scholarly journals COMPUTER ANIMATION IN 7TH GRADE ALGEBRA LESSONS: RESULTS OF EXPERIMENTAL WORK

2021 ◽  
Vol 58 (4) ◽  
pp. 126-133
Author(s):  
S.V. Saryglar ◽  
Keyword(s):  
Experimental Work ◽  
Computer Animation ◽  
Work Experience ◽  
Mathematical Knowledge ◽  
Research Work ◽  
Educational Activity ◽  
Teaching Mathematics ◽  
Mathematical Education ◽  
Mathematical Concepts ◽  
School Research

Statement of the problem. The article deals with the problem of visualization in teaching mathematics using animated drawings. The purpose of the article is to present the analysis of the experimental work on computer animation in the GeoGebra environment as a means of improving mathematical education at school. Research methodology. The methodological foundations of the research include activity-based, informational and visual approaches to teaching mathematics, a synthesis of the author’s work experience in testing computer animation at school. Research results. The results of the experimental work confirmed the expediency of using computer animation in the process of teaching algebra in the 7th grade (educational activity of students increased, as well as interest in research work and quality of mastering mathematical knowledge and skills). Conclusion. The use of computer animation in math lessons at school increases the level of understanding and assimilation of mathematical knowledge by providing clear illustrations of mathematical concepts and statements. The analysis of experimental work using the animation capabilities of computer environments shows an increase in the technological equipment of modern mathematics teachers, which help them achieve higher educational results.

The role and significance of computer animation in school algebra of complex numbers

2021 ◽  
pp. 22-27
Author(s):  
S. V. Larin
Keyword(s):  
Computer Animation ◽  
Research Work ◽  
Complex Numbers ◽  
Teaching Mathematics ◽  
Research Approach ◽  
Mathematical Concepts ◽  
Teaching Aids ◽  
Tenth Grade ◽  
Relevant Topic ◽  
Approach To Teaching

The article discusses computer technologies in teaching mathematics, which is relevant in the light of the digitalization of education. The role and importance of computer animation in algebra lessons in the study of complex numbers in the tenth grade in accordance with the current school textbooks are presented. Animation drawings can be used as demonstration drawings when studying the relevant topic, as a tool for testing knowledge, they provide an opportunity for experimentation, support the research style of developing learning. The use of animated drawings effectively replenishes the arsenal of teaching aids for a practicing mathematics teacher. This allows you to eliminate unnecessarily burdensome computational difficulties, to visualize mathematical concepts and statements, turning some of them into obviously correct ones, to facilitate the teacher's work in compiling tasks of the same type with different data. The management of the student's educational and research work on the manufacture of animation-geometric models of objects and phenomena contributes to the successful assimilation of knowledge by students, stimulates an experimental research approach to teaching.

scholarly journals ANIMATED IMAGES AS A MEANS OF DIGITAL TECHNOLOGIES IN TEACHING MATHEMATICS

2020 ◽  
Vol 53 (3) ◽  
pp. 54-61
Author(s):  
S.V. Larin ◽  
◽  
S.V. Chilbak-ool ◽  
Keyword(s):  
Public Relations ◽  
Work Experience ◽  
Mathematical Knowledge ◽  
School Teacher ◽  
New Technology ◽  
Effective Means ◽  
Digital Technologies ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Computer Environments

Statement of the problem. Universal digitalization of economy and public relations is a reality of today, and a school teacher is faced with the task of forming a personality ready to reveal his/her creative potential in the digital economy. The problem is to outline the ways of digitalization of teaching mathematics that meets the needs of society, and contribute to the understanding and assimilation of mathematical knowledge based on digital educational resources using the animation capabilities of computer environments. The purpose of the article is to present animated images in the GeoGebra environment as new means of digital technologies for teaching mathematics. Research methodology. Analysis of scientific, educational and methodological literature, synthesis of the authors’ work experience at school and university in approbation of elements of the mathematics teaching system using animated images. Research results. Specific types of animated images are presented and the expediency of their use as effective means of digital technologies for teaching mathematics in the lessons of arithmetic, algebra, trigonometry and the beginnings of mathematical analysis is substantiated. Conclusion. The use of new technology with the use of animated images in mathematics lessons at school increases the level of understanding and assimilation of mathematical knowledge by providing clarity of mathematical concepts and statements. In addition, animated images are used to eliminate computational difficulties, to generate tasks of the same type, and to organize self-testing of students’ knowledge. The creation of digital educational content using the animation capabilities of computer environments increases the technological equipment of a modern mathematics teacher, which will allow him/her to achieve better educational results.

scholarly journals The Concept of Theoretical-Empirical Dualism in Teaching Math

2020 ◽  
Vol 29 (4) ◽  
pp. 85-95
Author(s):  
G. D. Gefan
Keyword(s):  
Mathematical Knowledge ◽  
A Priori ◽  
Research Work ◽  
Cognitive Activity ◽  
Teaching Mathematics ◽  
Mathematical Education ◽  
A Posteriori ◽  
Research Activities ◽  
New Knowledge

Among the problems of mathematical education, the article highlights: (1) insufficient attention paid to the fundamental, structure-forming role of mathematics; (2) speculative learning, its isolation from practice. The concept of theoretical-empirical dualism in teaching is formulated as the unity of the abstract-theoretical and experimental-empirical cognitive activity of students. According to the author, a priori and a posteriori mathematical knowledge should be distinguished. A priori knowledge either seems to an individual to be completely obvious, indisputable, or he assimilates it uncritically, “on faith”. A posteriori mathematical knowledge subjectively arises in the process of student’s intense theoretical and practical activity, and is being actively and comprehensively verified experimentally – either using mathematical applications, or through mathematical experiments. The empirical component of teaching mathematics implies a variety of forms and methods of active (including computer) and professionally oriented learning, giving experience in independent formulation of problems, joint search for ways to solve them, interaction and teamwork. Particular attention is paid to the use of mathematical experiments in those frequent cases when it is necessary to replace or supplement complex evidence, illustrate new knowledge, and give research skills. Monte Carlo mathematical experiments are demonstrated, which serve, in particular, as a bright, figurative, and convincing form of reinforcing theoretical knowledge in the field of stochastic branches of mathematics. The research work of students is considered as the highest stage of the students’ theoretical-empirical activity. The article proposes subjects of research activities of students in the process or upon completion of the study of probabilistic and statistical disciplines.

scholarly journals Digital Representations of Mathematical Objects in the Context of Various Forms of Representation of Mathematical Knowledge

2020 ◽  
pp. 58-86
Author(s):  
Semjon F. Adlaj ◽  
◽  
Sergey N. Pozdniakov ◽  
Keyword(s):  
Comparative Analysis ◽  
Digital Media ◽  
Mathematical Knowledge ◽  
Information Environment ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Mathematical Objects ◽  
Computer Tools ◽  
Digital Representations ◽  
The Impact

This article is devoted to a comparative analysis of the results of the ReMath project (Representing Mathematics with digital media), devoted to the study of digital representations of mathematical concepts. The theoretical provisions and conclusions of this project will be analyzed based on the theory of the information environment [1], developed with the participation of one of the authors of this article. The analysis performed in this work partially coincides with the conclusions of the ReMath project, but uses a different research basis, based mainly on the work of Russian scientists. It is of interest to analyze the work of the ReMath project from the conceptual positions set forth in this monograph and to establish links between concepts and differences in understanding the impact of computer tools (artifacts) on the process of teaching mathematics. At the same time, the authors dispute the interpretation of some issues in Vygotsky’s works by foreign researchers and give their views on the types and functions of digital artifacts in teaching mathematics.

scholarly journals Pedagogical conditions for implementing value and sense direction of training mathematics at higher school

2020 ◽  
pp. 80-92
Author(s):  
Larisa V. Zhuk
Keyword(s):  
Creative Thinking ◽  
Educational Process ◽  
Teaching Mathematics ◽  
Mathematical Education ◽  
Search Activity ◽  
Mathematical Concepts ◽  
Teaching Aids ◽  
Semantic Orientation ◽  
Cognitive Information ◽  
The University

The article actualizes the issue of updating the content, methods and means of teaching mathematics at the university within the sociocultural paradigm. A significant contradiction characterizing the crisis situation in the field of higher mathematical education is the mismatch between the traditional organization of the educational process and the powerful developing potential of mathematical disciplines. Being overloaded with a lot of information, altogether with its insufficiently developed anthropological, cultural-like and communicative components, mathematical education hinders the mental development of the learner’s personality in relation to such important qualities as search activity, creativity, and creative thinking. The solution to this problem can be the transformation of the cognitive-information model of learning, the introduction of pedagogical technologies that actualize the sociocultural aspect of mathematical education. The aim of the study is to develop methodological foundations for the implementation of the value-semantic orientation of teaching mathematics at the university, expressed in providing a set of pedagogical conditions related to the selection of content, determination of teaching aids and methods, ways of organizing the interaction of students and a teacher, in which students intelligently master mathematical concepts, and freely operate with them. The didactic conditions for the implementation of the value-semantic orientation of teaching mathematics at the university are: the transformation of mathematical content, expressed in learning from sociocultural experience; the psychodidactic approach, focused on building the students’ self-motivation; the use of teaching methods that provide cognitive and emotional empathy (educational mathematical discourse), the activization of productive mental activity (technology of problematic dialogue); inclusion of non-standard, creative tasks, training cases. Providing these conditions will allow to realize the humanitarian potential of mathematics, to reveal the social, practical and personal significance of the subject matter.

scholarly journals Development of a personalized model of teaching mathematics by means of interactive novels to improve the quality of pupils' educational results

2021 ◽  
Vol 53 (5) ◽  
pp. 306-322
Author(s):  
Mikhail I. Bocharov ◽  
◽  
Tatiana N. Mozharova ◽  
Elena V. Soboleva ◽  
Tatyana N. Suvorova ◽  
...  
Keyword(s):  
Short Story ◽  
Computer Games ◽  
Research Work ◽  
Digital Technologies ◽  
Personalized Learning ◽  
Teaching Mathematics ◽  
Mathematical Education ◽  
Non Linear ◽  
Educational Path

The problem and the aim of the study. The implementation of educational programs in different subjects of modern school, including mathematics, is based on the principles of personalized learning, the active use of digital technologies and means of interactive interaction to ensure a high level of mathematical education. The purpose of the article is to investigate the features of the development of a personalized model of teaching mathematics by means of interactive novels to improve the quality of educational results. Research methods. The theoretical analysis and generalization of scientific literature on the problems of improvement of the quality of mathematical education, of the personalization of education by digital technologies, of the didactic role of the visual interactive literature as a kind of computer games, are applied. The main methodological principle of the study is determined by the key condition of personalized learning. That is the freedom of students to choose their educational path. The empirical methods were used: observation, analysis of the results of work with AXMA Story Maker application (answer selection, number of attempts to find a solution and of publications read). The study involved 121 7th-grade pupils of school №11, Kirov. In the experiment, the Fisher criterion was used to process the results. Results. The members of the experimental group were involved in the study of mathematical theory, solving of the tasks according to their personalized educational path in the interactive AXMA Story Maker space. Personalization is supported by self-selection of the pupil's response in a non-linear visual novel environment. Statistically significant differences between the experimental and control groups in terms of the level of educational results were revealed (φcrit = 1.64 <φemp = 2.964). In conclusion, the features that should be considered when designing a personalized model of teaching mathematics by means of interactive novels are summarized: correlating the didactic goal and the result of educational research work in a non-linear environment, choosing a plot for a visual short story, considering the text component and the personalized trajectory of cognition etc.

scholarly journals ANOMALIES IN THE IMPLEMENTATION OF METHODS OF TEACHING MATHEMATICS AND THEIR CONSEQUENCES

2021 ◽  
pp. 8-12
Author(s):  
M. LUTFULLIN ◽  
V. LUTFULLIN ◽  
L. MATYASH
Keyword(s):  
High School ◽  
Educational Material ◽  
Inductive Method ◽  
Practical Implementation ◽  
Teaching Mathematics ◽  
Mathematical Education ◽  
Mathematical Concepts ◽  
Deductive Method ◽  
Inductive Methods ◽  
Main Thing

The article deals with the negative trends in the development of school mathematics education in the context of the relationship of inductive and deductive methods of teaching educational material. It is stated that the dominance of deduction in teaching of mathematics in high school and its separation from inductive explanations to students of mathematical concepts, definitions, rules, formulas indicates a complete disregard for pedagogical experience and K.F. Lebedyntsev and D. Polya’s methodical research. The historical causes of excessive application of the deductive method of teaching mathematics are revealed: the centuriesold practice of imitating the method of “Beginnings” by Euclid; historically short (about four centuries) period of induction method formation in scientific research; even shorter period of pedagogical induction applications practice. In order to more fully revealing the pedagogical significance of inductive methods of teaching mathematics, a brief analysis of the methodical features of lectures course on algebra, developed and delivered by I. Newton to the students of Cambridge University, was carried out.It is found out that this course has a strong inductive orientation and revealed this genius English scientist’s conviction that teaching mathematics is an art in which solving examples and problems is more important and useful than rules. It is emphasized that this I. Newton’s conviction was significantly ahead of other Western European mathematicians. The purposefulness and persistence of national mathematicians-teachers M.G. Kurganov, F.I. Busse, P.S. Guriev, O.M. Strannolyubsky, S.I. Shohor-Trotsky, K.F. Lebedyntsev in substantiating the pedagogical significance of the inductive method of teaching mathematics and its practical implementation were noted. The important general didactic significance of F.I. Busse’s views on the implementation of learning consciousness principle has been revealed. Examples of M.M. Luzin’s high school education and modern practice of training mathematics teachers are given. They show that the lack of inductive explanations of the main thing in the content of the lesson turns deductive learning into formal-deductive, accompanied by the substitution of understanding by thoughtless mechanical memorization of educational material. The exceptional relevance of the practical implementation of the methodical heritage of K.F. Lebedyntsev and D. Polya’s in the context of solving the problem of improving the quality of school mathematical education is substantiated. The most important task of of the considered problem – determinating the practical ways of its decision – is formulated.

scholarly journals THE DEVELOPMENT OF MATHEMATICAL CULTURE OF STUDENTS AS A COMPONENT OF PROFESSIONAL COMPETENCE

2020 ◽  
pp. 131-136
Author(s):  
Olena KHODAKOVSKA ◽  
◽  
Svitlana USTYCHENKO ◽  
Keyword(s):  
Mathematical Knowledge ◽  
Intellectual Development ◽  
Educational Activity ◽  
Mathematical Education ◽  
Mathematical Activity ◽  
Mathematical Language ◽  
Mathematical Culture ◽  
Holistic View ◽  
Study Results ◽  
Development Of Students

Introduction. In recent years, teachers of most technical and natural sciences faculties find the level of freshmen starting a course of higher mathematics insuf-ficient to comprehend the basics of logical constructions. It is difficult for students to clearly realize that, for example, they should learn to prove a statement as a theorem or give a counter-example; in mathematics there are such terms as necessary and sufficient conditions, cause and effect; the system of equations and their totality are dif-ferent things; the properties of mathematical objects are subject of study; solving inequalities or equations requires understanding but not mechanical memorization. All these semantic subtleties make up the concept of mathematical culture based on clear logic reasoning and conclusion. Logical thinking is required in most activities, from business to programming. The relevance of the research is caused by the neces-sity to create a new educational environment free from such negative facts that some students have a low level of mathematical knowledge, skills and abilities; they are enable to independently acquire new mathematical knowledge and skills; their experience in mathematical, communicative and cognitive activity, necessary for a successful future career, is insufficient. International and Ukrainian scientists in the field of pedagogy and psychology diversely studied the problems of intellectual development and mathematical culture of students. (Jean Piaget , Jerome Seymour BrunerLev Vygotsky, Yuriy Hilbukh, Leonid Zankov, Vasilii Davydov, Daniil Elkonin, G.S. Kostiuk, Z.I. Kalmykova, N.O. Menchynska, S. L.Rubinstein, V.F. Palamarchuk, N.F.Talysina etc).The purpose of the articleis to generalize the pedagog-ical essence of mathematical culture, determine the place and role of mathematical education in the formation of students' mathematical culture, study pedagogical pre-requisites and specific technologies of its formation while teaching mathematics and determine conditions for crea-tion of the culture of mathematical language. The methods of analysis, comparison, explication, ab-straction are used in the study. Results. The development of mathematical culture of students involves a number of stages: formation of the student as a subject of educational mathematical activity; awareness of the mathematical education value; creating a holistic view of mathematical activity of the student; understanding mathematical learning materials; reflection of the general structure of mathematical activity in the educational activity; mathematical language acquisition, ability to correctly express and explain operations, ability to use mathematical signs and symbols; gaining under-standing of mathematical modeling as a mathematical method of reality cognition; mastering the system of mathematical concepts, general methods of operations; intellectual and spiritual development of students, includ-ing the development of mathematical thinking, meeting the requirements of modern information society, the develop-ment of children's motivation, creativity, research skills. The culture of mathematical language can only devel-op if the student has a sufficiently strong scientific base that allows him not to concentrate on thinking about the scientific accuracy of a story but to focus on how to speak. Originality. The Internet provides lots of opportunities to develop mathematical culture and present information of different nature: 1) mathematical information for com-pulsory learning i.e. comprehensible knowledge, filled with personal meaning should become a student's acqui-sition; 2) mathematical information for expanding ideas about the subject i.e. elements of logic, combinatorics, probability theory; 3) background information plays an important role in acquiring information, realizing its value, and creating the interest and need to study mathematics.Conclusions. The level of mathematical culture of stu-dents significantly increases under condition of taking nto account the leading ideas of modern international and Ukrainian psychological and pedagogical science about intellectual development of the personality; theoreti-cal substantiation of the content of students' mathemati-cal culture; working out a science-based approach to the technology of development of mathematical qualities of the personality when studying mathematics. In order to improve the culture of mathematical lan-guage, it is necessary to increase the classroom time for the development of oral language skills; allocate 10-15 minutes for oral questioning at every lesson; organize home test papers with an oral performance report in the form of an interview; conduct credit tests orally. Such forms of work contribute to the development of students' mathematical language

scholarly journals Class teachers’ attitudes towards the importance of the activity of setting up the problem in teaching mathematics to beginners

2018 ◽  
Vol 50 (2) ◽  
pp. 247-268
Author(s):  
Aleksandra Mihajlovic
Keyword(s):  
Work Experience ◽  
Teaching Practice ◽  
Mathematical Thinking ◽  
Attitude Scale ◽  
University Education ◽  
Future Research ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Positive Effects ◽  
Teachers Attitudes

Besides the actual solving of the problem, the so-called setting up the problem plays a very important role in the field of mathematics and mathematical thinking. When students are engaged in the activity of setting up the problem, they are actually placed in the ?role? of the mathematician as a scientist and offered a possibility to experience a different aspect of mathematics. Still, regardless of the positive effects shown by the results of numerous research studies, this activity is not sufficiently represented in the actual teaching practice of mathematics. Since teachers have the key role in the preparation and implementation of the activity of setting up the problem and their actions can influence the quality of knowledge and understanding of mathematical concepts, as well as students? ideas, the main aim of the research was to determine whether class teachers recognised the importance of organising the activity of setting up the problem in teaching mathematics to beginners. The sample included 161 class teachers. Data were collected using an attitude scale. Combined standard quantitative and qualitative methods were used to process the data. Research results have confirmed that class teachers hold a positive attitude towards the activity of setting up the problem. The established differences with respect to class teachers? work experience and the level of education point to the fact that more attention should be devoted to university education and in-service teacher training when it comes to the activity of setting up the problem. Future research should analyse the extent to which class teachers? teaching practices actually reflect their attitudes.

The Role of the Subject “Mathematics” Content in the Learning Motivation

2019 ◽  
Vol 16 (12) ◽  
pp. 5243-5247
Author(s):  
Nailya Vakifovna Timerbaeva ◽  
Elmira Ildarovna Fazleeva ◽  
Kadriya Barievna Shakirova
Keyword(s):  
Beginning Teachers ◽  
Subject Matter ◽  
Educational Activity ◽  
Teaching Methodology ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Motivation For Learning ◽  
The Subject

The future of any country depends on the quality of education, in particular, mathematics. This paper represents an investigation of the possibilities of using motivation, which is one of the main conditions for improving the quality of teaching mathematics. Educational motivation, as a particular type of motivation, is determined by many factors: the educational system, the organization of the learning process, the subjective characteristics of a student and teacher. In our opinion, the factor associated with the very specificity of the subject matter “mathematics” remains insufficiently studied. Experience has shown that practice teachers and beginning teachers underestimate the role of motivation in teaching mathematics. They unconsciously or quite consciously skip the stage of motivation when introducing mathematical concepts, studying theorems, etc., not seeing the potential of the subject matter for the implementation of motivation. The purpose of the study is to identify the capabilities of the subject matter “mathematics” in the implementation of motivation, as well as the pedagogical conditions for preparing future teachers for its implementation. The research methods for this problem are the theoretical analysis of the knowledge of this issue, questionnaires, overt observation. The study showed that students and beginning teachers knowing the general techniques and methods of motivation do not see the potential possibilities of the subject of mathematics and specific topics for its implementation. At the same time, we have established that motivation can be carried out at any stage of training: by introducing mathematical concepts, algorithms, studying methods of action, methods for solving problems and theorems. Improving the training of future mathematics teachers is associated with the development of mathematical, pedagogical and methodological thinking of students, allowing motivation to introduce to study mathematics as a subject. To do this, in the classes on the teaching methodology, it is worth to purposefully teach the methods of motivation for educational activity in all substantive lines of the school course in mathematics to supplement the training content with courses on the choice of “Methods of student motivation,” “The role of motivation in teaching mathematics,” “Motivation for learning through the content of the subject.

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