Mathematical Disciplines Research Articles

Оценка эффективности применения электронных учебников по математическим дисциплинам методом анкетирования преподавателей и студентов

<p>The article presents the results of a sociological study aimed at assessing the effectiveness of the use of learning management systems (LMS) in a mixed form of conducting educational activities in mathematical disciplines with face-to-face seminars and lectures and organizing the independent work of students of technical specialties of the university using the LMS. The research is based on the results of a pedagogical experiment conducted in the spring semester of 2022/2023 on the introduction of an electronic textbook into the educational process at the Moscow Aviation Institute on the course "Theory of the function of a complex variable" using the distance learning system CLASS.NET. The studies are carried out by interviewing students and teachers participating in the pedagogical experiment. The most popular functions of an electronic textbook by teachers and students have been identified.</p>

Is there room for conjectures in mathematics? The role of dynamic geometry environments

Proof, as a central and integral part of mathematics, is an essential component of mathematical education and is considered as the basic procedure for revealing the truth of mathematical propositions and for teaching productive reasoning as part of human civilization. Is there therefore room for conjectures in mathematics? In this paper after discussing at a theoretical level the concepts of proof and conjecture, both in a paper-and-pencil environment and in a dynamic geometry environment (DGE) as well as how school practice affects them, we fully explain a task involving various mathematical disciplines, which we tackle using elementary mathematics, in a mathematics education context. On the occasion of the Greek educational system we refer to some parameters of the teaching of geometry in school and we propose an activity, within a DGE, that could enable students to be guided in the formulation and exploration of conjectures. Finally, we discuss the teaching implications of this activity and make some suggestions.

Interdisciplinary connections of Mathematics and Literature in the preparation for External Independent Assessment of Humanities students

This article examines the issue of finding new methodological approaches to the development of problems that can contribute to the preparation of ‘Humanities’ students to pass the state final certification in the format of External independent assessment (EIA). The study analyzes the existing development of methods of qualitative mathematical training of students of humanities classes who study Mathematics according to the basic level program. In particular, the authors of the article were interested in the use of interdisciplinary connections between Mathematics and humanitarian disciplines. The authors of the article identified cross-curricular problems as a means of forming students’ motivation to study Mathematics, as well as a toolkit for measuring their level of readiness to solve typical problems of EIA. The researchers set a goal to develop cross-curricular problems following the EIA program based on the plot of Bulgakov’s novel ‘The Master and Margarita’. An experiment was conducted to confirm the effectiveness of the use of the system of interdisciplinary problems in the preparation for the EIA of humanitarian students. The obtained results confirmed that the implementation of problems in which the intersubject connections of Mathematics and Literature are realized has a more significant effect on both increasing the motivation of students to study Mathematics and their mathematical preparation.

ПУТИ СОВЕРШЕНСТВОВАНИЯ МАТЕМАТИЧЕСКОГО ОБРАЗОВАНИЯ В ВУЗАХ МЧС РОССИИ

Substantiates the expediency of using the MS Excel spreadsheet processor and the Mathcad mathematical package to solve research problems. The theoretical foundations of the statistical testing method are presented. The applied aspects of the application of the statistical test method are considered. 
 The ways of improving the teaching of mathematical cycle disciplines in the conditions of digitalization 
 of education are determined.

Peer leader perspectives from a PLTL implementation in a Hispanic-serving institution.

Peer-Led Team Learning (PLTL) is a pedagogical approach that has been shown to benefit all students, especially underrepresented minority students and peer leaders in Science, Technology, Engineering, and Mathematics (STEM) disciplines. In this work, we present results from our study of the impact of PLTL on our peer leaders from a controlled implementation in general biology, general chemistry, and statistics courses at a Hispanic-serving, minority-serving institution. More specifically, we have measured our PLTL program's impact on our peer leaders' skill development, engagement with the subject material, and sense of belonging as peer leaders. Weekly peer leader reflections analyzed using the Dreyfus model exhibited a consistent set of skills, while those analyzed using the Pazos model revealed a consistent type of student-peer leader interactions, allowing for peer leaders to be assigned to specific levels in the hierarchy of each of the models. Analysis of eight skill-based Likert-scale questions on the SALG survey showed an overall positive shift at the highest level. Independent of the skill or interaction level of the peer leader, we observed several instances of peer leaders acknowledging development in their communication skills, sincere attempts at creating an engaging classroom, and a deep investment in their student's success. Peer leaders also reported improvements in understanding of the subjects they were teaching, wanting to persevere and solve problems independently, and feeling passionate about helping other students.

Connecting mathematics to STEM education: interdisciplinary teaching and learning facilitation

In interdisciplinary Science, Technology, Engineering and Mathematics (STEM) education, empirical evidence is required that points to the educational contribution of mathematics. Specifically, researchers are not clear how mathematics weaves itself through the STEM education meta-discourse. This article contributes to pedagogical practices in educational institutions where STEM has been newly introduced - What are the perceptions and experiences of South African teachers on interdisciplinary STEM education, and how do mathematics and interdisciplinary STEM discourses leverage each other at schools of specialisation (SoS) in South Africa? Participant teachers were drawn from ten SoS in South Africa. SoS are STEM-dense schools in South Africa’s Gauteng Province, the country’s industrial and commercial hub. Interview data was collected on teachers’ experiences and practices to explore the affordances of Mathematics and other STEM disciplines to influencing curriculum advancement. Situated cognition, mathematics as explorations and flow theory informed this qualitative study. In the findings, technology was regarded as raising learner motivation and mathematical achievement. Important to the study is that participants have a high regard for mathematics’ role in interdisciplinary STEM education. In the study, teachers had no autonomy to pursue the STEM agenda, as they were bound to adhere to a prescribed curriculum, which hardly refers to implementation of interdisciplinary STEM education. Various recommendations are proffered, such as maintaining the positive perceptions participants have on the role of mathematics in STEM curricula. The research calls for equality and equity of all the STEM disciplines, as one STEM curricula cannot succeed without the other.

“Mission on Mars” – Integrated STEM Lesson

Integrated STEM teaching reflects the effort to combine some or all four disciplines of Science, Technology, Engineering, and Mathematics into one learning unit or lesson. The following work describes good practice for collaboration between teachers in different subjects in order to create effective interdisciplinary lessons. Students are engaged in enjoyable activities in Science, Robotics and Technologies. The lesson is student-led, they prepare themselves for the different activities according to their interests and skills. Students explore Mars, make conclusion, analyze and give solution.

Transdisciplinary role of physical and mathematical disciplines in modern natural science and engineering education

Introduction. In recent decades, a gradual degradation of mathematics and physics training in schools and universities has begun. Obviously, this has caused a significant decrease in the quality of professional training of students in the conditions of commercialisation and continuous reforms of education, and its chaotic digitalisation. At the same time, modern mathematics and physics have become the leader of the transdisciplinary trend in the natural, engineering, and other sciences of the digital era. The transdisciplinary trend generates a universal methodology capable of solving complex multifactorial interdisciplinary problems of nature and society. As a result of the transdisciplinary trend in science, such scientific fields as cybernetics, general systems theory, catastrophe theory, synergetics, artificial intelligence, big data, etc. have emerged. All these concepts were developed on the basis of the achievements of mathematics and physics over the past 70–80 years, which gave rise to the most unique practical achievements in modern, natural, and technical sciences.Aim. The present research aims to explore transdisciplinarity role of physical and mathematical disciplines in modern natural science and engineering education.Methodology and research methods. The system-based approach was used to analyse the role of mathematical and physical science systems in modern education. The synergetic approach became the basis for the study of the transdisciplinary trend of these systems in historical retrospect. In the methodology of these approaches, an important role was played by the methods of students’ holistic scientific worldviews formation, including ideas about the modern picture of the world of mathematics and physics. The authors applied the methods to develop student systems thinking (with its important quality of nonlinearity), which underlies the solution of multifactorial interdisciplinary tasks of their professional activity.Results. The results of the analysis of the transdisciplinary role of physical and mathematical disciplines indicate the fundamental importance of the unique potential of these disciplines in the natural science and engineering education in the era of the computer revolution.Scientific novelty. The authors identified, justified and characterised transdisciplinary ideas and methods (in mathematics and physics), which bring natural and engineering sciences to a higher level of cognition, thus contributing to improving the quality of natural science and engineering training of students at universities using a computer.Practical significance. The research materials emphasise considerable practical importance to implement a transdisciplinary approach in didactics and methods of teaching physical and mathematical disciplines in the system of natural science, and engineering education. The research findings will be of interest to educational theorists and teachers, who conduct professional training of students of natural science and engineering fields and to everyone who is interested in the prosperous future of the educational system.

ИНТЕГРАЦИЯ МАТЕМАТИЧЕСКИХ МЕТОДОВ И ЦИФРОВЫХ ТЕХНОЛОГИЙ КАК ОСНОВА СОЗДАНИЯ КОМПЛЕКСА ФУНДАМЕНТАЛЬНЫХ КУРСОВ В ПОДГОТОВКЕ СОВРЕМЕННЫХ УПРАВЛЕНЧЕСКИХ КАДРОВ

The digital transformation of public administration requires a significant change in the training of students in the fi eld of state and municipal administration (SMA), who possess a wide range of digital competencies. The foundation for the formation of digital competencies is the basic and special disciplines of mathematics and computer science. The purpose of this article is to determine the optimal trajectory of students’ education to obtain the necessary competencies. For this purpose, the article consistently examines and solves the problems of the essence of digital competencies (1), the specifi c features of teaching mathematics and computer science to students in the area of SMA (2), the interaction of these courses with other courses in the area of SMA (3), the content, scope and sequence of these courses (4). Conclusions and suggestions are based on generalization rich experience of Lomonosov Moscow State University, one of the fi rst Russian universities that opened SMA education, based on the analysis of domestic and foreign literature, as well as regulatory documents governing the digital transformation of public administration.

Exploring Roughness in Left Almost Semigroups and Its Connections to Fuzzy Lie Algebras

This paper explores the concept of Generalized Roughness in LA-Semigroups and its applications in various mathematical disciplines. We highlight the fundamental properties and structures of Generalized Roughness, examining its relationships with Fuzzy Lie Algebras, Order Theory, Lattice Structures, Algebraic Structures, and Categorical Perspectives. Moreover, we investigate the potential of mathematical modeling, optimization techniques, data analysis, and machine learning in the context of Generalized Roughness. Our findings reveal important results in Generalized Roughness, such as the preservation of roughness under the fuzzy equivalence relation and the composition of roughness sets. We demonstrate the significance of Generalized Roughness in the context of order theory and lattice structures, presenting key propositions and a theorem that elucidate its properties and relationships. Furthermore, we explore the applications of Generalized Roughness in mathematical modeling and optimization, highlighting the optimization of roughness measures, parameter estimation, and decision-making processes related to LA-Semigroup operations. We showcase how mathematical techniques can enhance understanding and utilization of LA-Semigroups in practical scenarios. Lastly, we delve into the role of data analysis and machine learning in uncovering patterns, relationships, and predictive models in Generalized Roughness. By leveraging these techniques, we provide examples and insights into how data analysis and machine learning can contribute to enhancing our understanding of LA-Semigroup behavior and supporting decision-making processes.

Considerations about Ethnomathematics, the culturally relevant Pedagogy and social justice in Mathematical Education

One of the challenges internationally faced by education systems is related to the growing number of students from linguistically and culturally diverse origins, a fact that calls the attention of teachers and researchers. Because these fields are connected to traditional education systems, there is a growing urgency to solve such inability to effectively reach all students. With respect to the social justice context, it is necessary assessing the embodiment of mathematics’ cultural perspective in the classroom, as well as creating the very basis for the ethnomathematics approaches and for pedagogy in mathematics discipline matrices, since it aims at developing this knowledge production. This approach focuses on promoting social justice and on the quality of students’ educational experience. Thus, this sociocultural diversity has growing in educational research, since it is an area that seeks to connect the daily experiences of students with the teaching and learning process aimed at making education systems humanized. In the context of social justice, it is necessary to examine how mathematics is found in all cultures and, at the same time, to base it on ethnomathematical and culturally relevant pedagogies that can assume, in mathematical curricula, the various linguistic and cultural forms of knowledge. Thus, the main objective of this approach is the integral promotion of student daily experiences in the school mathematics curriculum.

Levels of mastering theoretical knowledge of higher mathematics in computerized testing

This paper deals with the problem of computer testing of students level of theoretical knowledge on Higher Mathematics. When assessing students in Mathematics, their mastery of skills and abilities to solve problems and to use theoretical material falls into different categories. Test tasks to assess the ability to solve typical problems are often based on the prediction of the success of their solution by students, taking into account teaching experience, task examples from published sets of tests on Higher Mathematics. The process of tasks development is rather complicated for many reasons. In particular, when discussing some tasks with the student during the exam, the teachers questions usually do not have a test form and it is more difficult to predict the success of the students performance in this case. Therefore, the paper proposes to correlate test tasks to assess the mastery of theoretical material in higher mathematics with a certain hierarchical system of levels of knowledge acquisition. Matching test tasks knowledge with mastering level allows you to take into account their development and the depth of the study of theoretical material in mathematical disciplines. The paper deals with the hierarchical system of four levels of knowledge assimilation (recognition, mechanical reproduction, fragmentary understanding, integral understanding), gives examples of tasks for each level and the results of the success in individual test tasks, which can be useful for teachers when developing tests to check the theoretical knowledge of Mathematics.

The SCI – DOT: A New dimension of scientific innovation for persons with BLV.

Throughout history, students with blindness and low vision (BLV) have been vastly underrepresented in science, technology, engineering, and mathematics (STEM) disciplines with regards to both K-12 education and post-secondary endeavors (Burgstahler, 1994; Supalo, 2010). This underrepresentation of students with BLV in STEM is due to limitations in technology that allow them to access data in a laboratory setting, thus inhibiting their abilities to partake actively in data acquisition with their peers. The Sci-Dot, a multiline, refreshable braille and tactile graphics display capable of logging scientific data in real time with the support of Vernier Science Education’s (VSE) Go-Direct Bluetooth sensors, stands as a unique innovation for persons with BLV given its capabilities to output multiline, tactile data in real time. The Sci-Dot allows individuals with BLV to collect and analyze data by supplying them with tactile data at their fingertips. The author reports findings from a usability study to ascertain the technical feasibility of the device – its capability to produce interpretable tactile data in real time. Participants provided feedback that proved the Sci-Dot was technically feasible as a scientific data logger, and more. The Sci-Dot also has the potential to provide a wealth of independence and inclusivity for educational and social activities beyond the laboratory.

An Operations Research–Based Teaching Unit for Grade 11: The ROAR Experience, Part II

In this paper, we continue describing the project and the experimentation of Ricerca Operativa Applicazioni Reali (ROAR; in English, Real Applications of Operations Research), a three-year project for higher secondary schools, introduced. ROAR is composed of three teaching units, addressed to Grades 10, 11, and 12, respectively, having the main aim to improve students’ interest, motivation, and skills related to Science, Technology, Engineering, and Mathematics disciplines by integrating mathematics and computer science through operations research. In a previous paper, we reported on the design and implementation of the first unit, started in Spring 2021 at the scientific high school IIS Antonietti in Iseo (Brescia, Italy), in a Grade-10 class. Here, we focus on the second unit, carried out in Winter/Spring 2022 with the same students, now in a Grade-11 class. In particular, we describe objectives, prerequisites, topics and methods, the organization of the lectures, digital technologies used, and a challenging final project. Moreover, we analyze the feedback from students and teachers involved in the experimentation. Funding: G. Colajanni and E. Taranto were partially supported by the research projects Programma Ricerca di Ateneo UNICT 2020-22 linea 2, EEEP&DLaD, and OMNIA, respectively, of the University of Catania. The research of G. Colajanni was also partially supported by the Italian Ministry of University and Research and the European Union for the PON project on Research and Innovation 2014–2020 [Grant D.M. 1062/2021]. A. Raffaele was partially supported by the Gruppo Nazionale per il Calcolo Scientifico. These supports are gratefully acknowledged. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ited.2023.0001 .

Actual Problems of Economics Teaching in Higher School

The article examines the current problems of teaching economic specialties in Russian universities. According to the author, modern higher economic education is not focused on training specialists with the knowledge and values necessary to solve the problems of ensuring the economic sovereignty of the country. The reasons for this are both inside and outside the education system. To identify these causes and areas of concentration of problems, the author analyzed the current admission rules approved by universities in accordance with the regulatory documents of the Ministry of Education and Science; approaches to the assessment of applicants; the content of educational programs, their relationship with professional standards; curricula in the areas of training 38.03.01 “Economics”. The study used publicly available information posted on the websites of universities-leaders of the Expert RA Rating Agency ranking for 2020 in economics and management. The analysis revealed areas where the problems of higher economic education have a high degree of concentration. These include: the lack of uniform requirements for the initial knowledge of applicants; heterogeneity of the quality of the student audience by the level of initial knowledge; the inability of professional standards to orient universities to the formation of popular educational programs; the predominance of mathematical disciplines in the curricula, while reducing the list and volume of disciplines that form the worldview; unjustified shift of emphasis towards financial disciplines, formation of calculation skills instead of obtaining fundamental economic knowledge. Awareness of these problems will make it possible to make changes to curricula purposefully, and university graduates will be quickly involved in solving problems related to ensuring the economic sovereignty of the country, along with representatives of technical specialties.

Vertex cover algorithm

Problem to solve P=NP, using the coverage problem of a graph that is NP and convert it to P. In the mathematical discipline of graph theory, a vertex cover, simply a graph cover, is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. The problem of finding the smallest vertex coverage in a graph is called the vertex coverage problem. In computational complexity theory, it has been shown that this is an NP-complete problem. An NPcomplete problem is that it is not known if it has a Polynomial solution. I have found an algorithm that proves that it is Polynomial.

The teaching of Robotics to prospective teachers and its application in the classroom

Research activities are one of the most successful strategies to apply STEM education in complete secondary education. It is carried out by the completion of specific tasks. The professional activity of teachers of science and mathematical disciplines in STEM education is targeted at the formation and development of students' mental, cognitive, and personal qualities. Their level impacts students' ability to advance in a successful specialty STEM industry. It also entails developing the skill and willingness to tackle complicated problems, which is attainable with the proper amount of critical thinking, creativity, cognitive flexibility, teamwork, and the ability to carry out research activities. The nature of the interaction between disciplines and the degree of integration are determined in this article. The place of project activity on robotics in school training is explored, and it defines the skills that are produced as a result of such project activities. The prospect of teaching robotics to future teachers within the context of existing curricula is also examined. STEM education can be defined in a variety of ways, ranging from a straightforward list of "exact" or "engineering" subjects to creative activity. This field has become synonymous with scientific and research work: research and experiments. In this regard, robotics is an effective technique of developing STEM education. The findings revealed that prospective instructors were mostly able to include robots into STEM-based science teaching. Furthermore, prospective teachers proposed that robots be introduced into all classes, particularly science, in order to improve students' problem-solving and algorithmic thinking skills. However, this is a novel instrument, and schools have shown little interest in researching it. As a result, our paper focuses on identifying chances to incorporate the fundamentals of robotics in education. The article developed course standards based on the educational needs of future science, mathematics, and engineering teachers. The study provides an example of project implementation in robotics, describes the stages of execution together with the educational outcomes.

Co-designing a framework for a persuasive educational technology tool for motivating female students for enrolment into Science, Technology, Engineering and Mathematics disciplines

Co-designing a framework for a persuasive educational technology tool for motivating female students for enrolment into Science, Technology, Engineering and Mathematics disciplines

Inspiring STEM education focused on solutions

Inspiring STEM education focused on solutions Nancy Butler Songer, from the University of Utah, makes a call for collective action to create a new curriculum focused on the design of solutions. June 5, 2023, marked The United Nations Environment Programme’s (UNEP) fiftieth anniversary of World Environment Day, the largest global platform for environmental public outreach. Hosted by Côte D’Ivoire, this year’s celebration emphasized a need for collective action and policy to realize known solutions, such as the sustainable design of products and materials to reduce how much plastic waste flows into aquatic ecosystems. World Environment Day helps us to recognize that to address many current environmental, educational, health, and economic challenges that have foundations in Science, Technology, Engineering, and Mathematics (STEM) disciplines, we cannot rely on individuals or even experts within one area of science, technology, engineering, mathematics, or education. We must innovate with, study, and empower students, teachers, community members, and university and industry partners toward collective action.

Math is cool – for school? Insights into preservice teachers’ views on the mathematics discipline between an academic and a job-related focus

In academic teacher education, preservice teachers may develop complex views on their chosen scientific discipline of study, as a tension may exist between a purely academic focus and a job-related focus. This study reports quantitative data from N = 259 preservice mathematics teachers indicating their views on the mathematics discipline in four facets of task value and enjoyment of mathematics as well as in an open statement. Cluster analysis of the five quantitative variables suggests three disjunct clusters, and qualitative data support the cluster structure. Data are discussed regarding higher education and the role of discipline content in teacher education.