Math and Modernity: Critical Reflections

Besides the birth of new revolutionary concepts and methods, and of new areas of research, mathematicians, logicians, and philosophers have put into question the foundations of the discipline itself and the whole meaning of “mathematical truth.” Before then, at the end of the eighteenth century, mathematics was mainly concerned with explaining the “real world” and its laws. At the beginning of the “modern era” things started to change, sometimes slowly, other times abruptly. Abstract mathematics was no longer intimately related to the real world and its description. This abstract approach, both on research and on mathematical education, generated critical reactions in the mathematical community, and some “modern” ideas were rejected or neglected after several decades of experimentation.

My Industry to Academia Research Journey And Energizing Innovations Among Malaysian Engineers

In this talk, the author would like to share her research journey from industry to academia, first in Malaysia and then in United States. She was fortunate to receive a strong science & mathematical education in Malaysia, trained as an engineer at University of Malaya, worked with a team of talented R&D engineers at Motorola Communication Sectors Sdn Bhd in Penang before she went to United States for graduate studies. In United States, again she was fortunate to have several mentors who helped to inspire her to conduct great research first in industry and then in academia. She will first share her research journal from Malaysia to United States. Next, based on her experience, she will share some main ingredients one needs to cultivate to conduct great research, e.g., curiosity, diligence, and perseverance. Subsequently, she will also share her thoughts on how industry leaders, academic leaders and Malaysian government can collaborate to energize innovations among Malaysian engineers as well as young generations aspiring to be our next generation engineers. Cultivating curiosity in STEM fields at young age, providing opportunities for high school students to appreciate science through solving real life problems with college students, and creating opportunities for faculty members in STEM fields to spend sabbatical semesters at top universities or industry R&D laboratories to horn their skills are necessary steps to energize innovations among Malaysian engineers.

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

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.

Advanced Training of Teachers of Mathematics and Computer Science on the Basis of a Team Approach to Eliminate Methodological Defi ciencies in the Implementation of a Criteria-Based Assessment of Students’ Educational Achievements

The widespread introduction of a criterion system for evaluating the educational results of schoolchildren is an actual and significant direction of the development of domestic education. The article is devoted to the problem of eliminating methodological deficits of teachers in the development of criteria assessment tools for the current control of subject results of teaching mathematics and computer science in primary and high school. The article describes the method of organizing advanced training of teachers of mathematics and computer science on the basis of a team approach that contributes to the practical implementation of the intra-school system of current control of students ' academic achievements on a criterion basis. The article presents an approach to the implementation of an additional professional training program for teachers of mathematics and computer science on the basis of "team training", focused on the development of professional skills necessary for conducting procedures for the current control of subject learning outcomes, the Department of Mathematical Education and Computer Science of St. Petersburg Academy of Postgraduate Pedagogical Education.

Methods of Formation of Computational Skills Using Information Technologies

The article is based on the main key ideas of the concept of the development of Russian mathematical education, one of which is the idea of using information technologies in mathematical education as a basis for advancing at the world level. The article introduces mathematics teachers to the possibilities of using interactive simulators for the formation of students ' computational skills in the process of organizing oral and written counting in a playful form. Methodological recommendations on the topic "Actions with decimals" are given. The article is addressed to teachers and students of pedagogical universities, methodologists, mathematics teachers.

THE TECHNOLOGY OF WINTER CONCRETING OF MONOLITHIC FRAME STRUCTURES WITH SUBSTANTIATION OF HEAT TREATMENT MODES BY SOLUTIONS OF THE DIFFERENTIAL EQUATION OF THERMAL CONDUCTIVITY OBTAINED BY THE METHOD OF GROUP ANALYSIS

An innovative method for calculating thermal fields inside monolithic structures has been developed, based on the use and analysis of nonlinear differential equations. The innovativeness of the method lies in the approach to the analysis of nonlinear physical processes using nonlinear differential equations. Thanks to the method of group analysis, 13 expressions are obtained from complex mathematical equations, which are easy to use and depend on several empirical coefficients. It is assumed that this calculation method is a priori more accurate than the existing ones, as well as available to people at a construction site without higher mathematical education, which makes it a priority for research. The applicability of this method must be proven by linking empirical coefficients and variables to the conditions of the experiments, while obtaining reliable data that will turn out to be more accurate than the existing calculation methods. This article demonstrates a systematic approach to establishing the suitability of using the method of group analysis of differential equations for problems of winter concreting on the basis of laboratory experiments under stationary conditions. The equations were subject to verification, which, according to the physical description, correspond to the real conditions of the course of thermal processes inside monolithic structures. Based on the obtained processing results, it was decided that it was necessary to further study the innovative method in the conditions of the construction site, but only for some expressions that showed the best results at the stage of laboratory tests.

THE CONCEPT OF TEACHING MATHEMATICS IN THE 1ST GRADE OF A GENERAL EDUCATION SCHOOL

The teaching of mathematics should reflect the global trends in the development of mathematical and pedagogical scientific thought. The authors develop guidelines for studying mathematics in the 1st grade based on the Federal State Educational Standard. Thus, the structure and the form of the textbook content are described by chapter. The theoretical part should allow students to complete screening questions, univariate and multivariate tests, problems, and exercises. Each chapter of the developed textbook is divided into paragraphs, and each paragraph is divided into items. One item of theoretical material contains either a new idea to study or a set of interrelated concepts that define a new idea. According to this, it is possible to form mathematical knowledge trajectories. So, there are broad opportunities to transform knowledge elements into multimedia forms, including presentations, videos, test modules, and other newly emerging means of representation and visualization, using the achievements of artificial intelligence. It is possible to define main themes such as natural numbers counting, acquaintance with geometric shapes, comparison of objects in the value and quantity, acquaintance with a squared paper and measurement standards, the study of objects position, the sets consideration, introduction to the algorithm concept can. The authors’ conceptual directions of teaching mathematics in the 1st grade provide the foundation for mathematical education in general education schools for all the years of study.

Possibilities of Preparing Pupils for Proof Problems of Synthetic Plane Geometry Solvable by Deductive Methods

Proof problems, especially the ones of the synthetic plane geometry solvable by deductive methods, play a significant role in mathematical education and due to their demanding principle also in the above-standard education including mathematical competitions. Therefore, the issue of preparing pupils for solving the proof problems is very important. This study aimed to find out if the contemporary state of the system of pupils’ preparation for synthetic plane geometry proof problems is sufficient enough for the mentioned purpose. From the full set of schools of the Czech Republic, there were 14 schools identified as the successful ones based on the results of the national round of the Mathematical Olympiad. These schools were asked questions about literature used for pupils’ preparation and the publications named in the answers were then deeply inspected. The results showed a narrow range of the literature used by the schools and the didactic-methodical inspection of stated literature detected considerable space for improvements which led the author to the main theme of his dissertation.

The experiment in mathematical education: the escape room

In this article the use of the educational escape room in the process of teaching mathematics is presented.

Relação Professor-Aluno e Afetividade: um Estudo Sobre Dissertações e Teses Produzidas nos Últimos Sete Anos

ResumoEste artigo analisa dissertações e teses brasileiras, produzidas entre 2013 e 2020, que investigam questões ligadas à relação professor-aluno e à afetividade observadas nos anos finais do Ensino Fundamental. Para desenvolver este estudo, foi realizada uma Revisão Sistemática de Literatura (RSL), por meio da qual se buscou, na Plataforma Digital Brasileira de Teses e Dissertações (BDTD) e no Catálogo de Teses e Dissertações da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Capes), estudos que tratassem da temática aqui apresentada. Utilizando os critérios de inclusão e exclusão foram selecionadas uma tese e três dissertações. Para esta pesquisa foram consideradas como categorias de análise: objetivo, fundamentação teórica, participantes envolvidos, procedimentos de coleta de dados e principais resultados. Nas investigações analisadas foram observados indícios de consenso quanto ao papel fundamental desempenhado pelo professor nas relações de afetividade. É por meio da elaboração de situações contextualizadas e de uma condução que prioriza o bom relacionamento com seus alunos que são identificadas melhorias nos processos de ensino e aprendizagem da Matemática, proporcionado por uma aprendizagem significativa. De modo geral, a análise dos estudos permitiu identificar que há poucas produções que abordam a temática, uma vez que se foram encontradas apenas duas pesquisas desenvolvidas em programas de Educação Matemática, apontando a necessidade do desenvolvimento de pesquisas. Palavras-chave: Educação Matemática. Relações Afetivas. Revisão Sistemática de Literatura. AbstractThis article analyzes Brazilian dissertations and theses, produced between 2013 and 2020, which investigate issues regarding the teacher-student relationship and affectivity observed in the final years of elementary school. In order to develop this study, a Systematic Literature Review (RSL) was carried out through which studies that dealt with the theme presented here were searched, in the Brazilian Digital Platform of Theses and Dissertations (BDTD) and in the Catalog of Theses and Dissertations of the Coordination for the Improvement of Higher Education Personnel (Capes),. Using the inclusion and exclusion criteria, a thesis and three dissertations were selected. For this research, the following analysis categories were considered: objective, theoretical foundation, participants involved, data collection procedures and main results. In the investigations analyzed, there was evidence of consensus regarding the fundamental role played by the teacher in the affection relationships. It is through the elaboration of contextualized situations and a conduct that prioritizes the good relationship with their students that improvements in the Mathematics teaching and learning processes are identified, provided by a meaningful learning. In general, the analysis of the studies allowed to identify that there are few productions that address the theme, since it was found only two researches developed in Mathematics Education programs pointing out the need for the development of studies. Keywords: Mathematical Education. Affective Relationships. Systematic Literature Review.