Department Of Mathematics Research Articles

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.

Effects of mastery learning strategy on senior school students’ performance in mathematics in Osogbo, Nigeria

This study aimed to explore the effects of Mastery Learning Strategy (MLS) on senior school students’ performance in Mathematics in Osogbo, Nigeria. The quasi-experimental study’s goals were to investigate how MLS affected mathematics students' performance according to their gender and score levels. A purposive sampling technique was used to select two intact classes of 191 SS II students from two co-educational government senior secondary schools in Osogbo. The Geometric Constructions Test (GCT) which was made up of five theory questions adapted from WAEC mathematics past questions was used as the research instrument. GCT was revalidated by experts from the Department of Mathematics, University of Ilorin. The reliability index of 0.75 was obtained by test–retest method and Cronbach Alpha. Three research questions were raised from which three hypotheses were formulated. Data collected were analyzed using descriptive statistics, independent t-test and Analysis of Covariance (ANCOVA) at 0.05 level of significance. Findings revealed that MLS significantly improved students’ performance (t(189) = 10.22, p < 0.05) while there was a significant difference in the performance of male and female students in favour of males (F(1, 94) = 33.06, p < 0.05). The strategy apparently helped to bridge the gap among students’ scoring levels (F(2, 94) = 6.72, p < 0.05). The study found that, in comparison to the conventional method, MLS greatly enhanced students performance in mathematics. Hence, it was recommended that mathematics teachers should endeavour to adopt MLS in teaching Mathematics, especially in the perceived difficult topics.

«Любование стариной» в эпоху «великого перелома»: Н.И. Воробьев и преподавание этнографии в вузах Казани (1920-е – начало 1930-х гг.)

The paper examines the teaching activities of the famous ethnographer, geographer, researcher of the ethnography of the Tatars and other peoples of the Volga region, Nikolay Iosifovich Vorobyev, at Kazan University and the Eastern Pedagogical Institute in the 1920s – early 1930s. His role in organising special departments of these universities, where ethnography and related disciplines (anthropology, anthropogeography, ethnology, etc.) were taught, is shown. The views on ethnographic education of the Kazan teaching community, students and authorities at various levels are described. The paper shows that in the first years of the Soviet rule, ethnography was taught in large quantities at several Kazan institutes of higher education – Kazan University, North-Eastern Archaeological and Ethnographic Institute, and Eastern Pedagogical Institute. The main initiators of including ethnographic disciplines in the curriculum of institutes were employees of Kazan University, including N.I. Vorobyev. However, officials of the RSFSR People’s Commissariat for Education considered ethnography as a discipline that studies ‘backward peoples’ and ‘relicts’, and did not see it as a means of ideological education of students. Therefore, the number of hours assigned to this subject was reduced quite quickly. N.I. Vorobyev and his colleagues proposed a number of educational departments projects (geographical and museum-ethnographic sections of the Eastern Pedagogical Institute) in order to preserve ethnographic education in Kazan. As a result of their efforts, students of the Physics and Mathematics Department of Kazan University and the Eastern Department of the Eastern Pedagogical Institute studied ethnography and related subjects until its ‘defeat’ on the cusp of the 1920s and 1930s.

Practice-oriented tasks as a tool for testing the readiness of high school students for elective courses in informatics

The article substantiates the importance of incoming control for elective courses in informatics. It shows what didactic tools can be used to implement this control. Several elective courses in informatics developed by students of the Physics and Mathematics Department of the Mordovian State Pedagogical University named after M. E. Evseviev on the university discipline "Technology of development and methodology of conducting elective courses in informatics" are given. For each of them, developed practice-oriented tasks for the incoming control are given, which take into account the minimum set of knowledge and skills of schoolchildren necessary for successful assimilation of the material by the latter. Possible results of completing the tasks of the incoming control are demonstrated and it is shown what information a teacher can extract from them in order to effectively create an elective course, including the choice of forms and methods of teaching, organizing the activities of students, combining them into pairs or groups to perform joint project work.

Improving Mathematics Education through Teacher Professional Development: A Tanzanian Perspective

This study aimed to explore mathematics teachers’ perceptions of professional development. The study involved two public secondary schools in Ilala Municipality, Dar es Salaam. This was a qualitative study based on case study design. The study involved fourteen (14) participants that were selected purposefully. Two (2) heads of the schools, two (2) Academic Teachers, two (2) heads of mathematics departments, and eight (8) mathematics teachers were equally involved from both schools. Interviews, focus group discussions, surveys, and document analysis methods were used in data collection. Both interviews and focus group discussion were audio-recorded by using a protected smartphone with password to ensure data security. The documents reviewed includes; school policies, school calendars, and mathematics departmental meetings’ minutes. The data collected were analysed thematically to identify and interpret key themes. The data analysis was based on the following steps: transcription, data reduction, presentation, and discussion of findings. Fictitious names were used for names of people and schools to ensure confidentiality and anonymity. The study revealed that teachers perceived professional development as formal programs to improve teachers’ quality that were time-consuming and costly, while informal professional development programs were overlooked by teachers and other educational stakeholders. The study recommends that, in order to improve teachers’ quality as intended in professional development, there is a need to raise awareness for both formal and informal professional development programs among teachers and a learning community as a whole.

Perceptions and Attitudes of the Mass Promotion Policy Relative to Mathematics Learning at the Senior High School Level, Ghana

The study investigated the perceptions and attitudes of the mass promotion policy relative to students’ mathematics learning in senior high schools. Two research questions were used to guide the study. The researchers employed Social Cognitive Theory and the theory of self-determination to back the study. The study was linked with a pragmatist worldview that made use of a mixed methods approach. The design employed by the researchers as a convergent parallel design. A simple random sampling technique was used to sample students and teachers while a purposive sampling technique was employed in the case of heads of mathematics departments of the sampled schools. Three hundred and twenty-five (325) respondents or participants responded to questionnaires and interviews for the data collection. The methods of data analysis were descriptive statistics and thematic analysis. The findings showed that the mass promotion policy does not promote effective learning of mathematics but rather promotes indiscipline behaviors among students. Students' absenteeism, refusal to do class tasks, inattentiveness, disrespect, sleeping during lessons, and skipping classes were the attitudes put up toward mathematics learning. The researchers recommended that stakeholders, policymakers, and authorities should revise the mass promotion policy based on as per the findings revealed.

Towards a Better Transition to University: A Student-Centric Welcome Day for the New Undergraduate Students in a Mathematics Department

This case study delves into a Welcome Day event organised by the Department of Mathematical Sciences at a UK university for the incoming first year students in the department. This report reflects some of the practicalities and the evaluation of the event. The event, primarily focused on student engagement activities along with reduced amount of traditional presentations, was aimed at facilitating peer networking and smoothing the transition from school to university, hence nurturing a sense of belonging within the student community. The structure of the event was crafted to align with the department's unique ethos, with an emphasis on activities that resonate with the field of mathematics. Evaluation of the event is done based on the responses from the students during the event via an online questionnaire. The event not only demonstrated high levels of student satisfaction but also served as a good example of department-specific orientation programs. These localized events can complement university-wide initiatives, offering a more tailored setting for new students to acclimate to their specific academic environment. This paper has the prospect to guide others and to reinforce the notion of seeking to tailor welcome days to match the needs of new cohorts.

Analysis the Implementation of Independent Learning-Independent Campus Program based on Students’ Perceptions

Investigations of the independent learning-independent campus program still encounter obstacles in its implementation. This research is research that is motivated by the phenomenon of certain obstacles and problems faced by students when implementing independent learning-independent campus program in the mathematics department, FMIPA UNM, so it needs to be reviewed and carried out further analysis as material for further improvements. This research aims to explore student perceptions regarding the implementation of independent learning-independent campus program which is focused on the implementation of existing programs at independent learning-independent campus program which is implemented in the Mathematics Department of FMIPA UNM. This research is quantitative descriptive research using survey methods. The research was carried out at the Mathematics Education Study Program, Department of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Makassar. The sample in this study were students in semester IV and semester VI from the FMIPA mathematics department who were selected purposively based on research interests and needs, namely students who took part in the independent learning-independent campus program. Data was analyzed descriptively to see students' perceptions of the implementation of the independent learning-independent campus program. Research finds that students majoring in mathematics at FMIPA UNM responded well to the MBKM program, it can be seen that the majority of students were interested in joining the program.

Developing English Speaking Skills of 4th Year Students by Using the Cooperative Learning Strategy on Team-Pair-Solo Technique A Case Study of Faculty of Education, Souphanouvong University

The purposes of this study were to (1) study the effectiveness of using the cooperative learning strategy on team-pair-solo technique to enhance the students’ English speaking skills, and (2) to investigate the students’ satisfaction with the use of its teaching technique. The target groups consisted of 19 students from the fourth-year majoring in mathematics in the first semester, academic year 2020-2021 at Department of Mathematics, Faculty of Education. The instruments used in this research consisted of 4 five-hour lesson plans, one students’ English speaking skills assessment form, one English speaking skills test, one observation check list, and one questionnaire about students’ satisfaction. The obtained data were analyzed to calculate means, standard deviation and t-test (dependent samples) by SPSS program, version 21.0. The findings were as follows: Overall, the students’ English speaking ability was significantly higher after learning with the use of cooperative learning strategy on team-pair-solo technique, at the 0.05 level, indicating that the teaching strategy was effective in enhancing students’ English-speaking skills, and generally, the students’ were satisfied with their improvement in English speaking through the use of cooperative learning strategy on team-pair-solo technique, which is viewed at a high level.

Improving the Usability of Graphical Authentication Systems Using Subject-Based Images

Recognition based graphical authentication systems rely on a system user’s ability to recognize previously chosen images and use those images to gain access into a computing systems, devices or application. Recognition based systems that utilise several types of images have been developed and studied. The déjà vu scheme depends on the use of abstract (meaningless) images. Images in the déjà vu scheme have no exact meaning. This scheme has also been actively studied. This article presents a between user study conducted on two recognition-based schemes using system prototypes. The Abstract Based Graphical Authentication (ABGA) was designed to simulate the déjà vu scheme. The performance of this system was compared with the performance of a novel system developed for this research. The novel system, called Subject Based Graphical Authentication (SBGA), in which the system used images from the various disciplines of the research participants. The researcher conducted a lab-based study with 100 participants, 50 participants for each of the prototypes. The study investigated the impact of using subject based images to enhance the usability and security of recognition-based graphical passwords. Two graphical models were thus developed and presented to the 100 participants, which comprised of staff and students from the departments of Computer Science, Mathematics, and Engineering. In the experiments, participants selected their graphical passwords from sets of images representing their various disciplines. The researcher observed that the memorability rate for graphical passwords consisting of subject based images aligned with participants' disciplines surpassed the rate for passwords with purely abstract images. The results indicated 81.7% successful login rate and 18.3% failure rate for Subject Based Graphical Authentication (SBGA). In contrast, Abstract Based Graphical Authentication (ABGP) exhibited a 51.5% successful login rate and a 48.7% failure rate. The findings provide significant insights for graphical password designers and developers seeking to enhance system memorability. Balancing image familiarity with security considerations can lead to more user-friendly and effective recognition-based authentication systems. This study provides valuable insights into the benefits of incorporating familiar images in recognition-based graphical passwords, showcasing a significant improvement in memorability and user authentication success. The findings underscore the importance of considering the user’s familiarity with portfolio images in the design of graphical authentication systems.

A Department-Wide Transition to a New Mode of Computer-Aided Assessment Using STACK

AbstractWe focus on the integration of STACK—a Computer-Aided Assessment (CAA) technology—in the mathematics department of a high-ranking University in the United Kingdom. We study a department-wide project where instructors were expected to implement STACK into continuous assessment tasks for (nearly) all core modules across the first two years of undergraduate study. We present this work as a departmental case study, drawing on semi-structured interviews with six novice STACK assessment designers (and module leaders), supplemented by students’ responses to an open-response feedback questionnaire, and the reflections of a co-project lead (also first author). Our thematic analysis identified four themes related to the design of STACK-based assessments by novice to STACK tutors: the process of ‘STACKification’, technical challenges, users’ perspectives on the role of CAA, and finally, variations in assessment designers’ approaches to the role of feedback. In presenting our results, we are guided by Sangwin’s (2013) design principles for mathematics assessment. We consider various technical aspects of implementing STACK-based assessments as a first-time user, and the knowledge required to do so effectively and coherently. We conclude with a series of reflections on the role of CAA in undergraduate mathematics, and the ways in which such technology can be productively integrated with established practice.

Exploring the teaching methods used in graduate teaching assistant-led calculus recitations

ABSTRACT Many universities offer recitation sections taught by graduate teaching assistants (GTAs) as a way to supplement their large enrolment calculus courses. While some mathematics departments have revamped their calculus recitations to feature more evidence-based teaching practices, other departments rely on GTAs to decide how to run the recitation and what content to cover. In this latter context, more needs to be learned about the teaching practices of GTA recitation leaders and their impact on different student outcomes. As such, this study examines the teaching methods that twelve GTAs chose to implement in their calculus recitation sections. The goal of this study was twofold: (1) to examine whether GTAs utilised evidence-based teaching practices such as student-centred instruction and conceptually-oriented instruction, and (2) whether these practices were related to calculus students' attitudes toward the recitation, student engagement in the recitation, and students' expected final course grades. Using quantitative dominant mixed-methods, findings demonstrate that GTAs used a range of student-centred practices; however, they primarily emphasised the procedural aspects of calculus. Student-centred instructional practices were found to have a positive relationship with students' course attitudes, engagement, and predicted final examination grades. Focusing on concepts, had less of a relationship with these outcomes.

On Application of Absorbing Markov Chain Model to Determine Students’ Academic Progress: A Case Study of Mathematics Department, Ekiti State University, Nigeria

On Application of Absorbing Markov Chain Model to Determine Students’ Academic Progress: A Case Study of Mathematics Department, Ekiti State University, Nigeria

PROGRAM RUMAH CERDAS DIGITAL SEBAGAI UPAYA PENINGKATAN LITERASI DIGITAL DI DESA MALLONGI-MALLONGI

Digital literacy can be defined as the ability to use and understand information from a very wide range of sources that can be displayed on computer devices. The measurement of the digital literacy index is seen from four dimensions, namely, digital skills, digital ethics, digital security, and digital culture. When measured against these four dimensions, the level of digital literacy, Mallongi-Longi Village is considered as low in its application. Therefore, the Student Activity Unit (PPK Ormawa) of the Mathematics Department at FMIPA UNM seeks to address the issues in Mallongi-Longi Village by implementing a work program called the Digital Smart Home Program. It is hoped that this Smart Home Program can broaden the knowledge, attitudes, and skills of the Mallongi-Lonngi Village community regarding digital literacy. This program is conducted through classes and seminars. It consists of two main activities, namely digital classes and digital workshops, targeting the Mallongi-Longi Village community. This program runs for 58 days. Based on the program evaluation results, it was found that the target participants have responded well, the target community wants the sustainability of this program and this program has achieved all the objectives of the program implementation.

Sustaining Active Learning in Undergraduate Precalculus: Results and Challenges of a Course Redesign

Addressed toward course coordinators and departmental leaders interested in redesigning undergraduate mathematics courses with a focus on active learning, this report provides an update on progress in redesigning the Precalculus course offered by the Department of Mathematics at the University of Maryland, College Park, following initial indicators of success. We begin by discussing our team’s challenges due to the COVID-19 pandemic and our attempts to navigate these challenges. We then provide results related to student achievement, self-efficacy, and STEM intentions, in addition to addressing the remaining goals of the redesign.

Students' Numeracy Literacy Ability through the Implementation of Problem-Based Learning and STEM Approach

This research describes the numeracy literacy abilities of students from the Mathematics Department, Faculty of Mathematics and Natural Sciences, Gorontalo State University in solving problems in the MNA and Boundary Conditions courses. The results of the research show that the numeracy skills of students from the Mathematics Department at Gorontalo State University who program the MNA and Boundary Conditions courses in solving mathematical problems are sufficient in using various kinds of numbers or symbols to solve daily life problems and analyzing information displayed in various forms such as graphs. , tables, charts, diagrams and so on. In general, the results of this analysis cannot be used by students to predict and make appropriate decisions. This is shown in the results that only 11.84% of students were able to use various kinds of numbers and symbols in the first question, 21.05% of students were able to analyze information displayed in various forms and only 9.21% had the ability to interpret all question analyzes to take the right decision

Significant Differences Between the IQ Scores of Mathematics Students based on Regression Analysis and Factorial Experimental Design

In this research, data on general intelligence and emotional intelligence scores were analyzed and the difference between them was studied in terms of their application to students of the Mathematics Department in the four stages in the College of Computer Science and Mathematics at the University of Kufa for the academic year 2023-2024. Four statistical methods were used. The first was multiple regression analysis to study the extent to which each student's mathematics score was affected on the general intelligence and emotional intelligence tests (Y), by the student's gender (X1) and his type of residence (X2). The second statistical method is to analyze the design of a factorial experiment to study the presence or absence of significant differences between the grades of students in the four stages by classifying the students in the four stages into males and females, as well as studying the significant difference in the scores of the two intelligence tests (general and emotional) for students in the Mathematics Department in general and divided according to gender. requester. The third method of analysis was to analyze the design of a completely randomized experiment to study the significant differences in students’ intelligence scores between the four academic levels in the mathematics department. If there is a significant difference in the results of analyzing the data in the above methods, then we use the fourth statistical method in this research, which is the analysis of the least significant difference test to study the differences between each two groups separately. The results of the data analysis were numerous, the most important of which is that the intelligence scores in the two tests (general intelligence and emotional intelligence) do not depend on nor are affected by the student’s gender or type of residence. In addition, intelligence scores were not affected for the four educational levels.

Innovative Teaching Techniques for Alleviating Mathematics Phobia Among Secondary School Students in Anambra State

This study explores innovative teaching techniques to address mathematics phobia among secondary school students in Anambra State. Recognizing the pervasive impact of mathematics anxiety on academic performance and psychological well-being, the research focuses on the efficacy of two innovative approaches: inquiry-based learning and peer teaching. The study involves 50 secondary school students and employs a self-designed questionnaire validated by mathematics department lecturers, a measurement and evaluation expert, and an experienced secondary school teacher. Data collection was conducted through an online survey designed using Google Forms, providing a convenient and efficient method for participants to respond. Results from the online survey reveal insights into the comparative effectiveness of these techniques, highlighting gender-specific variations. Notably, peer teaching emerged as a more favorable technique. The slightly higher variability in scores in the peer teaching method, as indicated by the standard deviation, suggests that while it may lead to higher average performance, it also introduces greater variability, emphasizing the need for tailored approaches to accommodate diverse learning styles. The study contributes localized data to the broader literature, addressing gaps in understanding mathematics phobia in Anambra State. Findings aim to inform educators, policymakers, and practitioners about evidence-based strategies to create a positive and inclusive learning environment for mathematics in secondary schools.

Determinants of career choice among secondary school students in Enugu east education zone

This study examined determinants of career choice among secondary school students in Enugu East Education Zone. The study specifically examined the influence of parental factors on the choice of career among secondary school students in Enugu East, ascertained the influence of societal culture on the choice of career among secondary school students in Enugu East, evaluated the extent peer groups influence the choice of career among secondary school students in Enugu East and also investigated the influence of the school environment on the choice of career among secondary school students. Four research questions and four hypotheses guided the study. Related literature was reviewed under the conceptual framework, theoretical studies, theoretical framework, related empirical studies, and summary. The study adopted a census survey research design. The study was conducted among secondary schools in Enugu education zone. The population for the study was 334 students. There was no sampling of the study because of the manageable size of the population. A questionnaire was used as the instrument for data collection and was designed to elicit appropriate information from the respondents. To ascertain the face validity of the instrument, the questionnaire was given to two experts in the Department of Educational Management and one expert from Measurement and Evaluation in the Department of Mathematics and Computer Education all from the Faculty of Education, ESUT. The reliability coefficient of the instrument was calculated using the Cronbach Alpha method. The results of the analysis indicated reliability indices of 0.85, 0.81, 0.76, 0.83, and 0.84 for clusters A, B, C, D, and E. The overall reliability index was 0.82 which made the instrument reliable. Mean and standard deviation were used to answer the research questions, while t-test statistic was used to test the hypotheses at 0.05 level of significance. The findings of the study revealed among others that there is no significant difference in the mean ratings regarding the influence of parental factors on the choice of career between male and female students. Based on the findings, the study recommends among others that parental impositions regarding their children's choice of career often result in career failure. In realization of this, parents should guide their children through the decision-making process. Parents are advised to allow their wards free hands in their career choices that will relate to their interests, aptitude, passion, and ability.

Performance Analysis of Fifth-Semester Physics Education: Assessing an Online Pascal Compiler in the Department of Mathematics and Natural Sciences Education at University of Mataram

This study evaluates the integration of online Pascal compilers in undergraduate physics education at the University of Mataram, focusing on its impact on students' programming skills. Over one semester, three classes (A, B, and C) of physics education students from the Department of Mathematics and Natural Sciences Education (PMIPA), Faculty of Teacher Training and Education (FKIP), University of Mataram, participated in lectures, discussions, and practical exercises using the GDB Online Pascal Compiler. Course content included Pascal fundamentals, arrays, matrices, and applications in physics, evaluated through assignments, mid-semester, and final exams. Quantitative analysis of student performance data revealed significant differences in mean scores and variability among the classes, with Class A achieving the highest average score and Class C exhibiting the greatest variability. Statistical tests confirmed that performance data for all classes deviated significantly from normal distribution, necessitating non-parametric tests. The Mann-Whitney U test indicated no statistically significant differences in median scores between class A vs. class B, class A vs. class C, and class B vs. class C, suggesting consistent performance outcomes across classes post-course. These findings underscore the potential of the online Pascal compiler in enhancing students' programming skills within the context of physics education.