Conceptual provisions of fractal development of probabilistic thinking study in teaching mathematics and instruments for their implementation

Dvoryatkina, Svetlana N.; Shcherbatykh, Sergey V.

doi:10.32744/pse.2020.2.16

Cited by 5 publications

(4 citation statements)

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“…-Theory of fractal approach in teaching (Byshmeleva and Razova, 2017;Dvoryatkina and Shcherbatykh, 2020;Dvoryatkina and Kuznetsova, 2016;Shcherbatykh and Polyakova, 2020;Travkina, 2018); -Research on the theory and methodology of teaching the elements of the probabilistic- The use of these technologies gives the teacher high creative potential and develops the ability to see the educational problem from non-trivial perspectives. Humanitarian technologies put the teacher's organizational skills and the ability to act here and now, that is, in real-time, to the forefront.…”

Section: Methodsmentioning

confidence: 99%

Modern Educational Technologies in a Fractal Approach Implementation in the Math Lessons (on the Example of Learning a Probability-Statistical Line Elements)

Shcherbatykh

Polyakova

2022

Int. J. Criminol. Sociol.

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The article aims to reveal the didactic potential of modern educational technologies used within the framework of the fractal approach in teaching stochastics to learners, to show the effectiveness of fractal approach technologies in practice experimentally. In the course of the scientific research, the authors employed scientific analysis of literary sources on philosophical and methodological problems associated with the introduction of a fractal approach in teaching and informatization of education; systematization and generalization of the principles of fractal pedagogy; study, analysis, and concretization of advanced pedagogical experience in the use of modern educational technologies in the educational process; observation and analysis of the results of educational activities of seventh graders; and pedagogical experiment. This research allowed for identifying a group of modern educational technologies in the implementation of the fractal approach in mathematics lessons and identifying their didactic potential and possibilities of using, which is reflected in Table 1 of the main text of this publication. At the same time, it was found that the technologies of the fractal approach in teaching are quite useful: the experimental group received the best result.

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Section: Methodsmentioning

confidence: 99%

Modern Educational Technologies in a Fractal Approach Implementation in the Math Lessons (on the Example of Learning a Probability-Statistical Line Elements)

Shcherbatykh

Polyakova

2022

Int. J. Criminol. Sociol.

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“…Linn, A.C. Petersen, M. Sjölinder [24] на три соответствующие познавательным процессам категории: пространственное восприятие, пространственная визуализация, мысленное вращениепозволяет из IQ-тестов конструировать измерительные материалы. Субтесты измерения уровня интеллекта (IQ) «Пространственное воображение» и «Пространственное обобщение» из «Теста структуры интеллекта» Р. Амтхауэра «IST Intelligence Structure Test» (IST 2000-R) использованы авторами для конструирования измерительных материалов [6,12,29]. «Тест пространственного мышления» (ТПМ) И.С.…”

Section: материалы и методыunclassified

A new structural model for measuring spatial intelligence

Чикова

Zolotavin

Kamenev

et al. 2021

Vestn. Mininskogo univ.

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Introduction. The task of studying the structure and dynamics of spatial thinking of schoolchildren and students is relevant for general and educational psychology and private teaching methods. The research goal of the article is to theoretically substantiate, develop and test a structural model for measuring the spatial intelligence of students and schoolchildren.Materials and Methods. On the basis of a comparative analysis of the content of the definition of "spatial intelligence" in domestic and foreign educational psychology (I.S. Yakimanskaya, H. Gardner), a structural model and a rapid test for measuring the spatial intelligence of students and schoolchildren have been developed. The Structural Equation Modeling methodology was used to validate the developed express test. The research sample consisted of 688 schoolchildren from Novosibirsk at the age from 10 to 15 years.Results. The model for measuring the spatial intelligence of students and schoolchildren is developed by correlating the components of spatial intelligence: spatial knowledge, spatial abilities, spatial skills, with the corresponding cognitive processes: perception of space, spatial representation (thinking), spatial imagination. Based on the classification of intelligence tests into three separate categories: spatial perception, spatial visualization, mental rotation from intelligence subtests (R. Amthauer, M.C. Linn, A.C. Petersen, M. Sjölinder), a rapid test was constructed. The reliability (validity) of the express test was confirmed using structural equation modeling by the method of confirmatory factor analysis of models consisting of 15 indicators and one factor (spatial intelligence) or three factors (spatial knowledge, spatial abilities and spatial skills).Discussion and Conclusions. The theoretical significance of the developed structural model is that it reveals the mechanisms of the natural development of spatial intelligence, depending on the degree of formation of its substructures. The practical significance of the obtained result lies in the development of methodological foundations for screening diagnostics of the spatial intelligence of schoolchildren and is due to the high importance of spatial thinking for solving educational problems.

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“…At the same time, according to the classification of Ostroukh and Surkova (2020), as demonstrated in their monograph, the system that is developed by the authors should be soft and hybrid, with an intellectual interface, with expressed features of expert, self-learning, and adaptive systems. The use of the new technology implies taking into account the specifics of the following set of the system synergistic features: the quality and operability of decision-making; the fuzziness of goals and institutional boundaries; the multiplicity of subjects involved in solving the problem; the randomness, fluctuating and discrete behavior of the environment; the multiplicity of mutually influencing factors; the weak formalizability, uniqueness, and irregularity of situations; the latency and implicitness of information; deviation of plan implementation and the importance of small actions; paradoxicality of decision logic, as is proven in works (Dvoryatkina, Melnikov, and Smirnov, 2017;Dvoryatkina, Smirnov, and Lopukhin, 2017;Dvoryatkina and Shcherbatykh, 2020). The quality assessment system of trainees' knowledge on the basis of neural networks has been proposed by Zhuikov (2014).…”

Section: Introductionmentioning

confidence: 99%

“…Development of methods and quality models of educational activity at school and university with the application of modern digital technologies was carried out by Kozlov and Kozlova (2012), Kozlov, Mikhailov, and Vershinina (2017), Makhnytkina (2011), Monakhov (2014), Rudinskiy and Davydova (2014), Robert (2016), Uglev (2010), Guner and Pyatkovsky (2012) studied issues related to the competence assessment of trainees. The issues of computer control in adaptive learning systems on the basis of fractal modeling, as well as methods of fuzzy logic were studied by , Dvoryatkina and Shcherbatykh (2020), Dvoryatkina and Smirnov, 2016;Dvoryatkina, Masina, and Shcherbatykh (2017).…”

Section: Introductionmentioning

confidence: 99%

Parameters and Structure of Neural Network Databases for Assessment of Learning Outcomes

Smirnov

Dvoryatkina

Shcherbatykh

2022

Int. J. Criminol. Sociol.

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The purpose of this study is to determine the methodology, develop a theory of construction, put into practice algorithmization and implement the functionality of a hybrid intelligent system for assessment of educational outcomes of trainees on the basis of the identified keyword parameters and structure of the artificial neural network using expert systems and fuzzy simulation; to develop a methodology for the construction of structural-logic, hierarchical, functional and fractal schemes for structuring databases of the didactic field of learning elements; to determine the content, structure of parameters and database components, selection criteria and the content of complexes of educational standards. The methodology of introducing intelligent systems into mathematical education is on the basis of the Hegelian triad: thesis (implementation of the coherence principle) – antithesis (implementation of principles of the fractality and historiogenesis) – synthesis (implementation of the principles of self-organization and reflection of the complex system inversion integrity). Requirements for the organization and construction of the artificial neural network for assessment of personal achievements on the basis of fuzzy simulation have been developed. In the direction of using elements of fractal geometry, the technological structures of clusters that constitute the basis of generalized structures have been developed. In particular, it is revealed that the didactic field of learning elements is equipped with a system of multi-level hierarchical databases of exercises, motivational-applied, research, practice-oriented tasks using expert systems and integration of mathematical, information, natural-science and humanities knowledge and procedures.

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Conceptual provisions of fractal development of probabilistic thinking study in teaching mathematics and instruments for their implementation

Cited by 5 publications

References 0 publications

Modern Educational Technologies in a Fractal Approach Implementation in the Math Lessons (on the Example of Learning a Probability-Statistical Line Elements)

Modern Educational Technologies in a Fractal Approach Implementation in the Math Lessons (on the Example of Learning a Probability-Statistical Line Elements)

A new structural model for measuring spatial intelligence

Parameters and Structure of Neural Network Databases for Assessment of Learning Outcomes

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