Mathematical Issues Research Articles

Geometry to Build Models, Models to Visualize Geometry

In the seventeenth century, Guarino Guarini, mathematician and architect, affirmed that architecture, a discipline that primarily deals with measures, relies on geometry: therefore, the architect needs to know at least its basic principles. On behalf of Guarini’s words, we designed a set of interdisciplinary teaching experiences, between mathematics (via a calculus course) and drawing (via our Architectural Drawing and Survey Laboratory courses) that we proposed to first-year under graduate students studying for an Architecture degree. The tasks concern mathematical and representational issues about vaulted roofing systems and are based on the use of physical models in conjunction with digital tools, in order to make the cognitive geometric process more effective, thus following a consolidated tradition of both disciplines.

Neutrosophic Soft Fixed Points

In a wide spectrum of mathematical issues, the presence of a fixed point (FP) is equal to the presence of a appropriate map solution. Thus in several fields of math and science, the presence of a fixed point is important. Furthermore, an interesting field of mathematics has been the study of the existence and uniqueness of common fixed point (CFP) and coincidence points of mappings fulfilling the contractive conditions. Therefore, the existence of a FP is of significant importance in several fields of mathematics and science. Results of the FP, coincidence point (CP) contribute conditions under which maps have solutions. The aim of this paper is to explore these conditions (mappings) used to obtain the FP, CP and CFP of a neutrosophic soft set. We study some of these mappings (conditions) such as contraction map, L-lipschitz map, non-expansive map, compatible map, commuting map, weakly commuting map, increasing map, dominating map, dominated map of a neutrosophic soft set. Moreover we introduce some new points like a coincidence point, common fixed point and periodic point of neutrosophic soft mapping. We establish some basic results, particular examples on these mappings and points. In these results we show the link between FP and CP. Moreover we show the importance of mappings for obtaining the FP, CP and CFP of neutrosophic soft mapping.

درجة ممارسة معلمات الریاضیات لتدریس مهارات حل المسائل الریاضیة اللفظیة بالمرحلة المتوسطة The Degree of the Practice of Mathematics Teachers to Teach the Skills of Solving Verbal Mathematical Issues in the Middle Stage

المستخلص: هدفت الدراسة إلى قياس درجة ممارسة معلمات الرياضيات لتدريس مهارات حل المسائل الرياضية اللفظية بالمرحلة المتوسطة، ولتحقيق هدف الدراسة اتبعت الباحثة المنهج الوصفي المسحي، کما أعدت بطاقة ملاحظة کأداة لقياس درجة الممارسة، وتکونت البطاقة من (25) مهارة موزعة على خطوات حل المسألة الرياضية: فهم وتحليل المسألة الرياضية، وضع خطة أو استراتيجية للحل، تنفيذ خطة الحل، التحقق من صحة الحل. وطبقت الأداة على عينة الدراسة، وهن (30) معلمة من معلمات الرياضيات بالمرحلة المتوسطة، وقد تم تطبيقها في (17) مدرسة من مدارس المدينة المنورة في الفصل الدراسي الثاني من العام الدراسي 1440ه، وقد أسفرت الدراسة عن النتائج التالية: أن درجة ممارسة معلمات الرياضيات لتدريس مهارات حل المسائل الرياضية اللفظية بالمرحلة المتوسطة بالمدينة المنورة جاءت بدرجة متوسطة، حيث بلغ المتوسط الحسابي لها (2.79). Abstract: The aim of the study was to measure the degree of mathematics teacher practice to teach the skills of solving verbal mathematical issues in the intermediate stage, to achieve this study, the researcher followed the descriptive Survey Methodology , and she prepared a note cart as a tool to measure the degree of practice, The card consists of 25 skills distributed on the steps to solve the mathematical issue: understanding and analysis of the mathematical issue, the development of a plan or strategy for the solution, implementation of the solution plan, validation of the solution. The tool was applied to the sample of the study, which are 30 teachers of mathematics in the intermediate stage, and it was applied in 17 schools of Madinah in the academic year 1440 AH. The study produced the degree of practicing mathematics teachers to teach the skills of solving verbal mathematical issues in the intermediate stage in Madinah came at a medium degree, with an arithmetic mean (2.79).

The Preface of the Second Ahmad Dahlan International Conference on Mathematics and Mathematics Education (ADINTERCOMME) 2019

Preface The Ahmad Dahlan International Conference on Mathematics and Mathematics Education, abbreviated as AD INTERCOMME, is a biennial international conference hosted in a cooperation by the Mathematics Department - Faculty of Science and Applied Technology - and the Mathematics Education Department - Faculty of Teacher Training and Education - of Universitas Ahmad Dahlan, Yogyakarta, Indonesia. It aims to provide a great forum for worldwide mathematicians, professors, teachers, and researchers to share their ideas about the trends and the emerging issues both in mathematics and mathematics education. In 2019, the AD INTERCOMME would be implemented for its second edition. We invite researchers and practitioners to come and to contribute in this conference. We would be very happy to welcome you in Yogyakarta.The keynote presentations are provided especially to show the contribution of Mathematician and Mathematics Educators in the world of mathematics and mathematics education towards research and knowledge sharing where our conference theme for this year is the contribution of Mathematics and Mathematics Education in Industrial Revolution Era 4.0. The main event is the talk of three keynote speakers. The first keynote speaker is Associate Professor Dr. Mazlini Adnan form Universiti Pendidikan Sultan Idris, Malaysia. The second keynote speaker is Associate Professor Martianus Frederick Ezerman, Ph.D from Nanyang Technological University, Singapore. The third keynote speaker is Associate Professor Dr. Sitti Maesuri Patahuddin from University of Canbera, Australia.We also have speakers in workshop session coming from Universitas Ahmad Dahlan, Dr. Rully Charitas Indra Prahmana, S.Si., M.Pd who deliver the talk on the Publishing Manuscripts in a Scopusindexed Journal and M. Rizky Alif Yuza who deliver the talk on the Workshop Big Data: “Sentiment Analysis Using Pyhton, Elastic Search and Kibana. ADINTERCOMME 2019 was an overwhelming success, attracting the delegates, speakers and sponsors from many countries and provided great intellectual and social interaction for the participants. Without their support, the conference would not have been successfully organized. We trust that all the participants found their involvement in the Conference both valuable and rewarding. Our wish is that all participants would enjoy this conference, contribute effectively toward it and take back with you knowledge, experiences, contacts and happy memories of this conference and especially with this beautiful kingdom of Yogyakarta.Dr. Puguh Wahyu Prasetyo, S.Si., M.ScEditor in Chief

Money Knowledge or Money Myths? Results of a population survey on money and the monetary order

AbstractPeople use money in everyday life in ubiquitous ways. In addition, they know that money has quite different and multiple meanings in different social contexts, depending on the situation in which it is used. That said, what do people actually know about money, money creation, money backing and the institutional foundations of the monetary order? While contributions in the rapidly extending field of financial literacy have empirically studied people’s knowledge about mathematical and financial issues, people’s knowledge about the functioning of the money system and monetary institutions remained mostly unexplored. To improve our understanding of people’s knowledge of the money system and the most important money institutions, we questioned 2,000 individuals in Austria using a standardized population survey. In this paper, after a short critical review of the sociology of money and the literature on financial literacy, we present and critically discuss the results of the survey. We found that, independently of age, gender, education and income, people know very little about the money system or money institutions and mostly believe in money myths, such as the notion that money is still backed by gold. Finally, we discuss our empirical findings against the backdrop of the state of research on the sociology of money1.

A Method to Balance Dynamic Current of Paralleled SiC MOSFETs With Kelvin Connection Based on Response Surface Model and Nonlinear Optimization

Multichip SiC power modules with Kelvin-source connection are popular in applications with large capacity and high switching frequency. However, dynamic current imbalance among paralleled dies due to asymmetric layout limits the available capacity. Thus, this article proposes a method to mitigate the mismatched dynamic current by adjusting the connection points of bonding wires and copper traces. The response surface models and nonlinear constrained optimization algorithms are introduced for the first time to help determine the optimized positions for the connection points. By this method, the dynamic current imbalance can be well suppressed under various working conditions. Besides, the method is cost-efficient and well compatible with the conventional manufacturing technologies because there need no additional efforts but some modifications on bonding wires. At first, the optimization guidelines are obtained after analyzing the mechanism of dynamic current imbalance among paralleled SiC MOSFETs with Kelvin-source connection. Based on the optimization guidelines and response surface models of parasitic inductance, the dynamic current sharing problem can be transformed into a nonlinear constrained optimization issue in mathematics. According to the solution of the mathematic problem, the optimized positions for connection points of bonding wires and copper traces can be determined. Finally, some simulations and experiments are conducted to verify the effectiveness of the proposed method.

Variable-order space-fractional diffusion equations and a variable-order modification of constant-order fractional problems

ABSTRACT Fractional diffusion equations (FDEs) were shown to provide very competitive descriptions of challenging phenomena of anomalously diffusive transport or long-range interactions. However, FDEs introduce mathematical issues that are not common in the context of integer-order diffusion equations. For instance, the homogeneous Dirichlet boundary-value problems of linear elliptic FDEs with smooth data in one space dimension may generate solutions with singularities that do not seem physically relevant, which are in sharp contrast to their integer-order analogues do. We prove the wellposedness of the Dirichlet boundary-value problem of one dimensional variable-order linear space-fractional diffusion equations (sFDEs). We further prove that their solutions have the similar regularities as their integer-order analogues if the order has an integer limit at the boundary or have the same singularity near the boundary as their constant-order sFDE analogues if the order has a non-integer limit at the boundary. In particular, we prove that constant-order sFDEs with a variable-order modification indeed generate solutions with significantly improved regularities.

Facilitating pedagogical content knowledge development through professional development intervention

Teacher has main responsibility to accommodate all students and their learning needs in dynamic classroom situations. This goal can be accomplished if teacher can organize high quality teaching practice to support student’s success. So that teachers must be equipped with wide range of knowledge about how particular mathematics topics, problems, or issues are organized, represented, and adapted to the diverse interests and abilities of learners. Such knowledge is known as Pedagogical Content Knowledge (PCK). Many studies have proven PCK as professional knowledge that should be acquired by teacher to make effective teaching. Considering its importance, there must be systematic effort to develop pedagogical content knowledge through professional development. Teacher professional development has been used as the most effective approach to promote teacher change. Accordingly, the purpose of this paper is to explore ways to develop PCK in professional development intervention. The method used in this study is literature review. The review revealed that professional development intervention with collaborative-reflective situation such as: lesson study, analysing student’s work, analysing video of classroom practices, or construction of Content of Representation (CoRe) and Pedagogical and Professional Experience Repertoires (PapeRs) – based program, has positive impact to develop teacher’s pedagogical content knowledge.

Hopf Bifurcation of a Generalized Delay-Induced Predator–Prey System with Habitat Complexity

A delay-induced nonautonomous predator–prey system with variable habitat complexity is proposed based on mathematical and ecological issues, and this system is more realistic than the published models. Firstly, the permanence of the nonautonomous predation system is studied and some sufficient conditions are obtained. Secondly, the dynamical behaviors of the corresponding autonomous predation system are investigated, including the positivity and boundedness, and local and global stabilities. Thirdly, the properties of Hopf bifurcation of the autonomous predation system without/with delay are investigated and the explicit formulas which determine the stability and the direction of periodic solutions are obtained. Finally, a numerical example is given to test our theoretical results.

Mathematics Teaching in Vietnam in the Context of Technological Advancement and the Need of Connecting to the Real World

In the context of fundamental and radical reform of education and training in Vietnam, the educational goals are changing towards students’ competencies instead of knowledge and skills for students as in the past. Vietnam’s mathematics curriculum is going to innovate after 2018. Mathematical education constructs the connection between mathematical ideas, between mathematics and other subjects, and between mathematics and real life. This article investigates two significant issues in mathematics teaching in Vietnam: the purpose of learning mathematics among Vietnamese pupils and mathematics teaching methods concerning reality. Based on the findings from these questions, the article proposes some recommendations for mathematics teaching regarding the methods and appropriate extent to which teachers should connect mathematics to the real world in the context of rapid science and technology development as well as the adjustments to the current mathematical content at schools. Also, this article presents some examples of exploring practical content problems and designing real-life contexts in mathematics teaching to develop students' competency in Vietnam. The researchers also suggest that Vietnam's national mathematics curriculum needs reforming to keep up with the pace of development in the field of information and communication in the country. https://doi.org/10.26803/ijlter.19.3.14

Lagrangian Description of Three-Dimensional Viscous Flows at Large Reynolds Numbers

Boundary layer theory is used to show that, at large Reynolds numbers, the three-dimensional Navier–Stokes equations can be rewritten in a form with diffusion velocity that was previously known for the cases of two-dimensional and axisymmetric flows. Relying on this hypothesis, a closed system of equations that is a development of a similar model for the indicated special cases is derived to describe fluid flows in the Lagrangian approach. Simultaneously, a number of mathematical issues are investigated. The existence of an integral representation for the velocity field with integrals with respect to Lagrangian coordinates is proved by analyzing the equations of motion of selected Lagrangian particles and applying the theory of ordinary differential equations with parameters. An equation describing the vorticity flux from the body surface is derived.

Hyperreal Numbers for Infinite Divergent Series

Treating divergent series properly has been an ongoing issue in mathematics. However, many of the problems in divergent series stem from the fact that divergent series were discovered prior to having a number system which could handle them. The infinities that resulted from divergent series led to contradictions within the real number system, but these contradictions are largely alleviated with the hyperreal number system. Hyperreal numbers provide a framework for dealing with divergent series in a more comprehensive and tractable way.

Asymptotic flocking in the Cucker-Smale model with reaction-type delays in the non-oscillatory regime

We study a variant of the Cucker-Smale system with reaction-type delay. Using novel backward-forward and stability estimates on appropriate quantities we derive sufficient conditions for asymptotic flocking of the solutions. These conditions, although not explicit, relate the velocity fluctuation of the initial datum and the length of the delay. If satisfied, they guarantee monotone decay (i.e., non-oscillatory regime) of the velocity fluctuations towards zero for large times. For the simplified setting with only two agents and constant communication rate the Cucker-Smale system reduces to the delay negative feedback equation. We demonstrate that in this case our method provides the sharp condition for the size of the delay such that the solution be non-oscillatory. Moreover, we comment on the mathematical issues appearing in the formal macroscopic description of the reaction-type delay system.

Mechanical challenges of electrical transmission lines inspection robot

In this article, the dynamics of electrical transmission lines inspection robot while moving on the line has been investigated and mathematical modeling issues of its movement along the conductors have been considered. In order to achieve dynamical stability during the movement of inspection robot on the electrical line variation methods for problems of stretched string has been considered and solved. However, line inspection robot operation might be subject to failures because of conductor vibration. In this article, the robot-inspector considered as moving load and pendulum. As a result of even steady motion of inspection robot on the line, saw-tooth oscillations have been observed in the vertical plane that causes parametric oscillations in the perpendicular plane. In order to avoid dangerous oscillation, dynamic vibration absorber has been designed. The behavior of electrical line inspection robot motion through transmission lines has been studied.

Should N95 Respirators be Recommended for the General Public

Public health advisories recommend against the use of the N95 respirator by the general public in the current COVID-19 pandemic. These advisories are primarily motivated by the collective goal of reducing the reproduction number to below one. However, cultural factors may dissuade the public from adopting recommendations from models optimized for the collective good. This article presents a discussion of mathematical issues that ought to guide an advisory from an individualistic perspective. In particular, we argue that the public health advisory does not appear justified if one considers non-linearity in the dose-response relationship and heterogeneity in infection load in the context of the COVID-19 pandemic. The N95 respirator promises far greater effectiveness than homemade or surgical masks. However, due to a considerable variation in masks' brands and efficiencies, the public should look into the specific details of each available mask option.

Opinion propagation on social networks: a mathematical standpoint

These lecture notes address mathematical issues related to the modeling of opinion propagation on networks of the social type. Starting from the behavior of the simplest discrete linear model, we develop various standpoints and describe some extensions: stochastic interpretation, monitoring of a network, time continuous evolution problem, charismatic networks, links with discretized Partial Differential Equations, nonlinear models, inertial version and stability issues. These developments rely on basic mathematical tools, which makes them accessible at an undergraduate level. In a last section, we propose a new model of opinion propagation, where the opinion of an agent is described by a Gaussian density, and the (discrete) evolution equation is based on barycenters with respect to the Fisher metric.

Learning to be an opportunistic word problem solver: going beyond informal solving strategies

Informal strategies reflecting the representation of a situation described in an arithmetic word problem mediate students’ solving processes. When the informal strategies are inefficient, teaching students to make way for more efficient ways to find the solution is an important educational issue in mathematics. The current paper presents a pedagogical design for arithmetic word problem solving, which is part of a first-grade arithmetic intervention (ACE). The curriculum was designed to promote adaptive expertise among students through semantic analysis and recoding, which would lead students to favor the more adequate solving strategy when several options are available. We describe the ways in which students were taught to engage in a semantic analysis of the problem, and the representational tools used to favor this conceptual change. Within the word problem solving curriculum, informal and formal solving strategies corresponding to the different formats of the same arithmetic operation, were comparatively studied. The performance and strategies used by students were assessed, revealing a greater use of formal arithmetic strategies among ACE classes. Our findings illustrate a promising path for going past informal strategies on arithmetic word problem solving.

Characteristics of teacher knowledge produced by pre-service mathematics teachers: the case of open-ended problem-based learning

One major issue in mathematics teacher education regards the role of university-level mathematics in teacher knowledge. In the context of a design-based research project, an advanced mathematics teacher education course aimed at strengthening the connections between university-level mathematics and school mathematics was developed. In this paper, I present a case study, conducted within the education course, in which I analyse the characteristics of teacher knowledge produced by five small groups of pre-service teachers in an open-ended problem-based learning task. The results indicate the problem-based learning approach has the potential for enhancing specialised content knowledge such as knowledge of different representations of and applications of mathematical concepts. The results also highlight the challenges in using this approach for enhancing horizon content knowledge such as knowledge about the relationships between mathematical concepts. The findings in this case study suggest that problem-based learning can be used to develop mathematics teacher education, although further research is needed to design instructional practices that enhance pre-service teachers’ horizon content knowledge.

Combined Intervention of Working Memory and Arithmetic Reasoning in Students with ADHD

ABSTRACT This study compared the effects of a combined intervention of working memory (WM) and arithmetic reasoning (AR) vs WM intervention alone on the arithmetic reasoning performance of students with ADHD. Third- and fourth-grade elementary school students (n = 46) completed measures for AR, mathematical calculations, and WM. Participants were randomised using a minimisation approach taking age and IQ as variables of interest and assigned to one of the two groups: Combined Intervention (CI, n = 24) and Working Memory Intervention (WMI, n = 22). The results using GEE analysis indicated a significant group × time interaction (Waldχ2 = 6.414; gl = 2; p = 0.04) in AR performance in the immediate post-test. CI students showed significantly better performance on AR than WMI students immediately after intervention (pB = 0.042). There was an effect of time on mathematical calculations in the post-test (Waldχ2 = 48.305; gl = 2; p < 0.001). Despite the fact that the results for AR were not maintained in the deferred post-test, a combined intervention of WM and AR seems to be more efficient in improving arithmetic reasoning in ADHD students than a WM intervention alone. Nevertheless, this is not the case with other mathematical issues, such as calculation, where there was no significant difference between groups, but the effects had been maintained in the deferred post-test for both.

A abordagem CTS e a educação matemática crítica como estratégia de ensino-aprendizagem na formação de professores de matemática

Este artigo está embasado em uma pesquisa de mestrado e tem como objetivo discutir aspectos relevantes de um curso de formação continuada, para professores que ensinam Matemática, com base nas abordagens CTS (Ciência, Tecnologia e Sociedade) e EMC (Educação Matemática Crítica). A pesquisa, de natureza qualitativa, ocorreu em dois momentos. Primeiramente, realizamos uma análise das questões de Matemática contidas no ENEM (Exame Nacional de Ensino Médio) (2012-2016), para investigar se tais questões possuíam em seu contexto, questionamentos relacionados à abordagem CTS. Em um segundo momento, considerando o tripé: Ensino, Pesquisa e Extensão, desenvolvemos um curso de extensão, com base nas abordagens CTS e EMC, com o objetivo de identificar como os professores compreendem as abordagens CTS e EMC e de que maneira eles incorporam a temática em sua prática, além de construir com os professores, estratégias contextualizadas para o ensino da Matemática. As questões analisadas foram utilizadas como instrumento de ensino-aprendizagem para discutir possibilidades de incluir as abordagens CTS e EMC no ensino de Matemática. Observamos que os professores não conheciam as abordagens CTS e EMC, tampouco contemplavam a temática em sua prática. Desta forma, ressaltamos a importância dos cursos de formação continuada, pois apresenta ao professor novas estratégias didático-pedagógicas, bem como, possibilita discussões importantes sobre a sua prática.