University Mathematics Education Research Articles

Guest Editorial for Special Issue “Digital Experiences in University Mathematics Education: Advances and Expectations”

Guest Editorial for Special Issue “Digital Experiences in University Mathematics Education: Advances and Expectations”

CoCoSo Technique for Teaching Effectiveness

University mathematics, as an important core foundational course, is closely related to professional courses and occupies an important position that cannot be underestimated. University mathematics courses focus on cultivating students' abilities such as logical reasoning and abstract thinking, but the current teaching effectiveness of university mathematics courses is not optimistic. The teaching effectiveness evaluation of university mathematics education major is MADM. Currently, the CoCoSo and CRITIC technique was put forward MADM issue. The double-valued neutrosophic sets (DVNSs) are put forward characterizing fuzzy data during the teaching effectiveness evaluation of university mathematics education major. In this study, CRITIC technique was put forward the determination of attribute weights and double-valued neutrosophic number CoCoSo (DVNN-CoCoSo) technique is administrated for MADM. Finally, numerical example for teaching effectiveness evaluation of university mathematics education major is put forward to show the DVNN-CoCoSo technique.

Enhanced GDM Algorithms for College Mathematics Teaching Quality Evaluation Under Interval-Valued Intuitionistic Fuzzy Sets

The college mathematics teaching quality evaluation is the multiple-attribute group decision-making (MAGDM). Currently, the Exponential TODIM (ExpTODIM) and MABAC was executed to put forward MAGDM. The interval-valued intuitionistic fuzzy sets (IVIFSs) are executed for portraying fuzzy data during the college mathematics teaching quality evaluation. In this study, the interval-valued intuitionistic fuzzy number ExpTODIM-MABAC (IVIFN-ExpTODIM-MABAC) approach is put forward the MAGDM with IVIFSs. At last, numerical example for college mathematics teaching quality evaluation is executed to verify the IVIFN-ExpTODIM-MABAC. The major contributions are executed: (1) the ExpTODIM-MABAC based was extended to IVIFSs along with Entropy model; (2) the entropy is employed to execute the weight under IVIFSs. (3) the IVIFN-ExpTODIM-MABAC approach is put forward MAGDM with IVIFSs; (4) numerical example for college mathematics teaching quality evaluation and comparative analysis is executed to proof the IVIFN-ExpTODIM-MABAC approach.

New trends in didactic research in university mathematics education

Recent research in university mathematics education has moved beyond the traditional focus on the transition from secondary to tertiary education and students' understanding of introductory courses such as pre-calculus and calculus. There is growing interest in the challenges students face as they move into more advanced mathematics courses that require a shift toward formal reasoning, proof, modeling, and problem-solving skills. This survey paper explores emerging trends and innovations in the field, focusing on three key areas: innovations in teaching and learning advanced mathematical topics, transitions between different levels and contexts of mathematics education, and the role of proof and proving in advanced university mathematics. The survey reflects the evolving landscape of mathematics education research and addresses the theoretical and practical challenges of teaching and learning advanced mathematics across various contexts.

Building the educational future: Exploring the dimensions of STEM education through 3D printing and platonic solids in university mathematics teaching

This essay addresses the convergence of STEM (Science, Technology, Engineering, and Mathematics) education, exploring the opportunities and challenges of this multidisciplinary integration in the context of university mathematics education. Focusing on Platonic solids, the study examines how 3D printing becomes a transformative vehicle for mathematical understanding by providing tangible representations of abstract concepts. The tangible dimensions of teaching and the intersection between science, mathematics, and art are highlighted as key factors that enrich the educational experience. Additionally, the technological, ethical, and pedagogical challenges associated with the implementation of 3D printing in STEM education are addressed. This analysis culminates in the conclusion that this integration not only prepares students for an interconnected world but also raises new questions about ethics and responsibility in the evolution of university mathematics education.

How would future mathematicians embrace digital literacy? An TAM model-based analysis

Mathematical practice by working mathematicians is rapidly reshaping the structure and form of modern mathematics. Old intuitions relying on set-theoretic mathematics are receding, replaced by new mathematics based on (higher) category theory. Vladimir Voevodsky, a Fields Medalist, proposed in 2010s a project for reconstructing mathematical proofs using programming languages, known as homotopy type theory (HoTT). At the 2022 International Congress of Mathematicians, Kevin Buzzard gave a plenary talk titled “The Rise of Formalism in Mathematics”, calling for the mathematical community to pay attention to the new trend in research, paper writing and publication review. Undergraduate-level mathematics education is the foundation of mathematical research, but it is also deeply affected by the cutting-edge developments in mathematics. Some universities have already begun various teaching practices to adapt to this new trend, such as UCL's Xena project. This paper adopts multiple case studies and explores emerging impacts of digital literacy on university mathematics education - including both mathematics majors and other STEM majors that heavily apply mathematical tools. The authors believe that TAM model-based analysis could help evaluate the potential impact of this new trend rigorously, rather than relying solely on the propaganda of individual mathematicians. More specifically, we will examine in depth several undergraduate curricula, textbook writing programs, and mathematics education association based on a specific digital platform from the United States and Europe, and compare their successes and failures in various dimensions.

Comparative analysis between three theoretical approaches through empirical experiences at university level

Research into mathematics education at university level includes a wide range of theoretical approaches. This poses considerable challenges to researchers in terms of understanding and harmonizing the compatibility and commensurability of those approaches. The research community has already problematised and studied these challenges using networking theories. The networking theories framework is taken as a starting point in this study to contrast different approaches and to broaden the comparison of different frameworks. In particular, three case studies framed in the Action, Process, Object, Schema Theory, in the Problem-Solving approach, and in the Anthropological Theory of the Didactic are analysed. The differences and possible similarities between the three with regard to the research questions addressed, their objects of study, their empirical bases, as well as their research ends are considered. The analysis offers an insight into the potential for collaboration and the networking of theories in the field of university mathematics education.

On-the-Go Android-Based Learning Tool for Mathematics in Geographically Challenged Areas

One of the important challenges for mathematics educators during the Covid-19 pandemic was ensuring productive mathematics learning despite hindrances. This study explored the mathematics learning experiences of geographically challenged students during the pandemic and developed an on-the-go Android-based learning tool (OTG ALT) for mathematics learning in the challenged areas. The study employed educational design research (EDR) with three phases. A semi-structured in-depth interview guide and student satisfaction survey instrument were utilized. Six geographically challenged university students for interviews and forty students for the tryout of the OTG ALT were purposively selected as participants. Mean and standard deviation scores were used to analyze and interpret the quantitative data. The phenomenographic method was used to analyze the qualitative data. Results show that the experiences of the geographically challenged students in pandemic mathematics education were encapsulated in four different categories: 1) pandemic mathematics learning, a new experience, 2) teachers’ agency in mathematics, 3) tribulations and triumphs, and 4) mathematics that works. The developed learning tool for the course Mathematics in the Modern World (MMW) follows the i?SPARK model (introduce, study, practice, assess, reflect, and key to correction), with a video explainer per topic. Students were highly satisfied with the developed learning tool, in general and in terms of all indicators. Hence, the developed OTG ALT met the instructional standards for mathematics learning in the challenged areas. School administrators may improve the quality and effectivity of mathematics education in universities by considering minority perspectives. To make mathematics education inclusive and equitable, policymakers and curriculum designers can review the suitability of teaching materials and adapt them to the level and needs of the students.

Representation Process of Prospective Teachers in Solving Mathematical Problems Based on Cognitive Style

This study investigates the correlation between cognitive styles and the thinking process utilized when solving mathematical problems, emphasizing the significance of aligning problem-solving strategies with problem representations. Employing a qualitative approach, the research examines two cognitive styles—Field Independent (FI) and Field Dependent (FD)—chosen based on participants' mathematical abilities. Conducted at Cenderawasih University's Mathematics Education Study Program, the study reveals that students' mathematical problem-solving proficiency remains relatively low, warranting further exploration of their thinking processes. While FI subjects demonstrate competence in aligning thinking processes with mathematical representations, particularly in structuring problem-solving steps, FD subjects exhibit limitations in articulating meaning and verbal representations. These findings underscore the importance of instructing educators not only in teaching mathematical concepts but also in guiding students to articulate problem-solving steps using verbal representations. This study highlights the need for a holistic approach to mathematical education, integrating conceptual understanding with effective problem-solving strategies tailored to individual cognitive styles.

Unveiling the complexities of ‘Abstract Algebra’ in University Mathematics Education (UME): fostering ‘Conceptualization and Understanding’ through advanced pedagogical approaches

Unveiling the complexities of ‘Abstract Algebra’ in University Mathematics Education (UME): fostering ‘Conceptualization and Understanding’ through advanced pedagogical approaches

The Measures of Cultivating Students' Mathematics Application Ability in College Mathematics Teaching

Under the background of the new situation, the comprehensive ability of advocating quality-oriented education and talents cultivation, puts forward higher requirements on college students, the mathematics as a compulsory course in university, its status is self-evident, it can effectively promote students' thinking ability, innovation ability, the progress of the ability to solve the problem, then, still need professional teachers attaches great importance to the application ability training, as education the main line, To improve the traditional teaching malpractice, create a good teaching environment. This paper takes mathematics application ability as the theme, discusses the existing situation and concrete solutions, hoping to provide opinions and suggestions for the education industry.

Development of professional competencies of future technical university specialists through professionally-oriented teaching of mathematics

Relevance. In modern conditions of globalisation, the issue of the prospects for the organisation of professionally oriented mathematics education in the Republic of Kazakhstan is one of the most important problems for improving the quality of technical education in the state. Purpose. The purpose of the study is the analysis and practical implementation of the methodological component to increase the levels of readiness of future specialists of a technical university for the development of professional competencies, as a guarantee of the education of a competent specialist ready to carry out professional activities. Methodology. The following methods are used: analysis, comparison, systematisation, classification, generalisation and experiment, and methods of mathematical statistics. Results. The study conducted at Korkyt Ata Kyzylorda University developed a methodological toolkit aimed at enhancing the professional competencies of future technical university specialists through professionally-oriented mathematics education. Key findings include the identification of effective pedagogical conditions, such as diverse educational activities, the activation of independent cognitive work, the integration of digital technologies in mathematics education, and the use of professionally-oriented tasks, which collectively contribute to higher levels of readiness among students. Conclusions. The research underscores the importance of a structured approach to professionally-oriented mathematics education in technical universities. By implementing a methodological system that incorporates components and criteria of readiness, educational institutions can significantly improve the professional competencies of future specialists. The study suggests that further refinement of these methodologies can continue to elevate the quality of technical education in the Republic of Kazakhstan, ensuring that graduates are well-prepared for professional activities. Keywords: higher education; teaching methods; components of readiness; pedagogical conditions of training; digital technologies

“Mathematics is a battle, but I’ve learned to survive”: becoming a disabled student in university mathematics

AbstractIn university mathematics education, students do not simply learn mathematics but are shaped and shape themselves into someone new—mathematicians. In this study, we focus on the becoming of disabled mathematical subjects. We explore the importance of abilities in the processes of being and becoming in university mathematics. Our interest lies in how teaching and assessment practices provide students with ways to understand themselves as both able and disabled, as disabilities are only understood with respect to the norm. We analyse narratives of nine university students diagnosed with learning disabilities or mental health issues to investigate how their subjectivity is constituted in discourse. Our analysis shows how the students are shaped and shape themselves as disabled mathematicians in relation to speed in mathematical activities, disaffection in mathematics, individualism in performing mathematics, and measurability of performance. These findings cast light on the ableist underpinnings of the teaching and assessment practices in university mathematics education. We contend that mathematical ableism forms a watershed for belonging in mathematics learning practices, constituting rather narrow, “normal” ways of being “mathematically able”. We also discuss how our participants challenge and widen the idea of an “able” mathematics student. We pave the way for more inclusive futures of mathematics education by suggesting that rather than understanding the “dis” in disability negatively, the university mathematics education communities may use dis by disrupting order. Perhaps, we ask, if university mathematics fails to enable accessible learning experiences for students who care about mathematics, these practices should indeed be disrupted.

Evalution of Using Virtual Laboratory Media to Learning Geometry in Mathematic Programe Open University

The current condition of the virtual laboratory is developing so rapidly, one indicator is the number of Mathematics students in open university who are looking for references related to practical geometry courses via online between lectures, this raises concern as a lecturer in adding value to lectures, which are adapted to the 21st century learning era today by creating virtual laboratories based on Virtual Reality, research methods using the ADDIE R & D model (Analysis, Design, Develop, Implementation and Evaluation), the science virtual lab product has not been developed much in Indonesia, another thing that makes the appeal of this virtual lab product is that it is able to display virtual reality which can increase motivation and learning outcomes. Student, based on the validation of media experts and material experts on the virtual geometry lab product, it scores 91 and 94 meaning that the virtual geometry lab product is very suitable for use, then more than 90% of lecturers and students at the Open University are very happy to use it. This research has shown that using virtual geometry labs in geometry learning at the Open University shows that all students show enthusiasm in using virtual geometry lab products as a supplement to geometry learning inside and outside the classroom. This was shown that after limited testing of virtual geometry lab products in the open university mathematics education study program, it showed that the majority had completed B+ or a score above 85 in geometry learning.

Investigating problem-solving behaviours of university students through an eye-tracking system using GeoGebra in geometry: A case study

Problem solving is one of the high-level thinking skills and essential in teaching mathematical concepts and procedures. The eye-tracking method allows educators to see and interpret different problem-solving behaviours of students. The purpose of this study was to investigate the problem-solving behaviours of university students based on eye tracking statistics when faced with a geometry problem, and to explain these behaviours in terms of the students' success and learning styles. The research design was a case study approach that combined quantitative and qualitative data. Eight first-year students from the department of elementary mathematics education in a private University, Turkey, participated in this study. They were asked to solve a specific geometry question using the GeoGebra software. While solving this question, their eye movements were recorded and analysed using an eye-tracking program. Results were analysed to investigate their problem-solving skills and behaviours based on Polya’s mathematical problem-solving stages. Results of the study suggest that the effort devoted to the understanding and planning stages of problem-solving are important factors that contribute to success in this case. Results also revealed that participated students with a converger learning style were more successful in each step of the problem-solving process. Additionally, it could be concluded that the input area had only been used by converger students, indicating that they devoted time and effort to creating and trying formulas.

On the Infiltration of Aesthetic Education in College Mathematics Teaching

In the process of implementing the relevant contents of deepening the reform of the educational system, the relevant departments of the state put forward higher demands on the educational work, and made clear the prominent position of aesthetic education in the educational work of colleges and universities, therefore, relevant educators should pay attention to the effective infiltration of aesthetic education in the process of education and teaching. The following will be from the perspective of college mathematics teaching to explore how to combine teaching activities to enhance the level of aesthetic education.

Infiltration Strategies of Mathematical Culture in College Mathematics Teaching

Infiltration Strategies of Mathematical Culture in College Mathematics Teaching

Exploration of the Path of Computational Thinking Cultivation in University Mathematics Teaching

Exploration of the Path of Computational Thinking Cultivation in University Mathematics Teaching

Experience on the Teaching of Higher Mathematics in Vocational Colleges

Experience on the Teaching of Higher Mathematics in Vocational Colleges

A study on the ecological teaching reform of college mathematics supported by Internet technology

This paper combines the relevant theories and methods of educational ecology to study the interrelationship of various ecological factors in the ecological environment of college mathematics classrooms under the Internet environment, in order to construct a new ecological teaching model of college mathematics, further improve students' mathematical proficiency and provide a novel perspective and practice for deepening the reform of college mathematics teaching. The research adopts the methods such as questionnaire survey, literature research, in-depth interview and classroom observation. 3 survey statistics tables are provided with a total of 82 teachers and students participating in the survey. The survey results show that it is highly necessary to carry out ecological teaching reform of college mathematics supported by Internet technology. The specific measures adopted are also given as shown in Table 4. Facts have proved they are conducive to improving the quality of college mathematics teaching and cultivating talents for the country and society.