University Mathematics Education Research Articles

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.

“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

AbstractProblem 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.

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.

Development of Geogebra-Based Interactive E-Modules to Improve Students' Digital Literacy Abilities

Many students of Ivet University's mathematics education study program think that mathematics courses are very difficult and boring. This happens because students are positioned as listeners in the learning process so that what happens is that the learning process is too monotonous. So far, teaching and learning activities have only used books as a learning resource, an interactive approach will be able to make students more interested in the learning process. One interactive approach in the learning process is using geogebra-based interactive e-modules. The existence of geogebra-based interactive e-modules will further attract students in the learning process and improve students' digital literacy skills. The aim of this research is to produce a geogebra-based interactive e-module to improve students' valid digital literacy skills. The urgency of this research in learning is very important due to the low level of learning resources used in the learning process and the low level of digital literacy for students. The research that will be carried out will have a big impact on student understanding. It is hoped that the development of this interactive e-module will be able to overcome problems that arise in teaching students. It is hoped that limited learning resources can be overcome by having e-modules as a learning medium to prevent misunderstandings arising when teaching integral material. The result of this research is to produce a geogebra-based interactive e-module to improve students' valid digital literacy skills.

Exploration of cultivating students' autonomous problem-solving ability in college mathematics teaching

With the continuous development of information technology and the arrival of globalization, the demand for talents in society is becoming increasingly urgent. At the same time, talents from all walks of life also need to continuously improve their ability to independently solve problems in order to adapt to the requirements of the rapidly developing era. College mathematics education also faces the challenge of cultivating students' ability to solve problems independently. This situation makes it difficult for the traditional teaching mode that focuses on "teaching" and "training" to meet the needs of cultivating high-quality talents. Therefore, this article explores the cultivation of students' autonomous problem-solving ability in college mathematics teaching.

Research of Online and Offline Blended Teaching of College Mathematics

The traditional teaching model faces significant challenges in the era of information technology, while the blended learning model that integrates information technology and educational instruction has become an undeniable trend. Blended learning, which combines online and offline elements, can achieve complementary advantages to a greater extent, effectively enhancing the quality of teaching and promoting students' competence. This article explores the blended learning model, using higher mathematics courses as an example.

A practical study on integrating ecological education in university mathematics education in the context of deep learning

Abstract This paper combines the deep learning model and the concept of environmental education to construct an ecological education model of university mathematics based on deep learning and designs an index evaluation system for the ecological teaching quality of university mathematics under deep learning. The indicators that affect the quality of ecological teaching of university mathematics are analyzed by partial correlation analysis and factor analysis, and then the indicators after partial correlation, as well as factor analysis, are further analyzed by multiple linear regression, and the teaching model is put into practice. The correlations of student engagement, classroom culture, and clear objectives with teaching quality were 0.99, 0.99, and 0.98, respectively, and the evaluation satisfaction of each indicator was above 0.8, which could be effectively integrated.

Artificial Intelligence and Its Relationship to Teaching School and University Mathematics in Jordan

This study aims to study the scenarios that may arise with the introduction of artificial intelligence in education, especially in mathematics education in Jordanian schools and universities, and what its implications are for the future of schools. The study design was phenomenological, a qualitative approach that looked at the perspectives of participants from various fields. The findings suggest that as AI in education becomes more prevalent, schools and teachers will encounter new products, advantages, and disadvantages. The findings highlight several recommendations for using AI and preventing potential problems and while participants generally seemed to have positive views of AI, there were some negative aspects as well, to which mathematics teachers and academics in particular drew attention in relation to the future of education. While educators view AI as a tool to bring quality and benefit to all in the education sector, they are more focused on the rationale for AI in education and potential future issues.

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.

Values in college mathematics learning: Student teachers’ preference

This study explored what Ghanaian student teachers value in college mathematics learning. A cross-sectional survey involving 180 student teachers from College of Education in Ghana was conducted using the What I Find Important (WIFI) in mathematics learning questionnaire. The study employed principal component analysis with Oblimin rotation and one-way multivariate analysis of variance in analyzing the data gathered. Among the findings, it was found that student teachers value exploration, connections, understanding, and fluency in their study of college mathematics. Also, the findings of the study revealed a statistically significant difference in what student teachers value in college mathematics learning across college class levels. To facilitate a clearer understanding of valuing in the colleges of education in Ghana, it is considered important to establish through research the values of teacher educators regarding college mathematics learning and teaching, and how these values reflect what student teachers value and those values espoused in the new 4-year Bachelor of Education (B.Ed.) curriculum in Ghana.

Proof and proving in school and university mathematics education research: a systematic review

This systematic review aims to provide a complementary to existing synopses of the state-of-the-art of mathematics education research on proof and proving in both school and university mathematics. As an organizing framework, we used Cohen et al.’s triadic conceptualization of instruction, which draws attention not only to the main actors of the didactical process (i.e., the Teacher and Students) and the Content around which the actors’ work is organized (herein, content related to proof and proving), but also to the relationships among the actors and the content. Out of the 103 papers we reviewed, almost half fell in the Student-Content category, which is consistent with the existence of a substantial number of frameworks, methods, and research findings related to students’ engagement with proof and proving. About a quarter of the papers fell in the Student–Teacher-Content category, which reflects an emphasis on viewing instructional practice in proof and proving in a holistic, systemic way. Only few papers fell in the categories that did not include Content in them, namely, the categories of Student, Teacher, and Student–Teacher; this suggests mathematics education research on proof and proving has a strong disciplinary identity, which potentially differentiates it from other mathematics education research strands. About a fifth of the papers were oriented towards ‘breaking ground’ through making an explicit theoretical and/or methodological contribution (Student–Teacher-Content and Content were the main categories where such contributions appeared), whilst the majority of the papers were focused on ‘building ground’ through elaborating or employing existing methodological and/or theoretical approaches.

Exploring the "Teaching and Learning" of Calculus Course from the Perspective of Teaching Connection

In the current Mathematics education system, there is an obvious disconnection between college mathematics (taking calculus as an example) and middle school mathematics. If the connection is not smooth, it will directly affect the teaching effect of college mathematics. This article analyzes the causes of poor connection from the perspectives of differences in teaching objectives and methods, disconnection and overlap in teaching content, differences in learning methods, external environmental influences, and individual differences in student sources. We have proposed bridging strategies from the perspectives of teachers' "teaching" and students' "learning", providing teaching references for improving the effectiveness of university mathematics teaching and cultivating high-quality mathematics talents.

Conflicting mathematical worldviews

University mathematics education and civic education through mathematics emphasise different aspects of the mathematical worldview. The present study qualitatively analyses 21 mathematics students’ mathematics-specific intrinsic motivation for choosing a mathematics study programme referring to different aspects of their mathematical worldview before the beginning of their study. The results show that many preservice teachers enjoy schematic aspects of mathematics, which does neither correspond to the type of mathematics taught at universities nor to civic education through mathematics. These findings contribute to explaining demotivation and frustration of preservice teachers with university mathematics as well as challenges for implementing civic education through mathematics in classrooms.

Digital Twin for Math Education: A Study on the Utilization of Games and Gamification for University Mathematics Education

Gamification has emerged as a promising strategy for engaging students and enhancing learning outcomes across various disciplines, including education. It involves incorporating game-like elements into non-game contexts to motivate and engage users. Extensive research has demonstrated the positive impact of gamification on student engagement, motivation, and learning outcomes in diverse subjects, including mathematics. Nevertheless, there is a paucity of research on the effectiveness of gamification in mathematics education. To bridge this gap, we investigated the effects of gamification in college mathematics education, with a specific emphasis on students from liberal arts backgrounds who may lack foundational mathematical knowledge. In this work, we designed and implemented a gamified mathematics course tailored for liberal arts students in a Korean university. Leveraging digital twin technology for game and gamification, we created an immersive learning environment that allows students to visualize mathematical concepts through games, pair gamification factors on physical and virtual worlds, and engage in interactive problem-solving activities. The effectiveness of this gamified course in improving students’ engagement, motivation, and learning outcomes was thoroughly evaluated. Digital twin technology, in conjunction with gamification, holds immense potential to revolutionize the way mathematics is taught and learned, making it more accessible, interactive, and engaging for students from diverse educational backgrounds.

An updated conceptualization of the intuition construct for mathematics education research

To improve instruction, conduct communicable studies on student intuition, and provide an entry point for researchers interested in this area, the meaning of intuition in mathematics education needs to be addressed. This paper reviews 816 journal papers from top tier mathematics education journals to obtain an updated conceptualization of the intuition construct. Different research camps, such as a camp focused on instructional design that leverages learners’ primary intuitions in the classroom and a camp concerned with sources of errors through the lens of intuitive rules theory, emerged. A critical discussion of theoretical choices for intuition research will be followed by several directions for future research on intuition specific to university mathematics education.

Theorizing university mathematics teaching: the Teaching Triad within an Activity Theory perspective

In this paper, we draw on our recent research to inspect again some of the theoretical perspectives we have been using to analyze data and to characterize teaching-learning in university settings. We focus particularly, within a sociocultural perspective on Activity Theory and the construct the “Teaching Triad,” seeking to embed the Triad within an Activity Theory perspective. To achieve this, we relate the Teaching Triad with aspects of the sociocultural setting both in and beyond direct interactions in face-to-face teaching. While this is mainly a theoretical paper, an example is taken from observations of teaching in university lectures in a Greek university to show how these theoretical perspectives have provided insights to the institutional and cultural complexities involved and in what ways the Triad construct has evolved.

Research on the Mixed Teaching Mode based on the New Form Textbook of Linear Algebra

The new form of textbooks combines paper textbooks with new media resources, teaching with modern technology, and compensates for the content that paper textbooks cannot carry. The new form teaching materials of Linear algebra, including the integrated design of teaching content, strengthen the problem orientation, fully reflect the concepts of Flipped classroom, mixed teaching mode, inquiry learning, etc., improve the creativity, progressiveness and effectiveness of college mathematics teaching activities, and promote the benign development of college mathematics teaching.