determination of reasoning applied to different types of statistical graphs and in some cases to determine what type of calculation is required to do it. The instrument was applied to 138 undergraduate students from the economic-administrative area of the University of Guadalajara during January-June 2018. The results show that a large percentage of students confuse a normal distribution with a uniform one and that they are unable to distinguish that a bias can be determined from the measures of central tendency and dispersion, as well as other statistical reasoning difficulties. This may be as a result of a deficiency that exists in statistical teaching, an insufficient mathematical preparation on the part of the students, among other factors.

Web-quest as a means of pedagogical stimulation of students’ positive motivation to mind work

The article is devoted to the consideration of peculiarities of the use of web-quest technology in the mathematical preparation of students for the formation of positive motivation for mental work. The structure of the web-quest is considered. It is pointed up that 4 elements must be present necessarily in every educational web-quest: introduction, assignment, execution, evaluation. The classification of all forms of web-quests is given. The main stages of working on a web-quest are stood out.

Teaching Mathematical Disciplines Under Digitalization

The article focuses on the issues of modernizing the teaching of mathematical disciplines in the context of the digitalization of pedagogical objects: the educational process, methodological systems for teaching mathematical disciplines, educational paths for the development of key and subject competencies in the field of mathematics, mathematical and simulation modeling. The demand for digital technologies and digital products for the practice of mathematical preparation of the future bachelor is noted. From a methodological and research point of view, digital technologies are described that are essential for improving the quality of mathematical training.

Mathematical preparation of students for their professional self-realization in modern innovative society

The article analyzes the problems of mathematical university preparation of specialists in the context of their professional self-realization in the modern labour market. The structure of mathematical competence of students is considered, its most important components are substantively described (the ability to ask and answer questions in and with mathematics, the ability to deal with mathematical language and tools). As a result of the first (ascertaining) stage of pedagogical experiment allowed to establish the level of students’ mathematical competence formation according to the specified structure was established. It is proved that students of both mathematical and non-mathematical majors have poor mathematical knowledge and skills for solving problems that require their complex application, in particular, modeling problems in the context of future professional activity. The basic approaches to formation of mathematical competence of students are substantiated: research-oriented teaching; interdisciplinary approach and practical orientation; use of digital learning environments and related tools. The methods of implementation of these approaches are disclosed in the authors’ elective discipline for the students of mathematical specialty “Methods of formation of students’ mathematical competence for the future successful career”. The continuation of the research will be the introduction of the discipline above to the educational process which contains the next monitoring of future teachers’ readiness to use indicated approaches in their professional activity.