College Mathematics Research Articles

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.

The cognitive gap in the mathematical thinking abilities of high school leavers for college: Are they ready?

After students spend approximately 12 years of formal math learning from high school, they bring a store of enormous “learned” mathematics factual knowledge to face the challenges and prepare for college/tertiary level learning. However, research has shown that early tertiary-level students struggle to learn college mathematics. The ability to think mathematically and use this learned factual knowledge (mathematical thinking) to solve higher-order thinking skills (HOTS) problems is essential to tertiary education. Thus, do these high school leavers have access to previously learned factual knowledge and use it effectively in solving these HOTS problems? This sequential research design study was conducted among 640 high school leavers who received an A in their national examination. In the first phase, the researchers investigated their mathematical thinking ability, followed by interviews with selected students on the difficulties and challenges they faced in solving the underlying problems. The findings showed that these students lack the ability to effectively use the previously learned factual knowledge from school mathematics to solve mathematical thinking problems. Secondly, they lack the habitual mind to check their answers after deriving a solution to a given problem. Thirdly, most rarely used heuristics to devise a strategy to solve fundamental math problems. Although the expectation of the school math curriculum over the last decade has been re-engineered towards “teaching students to think,” this expectation has yet to be fulfilled. Thus, university educators must do more to guarantee that high school leavers can deconstruct their mathematical knowledge and reconnect it with the underpinnings and linkages of college mathematics requirement.

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.

Analyzing the Impact of AI-Based Personalized Learning on College Mathematics

Analyzing the Impact of AI-Based Personalized Learning on College Mathematics

Quadratic equations with absolute values: an example of developing proof in mathematics students

Proof is the most important and fundamental aspect of mathematics. However, it is generally agreed by mathematics teachers at upper high school and first year university that students lack the ideas of proof. How to develop this in students is a common, difficult and perennial problem. In this paper, we develop some ideas of proof based on the number of solutions of an equation involving a quadratic polynomial and absolute values of linear functions. We begin with the simple idea of making more precise a question that is posed, investigating the problem through exploration, and arriving at some conjectures. We proceed to determine ways to prove the conjectures and thus convert them into theorems. The question discussed in this paper arose in a session for high school students held at the Department of Mathematics and Statistics of the University of Western Australia. The result is an excellent and interesting illustration of problem posing and solving in mathematics that underpins mathematical thinking. The paper is accessible to final year high school and first-year university mathematics students. We expect that it will serve as a resource for and inspire further ideas and examples for mathematics teachers, for teaching proof to students.

New trends in didactic research in university mathematics education

AbstractRecent 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.

Teaching Statistics for the Social Sciences Using Active Learning: A Case Study

US college students are typically required to take at least one mathematics or statistics course, either as part their major area of study, or as a general education requirement. College mathematics requirements are an obstacle for many college students. Active learning, a pedagogical approach that places emphasis on students’ collaborative work, has been shown to increase student learning and course success in STEM fields of study and in mathematics courses. Active learning has also been shown to be adaptable to courses involving computer software and programming, such as introductory statistics. This case study is based on the author’s experience implementing an active learning model in an introductory statistics course for students majoring in sociology and related social sciences. Results indicate that the active learning approach was adaptable to the structure and particular learning goals of the course. Students perceived greater learning relative to other courses despite doing less work outside of class, and attributed this to the active learning structure of the course. These findings align with more systematic studies on the impacts of active learning in science and mathematics courses.

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.

지수함수 미분법의 정당화에 관한 예비 교사들의 수학 내용 지식과 인식

The purpose of this paper is to examine pre-service teachers' mathematical content knowledge and perceptions regarding the justification of the differentiation of the exponential function in relation to the connection between school mathematics and university mathematics. We analyzed and categorized how pre-service teachers justified the differentiation of the exponential function through semi-structured interviews, examined whether the gaps in the learning trajectory in school mathematics were rigorously addressed, and surveyed their perceptions about these gaps. This study revealed that the justification methods of pre-service teachers could be categorized into seven types, and they had difficulty rigorously addressing the gaps. Many pre-service teachers were unaware of the gaps in the learning trajectory and agreed on the need for consistent learning trajectories between school and university mathematics. This study highlights the need to improve pre-service teacher education by examining the mathematical content knowledge required for mathematics teachers in connection to school mathematics.

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.

Publisher Correction: How can university mathematics overcome Klein’s second discontinuity? Specific course design

Publisher Correction: How can university mathematics overcome Klein’s second discontinuity? Specific course design

Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures

AbstractSpecial tasks for pre-service teachers (PSTs) in university mathematics courses (“interface tasks”) are a common innovation in recent years to overcome the second discontinuity. By this, we mean tasks that are situated by typical everyday challenges of mathematics teaching and in which PSTs must use their mathematical knowledge and skills in a professionally relevant way. In this paper, we analyze answers that PSTs have created to an interface task on symmetry. The PSTs were asked to clarify a student’s question from a mathematical perspective and then give a suitable elementarized answer. We situate these two steps theoretically and reconstruct the mathematical reasoning in PSTs' answers. Through qualitative content analysis, we examined how PSTs justify figures' symmetries from a university mathematics perspective and when responding to the fictitious student. The scenario of a student questioning the existence of 100° rotationally symmetrical figures elicited rich and varied responses, proving suitable for an interface task. We compared PSTs' reasoning related to mathematical clarification with the reasoning related to elementarization. In many cases, this revealed a productive use of course content. An interesting result is that there is no uniform picture as to whether the arguments are more detailed in the mathematical clarification or in the elementarization.

From knowledge acquired at academic mathematics courses to significant changes in instructional practices

This non-interventional study investigates the contribution of university mathematics to teaching high-school mathematics. Data sources included interviews with five teachers who taught high-school mathematics before, during, and after their academic mathematics studies. All teachers provided tangible examples of fundamental changes in instructional practices that they explicitly linked to new knowledge acquired in the academic mathematics courses. The domain of analysis in general, and the topics of integrals and derivatives in particular, were central in the teachers’ illustrations of changes they made in their teaching, although other mathematical topics and domains were also mentioned. The reported changes were mostly associated with emphasis on mathematical explanations, exposition of two key elements of the deductive structure of mathematics: definition and proof, an increased focus on formal mathematics, and portrayal of mathematics as a wide and varied discipline. The study results are discussed in light of the relevant literature.

A Case Study on Item Analysis for College Mathematics Ability Test of Freshmen Reflecting Curriculum

A Case Study on Item Analysis for College Mathematics Ability Test of Freshmen Reflecting Curriculum

Research on the Practice of Ideological and Political Theories Teaching Innovation in College Mathematics Courses Under the Concept of Comprehensive Development

Research on the Practice of Ideological and Political Theories Teaching Innovation in College Mathematics Courses Under the Concept of Comprehensive Development

What do university mathematics students value in advanced mathematics courses?

What do university mathematics students value in advanced mathematics courses?

Teaching mathematics in college: The need for a set of professionally oriented tasks

The purpose of the study is to solve this problem, which consists of substantiating, developing, and implementing a methodological system for preparing students for professionally oriented mathematics education in college. Professionally oriented mathematics education in colleges is advisable, as it helps students see the practical benefits and importance of mathematics in their future professional activities. This approach allows us to better prepare students for their future professions. Research problem: what are the leading directions, principles, content, and forms of methodological preparation of students for professionally oriented mathematics education in college? In achieving this goal, we distinguish a complex of professionally oriented tasks in the fact that they reflect specific scenarios and difficulties that specialists face in their professional activities, and this allows students to gain experience in specific tasks from their field. Research methods: interviewing and testing students, teachers; observation, study, and generalization of pedagogical experience; development of an author's methodology for preparing students for professionally oriented mathematics education in college. We identified criteria to verify the effectiveness of the training methodology, assessing the students’ assimilation of subject knowledge and their increased motivation for learning. The results of the pedagogical experiment show that the process of teaching mathematics in a college with a professionally oriented methodological learning system, implemented through the use of a set of professionally oriented tasks, contributes to an increase in the level of mathematical training and educational motivation of students.

Example-Generation Tasks for Computer-Aided Assessment in University Mathematics Education: Insights From A Study Conducted in Two Educational Contexts

Example-Generation Tasks for Computer-Aided Assessment in University Mathematics Education: Insights From A Study Conducted in Two Educational Contexts

How university mathematics instructors form groups and how students experience them

‘Group work’ is a vague description of an instructional activity, because many factors shape its character and effect on students. One important factor is group formation, that is, how groups are formed by the instructor. In this paper, we sought to better understand the variation of group work with respect to group formation by addressing: How do university mathematics instructors form groups over the course of a semester? To this end, we examined eight instructors' methods of forming groups in one multi-section introduction to proof course. Our findings include a classification of group formation methods and descriptions of how instructors varied their formation methods across the semester. Further, we sought to understand: How do students experience different group formation methods? We analysed interviews with 29 students from the eight instructors' classes and identified central themes among students' experiences of different group formation methods. Finally, we discuss the sometimes conflicting research on (when) which group formation method is most appropriate and offer our thoughts on how the differences between typical undergraduate and K-12 mathematics classrooms may contribute to different recommendations.

Integration of Augmented Reality and Modeling Techniques in Dynamic Systems for Teaching Theorems and Demonstrations in University Mathematics Courses: A Differential Equations-Based Approach and Its Applications.

Teaching theorems and proofs in mathematics at the university level poses a considerable challenge due to their high abstraction and conceptual complexity. Augmented reality (AR) emerges as an innovative tool that transforms learning by facilitating the visualization and understanding of complex mathematical concepts, particularly in the realm of differential equations, which are fundamental for modeling dynamic systems. This technology allows students to interact with three-dimensional representations, enhancing their comprehension and analytical skills by visualizing the effects and solutions of equations in real time. Despite technological advancements in education, traditional teaching methods remain static and abstract, limiting the assimilation of concepts. The research employed a quantitative approach and a documentary methodology to analyze the effectiveness of integrating AR and modeling techniques, providing data that evidences their positive impact on academic performance. A thorough review of relevant literature was conducted, consolidating a theoretical framework that highlights the importance of these emerging technologies. The findings suggest that implementing AR in the classroom not only improves knowledge retention but also enriches the discussion on mathematics education in higher education.