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In recent years, with the increase of online learning platforms, obtaining learning behavior data from students, are becoming easy. However, analyzing the data to extract meaningful information remains challenging due to the data volume and complexity. Here, we apply Self-organizing Maps (SOM) to visualize the learning characteristics of many elementary students over many online assignments in mathematics class. As a case study, this research used the data log of MONSAKUN, a digital learning environment that focuses on exercising arithmetic using story-based questions by using a problem-posing approach with the integration of mathematical sentences. Our primary objective is to give intuitive understanding to the teachers regarding the students' performance that subsequently allows the teachers to generate meaningful advices. Here, SOM generates a two-dimensional map that preserved the topological order of high-dimensional learning characteristics data, in which students with similar learning characteristics are located close to each other, while students with significantly different characteristics are distanced from each other. We are interested especially in locating low-performing students, as they are the most important to be given advice by the teachers. By locating the low-performing students and other students in their vicinity on the map, the teacher may be able to use other students as references for improving the low-performing students' performances. The idea is to mimic the learning characteristics of the students designated as references. Due to the learning characteristics similarity, the low-performing students do not need to make drastic changes in their learning styles. It can be expected that by iterating this process over many assignments, the students' performances will gradually be improved. In this paper, we utilized a digital learning platform MONSAKUN, for learning arithmetic used in Japan. In this paper, we present our preliminary results in the form a learning-visualization of characteristics students of analytical and advisory tools and described our future goals for building a more flexible and general tool that can be deployed in Indonesia. [ABSTRACT FROM AUTHOR]

This paper explores the correlation between mental calculation performance and the frequency of using written algorithms in mental calculation tasks. Mental calculation is a mathematical tool used in everyday life situations during and after our formal education. After presenting an overview of the professional literature on this topic, the paper will present calculation methods and show how represented they are in the Curriculum. For the empirical part of the research, a total of 233 Croatian students aged 10 to 22 years were tested and interviewed. The previously mentioned correlation was then analyzed. An overview of the interview results will be presented as well. It was found that school mathematics does not always contribute to the development and flexibility in using mental calculation strategies because of the student preference for acquired written algorithms. Definitely, recommendation is shifting the focus from written calculation and procedures to the mental, discussing the associated strategies and different concepts of number. In this way, formal education could contribute to what students really need later on, in both private and professional situations in which they may find themselves on a daily basis. [ABSTRACT FROM AUTHOR]

This paper showcases an example of how mathematics was utilized to debunk a suspected anomaly in election returns in the aftermath of the Philippine national elections last May 2022. Initial results of the automated elections yielded numbers that the public deemed suspicious. In response to a call for experts' opinions on the matter, we processed and analyzed large samples of preprocessed data to which we have been given access. Using data analytics techniques, we examined transmission arrivals of election returns and compared them against the total votes transmitted, with the analysis performed at different aggregation levels. Our analyses showed that the seemingly suspicious numbers can be explained by examining the distributions of the transmission arrivals of election returns and analyzing those distributions using different levels of aggregation. From the perspective of critical mathematics education (CME) particularly, focusing on mathematics for critical citizenship, we highlight the importance of mathematics to help fight disinformation and spread of unfounded rumors. The paper concludes with recommendations for enriching students' mathematical experiences that could pave the way for a responsive and engaged citizenry in our country. [ABSTRACT FROM AUTHOR]

In physics and mathematics educational environments, meaningful learning paths should be balanced interactive explorations of the different epistemological and cognitive phases of the modelling cycle. Our approach in this context involves sequences of interactive engagement learning activities with computational modelling that explore the different kinds of modelling, progressively introduce scientific computation, generate, and resolve cognitive conflicts in the understanding of physics and mathematics, and comparatively analyze complementary mathematical model representations. In this work we present a learning sequence about light polarization for intermediate science, technology, engineering, and mathematics (STEM) university courses during which students can create and explore in the computer relevant mathematical physics models and animations that help and complement the learning processes in theoretical lectures and problem-solving paper and pen activities. [ABSTRACT FROM AUTHOR]

The field of numerical mathematics is one of the basic mathematical areas of training of future mathematicians. It plays an important role in the sense of connecting theoretical knowledge with practice. At the same time, it is one of the courses that specifically applies students' computer knowledge in solving mathematical problems. As a number of mathematical software and programming languages are emerging with the rise of IT technology, the question arises as to how to build the concept of teaching numerical mathematics. Models that have been used for a long time are already proving to be non-functional and significant innovation is needed. The paper will describe the structure of teaching numerical mathematics at the University of Ostrava, its innovations and teaching experience. [ABSTRACT FROM AUTHOR]

Mathematical representation is one of the fundamental abilities used in mathematics to build the connection between abstract ideas and logical thinking to understand and solve mathematics problems. The level of student representation ability will affect the way students convey the idea of solving mathematics problems. This shows how important this ability is in mathematics. But in fact, the ability of mathematical representation is felt to be less comprehensively mastered. This is indicated by the large number of students having difficulty conveying their ideas in solving mathematics problems. This paper describes students' abilities in mathematical representation to solve math problems. The indicators for mathematical representation ability in this research are classified as verbal representation (written text), visual representation (picture, diagram, graph, or table), and symbolise representation (mathematical statement, numerical/algebra symbol, mathematical notation). The subject of this research was 8-grade students of one of the junior secondary schools at Bukittinggi. The results showed that 22 out of 34 students have difficulty in conveying their ideas to solve math problems, while the rest feel quite good about it. [ABSTRACT FROM AUTHOR]

This paper aims to examine the learning of mathematics using philosophy-based teaching materials for high school students. Philosophy-based teaching materials are in the form of Student Activity Sheets (LKPD) consisting of LKPD based on Anthology, LKPD based on Epistemology, and LKPD based on Axiology. [ABSTRACT FROM AUTHOR]

The goal of this study is to outline the outcomes of analysis on the creation of useful math learning resources during the COVID-19 pandemic. The issue is that goods from the creation of math learning resources are required to counteract an acceleration in learning following the COVID-19 epidemic. Many of the results of development research, however, are only kept as study materials and are only preserved in Study Program documents or on Google Drive. The study was conducted utilizing the survey methodology, questionnaire data collection strategies, and development research outcomes papers completed by students of the Mathematics Education Study Program FKIP UPGRI Palembang during the COVID-19 epidemic. strategies for analyzing quantitatively described data. The outcomes of the development research take the form of products for math learning devices, with PBL/PBM, RME, CTL, and mathematics software being the most widely utilized learning models and methods. E-modules, LKPD/LKS, learning media in the form of video, and PPT are the most common product kinds. Algebra, Geometry, Calculus, trigonometry, statistics, and Arithmetic are among the mathematics topics covered throughout the development. The development's validity yields a product quality of 87.19%, while its practicality comes in at 85.48% and its potential impact is at 83.48%. According to the development research's findings, it should be given some thought if mathematics instruction is to be changed following the COVID-19 pandemic. [ABSTRACT FROM AUTHOR]

This paper aimed to describe the implications mathematics education in finance. Calculation of interest rates, discounts, profits, taxes, GDP growth requires basic arithmetic skills such as percentages. By imbuing financial literacy in math learning, not only do students know firsthand the use of percent in financial situations, but they are also increasingly knowledgeable about finance. Financial literacy in our study spans three dimensions: content, context, and process. By using the proportion and equation approach as well as two types of construction, namely the bar model and the circle model, we present the learning situation of monthly salary allocation table. Through this situation, students are expected to be able to construct fractional material and financial knowledge on salary and income content. [ABSTRACT FROM AUTHOR]

This paper aims to develop a valid and practice the development of PISA-Like Mathematics Problems and produce a potential effect on creative thinking skills of 7th grade junior high school students in solving the development of PISA-Like Mathematics Problems in the context of Palembang tourism. This research is type of qualitative research. The result of this research is the development of PISA-Like Mathematics Problems with the characteristics of creative thinking skills using Merdeka curriculum, which in the curriculum is related to number material. In content using Quantity content. In context using a social context, namely "Wisata Sungai Musi". In terms of difficulty level categorized as application level. To conclude, the development of PISA-Like Mathematics Problems can teach students to learn mathematics and at the same time introduce students to the culture and tourism of Palembang. [ABSTRACT FROM AUTHOR]

The effectiveness of Game-based Learning (GBL) in fostering students' motivation to learn mathematics is examined in this systematic review. Nine related papers published between 2018 and 2022 were found after an extensive search of the electronic databases of ERIC. A systematic review methodology was used to analyze the studies, and the results were then synthesized and summarized. None of the research in this review found evidence of a negative impact of GBL on students' motivation to learn mathematics; instead, all studies found evidence of a positive impact. It benefits students' motivation for several reasons, including the engaging and dynamic learning environment, the quick feedback and rewards, and the demanding and goal-oriented learning experience that games may give. The game's design, degree of difficulty, student autonomy, use of feedback and rewards, and other factors play significant roles in determining how effective GBL is at encouraging students' motivation to learn mathematics. However, this effectiveness is not guaranteed. The design and implementation of GBL in the mathematics classroom should consider these elements seriously. Generally, the results of this review point to GBL as a potentially successful strategy for increasing students' motivation to learn mathematics. Game-based Learning (GBL) is a strategy educators should consider employing to engage students and increase their interest in and love of mathematics. However, the game's design and other elements that may affect it must be carefully considered. More research is required to completely comprehend GBL's potential in mathematics education and develop efficient implementation methods. [ABSTRACT FROM AUTHOR]

COVID-19 pandemic requires professional teachers to use digital technology, but some students experience obstacles in technology so that it has an impact on their low critical thinking abilities. This paper aims to analyze mathematical critical thinking abilities between students who carry out learning models eliciting activities assisted by Edmodo and conventionally assisted by WhatsApp based on prior knowledge of mathematics. The research method used a quasi-experimental, non-equivalent pretest-posttest control group design. The sample was selected through a homogeneity test from 4 parallel classes of one junior high school in Bandung Indonesia, two classes were selected, namely class VIII A as the experimental class and VIII D as the control class. The instrument uses an initial mathematical ability test and critical thinking abilities. Data analysis uses: Two-way ANOVA test. Findings: There is a difference in the improvement of mathematical critical thinking abilities between experimental class and control class students. There are differences in the achievement of mathematical critical thinking abilities based on prior knowledge of mathematics in the smart, medium and weak categories. Learning models eliciting activities assisted by Edmodo can facilitate the process of construction, interaction and reflection so as to improve students' critical thinking abilities. [ABSTRACT FROM AUTHOR]

In this paper proposed, a novel subclass of meromorphic univalent functions has been introduced and defined. 풥(a, ℷ, A, B, μ) using convolution operator in U*. We have obtained some properties, like, coefficient inequality, growth and distortion bounds, radii of starlikeness and convexity, linear combination, closure theorems and extreme points. Mathematics Subject Classification: Primary 30C45 [ABSTRACT FROM AUTHOR]

The use of Digital Twins (DTs) or the digital replicas of physical entities has provided benefits to several industry sectors, most notably manufacturing. To date, the application of DTs in the healthcare sector has been minimal, however. But, as pressure increases for more precise and personalized treatments, it behooves us to investigate the potential for DTs in the healthcare context. As a proof-of-concept demonstration prior to working with real patients, we attempt in this paper, to explore the potential for creating and using DTs. We do this in a synthetic environment at this stage, making use of data that is all computer-generated. DTs of synthetic present patients are created making use of data of synthetic past patients. In the real world, the clinical objective for creating such DTs of real patients would be to enable enhanced real-time clinical decision support to enable more precise and personalized care. The objective of the numerical experiment reported in this paper, is to envisage the possibilities and challenges of such an approach. We attempt to better understand the strengths and weaknesses of applying DTs in the healthcare context to support more precise and personalized treatments. [ABSTRACT FROM AUTHOR]

In the current scenario Programming in Python plays a vital role in research arena as it preserves much of the man power. Converting the research work into the format of coding helps any researcher across the globe as it serves as a ready reckoner. Topology is one of the main branches of Mathematics. A Polish Mathematician named Kazimierz Kuratowski defined essential axioms in Topology with the aid of a closure operator named after him. In this paper, we have developed a Python program to find the closure and interior for the subsets of the given set. We will be using dictionary in Python with each subset as the key and the respective closure as its value. Subsequently we will be finding int(cl(A)), cl(int(A)), int(cl(int(A))), cl(int(cl(A))), for any subset A of the given set. [ABSTRACT FROM AUTHOR]

In the digital era, most of the human work is now been performed using the computer system. The computer's capacity to detect and understand meaningful Handwriting input from sources such as touch screens, pictures, paper documents, and other sources is referred to as handwriting character recognition. The diversity in people's handwriting style increases the complexity of handwritten characters. Also, grading academic answer sheets manually and providing an unbiased genuine grade is a challenging task. The aim of the work is to create handwriting character recognition system that will be used to read handwriting notes and solve mathematical equations. The ultimate goal is to show that neural networks can solve equations from a handwritten source effectively. In this paper, we present a web application-based equation solver that uses a camera image of an equation to display the solution. The program has the ability to solve simple arithmetic equations (addition, subtraction, multiplication) and up to two systems of linear equation variables handwritten or typed in a computer font. [ABSTRACT FROM AUTHOR]

In this paper, a new operator was defined μ m , k j. v f (w)) : A → A. Associated with Hadamard product of the Komatu Integral operator [MATH] and the Dziok-Srivastava operator [MATH]. And done use the method of differential subordination to derive certain properties of the differential operator μ m , k j. v f (w)). And aim of this paper is to use the relation (α 1 k + 1) μ m , k j + 1 , v f (w) = w (μ m , k j , v f (w)) ' + α 1 k (μ m , k j , v f (w)) [ABSTRACT FROM AUTHOR]

Nowadays, the need of ICT as a learning aid has potential role at the global scope. However, it sounds contradicts with the teaching and learning habit of the boarding schools or pesantren environment. It is an educational institution with strong and large cultural products, but reluctant to see the urgency of ICT implementation. This article aimed to examine students' learning experiences in mathematics at the role of ICT. The study was conducted using a qualitative approach with phenomenological methods. Research data were obtained through interviews and observations. Furthermore, triangulation of sources and triangulation of theory using Dale's classification or "the Cone of Experience" was carried out with regard to student learning experiences. The results showed that at this place: 1) the learning experience symbolically dominated the implementation of mathematics learning; 2) the iconic and enjoyable learning experience was only experienced by some students; 3) ICT had an important role in creating a symbolic, iconic, and enjoyable learning experience for students. This study provides strategic recommendations on how it can adapt the positive impact of ICT to support the learning process. While it deems impossible to stem the flow of ICT developments, this paper can serve as a reminder and a form of wake-up call to keep up with the demands and developments of the times. When ICT integration has not been implemented in mathematics learning, teachers should be able to create concrete learning experiences for students. [ABSTRACT FROM AUTHOR]

This research aims to analyze gender difference in cryptarithmetic problem-solving with "funtastic" battle math game. The respondent 29 student of the 4th graders in the elementary school, 16 female and 13 male students. The research approach was qualitative and quantitative. The data were collected through paper and pencil test, observation, and interview. The data were analyzed by descriptive and effect size methods. The results showed the average score of male students is lower than female students, however effect size on male students is higher than female. The findings are then elaborated using some related theories to justify the results. [ABSTRACT FROM AUTHOR]

Students' pattern of learning that does not involve active thinking will make it difficult for them to master the elements of higher order thinking skills (HOTS) in mathematics. Therefore, more effective learning methods need to be implemented to help students deal with this problem. This paper presents the results of a study after a cooperative method through paired learning was conducted on a selection of Year 6 students for the subject of Mathematics. The purpose of the study was to see the effectiveness of paired learning methods in the teaching and learning process of mathematics that apply the elements of HOTS. A total of twenty-eight Year 6 students from a school in Penang were selected as the sample for this study. Students' performance was tested before and after treatment to see if there was a difference between their performances. After that, a questionnaire was given to see the level of students' motivation and identify the factors contributing to their difficulties in mastering HOTS. From the results of this study, all students (100%) have shown an improved performance in the post-test. The mean scores from the questionnaire responses also indicated that students had a positive perception of the paired learning method. [ABSTRACT FROM AUTHOR]

Teaching and Learning Mathematics in the 21st centuries highly related to the digital technology used in the classroom. Mathematics is the best practice in the standard teaching and learning (T&L) process where the teacher and student physically attend the class. There is where the interaction and discussion on subject matter happened. However, due to the COVID-19, the practice needs to be changed drastically in which both sides of teacher and student are not allowed to have a physical class to avoid any contact. The learning process must proceed and adapt well to the current situation. A Learning Management system must be developed as a platform to digitally organize educational material. Due to that, this paper aims to illustrate the development of a website that is beneficial in T&L Mathematics courses. The content of the mathematics course chosen is Linear Algebra. There are various learning management systems, but the one that customizes the purpose and requirement of our class content can be developed by ourselves. Google offers a good package where google sites can be easily set up for that purpose. The content is arranged according to based on topics. In addition, the interactive learning environment is also embedded in developing the system to attract the student's attention during class hours. Live chat is also provided for the student to ask questions at their convenience time. Developing a customized learning management system can be an alternative for teachers to provide a digital environment to their students so that the process of T&L can be continued. Our website has been introduced to students, and their feedback is recorded. The result shows that students show positive responses while describing the website [ABSTRACT FROM AUTHOR]

Prior to the COVID-19 pandemic, majority of universities in Malaysia commonly implement the teaching and learning practices on physical face to face basis. However, the pandemic had drastically changed the norm of the teaching and learning practices into online teaching and learning as one of the measures to curb the spread of the virus among the community. The drastic move had greatly affected the academic communities particularly the students. Some of the possible factors influencing online learning difficulties faced by the students include poor internet accessibility, lack of self-motivation, lack of active interaction with lecturers and peers, lack of conducive learning environment and poor time management. In this paper, the technique of Fuzzy DEMATEL is employed in analyzing the level of influence and relationships of the aforementioned factors in contributing to learning difficulties particularly among fifty mathematic students at a public university in Shah Alam, Selangor, Malaysia. The cause-and-effect analysis that take into consideration the interactions or interrelationships between factors discovered that poor internet accessibility was classified in the cause group whereas the remaining factors which are lack of self-motivation, lack of active interaction with lecturers and peers, lack of conducive learning environment and poor time management were in the effect group. The results indicate that poor internet accessibility has the highest degree of relation in terms of influencing other factors. Based on the prominence value, the lack of self-motivation turns out to be the leading factor contributing to online learning difficulties. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present the concept of a parametric b-2 Metric space, which is a nonlinear version of the parametric b-metric, as well as to establish several fixed point theorems in these spaces. Before extending the finding of O. Ege and I. Karaca [Azerbaijan Journal of Mathematics, 7(1), 2017] to parametric b-2 metric spaces, some basic definitions and notions of parametric b-2 metric space are provided. We also present an example to show how our findings are applicable. [ABSTRACT FROM AUTHOR]

This paper aims to describe mathematics teachers' perception of mathematical proof. Proving in mathematics for the teacher is crucial as the foundation of developing students' skills in generating correct proof to some conjectures which require good mathematical reasoning. It has been highlighted in some works of literature that mathematical reasoning which is closely related to proving in mathematics also contributes to the development of a chosen set of 21st-century skills. A total number 152 of Indonesian in-service mathematics teachers were given a survey concerning their perception of mathematical proving. The description of the result consists of five important categories including the process of mathematical proof, thinking ability in mathematical proof, appropriate school level in learning proof, topic, and understanding in a mathematical proof. It is found that Indonesian in-service mathematics teachers had a positive attitude towards mathematical proof as a teaching approach in their classrooms, as the opportunity for students to improve helped students improve their thinking ability. [ABSTRACT FROM AUTHOR]

In Graph theory, colouring is the best and most well-considered amplitude. The four-colour problem has contributed to great change in the world of mathematics. Graph colouring has become an essential of interest in graph theory. This often includes its disparate theoretical conclusions, its unconcluded issues and its several utilizations. Throughout this paper, the Conjecture Steinberg is studied with a counter example. Conjecture Steinberg states that "Each planar graph except cycles of length four or five is 3-colourable". Whereas an example by which there exists a planar graph with four or five cycle is 3-colourable is encountered for the Steinberg conjecture. [ABSTRACT FROM AUTHOR]

This paper presents results from research that investigated the participation and attrition rate of male and female candidates in two post-secondary mathematics courses (Pure Mathematics and Applied Mathematics). The data for this study consisted of the course results over five years from 2013–2017 for 15,220 candidates (N = 19,585) from 71 post-secondary educational institutions in Jamaica. They were analysed using frequencies (totals and percentages) and descriptive statistics. The data analysis revealed that, on average, over the five years and across each of the five years, approximately 18% of the students who engaged in postsecondary education opted to participate in a mathematics course. However, there was a sharp decrease in the Year 2 student participation after completing the related Year 1 course. Another key finding was that a higher percentage of males chose to undertake Applied Mathematics in Year 2 and equal proportions of male and female candidates in the other three courses. These findings suggest that initiatives are needed which improve student achievement and experience in the first year of each mathematics course which could potentially decrease student attrition across years and curb the leakage at this juncture of the STEM pipeline. [ABSTRACT FROM AUTHOR]

The objective of the present paper is to study and investigate new notion of separated sets namely, δ-ß-Separated sets by using δ-ß- open sets. Moreover, with this notion we introduce new classes of connected spaces which are called strongly δ-ß-connected spaces and study some essential properties concerning of δ-ß- connected spaces. Several characterizations and fundamental properties concerning of such these classes of connected spaces with some δ-ß- Separtion axioms and compact spaces are obtained. The behavior of δ-ß- connected spaces with respect to several types of well-known mappings is discussed. Also, the digital spaces in the context of these new concepts are examined. Mathematics Subject Classification: 54B05, 54B10 ,54C10 ,54D18,90D42. [ABSTRACT FROM AUTHOR]

Graph theory is a branch of mathematics which is quit rich and interesting. The study of domination is one of the fastest growing area in graph. There are different types of domination such as connected domination, independent domination, total domination, paired domination, secure domination , etc. "The secure dominating set S of a graph G is a dominating set with the property that each vertex u∈V\ S is adjacent to a vertex v∈S such that (S\ v) Uu is a dominating set. The minimum cardinality of such a set is called the secure domination number and denoted by γs(G)". In this paper we discuss about the secure domination for some special graphs. [ABSTRACT FROM AUTHOR]

A teacher, who is the provider of the proven educational knowledge, should be adequately competent in terms of expertise, trust, dedication, positive attitude, effective communication and patient listening. All these attributes can surely be inculcated in pupil teacher but only if the training is provided with maximum commitment, with specified objectives, taking into account the needs of todays' educational scenario and the needs of students. This paper emphasize on the system of training being provided to pre-service Mathematics' teachers, to develop their teaching skills. It includes the use of some creative teaching concepts to increase the interest, level of satisfaction and the outcome of their targeted Mathematics' students. Several studies, researches have shown that the students, who have been studying Mathematics since their childhood, are unable to perform simple calculations and are unable to solve simple numerical problem of their everyday life. This study will conclude with some suggestive facts that pre-service trainees should be trained in a way that other than the prescribed curriculum/syllabus, they should spend time to improve quantitative skills using some innovative techniques in regular class practice. As an example, the inventive methodology will also be discussed. And the second highlight will be the the emphasis on continual and rigorous assessment of the trainees during teaching practice, so that they can resolve the dearth and can go ahead with a handful of approaches to serve the purpose of fruitful teaching and learning. [ABSTRACT FROM AUTHOR]

STEM education is one of the primary priorities in the Malaysian Education Blueprint (PPPM) 2013-2025, in line with the relevance of STEM at the global level. In keeping with the educational needs of 21st-century learning, the use of technology in education is also highly encouraged. Unfortunately, the Malaysian government's goal of producing one million experts in Science, Technology, Engineering, and Mathematics (STEM) by 2020 was not met because the 60:40 STEM: non-STEM policy failed to meet the goal. Students' interest in different STEM disciplines has been linked to their interest in integrated STEM in previous studies. Students' lack of interest in STEM fields appears to have an impact on their low mathematics achievement at the international assessment level, including in the field of geometry. Geometry is one of the most important branches of mathematics, and spatial thinking goes hand in hand with it. This paper presents the results of a critical review as well as a brief overview of ongoing research targeted at developing a model for the formation of interest among secondary school students in STEM through geometry learning based on augmented reality (AR) technology and visual-spatial abilities. The first part of the paper provides an in-depth review of these matters based on rather limited resources. The review revealed various difficulties and limitations in piquing students' interest in STEM and mathematics. The second part describes research being conducted by the researchers to examine the implementation of using AR in geometry learning based on visual-spatial abilities. For the pilot and main stages of the study, pre-and post-test, observations, and semi-structured interviews will be conducted. The data will be analysed quantitatively and qualitatively, and the theory of change approach will be applied. The findings will be used to develop a model for the formation of interests among students as a result of geometry learning. The model aims to provide some relevant information for technology-assisted mathematics instruction, and it aligns with national STEM policy goals of increasing the number of students selecting STEM disciplines in secondary and higher education. [ABSTRACT FROM AUTHOR]

The mode of assessment is one of the most important factors influencing learning as it affects how students organize their time and what subjects they focus on. It is well known fact that students may exhibit different abilities in different forms of assessment. In this paper, we show how e-assessment with the Halomda educational platform can enhance students' learning experiences. In addition, we present how technology-assisted math education can help students study at home and in the classroom, as well as support teachers in their routine work of checking student assignments. Results from teaching courses with Halomda demonstrate not only high student learning outcomes on the final exam, but also a good correlation between exam marks and weekly assignment marks. [ABSTRACT FROM AUTHOR]

Lie algebras appeared in mathematics at the end of the 19th century in connection with the study of Lie groups. A Lie algebra is a vector space over some field together with a bilinear multiplication is called the bracket which satisfies two simple properties: skew symmetric and Jacobi identity. The universal property of tensor product for representations of Lie algebras is a supporting conjugate of tensor product, which guarantees obtaining a linear map from a bilinear map. The main objective of the paper is to obtain results in representations for Lie algebra through the new structure consisting of four and five representations, by action of representation for Lie algebra. As well as obtaining new generalizations using dual action of representation for Lie algebra. [ABSTRACT FROM AUTHOR]

Isabelle/HOL is a generic proof assistant. Using an Isabelle/HOL requires insight into procedures as well as into the concepts involved. In addition, the way computer manages the procedures can affect mathematical concepts. We can clearly understand mathematical concepts and can minimize the burden of operation opportunities. "Foundations of Geometry" is a book of mathematics written by Hilbert in 1899. The book is famous as the most rigorous study of the axiom system of Euclidean geometry by axioms and formalism. The purpose of this paper is to complement the axiom system by theorizing a part of the problems in this book. [ABSTRACT FROM AUTHOR]

Stereotypes about men being better than women at mathematics appear to influence female students' interest and performance in mathematics. Given the potential motivational benefits of digital learning games, it is possible that games could help to reduce math anxiety, increase self-efficacy, and lead to better learning outcomes for female students. We are exploring this possibility in our work with Decimal Point, a digital learning game that scaffolds practice with decimal operations for 5th and 6th grade students. In several studies with various versions of the game, involving over 800 students across multiple years, we have consistently uncovered a learning advantage for female students with the game. In our most recent investigation of this gender effect, we decided to experiment with a central feature of the game: its use of prompted self-explanation to support student learning. Prior research has suggested that female students might benefit more from self-explanation than male students. In the new study, involving 214 middle school students, we compared three versions of self-explanation in the game - menu-based, scaffolded, and focused - each presenting students with a different type of prompted self-explanation after they solved problems in the game. We found that the focused approach led to more learning across all students than the menu-based approach, a result reported in an earlier paper. In the additional results reported in this paper, we again uncovered the gender effect - female students learned more from the game than male students, regardless of the version of self-explanation - and also found a trend in which female students made fewer self-explanation errors, suggesting they may have been more deliberate and thoughtful in their self-explanations. This self-explanation finding is a possible key to further investigation into how and why we see the gender effect in Decimal Point. [ABSTRACT FROM AUTHOR]

We implemented a project to create transformative changes in the STEM Education at a Hispanic-serving institution by revamping mathematics curriculum and building a system of support in mathematics learning. The project accomplished three main areas of curriculum development: (1) Restructuring the first-year mathematics courses at the college algebra level using a corequisite model; (2) designing and implementing active learning and problem-solving oriented curriculum in Calculus; (3) building a student support system of peer-tutoring and mentoring through peer-led team learning. High impact strategies were used for increasing and sustaining the participation of women and underrepresented minority students in computing. Strategies included hands-on active and collaborative learning pedagogy, experiential learning with real world relevance and applications, and curriculum that incorporates data analysis, data visualization and computational thinking. The support targeted introductory courses to provide early exposure and engagement. This paper describes the curriculum restructuring and development, which led to the institutional implementation and transformation of mathematics curriculum. The paper also reports on the success of the redesigned courses. [ABSTRACT FROM AUTHOR]

Two short university courses of recovery of logical-mathematical deficiencies were completed by 210 students of a degree course in Primary Education Sciences, for future elementary school teachers. The courses were held during the years of the pandemic and were therefore online. Students had completed an entrance test with pen and paper, in person, when they first applied for university. The test was organized by an external organization given that there were more than 1000 candidates. Many deficiencies in logic and mathematics were revealed, but without specifics. We therefore transformed some of the test questions into electronic form, with automatic assessment so that students could verify their level themselves and lecturers could plan teaching activities. These questions were used in the courses of recovery. Having to verify the results of more than 1000 students at the original entrance tests, this method for identifying specific deficiencies of the successful candidates was of great support. [ABSTRACT FROM AUTHOR]

The soft set is a concept which is considered as a common mathematical tool to deal the unpredictability in all the fields that deals mathematics. The problems that trouble the theoretical approaches are solved using soft set. The soft topology is formulated using soft sets. Based on variable values, soft topology induces topology. Using soft topological spaces soft tritopological spaces are framed. This research paper deals some new definitions of trio open soft b cover, trio compact soft b. Also investigates trio compact soft b spaces properties in soft tritopological spaces. In further studies the outcome of this research paper can be done on soft tritopological spaces. [ABSTRACT FROM AUTHOR]

This paper attempts to provide information about designing digital holographic learning media especially in teaching and learning mathematics at University. To be detail, this study was conducted to provide educators at university information towards things need to be considered in designing such instrument. In this case, we depict several activities in making holograms to deliver mathematical insights for students for Calculus course. The study was carried out through developmental steps ADDIE, such as Analysis, Design, Development, Implementation, and Evaluation. This study was conducted at Mathematics Education Program, Medan State University, especially for students who enrolled Calculus course. The activities were described explicitly in each phase. The results of this study show that it takes time to make holographic digital media in teaching and learning process of mathematics, including university. In this case, there are several aspects that need to be considered in designing the media, such as (1) the learning topics; (2) contents; (3) object video/animation; (4) hologram application. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a result on the existence of fixed points for a system of mappings which generalizes the results of Edelstein (J. London Math. Soc. 37 (1962), 7479), Suzuki (Nonlinear Anal. 71 (2009), 11, 53135317.), Matkowski (Bull.Acad.Polon.Physics. 21 (1973), 323324) and many others. As an application, we establish a result on the existence of common fixed points for two systems of mappings, which supports our main finding. In addition, we also have an example to validate our main finding. [ABSTRACT FROM AUTHOR]

Education for children with special needs, especially with mild intellectual disabilities, has not received much attention from researchers and practitioners. The education of intellectual disabilities children also has the same right to develop according to the needs of the times as regular children's education in general. The changing and evolving needs of the times should also be followed by changes in the curriculum used, considering that one of the learning goals in special schools for intellectual disabilities children is to make the children who can live independently. In special schools for intellectual disabilities children in Indonesia, mathematics learning is combined with other lessons to discuss specific themes in everyday life. Based on an extensive literature search on the mathematics curriculum in special schools for intellectual disabilities children, this paper aims to review the literature involving two things: (1) mathematics education curriculum in special schools for intellectual disabilities children in Indonesia, and (2) mathematics curriculum in special education in Australia and Singapore. A view is also provided. This paper concludes that: (1) learning in special schools for intellectual disabilities children in Indonesia uses thematic learning where mathematics learning is focused on its usefulness in everyday life, (2) numeracy is the focus of education in Australia, not least for intellectual disabilities children, and learning Mathematics for mild intellectual disabilities children in Singapore includes the concepts of numbers, spaces, arithmetic procedures, problem solving and measurement. [ABSTRACT FROM AUTHOR]

In this paper, we present the preliminary results of testing an adaptive learning system on tablet computers developed for mathematics classes in the lower grades of primary school. The developed system consists of two parts: the mobile application for repetition and revision of math exercises, and an administrative interface, through which teachers can create new tasks, monitor students' progress, and analyse the results of each student. The adaptivity algorithm, based on various available information, assesses the current knowledge level of each student and populates a list of next tasks with ones of appropriate difficulty. The preliminary study was conducted with a small class of third-grade students, and the results show that the adaptivity algorithm generally successfully assessed the students' knowledge level (the level which coincides with the teacher's assessment). Exceptions and border case issues are analysed in detail, and improvements to the algorithm are suggested. [ABSTRACT FROM AUTHOR]

In a typical elementary mathematics(math) class, Students with Writing Disabilities (SWD) operate at a disadvantage. Math lessons and techniques are geared towards students who are able to actively 'work out' math problems with pencil and paper. We conducted interviews with special educators in elementary schools to learn about the pros and cons of current writing assistive technologies that are used in classrooms for math. Informed by the interviews findings, we designed a prototype called SMPL that enables SWD to work out math problems digitally. We ran a user study with 8 SWD to obtain feedback on SMPL. We present the interviews and user study findings. We found that: 1) There is a lack of writing assistive technologies that are designed specifically for elementary math learning; 2) It is feasible to provide SWD with a math learning experience similar to their peers; and 3) The writing assistive technology should be adaptive to students' skills and backgrounds. [ABSTRACT FROM AUTHOR]

This article provides brief guidance for a successful graduate teaching assistantship at our school. Although the com-ponents mentioned in this article are primarily aimed at mathematics courses designated as the "Basic Science and Mathematics" (BSM) modules with multiple sections, the principle can also be applied and adapted to other courses and institutions as well. [ABSTRACT FROM AUTHOR]

Fractional calculus is not a new topic, in reality it has almost the same history as that of classical calculus. In this paper, new approaches are developed to solve a class of nonlinear fractional differential initial value problems with fractional derivative defined in Caputo sense. Two numerical methods have been presented, Fractional Adams-Bashforth-Moulton Method (FABMM) and Fractional Differential Transformation Method (FDTM) compared with Adomian Decomposition Method (ADM), used for very specific type of problems. The methods are used on two different nonlinear fractional differential equations of the form, Dα y(t) = f(y(t)), with and without exact solution for the same initial condition y (0) = 0. We present new results that deal with the Adomian Decomposition Method (ADM), suitable to handle fractional calculus applications. The results are obtained with comparisons made between FDTM, FABMM and the exact solutions at each integration point, given, both graphically and tabularly, for different fractional orders 0 <α ≤1, constant step-size h = 0.01 and small time interval t∈[0,0.5]. Our work, with using symbolic software packages as Wolfram Mathematica, can be considered as an alternative to existing techniques, and will have wide applications in science and engineering fields. [ABSTRACT FROM AUTHOR]

This paper presents a preliminary result of ongoing research on monitoring natural disasters induce structural infrastructures damages by using off-the-shelf digital camera. It's Orientation and calibration algorithm that steamed from a more general pinhole camera model can be varied into two distinct approaches: projective collineation and perspective collineation which widely embraced by computer vision community and photogrammetric community respectively. This research investigates reliabilities of those varying methods for computing orientation and calibration of the captured images of a bridge. Some photographs of the surveyed bridge were processed using two proprietary software which each employs different collineation algorithm. Some findings reveal that the projective collineation algorithm uses more robust matrix operation but requires more parameters and consequently need more correspondent points on each captured image. On the other hand, fewer parameters and common points are required for the more rigorous perspective model although it requires a nonlinear relationship of matrix operations. Results show that the projective collineation algorithm gives higher model stability but requires more stable camera and optics. Furthermore, figures and numbers are provided to support our findings that both algorithms produce approximately equal precision of the orientation and calibration parameters. [ABSTRACT FROM AUTHOR]

In this paper we computed and studied the types of the subgroups of the groups A5, C2 × A5, C3 × A5, C5 × A5andCp × A5 where p is an odd prime number. We also classification the subgroups of those groups into the abelian, non-abelian, solvable, and non-solvable groups. So, we computed the number of solvability degree parameters of some of those finite groups. Mathematics Subject Classification (2010): 20F12, 20F14, 20F18, 20D15. [ABSTRACT FROM AUTHOR]

The aim of this research is to experimentally prove that a set of forms and methods could provide self-efficacy of prospective EFL teachers. Bandura's theory of social learning demonstrates the central role of self-efficacy. The author opts for teaching through observation, underlining the role of social experience and mutual determinism in personality development. However, in the course of our research, there were not found enough scientific papers on the development of self-efficacy as a component of professional identity and as a factor of teachers' professional formation. The experiment was conducted with 80 final year students of KFU-prospective EFL teachers. The ascertaining stage of the experiment was to determine the initial values of self-efficacy: the level of formation of selfefficacy in learning; professional self-efficacy, communication self-efficacy. For this purpose, we employed 'Questionnaire about teaching experiences during the final school teaching practice' by Kaldi and 'Self-efficacy Scale' by Sherer et al. Statistical analysis of empirical research was done by means of standardized testing assessment in mathematical statistics (Wilcoxon T test). The results obtained at the ascertaining stage allowed to design a program for developing self-efficacy of prospective EFL teachers. Kaldi's questionnaire enabled to determine that majority of participants were certain to possess the qualities and skills necessary for pedagogical activity. This means that future EFL teachers adequately assessed their skills and knowledge and were convinced that the school teaching practices, and the final one specifically, would equip them with a wealth of experience and would permit to perform in the profession properly. Self-efficacy Scale revealed that 80 % of the participants in both the experimental and control groups had an average level of professional self-efficacy. This indicates future EFL teachers believe in possessing the qualities, skills and capabilities they have acquired from previous practices and in employing them successfully in their future professional activity. However, the experimental group showed low level of communication self-efficacy. These results indicate an unsuccessful past experience that has affected the self-efficacy of some students. This led to a lack of confidence and belief in solving communicative problems and realizing successful communication by future EFL teachers. A high level of communication self-efficacy, on the contrary, means that future EFL teachers are assured to communicate successfully, establish rapport with schoolchildren and eliminate communication problems. Based on the analysis of psychological and pedagogical papers, we considered training to be the most effective means of developing self-efficacy of future EFL teachers. A number of training theories and our personal experience served the basis to design a program for developing self-efficacy of prospective EFL teachers. The formative stage of the experiment resulted in noticeable improvement of self-efficacy level in the experimental group. [ABSTRACT FROM AUTHOR]

Today, worldwide, employers in the industry are often dissatisfied with modern engineering education, which is not adapted to the needs of business. Governments in all European countries face the problem of low student motivation to study science, technology, engineering and mathematics (STEM). Students are dissatisfied with university education, describing it as "outdated, impractical and uninteresting". University professors are dissatisfied with the declining competencies in STEM and motivation to learn of young people. A huge challenge for all university professors is to find teaching methods that increase the motivation of the new generation of students, "students of the digital era, students of the seven screens", especially when studying subjects related to mathematics, which are extremely difficult and repulsive according to the students in recent years. In the conditions of the pandemic of COVID 19, when it was necessary to immediately switch to online learning, in the last academic year (2019-2020), the teaching staff was faced with the need to generate many similar assignments for students to avoid the possibility of deception ("copy and paste") of the students during the tests, as well as by "filling in the time" in order not to allow one student to solve the assignment of another student for the duration of the test. All this necessitated the creation of the application in MS Excel, described in the paper, which would solve the task assigned to the students. The paper briefly presents the methods applied during the last academic year in the study of a STEM-based course, and in particular one of the sections studied in the course, which requires a fairly good mathematical background of students -- operating with fractions, solving systems of equations, matrix calculation, etc. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present the role of education in the professionalization of public administration, based on which the hypothesis was set that ethics education increases the professionalization of public administration. The methodology used in the paper to verify the hypothesis includes scientific methods of deduction and induction, methods of analysis and synthesis, and mathematical-statistical methods in the processing and presentation of the research results. Special emphasis is placed on the case study method based on the example of the Tax Administration of the Republic of Croatia regarding education carried out in the field of ethics and fight against corruption as part of the Anti-Corruption Strategy. The education was carried out live during 2018 and 2019 for 413 Tax Administration employees, while for all other employees it was organized in the form of E-learning seminars. Education participants' questionnaires were used in this paper as well as data of the Ministry of Justice and Administration on complaints filed about unethical behavior of civil servants, data of ethical commissioners of the Tax Administration and the Ministry of the Interior, and Tax Administration data. The statistical data analysis shows the trend of complaints filed about unethical behavior of Tax Administration employees after the education and it was compared with the Ministry of the Interior, in which there no education was carried out. Data on the identification of conflicts of interest as a potential form of corruption were also analyzed by comparing them before and after the education. The research results confirm the basic hypothesis that ethics education increases the professionalization of public administration. This research is also an important basis for future research that should find an appropriate hybrid model of live learning and online learning, especially in the pandemic conditions caused by the COVID-19 virus that has accelerated the existing processes and forced the implementation of new forms of learning and business. [ABSTRACT FROM AUTHOR]