Training Of Future Mathematics Teachers Research Articles

Future teachers’ reflections on mathematical errors made in their teaching practice

AbstractThis study answers the following research questions: 1) What types of mathematical errors do future teachers identify when they reflect on their practice? and 2) Which levels of development of the didactic suitability assessment competence for the “errors” component can be inferred when they reflect on their practice? To answer these questions, we explain the Didactic Suitability Criteria construct and describe the associated training cycle structure in the theoretical and methodological framework sections. We followed a qualitative research methodology that mainly consists of thematic analysis. The study conducted allows finding inductive categories of types of mathematical errors, such as error in the task instructions, error of proposition, procedural error, error in the representation, error in the definition and error in the argument. It also enables establishing levels of development of the didactic suitability assessment competence of future teachers for the “errors” component. The main conclusion of this research is the importance of the context to decide what a mathematical error is. The need to further examine the notion of mathematical error in the training of future mathematics teachers is also stressed. Another conclusion is the development of a rubric that allows for more accurate and deeper reflections of future teachers on the errors made.

Responsibilities and perception of course coordinating professors of the curso de Licenciatura em Matemática no IFSP regarding the scope of the function

This article, an excerpt from the author's thesis, presents the responsibilities and impressions of the teachers who served as Coordination of Degree in Mathematics, at the Federal Institute of Education, Science and Technology of São Paulo (IFSP), between 2008 (the first institutional offer of the course) and 2021 (date of data collection), regarding the exercise of the function. With the central objective of identifying how the function demands pedagogical and educational management dimensions, we started with institutional documents and qualitative research data, obtained in a questionnaire sent to all (former) coordinators of the aforementioned period. By opting to categorize the data, two dimensions were obtained: pedagogical and educational management. This movement resulted in the characterization of the function as articulating, formative and transformative, from the point of view of the pedagogical dimension. As well as educational management consisting of leadership, democratic processes, participatory management and organizational culture and climate. (In)directly impacting the initial training of future mathematics teachers.

Risks in Identifying Gifted Students in Mathematics: Case Studies

Abstract The article discusses the risks involved in identifying gifted students in mathematics in the school environment. Although the theory of gifted students is widespread and available today, school practice shows many cases of gifted students who have not been identified in the school environment. The reasons for this are various. The article will present the theory related to this topic. The research was conducted as two case studies using qualitative research methods. Semi-structured interviews with parents and pupils were used, and the pupils were observed for a long time by the researcher. In the first case, it was a mathematically gifted pupil with dyslexia, and in the second case, it was a mathematically gifted pupil with an extremely high IQ. The result of the study was to find out in which moments the school did not provide support to the pupil in the two cases mentioned and what kind of help the pupil would appreciate at school. Both pupils were involved in a 1-year intervention in which the intention was to cultivate their mathematical thinking and expressions with the help of appropriately chosen tasks. The stated findings are important for practice and discussion about the training of future mathematics teachers, for which consistent professional training focusing, among other things, also on the education of gifted students is essential. Both case studies are part of long-term research dealing with the identification of gifted students.

Применение цифровых инструментов обработки естественного языка для оптимизации подготовки учителя-предметника в полилингвальной образовательной среде

The aim of the research is to automate the analysis process of the most common grammatical forms and syntactic structures of a foreign or second language to optimize the content and acquisition of English language programs in the training of future Mathematics teachers for professional activities in a multilingual educational environment. The paper theoretically justifies the necessity of a comprehensive frequency analysis of language structures. Software tools for natural language processing (the Python programming language and the spaCy library) were developed, which were subsequently applied in the course “Methods of Mathematical Data Processing” to identify the most frequent grammatical forms and syntactic structures characteristic of the English language of Mathematics. Based on the data obtained, methodological recommendations were formulated for the content and outcomes of English language programs for future Mathematics teachers in a multilingual educational environment. The scientific novelty of the research lies in using digital natural language processing (NLP) tools for a quantitative and statistical analysis of language data, necessary for the development of methodological recommendations for the content and outcomes of foreign/second language programs for subject teacher training. As a result of the research, it was found that digital natural language processing tools can be used to improve the language training of subject teachers in a multilingual educational environment.

Features of Preparing Future Mathematics Teachers for the Implementation of Logical Tasks

This article describes the types of logical tasks in Mathematics textbooks of the main school according to the updated program and the characteristic features of the methodological training of future mathematics teachers in their implementation. The issue of preparing students for the implementation of logical tasks is considered. Methods and techniques for improving the logical thinking of students studying in the specialty of a mathematics teacher are outlined. The main task of teaching mathematics is the development of logical thinking and logical training of students. Accounting in the ability to think logically, along with the interest of a student who comes to school, is the main task of a mathematics teacher. Therefore, it is necessary to train future teachers of mathematics as young specialists capable of developing logical literacy of students using effective teaching technologies. This leads to the need to increase the requirements for the quality of teaching students in general schools and, accordingly, the quality of training of future teachers in pedagogical universities. However, only supplementing the process of training students with new content, increasing the amount of knowledge communicated to students is not able to solve the task of raising the quality of teacher training to the level of modern requirements. The solution to this problem, in our opinion, lies in the systematization of fundamental training of future teachers, should be logical training that allows students to be confident in critical thinking, analysis, reasoning and reasoning, maintain and justify their point of view.

ПРАКТИКО-ОРИЕНТИРОВАННАЯ МОДЕЛЬ МЕТОДИЧЕСКОЙ ПОДГОТОВКИ БУДУЩЕГО УЧИТЕЛЯ МАТЕМАТИКИ В УСЛОВИЯХ ИНДИВИДУАЛИЗАЦИИ ОБРАЗОВАНИЯ

The article describes the aspects of practical training of future mathematics teachers in the system of higher pedagogical education in the context of the development of the paradigm of education individualization. The experience of the Orel State University named after I.S. Turgenev on the implementation of the practice-oriented individualized model for the training of future teachers is represented.

Game-Based Learning and Gamification Technologies in the Preparation of Future Mathematics Teachers

Our paper advocates the preparation of future mathematics teachers for the use of game-based learning and gamification technologies. For this purpose, we created a university course that is dedicated to familiarizing the students with basic concepts of game-based learning and gamification and to conveying direct experience with their use. We support the concept and activities in this course by the positive results of the research on the opinions of 115 students. We hope that the positive results and our description of the course will be an inspiration for the broader incorporation of game-based learning and gamification technologies into the training of future mathematics teachers. Limitations of our research are the research sample, we investigated students’ reactions only at the author’s home university. Therefore, in the future, the research could be done with a broader sample and studying more in detail the students’ beliefs related to game-based learning and gamification before and after the course to get a better view of their development.

Болашақ математика мұғалімдерін геометриялық салу есептеріне даярлауда «деңгейлеп оқыту» технологиясын қолдану

The article examines the issue of methodological preparation of future mathematics teachers for teaching geometric construction problems, analyzing the educational program "Mathematics Teacher Training" prepared by the University from the subject and meta-disciplinary point of view. Based on the use of "level learning technology" in teaching future mathematics teachers to solve construction problems, students' creativity and research abilities, independent work, abstract thinking, etc. problems of improving methodological training by developing skills are studied. Mastering new technologies of teaching in the field of modern education helps the teacher to develop himself and effectively organize the educational process. The use of new technological methods of teaching increases the level of education of students in accordance with modern requirements. In the given article, the authors analyzed the state programs and concepts, the works of domestic and foreign scientists, the results of an online survey, and interviews conducted with students. 68 studentsofthe mathematics education program were involved in a pedagogical experiment, and the results were shown. As the analysis of the survey shows, after using the "level learning technology" in the lesson, students are recognized from a certain personal subjective point of view, which regulates their cognitive and practical activities. It has been shown that the use of "Level-level teaching technology" in the teaching of structural calculations allows effective and efficient organization of education, and increases the methodological training of future mathematics teachers.

Болашақ математика мұғалімдерін геометриялық салу есептеріне даярлауда «деңгейлеп оқыту» технологиясын қолдану

The article examines the issue of methodological preparation of future mathematics teachers for teaching geometric construction problems, analyzing the educational programs “Mathematics Teacher Training” prepared by the University from the subject and metadisciplinary point of view. Based on the use of “level learning technology” in teaching future mathematics teachers to solve construction problems, students’ creativity and research abilities, independent work, abstract thinking, etc. problems of improving methodological training by developing skills are studied. Mastering new technologies of teaching in the field of modern education helps the teacher to develop himself and effectively organize the educational process. The use of new technological methods of teaching increases the level of education of students in accordance with modern requirements. In the given article, the authors analyzed the state programs and concepts, the works of domestic and foreign scientists, the results of an online survey and interviews conducted with students. 68 students of the mathematics education program were involved in a pedagogical experiment, and the results were shown. As the analysis of the survey shows, after using the “level learning technology” in the lesson, students are recognized from a certain personal subjective point of view, which regulates their cognitive and practical activities. It has been shown that the use of “Level-level teaching technology” in the teaching of structural calculations allows effective and efficient organization of education, and increases the methodological training of future mathematics teachers.

Use of Media Educational Technologies to Increase Information Competence in the Process of Education of Future Mathematics Teachers

The article describes the experience of implementing media educational technologies in the process of training future mathematics teachers. The current situation in education dictates new requirements for the training of students of higher educational institutions, which consist in the fact that acquiring only special knowledge is not enough in order to be a competitive graduate, it is necessary to develop such abilities of the individual that reveal his individuality and creative potential to the greatest extent. The educational process can be improved by the modernization of the education system and the emergence of innovative learning technologies. The use of media educational technologies in the process of training future mathematics teachers improves the individual learning of students, their motivation and creative ways of creating media tools and increases informational competence in general. The modern educational space cannot be imagined without the use of Internet technologies, where electronic educational resources help to form the necessary qualities in students in an informational and educational environment. Therefore, the use of media educational technologies to increase information competence in the process of training future teachers in the educational activities of a higher educational institution is more relevant than ever. This means that teachers have a completely different approach to imparting knowledge. Using electronic educational resources of the new generation and technological methods of media education, teachers will be able to build courses in an active, interactive mode, in distance learning, in synchronous, asynchronous, and as it happens today, as well as during military operations in Ukraine. In this regard, it is necessary not only to form a modern and well-organized system of theoretical knowledge and skills of teachers, but also to prepare for the effective application of this knowledge in pedagogical activity and to overcome the difficulties that arise when using it. knowledge in practice. According to the results of the obtained empirical data, the effectiveness of the use of media educational technologies in distance learning during the training of future mathematics teachers has been proven.

The training of the future mathematics teachers for working in The new ukrainian school

The article presents the elements of the methodology of future mathematics teachers' preparation for work in the New Ukrainian School. The role of the teacher in the formation of the key competencies that students will acquire is analyzed. The need for changes in the training of future mathematics teachers in the context of the implementation of school education reform is revealed. The role of the discipline "Methods of teaching mathematics" in the training of future mathematics teachers during the transition to new state standards is highlighted. The methodological competences of the future mathematics teacher of the New Ukrainian School are given.

Оn the implementation of a transdisciplinary approach in preparing future mathematics teachers

Introduction. The disparate study of certain areas and branches of knowledge, characteristic of the disciplinary approach, has largely lost its position, recognising the inevitability of interdisciplinary cooperation. At present, interdisciplinarity is already being comprehended at a new level, creating the prerequisites for the introduction of a transdisciplinary approach to solving complex problems, including in the educational sphere.Aim. The current research aims to present the transdisciplinary teaching means, which are relevant in the process of training future teachers of mathematics, and which are identified on the basis of an analysis of the content of education.Methodology and research methods. General scientific and empirical methods were used to develop the ideological basis of the study. The aforementioned methods allowed the authors to draw up a complete picture of the problem under study, to identify its patterns and trends, to understand the essence. The search and selection of mathematics subject content with transdisciplinary properties was based on a systematic and interdisciplinary approach. At the stage of testing the research hypothesis, the competency-based approach was decisive, and tactical tasks were solved by referring to the activity approach. In addition, the main provisions of the concepts of humanisation and humanitarisation of education, as well as the principles of fundamentalisation of mathematical education, were taken into account.Results and theoretical significance. The expediency of using inequalities and convex functions in the training of future mathematics teachers in the context of a transdisciplinary approach is substantiated. A phased description of the work carried out allows us to trace the methods of reflecting the modern scientific content of the relevant topics, conditions, means and expected results of pedagogical interaction. The theory and methods of teaching mathematics at the university are enriched with a qualitatively new vision of the educational potential of the concepts of inequality and a convex function.Practical significance. The introduction of inequalities and convex functions in the process of future mathematics teachers training at Vyatka State University made it possible to demonstrate the possibilities of a transdisciplinary approach in the development of students’ worldview and the formation of professionally significant students’ competencies. The presented means of implementing the transdisciplinary approach can also be comprehended in teaching students of other areas of training.

THE VALUE-COMPETENT APPROACH IN THE PROFESSIONAL TRAINING OF FUTURE TEACHERS OF MATHEMATICS

The article highlights the pedagogical expediency of using the value-competency approach in professional training of future mathematics teachers. The content of the concepts “competence”, “value-semantic competence”, “value-competence approach” is outlined. It is noted that the value-competency approach to the organization of the educational activities of future mathematics teachersensures unity in the formation of professional competences and life values (general cultural competences) of the students of education. It is indicated that the value-competency approach is focused on the formation of value-semantic competence, which is one of the key components of the readiness of future teachers for professional activity and is connected with a personʼs value orientations, his ability to see and understand the world around him, to navigate in it, to realize oneʼs role and purpose, to act creatively, to be able to choose target and meaning settings for oneʼs actions and deeds, to make decisions. It was established that the formation of value-semantic competence in future mathematics teachers in particular involves: the formation of an intellectual, spiritually developed personality; formation of oneʼs own value orientations regarding the future profession and field of activity; formation of patriotism; development of humanism and morality; development of independence, personal initiative; mastery of methods of self-determination in situations of choice based on one's own positions; fostering activity, the ability to make decisions and take responsibility for their consequences; fostering kindness and tolerance towards colleagues, students and their parents, the ability to work in a team; education of love for the teaching profession, etc.Among the innovative teaching methods that ensure the implementation of the value-competency approach in the professional training of future teachers of mathematics, the case method and the method of educational projects are defined.
 Keywords: future teachers of mathematics; competence; value-semantic competence; value-competence approach; value orientations; case method; method of educational projects; professional training of future teachers of mathematics.

PROFESSIONAL TRAINING OF FUTURE TEACHERS OF MATHEMATICS: THE PROBLEM OF FORMING CRITICAL THINKING

The relevance of the problem under consideration. In the process of training at the pedagogical university, the educational activities of future mathematics teachers should acquire the features of his professional activity, so in addition to mastering knowledge, must have the ability to control mental processes, justify, identify problems and find their own solutions, be able to defend their opinions, choice of elements of educational content and teaching methods in lesson design. These provisions intensify the problem of developing critical thinking of future mathematics teachers in the process of their professional training. The purpose of the study is to reveal ways to organize the process of professional training of future teachers of mathematics, which will contribute to the effective formation of their critical thinking in the study of professional mathematical disciplines. Research methods: theoretical: analysis, systematization and generalization of pedagogical and psychological research. Critical thinking is the most important component of the training of future mathematics teachers. Critical thinking of the teacher is generally defined as a type of evaluative thinking activity, based on the formed skills of a certain type, which contributes to the understanding of theoretical knowledge, translating them into practical activities and predicting results. Methods of training future teachers of mathematics, focused on the formation of critical thinking skills, includes the organization of the educational process based on involving students in active cognitive activities using various methods of working with information and development of specially designed sets of tasks.

RETRACTED: The role of applied problems in the training of future mathematics teachers in the 21st century

• Improvement of the mathematical education for future teachers of mathematics and, accordingly, the training of students at universities and schools is a national priority task. • The educational process focuses on the application of theoretical knowledge in practical activities with the integrated presentation of disciplines (mathematics + technology + computer science). • The mathematical preparation of both future teachers and school students is one of the key elements of the intellectual development of youth. Improvement of the mathematical education for future teachers of mathematics and, accordingly, the training of students at universities and schools is a national priority task. The purpose of this article is to analyze existing scientific, practical, and theoretical works highlighting the applied problems use in preparing future mathematics teachers to assess the current situation and develop solutions. To disclose the research topic, an analysis of terminological interpretations of the concepts “applied task” and “applied/practical orientation” was carried out; analyzed the impact of the use of applied tasks on a set of competencies; the generalization method was used in the analysis of the usage of pedagogical software in teaching students; using a comparative analysis, provided information on the methodological and subject training of mathematics teachers in higher educational institutions of Ukraine, Poland, Bulgaria and the UK. This analysis demonstrates the interest and understanding by teachers and scientists of the didactic purpose of the applied orientation in teaching mathematics, as well as the use of applied tasks in the learning process. Based on the analysis of the sphere of usage and didactic orientation, author's interpretation of the term “applied problem” is proposed. The author's vision of the role and place of applied problems in the preparation of mathematics teachers is given. Along with the application of applied problems in local mathematical disciplines, there is an inclusion in the curriculum of a separate discipline “Applied Mathematics”.

Theoretical and practical bases of professional training of future mathematics teachers for differentiated learning

Theoretical and practical bases of professional training of future mathematics teachers for differentiated learning

RETRACTED: Methodology for using web technologies to develop the intellectual abilities of future mathematics teachers

• The current stage of development of Kazakh education is characterised by intensification of large-scale transformations. • The Internet has made significant changes in the organisation of public space. • In the process of teaching a discipline, the Internet can play the role of a source of information, a means of control, a field of communication, a way of organising the learning process itself. The article actualises the problems of professional-pedagogical education, in particular, the issues of using web technologies in the process of psychological and pedagogical training of future mathematics teachers. The authors outlined a range of relevant issues, the solution of which is possible under the condition of implementing elements of a mixed learning system using cloud technologies. The article presents the results of an online survey of students of the specialisation “Secondary education” to determine the degree of using web applications in the process of psychological and pedagogical training and the degree of their interest in the use of cloud technologies in their future professional activities. The scientific novelty is determined by the fact that the ways of implementing cloud services into the educational process of high school are highlighted. The study identifies the system of principles that contribute to the effective organisation of psychological and pedagogical training of future mathematics teachers using web technologies. The practical significance of the study is determined by the fact that the main lines of improvement of the psychological and pedagogical training of future mathematics teachers are characterised, provided that web technologies are used.

Competency approach to the study of the second-order surface interface as the geometric location of points in space

The necessity of the formation of students' functional literacy as a competency approach to the training of future Mathematics teachers is substantiated on the example of studying of one of the topics of analytical geometry. It has been established that a prerequisite for the development of any competency prescribed in the standards of secondary education is the initial existence of a sufficiently new concept of functional literacy for a student of a certain level. The basic literacy comes down to the ability to read, write and express of one's thoughts correctly. Let us consider the issue of functional literacy from the point of view of the pedagogic specialty. Acquaintance with the well-known textbooks of analytic geometry allows us to say that 2nd order algebraic surfaces in Euclidean space are determined in most cases algebraically by means of equations. A constructive approach is also of use – surfaces are obtained by rotating 2nd degree curves around their symmetry axes and by deformation of the resulting surfaces by compression. The metric approach, as it used for 2nd order curves, is restricted only by the formulation of problems to find the certain locus of points in space. The exception is the article Dmitriy Perepyolkin which was published in 1936. In this paper the locus of points in space with the following characteristic property is studied – the ratio of the distance to a given point to the distance to a given straight line is constant. The strait line is assumed not to contain the point. The study is held out in pure geometrical manner – it is done using the method of sections and known loci of points on the surface. In the present article we study the locus of points in space defined by metric relation to a certain set of pairs of points, lines and planes. It is shown that any non-degenerate 2nd order surface can be considered as a certain locus of points of space and this interpretation is not unique.

MATHEMATICAL MODELING AS A TOOL FOR INCREASING THE MATHEMATICAL LITERACY OF STUDENTS

Today, the problem of developing the functional literacy of schoolchildren is relevant at the community level. In this regard, new requirements are imposed on the level of professional training of future mathematics teachers. The authors consider the issue of preparing future mathematics teachers to develop students' mathematical literacy. The works of scientists on the development of functional literacy of schoolchildren were studied and the concepts of "model", "mathematical modeling" were explained. In addition, the specifics of the method of mathematical modeling in the process of teaching mathematics in secondary school have been clarified, and the pedagogical conditions for using the modeling method have been determined. It is shown that mathematical modeling is not only a tool for solving applied problems, but also a way of developing intellectual skills that a student must master.

Errores de profesores de Matemáticas en formación inicial al resolver una tarea de modelización


 
 
 Este trabajo describe los errores que han puesto de manifiesto un grupo de 27 estudiantes de la especialidad de Matemáticas del Máster de Formación de Profesorado de Secundaria en una tarea de modelización. A partir de la revisión de los antecedentes, se establece un sistema de categorías de los errores en las distintas fases del proceso de modelización y la coherencia entre las mismas. El análisis de los resultados muestra mayor frecuencia de errores en las fases en las que interviene la situación real original: la fase simplificación para obtener el modelo real y la fase de validación para interpretar los resultados obtenidos. Los tipos de errores manifestados aportan información para la formación de los futuros profesores de matemáticas.