A calculus student’s understanding of graphical approach to the derivative through quantitative reasoning

The concept of derivative is used in many areas including applied problems and requiring mathematical modelling in different disciplines. One of the most important approaches for teaching the derivative is to support students in visualizing the concept. Also, it is necessary to shift researchers and teachers’ focuses to students’ dynamic mental actions while learning derivative in order to conduct effective teaching process. With this necessity, I focused on the perspective of quantitative reasoning related to the graphical approach to the derivative. This study aims to reveal a calculus student’s mental actions related to the graphical approach to the derivative. The data were collected from a first-year calculus student engaged in the task requiring graphical interpretation of the derivative. Results showed that the student’s understanding of the slope shaped her inferences about the tangent line because the quantity of ratio is prior knowledge for learning the instantaneous rate of change. Besides, as the student had the idea of correspondence related to the concept of function, she had difficulties in interpreting the global view of the derivate. This result suggests that having global view of the derivative requires a strong understanding of function and rate.

Research on reflective-evaluative competence in pupils with intellectual disabilities

The aim is to conduct empirical research on the formation of reflective-evaluative competence in primary pupils with intellectual disabilities and to determine effective methods to develop it. Methods: tests with standardized questionnaires, methods for checking the logic of motivating dialogue, comparative analysis, quantitative and qualitative content-analysis. We established that disorders in the functioning of reflection in primary pupils are observed in changeable or unfamiliar situations: rejection to solve a problem, desire to simplify a task, justification of their inability, avoidance of difficulties. We registered that insufficient development of self-control and self-esteem causes faults in programming and performing activity. We identified difficulties in verbalizing a plan of actions showing the respondents’ inability to compare and substantiate practical and mental operations. Disorders in reflective-evaluative competence are insufficient development of reflection, self-control, self-esteem and self-correction that does not allow primary pupils to organize their mental actions purposefully.

DEVELOPMENT OF ANALYTICAL SKILLS OF UNIVERSITY STUDENTS: SCIENTIFIC AND ANALYTICAL REVIEW

Представлен аналитический обзор проблемы развития аналитических умений студентов в вузе. Дана сравнительная характеристика понятий «аналитические умения» и «аналитические способности». Сделан вывод, что аналитические способности являются свойством личности, а аналитические умения – освоенный опыт деятельности. Рассмотрены основные мыслительные действия, лежащие в основе аналитических умений. Дается сравнение двух групп аналитических умений: аналитико-прогностические и аналитико-рефлексивные. Обосновывается тезис о том, что развитие аналитических умений невозможно без получения новых знаний. Значительное внимание уделено структуре понятия «аналитические умения». Определена необходимость развития аналитических умений у студентов для профессионального становления будущих специалистов. Сделан вывод о том, что для развития аналитических умений требуется время, это длительный, системный процесс в профессиональном образовании. Выявлены факторы (позитивные и негативные), влияющие на развитие аналитических умений студентов. Уделено внимание заданиям и упражнениям (кейс-заданиям), направленным на изучение развития аналитических умения студентов. Для диагностики уровня развития аналитических умений студентов разработаны показатели, а также представлена характеристика уровней развития аналитических умений студентов вуза – низкий, средний, высокий. Представлены результаты пилотажного исследования по выявлению уровня развития аналитических умений студентов гуманитарных направлений подготовки. Исследование проводилось в вузах городов Ставрополя и Краснодара. Результаты исследования показали, что у студентов преобладает средний и низкий уровень развития аналитических умений. На основе полученных результатов выявлены причины низкого уровня развития аналитических умений у современных студентов. An analytical review of the problem of the development of analytical skills of students at the university is presented. A comparative characteristic of the concepts «analytical skills» and «analytical abilities» is given. It is concluded that analytical ability is a personality trait, and an analytical skill is the acquired experience of activity. The main mental actions underlying analytical skills are considered. Comparison of two groups of analytical skills is given: analytical-prognostic and analytical-reflexive. The thesis is substantiated that the development of analytical skills is impossible without obtaining new knowledge. Considerable attention is paid to the structure of the concept of «analytical skills». The need for the development of analytical skills among students for the professional development of future specialists is determined. It is concluded that the development of analytical skills takes time, this is a long, systemic process in professional education. The factors (positive and negative) influencing the development of students’ analytical skills are revealed. In the article, the authors focus on assignments and exercises (case assignments) aimed at developing students’ analytical skills. To diagnose the level of development of analytical skills of students, indicators have been developed, as well as the characteristics of the levels of development of analytical skills of university students - low, medium, high. The authors present the results of a pilot study to identify the level of development of analytical skills of students in humanitarian areas of training. The study was conducted in universities in the cities of Stavropol and Krasnodar. The results of the study showed that students have a predominantly medium and low level of development of analytical skills. Based on the results obtained, the authors identified the reasons for the low level of development of analytical skills among modern students.

Teaching Mathematics: Heuristics Can and Ought to Lead the Way

In contrast to problem-solving procedures that are the “bricks and mortar” of demonstrations in mathematics textbooks, heuristics, defined by Polya as “the study of means and methods of problem solving”, are those mental actions that enable the practitioner to make progress when it is not clear how to solve problems directly. Yet, as essential as heuristic tools are, they tend not to be included in presentations in mathematics textbooks. The overarching problem can be understood in terms of students’ not developing productive means for engaging problems. A few mathematics problems are included to argue for the validity, if not the priority, of the need for the incorporation of heuristics along with problem-solving procedures as standard content in mathematics textbooks.

DEVELOPMENT OF COGNITIVE ABILITIES IN CHILDREN WITH MENTAL RETARDATION THROUGH THE TECHNOLOGY OF STEP-BY-STEP FORMATION OF MENTAL ACTIONS IN THE PROCESS OF LEARNING THE ELEMENTS OF RESEARCH ACTIVITIES

Рассматривается возможность применения технологии поэтапного формирования умственных действий в процессе обучения детей элементам исследовательской деятельности как средства развития познавательных способностей младших школьников с задержкой психического развития. Материалом исследования послужил теоретический анализ научно-методической литературы по теме исследования: теория поэтапного формирования умственных действий П. Я. Гальперина; положения о развитии познавательных способностей младших школьников как результата развивающего обучения В. В. Давыдова, А. В. Запорожца, Л. В. Занкова, А. Н. Леонтьева; подходы к развитию познавательных способностей детей с задержкой психического развития Н. В. Бабкиной, Л. Н. Блиновой, А. Д. Вильшанской, Г. Н. Пениным, У. В. Ульенковой, Л. М. Шипицыной. Теоретический анализ научно-методической литературы позволил предположить, что технология поэтапного формирования умственных действий может эффективно применяться для обучения младших школьников с ЗПР элементам исследовательской деятельности на разном уровне самостоятельности и сложности и тем самым развивать у обучающихся познавательные способности. The purpose of this article is to consider the possibility of using the technology of step-bystep formation of mental actions in the process of teaching children the elements of research activity, as a means of developing the cognitive abilities of younger schoolchildren with mental retardation. The material of the study was a theoretical analysis of scientific and methodological literature on the topic of research: the theory of step-by-step formation of mental actions by P. Ya. Galperin; the provisions on the development of cognitive abilities of younger schoolchildren as a result of developing training by V. V. Davydov, A. V. Zaporozhets, L. V. Zankov, A. N. Leontiev; approaches to the development of cognitive abilities of children with mental retardation by N. V. Babkina, L. N. Blinova, A. D. Vilshanskaya, G. N. Penin, U. V. Ulenkova, L. M. Shipitsina. The theoretical analysis of the scientific and methodological literature suggests that the technology of step-by-step formation of mental actions can be effectively used to teach younger students with mental retardation the elements of research activity at different levels of independence and complexity, and thereby develop students’ cognitive abilities. The relevance of addressing the topic of the development of cognitive abilities in children with mental retardation (hereinafter referred to as PDA) is due to the fact that this category of children is one of the numerous groups represented in general education organizations that implement inclusive educational practice, since PDA can be observed in most categories of children with disabilities and is secondary in nature.

Imagination as a phenomenon of cognition

This article discusses the problem of imagination as a holistic phenomenon of cognition based on the concept of corporeality of mind. Imagination becomes an instrument for enactive subject – object interaction. They complement and revive each other in the activity of cognition and self-cognition. Imagination is a generative model of cyclical interaction between the subject and object in junction of the image and action. Imagination is a moment of visual culture, a means of shaping thoughts and feelings in the optical coherence of mental actions in the reproduction of the picture, scenic manifestations of the material in mental life of a person, interpretation of the imagery-symbolic language and action. Imagination creates the space of the game of feelings, mind, and body in the context of cognitive engagement of a person. The most vivid manifestation as a phenomenon of cognition imagination acquires in the practice of psychoanalysis. The scientific novelty of this work consists in the following statement: psychoanalytic description interprets imagination in realization of the image through body and mind. The article employs the method of enactive construction of knowledge, visualization and psychoanalytic description, which demonstrates imagination as an integrative dimension of a human, optically harmonizes body, thought, and external environment of a person. The article underlines the role of metaphors, transformation, and paradoxicality, which indicate the degree of depiction of the image through integration of the corporeal, social and imaginable in a circular, cyclical dependence. Imagination creates the syntheses of these dimensions in a “paradoxical system”, translation of the fiction into symbolic language, and symbolic substantiations of the living experience of a cognizing being. Imagination is the organic development of human nature. The interactant appears to be an external environment and part of the human organization that creates him through the living experience of cognition and self-cognition.

A TOOL OF INTERIOR ANALYSIS IN THE FRAMEWORK OF ANALYTICAL APPROACHES AND MERSIN TRAIN STATION BUILDING SAMPLE

Thinking is a skill that involves complex mental actions and shows individual differences. Thinking ability is the most important feature that makes humankind superior to other living things. Individual differences cause thinking to evolve into different types. Analytical thinking can also be defined as an act of thinking and understanding all parts of a whole. According to the philosophy of analytical thinking, all parts of the whole must be understood in order to understand the whole. There is a flow from piece to whole in the analytical thinking approach. In other words, it is an inductive approach. When considered in this context, the understanding of an interior space can be achieved by understanding all the parts of the interior one by one and establishing the relationship with the whole. A limited number of studies related to an analytical interior analysis tool were reached in the literature. For this reason, the aim of the research is to develop an analytical interior analysis tool and to evaluate this method developed within the scope of an example. For this purpose, an interior analysis tool has been developedin the light of the information obtained from the literature review. For an exemplary evaluation, Mersin Train Station Building, one of the works of the Second National Architecture Period, was chosen and was evaluated within the scope of this tool. As a result, it has been found that the use of an interior analysis tool in interior studies allows the examination of all elements of the entire interior, and enables the detection of erroneous and uncontrolled applications carried out in the process, especially in historical places without ignoring.

The use of educational and speech situations at the stages of learning the scientific style of speech

This article considers the stages of teaching the scientific style of speech of foreign students in pre-university training. Based on the analysis of the scientific literature, it is concluded that the effectiveness of classes in teaching oral language in a foreign language is achieved through the use of communicative and activity approaches, as well as the use of learning and speech situations that will help bring learning closer to natural communication. Therefore, the methodological basis is a threefold approach to learning theory. Given the classification of stages of formation in foreign listeners of full-fledged mental actions, four stages were identified, through which it is necessary to conduct foreign listeners in order to form in them speech skills and abilities within the scientific style of speech. The main task of the first stage (motivational-target) is to direct foreign students to study the scientific style of speech and develop interest in this discipline, mastering which will allow them to participate in communication in the educational and professional sphere and also partially prepare them for professional activity. At the content-preparatory stage, foreign students create guidelines for mental activity, ie there is an acquaintance and consolidation of grammatical constructions of scientific style of speech and the necessary scientific vocabulary, on the basis of which they will be able to perform any speech tasks. At the communicative stage, foreign students participate in communicative activities, forecasting and planning of speech, its production based on the studied grammatical constructions and the necessary scientific vocabulary, using speech etiquette, realization of skills of dialogic and monologue speech using educational speech terminology. At the final analytical-corrective stage the analysis and correction of formation of levels of oral speech of foreign listeners is provided and is realized through independent work on conversational educational and speech situations.

Psychological and pedagogical aspects of chemistry distant teaching to foreign university entrants

Chemistry is one of the most important courses in the system of pre-university training of prospective specialists with higher medical education. During the pandemic, we had to face some problems when organizing chemistry distance learning. There was a lack of data and opportunities for out-of-class interaction with students, since it was necessary to switch to the remote format in a very short time, literally within a few days. It was necessary to develop a model and methodological support to teach chemistry in the distant format and develop relevant professional competencies. The theoretical basis of the research is the theory of the planned development of mental actions and concepts and activities. Analyzing the results, we came to the conclusion that the implementation of this approach increased the motivation of university entrants to study chemistry. Methodological materials helped to improve the quality of training specifically for foreign entrants who did not know Russian well. The results of the final testing made it possible to conclude that the use of distance education or its elements in pre-university chemistry training is promising, necessary and expedient. All students in one way or another coped with the final certification and received certificates that allow them to continue their studies at a medical university.