Mathematics Lecturers Research Articles

Metric compatibility and determination in complete metric spaces

AbstractThe local slope operator was introduced in De Giorgi et al. (Atti Accad Naz Lincei Rend Cl Sci Fis Mat Nat 68:180–187, 1980) to study gradient flow dynamics in metric spaces. This tool has now become a cornerstone in metric evolution equations (see, e.g., Ambrosio et al. (Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics. Birkhauser, 2008). Very recently, in Daniilidis and Salas (Proc Am Math Soc 150:4325–4333, 2022), it was established that Lipschitz inf-compact functions are uniquely determined by their local slope and critical values. Compactness played a paramount role in this result, ensuring in particular the existence of critical points. We hereby emancipate from this restriction and establish a determination result for merely bounded from below functions, by adding an assumption controlling the asymptotic behavior. This assumption is trivially fulfilled if f is inf-compact. In addition, our result is not only valid for the (De Giorgi) local slope, but also for the main paradigms of average descent operators as well as for the global slope, case in which the asymptotic assumption becomes superfluous. Therefore, the present work extends simultaneously the metric determination results of Daniilidis and Salas (Proc Am Math Soc 150:4325–4333, 2022) and Thibault and Zagrodny (Commun Contemp Math 25(7):2250014, 2023).

Lecturers' use of questions in undergraduate mathematics lectures

Mathematics lecturers frequently ask questions in their lectures, and these questions presumably play an important role in students’ thinking about and learning of the lecture content. We replicated and developed a coding scheme used in previous research in the US to categorise lecturers’ questions in a sample of 136 lectures given by 24 lecturers at a research-intensive UK university. We found that the coding scheme could be applied reliably, and that factual questions were predominant (as in previous research). We explore differences in the lecturers’ use of questions – both between our UK sample and the previous US work, and between individual lecturers in our sample. We note the presence of strings of related successive questions from the lecturer, which we term ‘question chains’. We explore the nature of these, examine their prevalence, and seek to account for them in terms of the lecturers’ possible intentions.

Analysis of Topics Perceived Difficult by Pre-service Mathematics Teachers and Lecturers in Colleges of Education in Niger State, Nigeria

This study was conducted to investigate the topics perceived as difficult by pre-service mathematics teachers and Mathematics lecturers in Colleges of Education in Niger State, Nigeria. One Hundred and seven (107) 300 level Pre-service Mathematics Teachers and Seventeen (17) Lecturers were purposively selected from two (2) Colleges of Education in Niger State, Nigeria. A twenty-three items questionnaire named Mathematics Topic Analysis Questionnaire (MTAQ) with two sections was administered to respondents (Pre-service Mathematics Teachers and Mathematics Lecturers). The questionnaire was validated by experts, and its internal consistency was assessed using Cronbach's Alpha, which yielded a reliability coefficient of 0.87. Data analysis was done using Mean and Standard deviation and independent sample t-test. A criterion means of 2.5 was set as the basis for judgment. A mean score of 2.5 and above indicated an easy topic, while less than 2.5 indicated a difficult topic. Findings revealed that Pre-service Mathematics teachers perceived 9 topics as difficult to comprehend while 3 topics were perceived as difficult to teach by Mathematics lecturers. The study also showed that Pre-service Mathematics teachers’ gender has no significant influence on their perception of difficult topics in mathematics. It was therefore recommended that students should be encouraged and motivated to learn mathematics, curriculum developers should develop instructions that would improve students’ knowledge by laying more emphasis on the perceived difficulty areas in mathematics and further studies should be conducted to find out the factors responsible for the perceived difficulty and also if there is a relationship between perception and students’ achievement.

The influence of using Learning Videos for High School Mathematics Curriculum Subjects with Flipped Classroom Models on Learning Achievement in the UIN Walisongo Semarang

During the current pandemic, students are having difficulty understanding mathematical material; normally, they are taught by lecturers face-to-face, but now online. The obstacle that students face is that they believe that learning is not optimal because the signal is often poor and inconsistent, and they are unable to meet with the lecturer. To alleviate this issue, it is required to create a video of learning material that will be supplied by a mathematics lecturer by the lecturer who teaches, the video is published on YouTube, and the youtube link is given to students to study beforehand for the forthcoming meeting. This is consistent with the flipped classroom concept, in which students are expected to first understand the lecturer's video before being discussed directly by the lecturer.It is expected that students are able to think creatively about video content created by their professors, and students are able to examine material flaws that they have not understood and then clarified by their lecturers at the next meeting. In research on the development of instructional video media for high school mathematics curricular with the ADDIE stage model. This model, as the name suggests, consists of five main phases or stages, namely (A) analysis, (D) design, (D) development, (I) implementation, and (E) evaluation. The Implementation and Evaluation stage was carried out in the second year, with expanded tests carried out at UIN Walisongo Semarang in a fun and enjoyable manner, with posttests and user response questionnaires given with the following results: Based on research at UIN Walisongo, posttest results were processed using tests t results obtained are 0% <5%, then H0 is rejected. This means that we accept H1, which means that the results of learning mathematics using video learning media for high school mathematics curriculars are better than conventional learning models. Looking at the average learning achievement in the mean column, Group Statistics table, the experimental class average is 86.00, while the average -the average control class is 64.74. These results show that the learning outcomes of the experimental class are better than the control class. R Square value of 0.804 = 80.4%. This value means that the influence of virtual lab media on learning achievement is 80.4%, while 19.6% of learning achievement is influenced by other variables outside of the independent variables in this research.

AN EXPLORATORY STUDY: DEVELOPMENT OF ELECTRONIC MODULES IN MATHEMATICAL PHYSICS I COURSE

AN EXPLORATORY STUDY: DEVELOPMENT OF ELECTRONIC MODULES IN MATHEMATICAL PHYSICS I COURSE

Learning more about derivative: leveraging online resources for varied realizations

Recent literature underlines the increasing use of online platforms in learning undergraduate mathematics, where students refer to these as supplementary resources to develop their mathematical understanding. Through an intrinsic case study, we focus on a highly viewed YouTube learning resource for learning derivative. The selected case is from 3Blue1Brown, a YouTube channel whose founder has received an award from the American Mathematical Society. The video has garnered more than 3.3 million views in the past couple of years. Reflecting on the relevant literature, a realization tree for derivative is developed and then used as an analytical tool to analyze this resource to explore what realizations have been used in it to facilitate students’ understanding of derivative. The findings indicate that the analyzed YouTube resource discusses various realizations of derivative, including all its five main realizations, and effectively utilizes new digital technology for discussing these realizations. Such an exceptional resource for learning mathematics leads us to suggest that mathematics lecturers raise their awareness about such online free resources and incorporate them into their teaching packages when appropriate to facilitate student learning.

Facilitating note-taking with guided notes – students’ preferences regarding positions for blanks and preprinted parts

In traditional mathematics lectures given on the board, students are often busy taking notes and have trouble listening to the instructor simultaneously. One approach to address this problem is the use of guided notes. These are parts of the instructor’s notes containing blanks at certain positions. Such guided notes can help students process information presented during the lecture, because they have to write less and can be more attentive towards the instructor’s explanations. Furthermore, the blanks provide opportunities for fostering students’ active engagement with the content presented. But which positions of a mathematics lecture might be suitable for blanks in guided notes? While there exist some proposals from instructors, students’ perspectives have been rarely considered, although they are the ones who need to actively process the information presented in the lecture during their note-taking. We therefore investigated at which positions of a mathematics lecture students appreciate blanks within guided notes, and why they perceive the blanks at these positions as helpful for their note-taking. The results provide some indications about suitable positions for blanks or preprinted parts in guided notes, and explain why students might benefit from these during their note-taking.

Analysing the quality of real analysis lectures using a structured observation tool

This paper reports a study investigating the quality of advanced mathematics lectures following three goals. First, we present our conceptualisation and operationalisation concerning the quality of mathematics lectures. Second, we test the reliability of a structured observation tool that is based on the aforementioned conceptualisation. Third, we describe the quality of mathematics lectures based on data collected with the observation tool and illustrate its use. The results show that our observation tool is suitable for collecting data about characteristics of mathematics lectures observed on-site and from video recordings. The analysis of the data shows that our findings are in line with previous research: formal aspects of mathematical statements are presented in verbal and written forms mostly correctly; informal aspects of mathematical statements (such as examples, visual or mental representations) are, if they are presented, usually presented only verbally. Furthermore, students have the opportunity to participate during lectures, but there are seldom presentations of alternative solutions, examples or proofs and only a few opportunities for formative assessment. Finally, we discuss implications for future research.

Inquiry in mathematics: studying a professional development measure for university lecturers

This paper reflects on the Inquiry-Based Mathematics Education approach and the professional development of university mathematics lecturers. The main focus is on task re-design as a key aspect of subject matter focussed lecturer training. The professionalisation activity we have established is rooted in a framework developed by the European project Partnership for the Learning And Teaching IN University Mathematics (PLATINUM). The focus of this paper is a didactic instrument developed within this project and implemented in the training activity. We focus on challenges, leeways and scope for actions that arise in the design and implementation of mathematical tasks for an inquiry-based teaching. For the empirical analyses, we use data from a professional activity carried out at the Complutense University of Madrid in Spain, jointly by a team from Madrid and Hannover.

Detection of environmental pollutants from cobwebs found in selected lecture rooms at the Faculty of Science, Federal University Dutse, Nigeria

The aim of this study was to assess the environmental pollutants present in the cobwebs found in selected lecture rooms; Mathematics lecture room (MTH), Chemistry lecture room (CHM), Biology lecture room (BIO) and Environmental Science lecture room (EMT) in the Faculty of Science, Federal University Dutse. Bacterial pollutants coupled with Arsenic (As) Lead (Pb) in the sampled cobwebs were isolated and identified using standard procedures. One-way Analysis of variance was used to determine the variation in the concentrations of Pb and As in the sampled cobwebs. Staphylococcus aureus (28.1%), Bacillus sp. (37.5%), Streptococcus sp. (18.8%), and Streptobacillus sp. (15.6%) were detected in all the cobwebs samples. MTH 4 had the highest Pb concentration (1.2800 mg/kg) while CHM 3 had the lowest (0.470 mg/kg) Pb concentration. CHM 3 and BIO 3 had very low concentrations of Pb, which were significantly different from each other (p˂0.05). This study has revealed that spider cobwebs can be an effective bio-indicator in determining indoor air quality. Keywords: Indoor air, Cobwebs, Lecture rooms, Bacterial contaminants, Lead, Arsenic

Oxford mathematics at a low ebb? An 1855 dispute over examination results

ABSTRACT Between December 1855 and March 1856, a public dispute raged, in British national newspapers and locally published pamphlets, between two teachers at the University of Oxford: the mathematical lecturer Francis Ashpitel and Bartholomew Price, the professor of natural philosophy. The starting point for these exchanges was the particularly poor results that had come out of the final mathematics examinations in Oxford that December. Ashpitel, as one of the examiners, stood accused of setting questions that were too difficult for the ordinary student, with the consequence that, in Price’s view, further mathematical study in Oxford – never as robust as in Cambridge – would be discouraged. We examine this short-lived affair, and use it not only to gain insight into the status of mathematical study in Oxford in the mid-nineteenth century, but also to point towards the increasing importance of competitive examinations in British public life at that time.

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.

Exploring criteria for university mathematics teachers’ selection of calculus textbooks

This study delves into the nuanced process of calculus textbook selection by university mathematics lecturers. Drawing from a conceptual framework that encompasses various selection criteria, including culture-driven, student-driven, resource-driven, teacher-driven, mathematics-driven, and constraints-driven factors, the research examines the predominant criteria guiding lecturers’ choices. Data from participating lecturers reveal a multifaceted decision-making process. “Culture-driven selection” emerges as a significant criterion, indicating the influence of curriculum committees. Additionally, educators prioritize “student-driven selection,” valuing accessibility and contextualization, while also favoring textbooks with abundant resources and problems. The study underscores the complexity of textbook selection, shedding light on how instructors navigate educational, commercial, and student-centered considerations. These findings offer insights beneficial for textbook authors and publishers, useful for the creation of resources aligned with educators’ preferences.

Less is More: Improving by Removing

The pressures currently on teachers of mathematics at every level seem greater than ever, whether that is university mathematics lecturers, school teachers or those who work with very young learners. So, I began my Presidential Address with the hope that no one would leave the Joint Conference of Mathematics Subject Associations 2023 feeling as though they were not good enough and must do more. I did not want anyone to go home with a lengthy to-do guilt list of additional things they must try to incorporate into their practice. Instead, I advocated giving attention to the ancient proverb “less is more”, versions of which are found within many cultures; e.g., “brevity is the soul of wit” (Hamlet), “Sometimes diminishing a thing adds to it; Sometimes adding to a thing diminishes it” (Tao Te Ching). I offered five aspects of mathematics teaching and learning that might benefit from ‘less of’ something, in each case trying to see how this might create space for more of something else. In this article, I present these five suggestions for improving by removing.

Pengembangan Modul Sudut dan Garis yang Berbasis Etnomatematika

The purpose of this study was to produce a math module with an ethnomatics approach for class VII SMP and to describe the module on angles and lines with applied Mathematics Approach for Class VII Junior High School students to get an easier understanding and increase students' enthusiasm for learning. With introduce culture to class VII students are viewed from the 3 aspect of validity, effectiveness, and practicality. This type of research is the development of research with ADDIE development model. Which includes analysis, design, development, implementation, evaluation. Modules have been developed further validated by the validator 3 is 2 mathematics lecturer Budi Utomo Malang Teachers’ Training College and one teacher of Bahasa Indonesia as subject matter experts, media specialists, and linguists. The tests showed an average score of in the category invalid and declared effective student questionnaire responses with an average score of were categorized as excellent, and practical dinayatakan modules for which there are instructions for using the module, prerequisites, answer key, etc. From the research it can be concluded THAT math module with an ethnomatics approach to describe the module on angles and lines with applied Mathematics approach feasible to be used as teaching materials for junior high school students of class VII

Optimization of mathematics teaching and learning for the treatment of anxiety disorders in college students

BackgroundThe study attempts to integrate Civic and Political Psychoeducation to optimize the teaching content of traditional mathematics courses in colleges and universities, in order to alleviate college students’ anxiety in the process of mathematics learning, as the difficulty of mathematics courses in colleges and universities increases.Subjects and MethodsAs subjects for this study, 120 students majoring in Mathematics Applications at one of China’s universities were chosen. The 120 college students were randomly and equally divided into two groups, the control group and the experimental group, with 60 students in each group. The students in the experimental group were taught utilizing the Civic Psychology intervention in their mathematics courses, whereas the students in the control group were taught using the usual mathematics lecture approach. The trial ran for a semester. After one semester, the students’ anxiety psychological ratings under various instructional approaches were compared. The data changes during the experiment were recorded and analyzed using SPSS23.0.ResultsThe study’s findings demonstrate that after one semester of mathematics instruction, the average anxiety level of the experimental group dropped from 28.56 to 5.21, whereas the average anxiety score of the control group did not change appreciably. It can be demonstrated that the experimental group’s teaching style can more successfully ease college students’ anxiety during the arithmetic learning process.ConclusionsA college mathematics teaching strategy that mixes ideological and psychological education can successfully reduce college students’ anxiety during the mathematics learning process.

Web-based learning management system as media in teaching ESP for mathematics students in higher education

This study examines the techniques used by ESP Math lecturers, the challenges they have in providing ESP learning materials, how they overcome these challenges, and the implications for ESP design. This study employed a qualitative research design by interviewing five ESP Mathematics lecturers teaching at STKIP PGRI Sidoarjo in the 2022-2023 academic year. 15 items of interview guidelines were prepared to gain a deeper understanding of what respondents have done in implementing the techniques of teaching ESP for Mathematics. The data were then examined using an interactive analysis process. The survey found that several of the lecturers had issues with vocabulary, pronunciation, grammar, and speaking fluency. The instructors overcame the obstacles by working together with other instructors and studying from printed and digital resources to better their command of the English language. Additionally, they utilized a web-based learning management system to aid in their education and facilitate the creation of instructional materials. It meant that the development of ESP for math educators had to concentrate on four areas: vocabulary, pronunciation, grammar, and fluency. The ESP curriculum might be developed using any number of platforms, including ones that cater to linguistics and mathematics.

Experts‵ Perception on the Usage of Mathematical Representations in Biology Comics

Integrating biology and mathematics can potentially solve problems associated with students' inability to solve quantitative biology problems. To face this issue, we embarked on a project to develop biological and mathematical content-based comics for elementary school students. It would assist them in gaining early comfort with transdisciplinary work. However, we need experts’ perceptions to see if our comics are feasible. This exploratory interview research attempted to understand how experts perceive mathematical representation in biology comics. The three experts involved in the interview were a biology teacher, a mathematics lecturer, and a comics enthusiast. This study's empirical data were collected using semi-structured interviews and analyzed using thematic analysis. The research uncovered three major themes: 1) comic content, 2) graph type, and 3) graph modification. Experts have a positive opinion of our comics. We highlight the experts’ feedback for some revision, such as adding additional information, expanding the storyline, and modifying the graph through Concrete-Pictorial-Abstract approach.

A Study of Common Mathematical Errors Committed by the Students of Xth Class in Geometry

The study looked into the types of mistakes committed by the Xth class students in mathematics made when solving word problems that were concrete and formal. 240 students from five local government and Private schools were chosen using random and purposeful sampling approaches, respectively. The study's conclusions showed that Students committed more numbers of errors under the objective “Application” when compared to other objectives. Students committed more number of errors under the content area “Angles”. The study also concluded that the students confused greatly with the Terminology and students were very weak in fundamental operations especially in Angles. It is one of the fundamental subjects included in both primary and secondary education. The intellectual growth of an individual is aided by mathematics. The methods for solving issues, like as induction, deduction, and idealization, make up the syntactic framework. The person tackling the problem must have a sufficient comprehension of the two structures in order to solve the problem successfully. Therefore, it is advised that word problem solving receive sufficient attention in mathematics lectures.

Ethnomathematics: The exploration of fractal geometry in Tian Ti Pagoda using the Lindenmayer system

This study explores the concept of fractal geometry found in the Tian Ti Pagoda. Fractal geometry is a branch of mathematics describing the properties and shapes of various fractals. A qualitative method with an ethnographic approach is used in this study. Observation, field notes, interviews, documentation, and literature study obtained research data. The observation results were processed computationally using the Lindenmayer system method via the L-Studio application to view fractal shapes. The results show that the concept of fractal geometry is contained in the ornaments on the Tian Ti Pagoda. The length and angles of each part of the ornament influence the fractal shape of the Tian Ti Pagoda ornament. In addition, the length and angle modifications resulted in several variations of the Tian Ti Pagoda fractal. The findings from this study can be used as an alternative medium for learning mathematics lectures, especially in applied mathematics, dynamical systems, and computational geometry.