Higher Mathematics Teaching Research Articles

DEVELOPMENT AND IMPLEMENTATION OF THE TEACHING METHODOLOGY OF THE HIGHER MATHEMATICS COURSE BASED ON PRACTICE

The teaching of higher mathematics has traditionally focused on theoretical concepts, which often creates a gap between students' understanding of the subject and its practical applications. This article explores the development and implementation of a teaching methodology for the higher mathematics course based on practice-oriented learning. The objective is to bridge the gap between theory and application, improving students' problem-solving skills and enhancing their ability to apply mathematical concepts in real-world situations. By integrating practical activities, case studies, and applied projects into the curriculum, this methodology fosters deeper comprehension and equips students with valuable competencies for their future careers.

Transdisciplinary approach as a resource for the development of critical thinking in higher mathematical education

Introduction. In a modern digital and globalized society, the higher education system is faced with the task of developing critical thinking skills in graduates that allow them to solve complex problems through the integration of knowledge from various disciplines at a new transdisciplinary level of knowledge. Such integration seems possible based on the use of modeling methodology, methods of computational and discrete mathematics, and mathematical cybernetics, which form the foundation of the language of information technology and processes. The purpose of the study is to identify the role of the transdisciplinary approach in the development of students’ critical thinking through mathematics. Materials and methods. 76 students of the Vyatka State University majoring in 06.03.01 Biology took part in the study, covering 2022–2023. The main methods for measuring critical thinking, presented by the UF/EMI Critical Thinking Disposition Instrument and The Critical Thinking Barriers Scale (CTBS), were supplemented with diagnostic tools from specially designed tasks, taking into account specifics of teaching mathematics to future biotechnologists. Statistical analysis of the obtained results was performed using the Mann-Whitney U test. Results. A number of methodological conditions have been formulated to ensure the development of students' critical thinking in the process of teaching mathematics, which corresponds to the priority goals of modern higher education. The expediency of using contextual mathematical problems containing a real data set, the method of mathematical modeling, the inclusion of modern mathematical theories and their applications in the teaching content, a joint form of work in the classroom and work with scientific articles is substantiated. A quantitative analysis of the results confirmed the significance of the differences (Uemp = 65 < Ucr = 66; р < 0,01), which indicates the effectiveness of the intervention based on the proposed methodological conditions. Conclusion. The practical significance of the study is determined by the possibilities of using its results in improving the critical thinking skills of students in the process of teaching mathematics.

Case Design and Practice of Integrating Ideological and Political Education into Higher Mathematics Teaching

Case Design and Practice of Integrating Ideological and Political Education into Higher Mathematics Teaching

ОСОБЛИВОСТІ ВИКОРИСТАННЯ СУЧАСНИХ ІНФОРМАЦІЙНОКОМУНІКАЦІЙНИХ ТЕХНОЛОГІЙ У ВИЩІЙ МАТЕМАТИЧНІЙ ОСВІТІ

The article discusses the relevance of using information and communication technologies (ICT) in higher mathematical education within the context of the contemporary educational environment characterized by rapid technological changes. It is noted that effective utilization of ICT, such as electronic journals, multimedia technologies, testing systems, and computer mathematics systems, contributes to the improvement of the teaching and learning process. Emphasis is placed on the necessity of reviewing and modifying teaching methodologies for mathematical disciplines to integrate innovative solutions. Furthermore, the use of information and communication technologies in higher mathematical education is deemed highly relevant due to the rapid development of the modern technological environment and the needs of the contemporary job market. The implementation of electronic journals, multimedia technologies, testing systems, and computer mathematics not only enhances the efficiency of teaching mathematical disciplines but also helps create a solid foundation for the future professional success of students. Electronic journals serve not only as convenient tools for administrative processes but also as platforms for active interaction among students, teachers, and administration, fostering the development of academic community and stimulating discussions and collaboration. Multimedia technologies, such as video lessons, interactive exercises, and simulations, provide students with opportunities to better grasp material and understand complex concepts, opening up new possibilities for personalized learning and adaptation to various learning styles. Testing systems, particularly those based on interactive platforms, enable instructors to effectively monitor students' knowledge and track their progress, as well as provide opportunities for personalized learning through automatic adaptation of task complexity Computer mathematics systems, including software packages for numerical and symbolic computations, become an integral part of modern mathematical education, empowering students to efficiently solve complex mathematical problems and explore new concepts, thus stimulating their creative potential and innovative approach to problem-solving. Together with educational platforms and distance learning systems, these tools contribute to the modernization and optimization of the educational process, leading to the improvement of the quality of higher mathematical education and the preparation of qualified professionals for the contemporary world.

Enhancing Students’ Critical Thinking Through Mathematics in Higher Education: A Systemic Review

Critical thinking (CT) is an essential competency for global citizens in the 21st century. Few systematic reviews have evaluated and analyzed instructional interventions to enhance CT in mathematics at the university. This study includes 15 studies on cultivating CT among undergraduate students through instructional interventions within the mathematics curriculum. Quantitative and qualitative methods were employed to provide information and feedback on study and intervention characteristics, analyze the features and effects of multiple interventional strategies, and assess instruments by coding categories. The results indicate that it is essential for instructors to identify the specific CT objectives, including features, criteria, and standards of CT, before intervention. Several teaching strategies are alternatives for developing undergraduate students’ CT abilities through the mathematics curriculum; however, flexibility and availability are necessary to allow students and instructors to adapt and coordinate. Further, multiple assessment instruments are essential for the instructional intervention.

Factors affecting success and failure in higher education mathematics: Students' and teachers’ perspectives

BackgroundStudents from Bangladesh pursuing STEM education often encounter obstacles when tackling diverse mathematical problems within various educational settings. Frequently, they find themselves lacking the essential prerequisite knowledge and strong foundational skills necessary to engage with the teaching and learning resources utilized at the undergraduate level, resulting in a significant number of students needing to seek readmission annually. ObjectiveThe objective of this study is to explore the determinants of academic achievement among university undergraduates majoring in mathematics in Bangladesh. Employing a mixed-method research approach, the study combines quantitative and qualitative data analysis to examine the viewpoints of both students and educators concerning these factors. The authors primarily emphasize classifying the factors that impact the efficacy of mathematics pedagogical methods. MethodologyThe study is structured into three phases: i. An initial exploratory qualitative survey. ii. A quantitative triangulation survey. iii. Followed by explanatory semi-structured interviews. FindingsTo begin, the initial qualitative survey identified significant factors that contribute to students' achievements and setbacks in mathematics. Subsequently, the quantitative analysis verified both similarities and distinctions in the perspectives of students and educators. Furthermore, the correlation coefficient analysis revealed that male students frequently exhibit inconsistency and a lack of enthusiasm for studying, resulting in subpar performance. Conversely, female students frequently cited challenges like the difficulty of connecting mathematical theories to real-world applications, heavy course loads, and limited resources as reasons for their academic difficulties. Lastly, insights from interviews with students highlighted their acknowledgment of inadequate study practices, excessive reliance on memorization, suboptimal teaching methods, low motivation, and external distractions as key factors leading to their struggles. They also recognized the importance of consistent practice, a solid comprehension of concepts, regular study routines, and effective learning strategies for successful mathematics education. In contrast, educators emphasized the significance of students having clear concepts, natural aptitude, motivation, and a sense of curiosity as pivotal elements for successful learning in mathematics. ConclusionThis conclusion suggests a new beginning in the realm of local mathematics pedagogy, achieved by scrutinizing teacher-student feedback about the factors influencing success and failure, considering the diverse individual and contextual variables at play. To foster mutual trust and understanding between students and teachers, it may be beneficial to engage in open discussions and interactions.

Mathematics students’ self-reported resources used for solving real-life problems in a challenge-based modelling course

There are new educational approaches that are moving towards student-centred teaching and learning. One of them is challenge-based education, where students acquire and develop disciplinary knowledge and competencies by collaborating on solving real-life problems. Hence, in this paper, we report on a study of applied mathematics students’ learning experiences in the context of challenge-based education in a higher education mathematics course. Using a case study approach, we investigate how students perceive the role of the different resources to help them solve real-life problems during a one-week challenge-based modelling course. We collected data, from four groups of students (5–7 students each) who worked together and interacted with their mathematics supervisors and problem owners. Results show (1) the crucial importance of using and integrating different resources, such as social resources (e.g. mathematics supervisors and problem owner), for such learning environments to link mathematics to an authentic situation and develop the skills of an ‘applied mathematician in the real world’; (2) the relevance of mathematical knowledge in creating models to solve real-life challenges.

Teaching mathematics in an EFL context at higher education; before, during and after the COVID-19 pandemic: a comparative study

Teaching mathematics in an EFL context at higher education; before, during and after the COVID-19 pandemic: a comparative study

Experience on the Teaching of Higher Mathematics in Vocational Colleges

Experience on the Teaching of Higher Mathematics in Vocational Colleges

Research on the Method of Integrating “Curriculum Civics” into the Teaching of Higher Mathematics

Research on the Method of Integrating “Curriculum Civics” into the Teaching of Higher Mathematics

Digital Pedagogy for Self-Paced Learning in Mathematics Education

This paper examined the contribution of digital pedagogy (DP) to self-paced learning in higher mathematics education. The research question was: In what ways does DP contribute to a resourceful learning environment to address individual learning styles and preferences in higher mathematics education? The study used a quantitative approach, employing a critical Action Research design with pre-test and post-test measures. The study participants were 126 third-semester students taking a Differential Geometry course in 2017. The tool used was the self-paced learning (SPL) index survey questionnaire. Based on analysis and discussion with relevant literature, this paper highlights the benefits of digital pedagogy, including the promotion of 21st-century skills, the provision of anytime and anywhere learning opportunities, and the creation of an e-resource repository to ensure SPL. Moreover, digital pedagogy provides adaptive learning experiences that can be adjusted to each student’s learning pace and style, enabling them to learn effectively and achieve their full potential.

Online Teaching and Learning of Mathematics in Higher Education: Post-Covid 19 Lecturer Perspectives

Online learning offers excellent chances for both students and teachers because it is flexible, affordable, and convenient in terms of time and space. This paper examined the perspectives of lectures on online teaching and learning mathematics in higher education after COVID-19. This paper adopted the Technology Acceptance Model (TAM) as a theoretical framework. The theory was used in the study to understand the lecturers’ viewpoints on how they embrace the use of technology in their teaching of mathematics. This was a qualitative study that used a case study as a design. The study’s participants were ten (10) mathematics lecturers at the Mathematics Department in one rural university in the Eastern Cape Province purposefully selected as information-rich participants. Data was collected using face-to-face, semi-structured interviews which were analysed through thematic analysis. The findings of the study revealed that lecturers saw the importance of teaching mathematics using technology to close the resource gap as universities steadily shift to 21st-century learning environments. At the same time, lecturers in rural universities are impacted by the challenges they face, which include a lack of technology skills, teaching practical work online, classroom control during online teaching, shortage of resources such as poor internet connections and electricity load shedding in the country which had strained the smooth running of online mathematics classes especially while teaching mathematics online. Based on the findings the study recommended that lecturers should be provided with technology professional development in mathematics, strengthening of internet access points, and methods for monitoring and controlling mathematics classes. Keywords: Higher Education, Learning, Mathematics, Online, Teaching.

Characterizing the Effectiveness of Video Recordings in Mathematics Instruction within Higher Education: Minimizing Direct Teacher-Student Interaction through Technological Modalities

This study was conducted to characterize the effectiveness of employing video recordings as a teaching tool in mathematics in higher education, with a bid to minimize direct teacher-student interactions. The research employed an experimental design, utilizing pre-tests and post-tests with a sample of 45 randomly selected first- and second-year mathematics students at Mountains of the Moon University. Video recordings were compared with alternative approaches, including online (Zoom) classes and self-study materials/handouts, to gauge their effectiveness in the absence of physical teacher-student interactions. Three experimental units were established, each undergoing learning of sequences via video recordings, online (Zoom) classes, or self-study printable materials/handouts. Statistical analysis was done using SPSS including percentages, descriptive statistics, Pearson correlation, and independent sample t-tests. Results revealed the relevance of both tools in mathematics learning, with video recordings proving to be more effective and superior in enhancing understanding of the learned concepts compared to the alternative tools. The study recommends the incorporation of video recordings in mathematics teaching, particularly in situations where physical meetings between teachers and students are impractical.

Math phobia and maths anxiety: multidisciplinary aproaches for a more inclusive and equitable education in Brazil

Maths anxiety, commonly referred to as "math phobia", is a challenge in the context of mathematics education in Brazil. While research on the impact of math phobia in the classroom and its direct relationship to learning disabilities is not yet well established, it is widely accepted that math phobia has the potential to increase students' aversion to the subject. This study explores math phobia by analysing text fragments from the mathematics education literature, using lexicometric analyses with the IRaMuTeQ software and Textual Discursive Analysis (TDA). The results emphasise that math phobia is influenced by various cognitive and emotional factors that have a negative impact on learning. Addressing this issue requires a multidisciplinary approach, with a focus on teacher training to create inclusive and welcoming learning environments. Therefore, investment in teacher training is essential to reduce math phobia and promote equitable, high quality mathematics education in the country.

Learning Mathematics with Large Language Models

Artificial intelligence (AI) has permeated all human activities, bringing about significant changes and creating new scientific and ethical challenges. The field of education could not be an exception to this development. OpenAI’s unveiling of ChatGPT, their large language model (LLM), has sparked significant interest in the potential applications of this technology in education. This paper aims to contribute to the ongoing discussion on the role of AI in education and its potential implications for the future of learning by exploring how LLMs could be utilized in the teaching of mathematics in higher education and how they compare to the currently widely used computer algebra systems (CAS) and other mathematical tools. It argues that these innovative tools have the potential to provide functional and pedagogical opportunities that may influence changes in curriculum and assessment approaches.

Education-oriented Proof Assistant Based on Calculational Logic: Proof Theory Algorithms and Assessment Experience

This work presents an interactive proof assistant, based on Dijkstra-Scholten logic, aimed at teaching logic and discrete mathematics in higher education. The assistant interface is web and easy to use, since inferences can be made just with the mouse. The educational experience is presented showing a correlation between the grades of the assessments in class and those made with the application web. Additionally, an algorithm proof theory for the Disjktra-Scholten system are made and the following algorithms are shown: 1) a versatile printing algorithm that allows the administrator to configure the symbols of a theory, by assigning the desired presentation with LaTeX; 2) An algorithm, based on Broda and Damas combinators, for generate monotonic or anti monotonic inferences in the Dijkstra-Scholten logic; 3) An algorithm to generate the proofs of dual theorems in Boolean Algebra theory.

Mathematics education faculty members' perceptions of barriers to distance education: Q-method analysis

As a result of the great earthquake disaster in Turkey, mathematics education in universities was reorganized as distance education after the pandemic period. This article aims to identify the barriers to distance education practices in higher education. In line with the aim of this study; Q methodology was used to help determine the perceptions and perspectives of faculty members regarding the barriers to distance education in the process of teaching mathematics in higher education. Q methodology aims to reveal the internal frame of reference of individuals through their preferences. According to the findings of the study, participants identified barriers under 3 factors. These 3 factors, in order of weight, represent student, curriculum and technology barriers. In general, it was seen that the 4 factors revealed by the methodology in the study yielded results compatible with the literature. However, it was determined that the barriers arising from the teacher did not carry a factor load in the study. Another unique result was the identification of barriers arising from the nature of mathematics. It was understood that there are unique obstacles specific to the field of mathematics due to pedagogy and curriculum. In this respect, investigating the barriers to field-specific extended education will provide more accurate findings. In this study, which was conducted with Q methodology and supported by qualitative data, the identified barriers to distance education were consistent with the general literature. Q methodology reveals that it is a compatible tool for various research in similar situations.

A methodological framework for using cloud-based mobile mathematical environments in higher education

This research aims to develop a methodology for utilizing cloud-based technologies in the teaching of higher mathematics. The study tasks involve identifying the features of mobile mathematical environments as tools for cloud-based technologies, developing a mobile mathematical environment specifically designed to support mathematics learning for students in economic disciplines, and formulating a methodology for employing the mobile mathematical environment. The research focuses on the process of teaching higher mathematics to students in economic disciplines. The subject of investigation encompasses the use of cloud-based learning technologies in the teaching of higher mathematics. The research methods employed include studying, summarizing, and systematizing scientific, methodological, and psycho-pedagogical literature; analyzing current educational standards and curricula; conducting targeted pedagogical observations, testing, and surveys; and analyzing the experience of using cloud-based learning technologies in the teaching of higher mathematics. The findings analyze the main features of mobile mathematical environments as tools for cloud-based technologies. The ``Higher Mathematics'' mobile mathematical environment, designed to support the learning of higher mathematics for students in economic disciplines, is examined. Elements of the methodology for utilizing the ``Higher Mathematics'' mobile mathematical environment in the teaching of higher mathematics are identified. The study identifies instructional formats through which the implementation of the ``Higher Mathematics'' mobile mathematical environment occurs in the teaching of higher mathematics. The main conclusions and recommendations emphasize that the use of the ``Higher Mathematics'' mobile mathematical environment in the teaching of higher mathematics enables students to master the necessary educational material and contributes to the development of cognitive activity, the formation of independent work skills, and the consolidation and systematization of knowledge.

Embedding Sustainable Mathematics Higher Education in the Fourth Industrial Revolution Era Post-COVID-19: Exploring Technology-Based Teaching Methods

Higher Education Institutions have adopted technology-based teaching methods to prevent the spreading of the contagious coronavirus (COVID-19). In the Fourth Industrial Revolution (4IR) era, technology-based teaching methods are indispensable for scaffolding teaching, learning and assessment. Mathematics is an important discipline in education, and provides a basis for problem solving, critical thinking and analytical skills, which is important to consider when focusing on sustainability. Thus, to add knowledge to the field about integrating technology-based teaching methods in mathematics, Higher Education environments during and post-COVID-19 need to be interrogated. This added knowledge is be valuable in the 4IR era post-COVID-19 for sustaining mathematics in Higher Education. This study explored participants’ experiences, views, implications and suggestions for technology-based teaching methods for mathematics. These participants (N = 45) were postgraduate students and mathematics school teachers at the research site in KwaZulu-Natal, South Africa. The research location for this qualitative study was a South African Higher Education Institution, and the study was conducted during the COVID-19 pandemic. The Community of Inquiry theoretical framework and the Substitution, Augmentation, Modification and Redefinition (SAMR) theoretical model guided this study. Participants were invited to two interactive online workshops. At these workshops, participants were introduced to different technology-based teaching methods. Then, they were invited to individual online interviews. The findings of this study suggest important experiences, views and suggestions for using technology-based teaching methods in Higher Education mathematics contexts in the 4IR era. These findings provide important implications and further research possibilities for embedding sustainable mathematics in Higher Education in the 4IR era, post-COVID-19.

Assessing the Relevance of Information Sources for Modelling Student Performance in a Higher Mathematics Education Course

In recent years, most educational institutions have integrated digital technologies into their teaching–learning processes. Learning Management Systems (LMS) have gained increasing popularity, particularly in higher education, due to their ability to manage teacher–student interactions. These systems store valuable information which describes students’ behaviour throughout a course. These data can be utilised to construct statistical models that represent learner behaviour within an online LMS platform. In this study, we aim to compare different sources of information and, more ambitiously, to provide insights into which source of information is most valuable for inferring student performance. The considered sets of information come from (i) the Moodle LMS; (ii) socio-economic data about students acquired from a survey; and (iii) subject marks achieved throughout the course. To determine the relevance of the incorporated information, we use artificial intelligence (AI) methods, and we report the importance measures of four state-of-the-art methods. Our findings indicate that the selected methodology is suitable for making inferences about student performance while also shedding light on model decisions through explainability.