Mathematics Subject Research Articles

Q-Deformed and delta-parametrized A-generalized logistic function induced Banach space valued multivariate multi layer neural network approximations

Abstract. Here we research the multivariate quantitative approximation of Banach space valued continuous multivariate functions on a box or RN, N ∈ N, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We investigate also the case of approximation by iterated multilayer neural network operators of the last four types. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its partial derivatives. Our multivariate operators are defined by using a multidimensional density function induced by a q-deformed and λ-parametrized A-generalized logistic function, which is a sigmoid function. The approximations are pointwise and uniform. The related feed-forward neural network are with one or multi hidden layers. Mathematics Subject Classification (2010): 41A17, 41A25, 41A30, 41A36. Keywords: Multi-layer approximation, q-deformed and λ-parametrized A- generalized logistic function, multivariate neural network approximation, quasi-interpolation operator, Kantorovich type operator, quadrature type operator, multivariate modulus of continuity, iterated approximation.

Hankel and symmetric Toeplitz determinants for Sakaguchi starlike functions

Abstract. In this paper, we consider the class of starlike functions with respect to symmetric points which are also known as Sakaguchi starlike functions. We de- termine best possible bounds on Zalcman conjecture |a_n^2 – a_(2n-1) | and generalized Zalcman conjecture |aman − am+n−1| for n = 2 and n = 4, m = 2, respectively for such functions. Further, we compute estimate on third order and fourth order Hankel determinants. As well, we also obtain estimates on third and fourth symmetric Toeplitz determinants. Mathematics Subject Classification (2010): 30C45, 30C80. Keywords: Starlike function, Sakaguchi starlike functions, Zalcman conjecture, third and forth order Hankel determinants, second, third and fourth order symmetric Toeplitz determinants.

New results on asymptotic stability of time-varying nonlinear systems with applications

Abstract. In this paper, we present a converse Lyapunov theorem for the new notion of global generalized practical uniform h-stability of nonlinear systems of differential equations. We derive some sufficient conditions which guarantee the global generalized practical uniform h-stability of time-varying perturbed systems. In addition, these results are used to study the practical h-stability of models of infectious diseases and vaccination. Mathematics Subject Classification (2010): 35B40, 37B55, 34D20, 93D15, 92D30. Keywords: Epidemic models, generalized practical uniform h-stability, Gronwall’s inequalities, Lyapunov functions.

Fostering students' inquiry aptitudes and collaborative reasoning in higher education science courses with social annotation tools and collaborative platforms

AbstractInteractive digital technologies are playing an increasingly important part in education for enhancing collaborative learning processes and improving engagement. Social annotation (SA) tools and collaborative platforms are an innovative way to involve students to give and take feedback, annotate, and brainstorm on complex topics in science, technology, engineering, and mathematics (STEM). This article focuses on innovative practices that integrate inquiry‐based discussions using SA tools and collaborative platforms to promote undergraduate students' interest and curiosity about sciences. In this article, lectures were combined with inquiry‐based discussions using an open education SA tool and an open‐access collaborative platform to engage students in a meaningful dialog with peers on scientific topics. Students debated with peers on scientific content in an online environment. Findings show that the integration of inquiry‐based discussions using SA tools and collaborative platforms provides a practical way to effectively improve students interest in science. The information reported in this article can support STEM instructors in designing collaborative learning activities in online and hybrid settings that spark students' curiosity and inquiry attitude about natural sciences.

Impacting elementary STEM teacher leadership identities

AbstractLearning science, technology, engineering, and mathematics (STEM) subjects starting at a young age helps prepare students for a variety of careers both inside and outside of the sciences. Yet, addressing integrated STEM in an elementary school setting can be challenging. Teacher leadership is one way to address this challenge. The purpose of this qualitative, descriptive case study is to understand how participation in the NebraskaSTEM Noyce Master Teaching Fellowship project impacted elementary STEM teacher leadership identities. Our findings suggest participation in the project contributed to different layers of teacher leadership identity (as a STEM learner, as a STEM teacher, and as a STEM teacher leader). These findings suggest professional development should be tailored to address empowering specific layers of STEM teacher leaders' professional identity. Other teacher leadership development projects may want to consider how to structure their projects to empower teachers based on the identities and experiences of those teachers.

Exploring the Impact of TikTok Blended Learning on Mathematics Performance: A Hypothesis Approach

Studying engineering at the university level necessitates a strong foundation in mathematics. However, the diverse mathematical backgrounds of enrolled students pose challenges to educators in higher education. To address this issue, utilizing technology and visual representations alongside various examples can enhance understanding for students with different learning preferences. Therefore, this study aimed to examine the difference in mathematics final examination scores between students engaged in TikTok blended learning and those in traditional non-blended learning environments. Hypothesis testing and z-test were employed to analyze the mathematics performance. The R software code was included to prove the hypothesis testing. The result showed that students who practised TikTok blended learning performed better than students who were in the non-blended learning environments in mathematics subject of engineering technology in final examinations.

EFEKTIFITAS PENGGUNAAN APLIKASI QUIZIZZ TERHADAP MINAT DAN HASIL BELAJAR MATEMATIKA SISWA

This research aims to determine the effectiveness of using the Quizizz application on students' interest and learning outcomes in mathematics on exponents and root forms at Muhammadiyah 48 Medan Private Middle School. The background to this research focuses on the low interest and learning outcomes of students in mathematics subjects, which are often considered difficult and boring by many students. The method used is quantitative with a pre-experimental research design, namely one group pretest posttest design where the sample consists of 50 students selected using total sampling techniques. The results of the research show that there is a significant increase in student interest and learning outcomes after using the Quizizz application, namely scores The average interest in learning mathematics after using the Quizizz application is 76.54 with a gain value in the medium category of 0.448 and the average score for learning mathematics after using the Quizzizz application is 78.60 with a gain value in the medium category 0.478. The paired sample t-test produced a significance value of less than 0.05, namely 0.001, indicating that the use of the Quizizz application was effective in increasing students' interest and learning outcomes in mathematics. So it can be concluded that the integration of technology in learning, especially through the Quizizz application, has been proven to be able to make mathematics learning more interesting, fun and interactive, thereby increasing students' interest and learning outcomes in mathematics.

Analysis of Mathematical Connection Ability and Self-Confidence on Junior High School Students

This research is motivated by the importance of students’ mathematical connection abilities and self-confidence in learning mathematics. Mathematical connection ability is an important factor in understanding mathematical concepts. The aim of this research is to analyze the level of students’ mathematical connection abilities and junior high school students’ self-confidence. The method used in this research is a descriptive-qualitative method. The research subjects were 37 students in class VIII-C of SMPN 3 Margahayu. The instruments used were four items of mathematical connection test material on the System of Two-Variable Linear Equations and non-tests of students’ confidence in learning mathematics. The results of the analysis show that the average score of all mathematical connection ability test questions in indicator 1 using relationships between mathematical topics is 5%, indicator 2 is understanding equivalent representations of the same concept (36%), indicator 3 uses mathematics in everyday life (52%), and indicator 4 uses mathematics in other subjects (27%). So the average is 30%. So the students’ mathematical connection ability is included in the low category. Most students are unable to solve problems with indicators using relationships between mathematical topics. This is shown by the results of the mathematical connection ability test; students did not connect optimally. But in learning mathematics, students already have good self-confidence.

PENGARUH MEDIA KARTU DOMINO TERHADAP KEMAMPUAN HOTS PADA MATA PELAJARAN MATEMATIKA KELAS IV SEKOLAH DASAR

This study seeks to prove whether or not there is an influence of domino card media on higher order thinking abilities (HOTS) in Mathematics subjects in class IV elementary school. A quasi-experimental design employing a quantitative method was utilized. A posttest-only non-equivalent control group design was the research design applied. Class IV students, totaling 64, were the sample used in this research, divided into two classes: the experimental class and the control class. The method of data collecting uses saturated sampling. Data collection is carried out through test instruments that include HOTS indicators. Testing shows that there is an influence on students' higher order thinking skills (HOTS) between the control class and the experimental class. According to data analysis, it is proven that there is an influence of the implementation of domino cards on HOTS abilities in fourth grade elementary school mathematics lessons.

High school graduates’ perceptions of space studies in formal education

Science, technology, engineering, and mathematics (STEM) subjects are a significant concern in educational systems worldwide. Students who learn these subjects acquire skills and knowledge that enable countries to develop advanced technological infrastructures in industry and academia, ultimately driving local and global economies toward a more advanced future. However, many countries have reported reduced student interest in STEM studies. While students become interested in STEM subjects after joining space education projects, these are often informal activities that occur outside schools. Space education allows students to explore several subjects simultaneously through a multidisciplinary approach and facilitates the development of important skills required in the knowledge-intensive industry and academia. Hence, this research aimed to analyze the perceptions and attitudes of high school graduates exposed to school-based space studies within the formal educational framework in relation to their motivation to undergo STEM studies and other pedagogical issues. The results reveal students’ high degree of motivation to undergo STEM studies through space education, which is an expected but not obvious finding. As for the pedagogical aspect, the issues highlighted by space education include learning activities outside the classroom, the acquisition of skills, and the use of the project-based learning (PBL) approach.

Peningkatan Hasil Belajar pada Materi Volume Kubus dan Balok dengan Menggunakan Pendekatan TARL

This research aims to describe the improvement in learning outcomes in spatial volume material using the TARL approach for class IV students at SDN 01 Kanigoro. This research was carried out using a type of Classroom Action Research (PTK) which was carried out in 2 cycles which aimed to determine the increase in the completeness of student learning outcomes through the TARL learning approach. The research subjects were 12 class IV students at SDN 01 Kanigoro. The research results show an increase in student learning outcomes in mathematics subjects using the TARL approach at SDN 01 Kanigoro. Based on the results of pre-cycle action activities, there were 3 students who completed and 9 students who did not complete. In the first cycle, there were 7 students who completed and 5 students who did not complete. while in the second cycle there were 11 students who completed it and 1 student who did not complete it. In conclusion, by using the TARL approach, student learning outcomes in class can improve.

The Role of Teachers in Developing Students’ Reading Comprehension Through the Implementation of Webtoon Application

This research aims to describe the improvement in learning outcomes in spatial volume material using the TARL approach for class IV students at SDN 01 Kanigoro. This research was carried out using a type of Classroom Action Research (PTK) which was carried out in 2 cycles which aimed to determine the increase in the completeness of student learning outcomes through the TARL learning approach. The research subjects were 12 class IV students at SDN 01 Kanigoro. The research results show an increase in student learning outcomes in mathematics subjects using the TARL approach at SDN 01 Kanigoro. Based on the results of pre-cycle action activities, there were 3 students who completed and 9 students who did not complete. In the first cycle, there were 7 students who completed and 5 students who did not complete. while in the second cycle there were 11 students who completed it and 1 student who did not complete it. In conclusion, by using the TARL approach, student learning outcomes in class can improve.

The Application of Audiovisual-Based Learning Media to Increase Students' Learning Interest in The Material of Ratios and Diagrams in Grade 5 SD Negeri 101943 Bengkel

There is a gap in interest with one of the subjects that students do not like. The aim of this research is to grow and increase students' interest in learning, especially in learning mathematics using audio-visual media on student learning outcomes in ratio and diagram material. The subjects of this research were the VB SD class with a total of 19 students. The time for carrying out the PTK research in the form of applying audiovisual media to mathematics subjects regarding ratios was carried out from May 2024 to June 2024. The research instruments used in this PTK were question sheets, observation sheets and documentation. Meanwhile, data collection techniques include observation and documentation. Based on student learning outcomes, it was obtained at 42.1% and for student interest in learning, it was obtained at 26.31% in the pre-cycle carried out. The results obtained from cycle 1 were that student learning outcomes were 57.89% and student interest in learning was 47.36%. Based on the results obtained from cycle 2 activities, namely student learning outcomes and student interest in learning were at 73.68%, this shows that the media is proven and successful in increasing students' learning interest in ratio and diagram material.

Predictive models, as an idea, to advance the secondary to tertiary transition in science courses

Investigating the transition between the secondary and the tertiary levels is a main theme in mathematics and science education. More so, this paper considers the transition that intersects with the after-effects of COVID-19, or the transition together with an educational context dominated by sociocultural differences and educational disadvantages. With this knowledge in mind, we investigated the effects of predictive mathematical models (multiple regression, logistic regression, and decision trees) to predict <i>at-risk</i> students at three time intervals (weeks one, three, and seven) in the semester. The idea was implemented with a first-year life science class of 130 students. Variables from an academic readiness questionnaire along with early assessment grades were used to build these models. Through a Monte Carlo cross validation method, the performance of the executed predictive models was assessed, and limitations were reported. We argue that the results obtained from predictive models can support both lecturers and students in the transition phase. The idea can be expanded to other courses in STEM fields and other educational contexts.

Modelo didáctico basado en el Aprendizaje significativo para mejorar la competencia resolución de problemas en estudiantes de Ingeniería

The purpose of this research was to propose a didactic model to improve problem-solving competence in students of Materials Engineering, Mathematical Analysis subject. The qualitative approach was used, the research was applied, propositional modality. The investigation was carried out in two moments. A sample of 30 second cycle students was used in the diagnosis. The sampling was non-probabilistic. The data were collected from the auxiliary registry. In the model proposal, the foundations, characteristics, design and description of the model were raised. The results of the diagnosis show that the level of achievement of the problem-solving competence is good. The use of the didactic model allowed students to develop problem-solving skills in mathematics. Likewise, the didactic model allowed students to manage a systemic vision that allowed them to direct their learning, evidencing improvements in the planning, organization, execution and evaluation of their problem-solving processes. In conclusion, the strategy based on meaningful learning allowed students of materials engineering students to develop competence in solving mathematical problems through meaningful learning activities in solving problems consistent with the subject.

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

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

Enhancing Measurement and Calculation Education in High School through 3D Printing Technology

Mathematics education often grapples with the challenge of teaching abstract mathematical concepts, particularly those existing in 3D space. Visualizing, manipulating, and comprehending these abstract objects can be a formidable task for learners. While 3D printing technology has found applications in various fields, its utilization in mathematics education remains limited. This research explores the potential and effectiveness of 3D printing technology in enhancing the teaching of measurement and calculation topics in high school mathematics. We designed 3D printed models with a specific focus on shapes, polyhedra, pyramids, and cylinders. These models were created to facilitate hands-on learning experiences for students, enabling them to directly measure, calculate, and experiment with these tangible mathematical objects. The experimental results reveal that students not only learned how to employ measuring tools to gauge the dimensions of tangible mathematical objects but also conducted mathematical experiments related to the 3D printed models. This practical engagement allowed students to gain valuable experiences and foster a deeper understanding of abstract mathematical concepts.

Irrational Outputs from Rational Inputs in Theta-3 Functions Using Dirichlet’s Theorem

Theta Functions are not an easy subject of mathematics because new researches about this wide topic are still being published regularly. The findings about Theta Functions lead directly to many applications in different fields of applied mathematics and help also to develop old interesting mathematical topics such as Poisson summation and Riemann Zeta Function. This work proves by using a theorem of Dirichlet and a previously demonstrated useful approximation that the rational inputs of Theta-3 Functions give only irrationals as outputs of these functions. This paper applies only simple notions of sequences and represents an opportunity for the students of mathematics to easily understand the steps of the demonstrations.

Reduced basis method for non-symmetric eigenvalue problems: application to the multigroup neutron diffusion equations

In this article, we propose a reduced basis method for parametrized non-symmetric eigenvalue problems arising in the loading pattern optimization of a nuclear core in neutronics. To this end, we derive a posteriori error estimates for the smallest eigenvalue which is assumed to be simple and the associated left and right eigenvectors. The practical computation of these estimators requires the estimation of a constant called prefactor, which we can express as the spectral norm of some operator. We provide some elements of theoretical analysis which illustrate the link between the expression of the prefactor we obtain here and its well-known expression in the case of symmetric eigenvalue problems, either using the notion of numerical range of the operator, or via a perturbative analysis. Lastly, we propose a practical method in order to estimate this prefactor which yields interesting numerical results on actual test cases. We provide detailed numerical simulations on two-dimensional examples including a multigroup neutron diffusion equation.

Development of Game-Based Mathematics Learning Media to Improve Mathematical Understanding Abilities

This research aims to develop mathematics learning media in the form of games. Apart from that, this research aims to determine the feasibility and find out whether the learning media being developed is appropriate and can improve students' understanding abilities in mathematics subjects. This type of research is development research with the ADDIE model (Analysis, Design, Development, Implementation, and Evaluation). The research subjects were class VII students at YP Sunan Dalem Gumeno Middle School. The research instruments used in this research were (1) Interview Guide (2) Validation Sheet (3) Student Response Questionnaire (4) Mathematical Understanding Ability Test Questions. The mathematics learning media in the form of games developed is expected to improve students' mathematical understanding abilities. The validation results from media experts and material experts respectively obtained an average of 4.4 and 4.2 with valid criteria. The validation results of the mathematical understanding ability test obtained an average score of 4.2 with valid criteria. The results of the student response questionnaire obtained an average practicality of 4.2 with practical criteria. The results of the mathematical understanding ability test were carried out using a t-test using the SPSS program and the results showed that the significant value was 0.000 < 0.05, meaning that students' mathematical understanding ability after using game learning media was better before using the game learning media, so it can be concluded that the learning media Games can improve students' mathematical understanding abilities and can be said to be effective. The results of this research show that learning media is said to be valid, practical, and effective. In other words, game-based mathematics learning media can improve students' mathematical understanding abilities.