World Of Mathematics Research Articles

MATEMÁTICA: CONTRIBUIÇÕES E REFLEXÕES HISTÓRICAS

This article addresses a journey of historical discovery in the world of mathematics, where a chronology of science is presented, from its beginnings to the present. The research portrays important points referring to ancient mathematicians who contributed significantly to the progress of numbers, drawing a parallel between times. The methodology adopted was the bibliographic research, obtained through the analysis of previously published materials (articles, books, etc), where it was possible to conclude that the past study of science is of fundamental importance, so that students and researchers have a broader notion about the mathematical historical course.

Milieu, spirit, flesh and fusion in Le Corbusier’s life and work

How can a study of Le Corbusier’s post-war work – the Poème de l’angle droit and Modulor 1 and 2 – throw light on his earlier preoccupations. These works are retrospective and confessional. They are obsessed with the question ‘By what right may I create?’ The former work looks for answers in experience and the latter in the ‘divine’ world of mathematics. From at least 1906, when he bought and devoured Edouard Schoré’s Les grands initiés, Le Corbusier had a strong sense of predestination and a conviction that suffering was a necessary part of the voyage to enlightenment. His dualism, the belief in the separation of the spiritual and material worlds, encouraged him to view mathematics as part of the ‘hidden world’ of the spirit. His problem, in the research leading up to Modulor 1, was how to reconcile divine proportion and human experience. He invariably described the passage from the material to the spiritual worlds in terms of physical processes – smoking, simmering, brewing, giving birth. This idea, clearly described in one of his lectures in 1929, and his frequent discussion of ‘cosmic’ forces and symbolism during the 1930s, indicates that these ideas were well entrenched before the war.

Glimpses of contributions of some top Indian mathematicians: A review article

Indian mathematics has its deep roots in the Vedas, different from what is known as Vedic Mathematics. Vedic age gave rise to a new era of progress in the field of Science, Technology and Development. The Hindu Scripture Vedas is synonymous with all kinds of original source of knowledge and intellectual wisdom in the universe leading to modern knowlege in modern mathematics. Indian mathematicians made tremendous contributions to the entire world of Mathematics and Science. Decimal number system as well as the invention of zero (0) are among the greatest contributions of Indian mathematicians. The theory of trigonometry, Mathematical Modelling, Algebra, algorithm, modern arithmetic, sine and cosine functions leading to modern trigonometry, Diophantine equation, square root, cube root, negative numbers are also developed by Indian mathematicians. In this review article, the work of some of the renowned Indian mathematicians from Indus Valley civilization and the Vedas to modern times are covered in short with the hope that it may reveal hidden fundamental mathematical ideas as basic ideal tools which may usefully motivate for further research work in every domain of mathematical sciences, natural and applied sciences, engineering and social sciences. Moreover, there are many more remarkable Indian mathematicians who contributed to the origin of mathematical sciences. They have made several general contributions to mathematics that have significantly influenced scientists and mathematicians in the modern times.

Penerapan pembelajaran Team-Assisted Individualization (TAI) berbasis tahapan Newman untuk meningkatkan kemampuan siswa kelas VII SMP Brawijaya Smart School dalam menyelesaikan soal cerita matematika

the aim this research is to know applying Team-Assisted Individualization (TAI) based Newman Stages can increase ability of students to solving mathematics world problems. Data collected with document analysis and observation with descriptive qualitative approach. The result shows that the number of students in high-ability increase 42,43 percent and the number of students in low-ability decrease 33%, group distribution based on prior-ability and characteristic of students, the teacher assist student getting into difficulty, groups of learning to fare well, reflection of learning can unbend misconseption of students, and the appreciation be a motivation of students in learning

Matematik Öğretmeni Adaylarının Matematiksel Modelleme Döngüsü Üzerindeki Davranışlarının İncelenmesi

The aim of the study is to determine the behavior on individual modeling cycle of pre-service teachers who participate in mathematical modeling learning environment and who do not. An action research method was employed in the study. The research participants consisted of 32 pre-service mathematics teachers, 17 of whom attended the learning environment while the rest did not. Two mathematical modeling tasks were used in the pre and post interview. In pre interviews, pre-service teachers were interviewed individually, and the modelling routes of the pre-service teachers were closely monitored. At the end of the 11-week action plan, the post interview was made individually with the pre-service teachers. The recorded dialogues were analyzed during modeling cycles. It was determined that all pre-service teachers had a nonlinear cycle in the pre and post interviews. Pre-service teachers experienced in modeling repeated many steps back and forth. It was determined that they tried to revise the model when they reached a conclusion, so they had more complex modeling cycles. In addition, they mostly act in the world of mathematics. Pre-service teachers who are not experienced in modeling made a direct transition to real results without creating a mathematical model. It has been found that their areas of action are generally in the real world and they move less in the modeling cycle.

Design Mathematical Activity in Mathematics Classroom: Decimal Number

The research was aimed to investigate six-lesson study team members in designing mathematical activities to develop students’ mathematization using Open Approach in the second step of the Lesson Study process in teaching decimal numbers. A total of 16 Grade 4 students participated as the target group. Three instruments were used namely lesson plans, student worksheets, and observation field notes. Researchers employed ethnographic research design to study how the mathematical activities could assist students to develop their mathematical ideas from the real world to the mathematical world through a flow of lessons over the four stages of the Open Approach along with the Lesson Study process. The research results revealed that a series of five research lesson plans encompassing various mathematical activities were successfully encouraging students to elaborate their ideas and transmitting their ideas from the real-world to the mathematical world using semi-concrete aids. Moreover, the results of using the Open Approach have been proved to be relevant as students demonstrated their mathematization in fostering their mathematical thinking to transform their ideas smoothly. Therefore, designing mathematical activities is important to cultivate students’ mathematical thinking in problem-solving instantaneously. A limitation of the research was identified when the Lesson Study team members were reflecting on the teaching practice. This is because they found that the unclear illustration in the student worksheets has raised confusion. In conclusion, the overall results of this research have contributed significantly to our recognition of the practicality of Open Approach treatment in the Lesson Study process in developing students’ mathematization through their participation in mathematical activities.

The contribution of online mathematics games to algebra understanding in Grade 8

This study explores how online mathematics games contribute to Grade 8 learners’ understanding of basic principles and more sophisticated aspects of algebra. This project documents the trajectory of a purposive sample of 30 Grade 8 learners doing mathematics and one mathematics educator. The study is premised on the argument that learners with the guidance of the teacher can grasp algebraic concepts better and learn to manipulate these imaginatively and independently, by integrating new online mathematics games into standard classroom teaching of mathematics. The study was located within the interpretive qualitative research paradigm and used a case study approach. Data were collected by means of (1) lesson observations, (2) questionnaires and (3) semi-structured interviews. The data collected were analysed through the lens of the sociocultural theory, social constructivism and the activity theory. This study supports the view, set out in the literature reviewed, that the way in which resources are utilised can substantially improve the teaching and learning of algebraic concepts. Teachers should encourage learners to venture into the world of online mathematics games to learn algebra because they help learners to be creative, look for patterns, make conjectures, collect data, express their own thoughts, accept the ideas of others and establish structured forms of cooperation. The teacher’s role is to show and guide the learners how to use online mathematics games to solve mathematics problems. This study’s main recommendation, among others, is a revision of the curriculum to integrate online mathematics games into all subjects in classrooms at all levels.

DIGITAL LITERACY IN USING GEOGEBRA LEARNING MEDIA IN TERMS OF SELF-DIRECTED LEARNING

Digital literacy is important to improve the quality of education, especially in mathematics learning which can develop and engage students in exploring the efficient digital world for learning mathematics. The purpose of this study is to analyze the digital literacy of grade VIII students of SMP Negeri 1 Karangrejo in using GeoGebra learning media in terms of self-directed learning. This type of research is descriptive qualitative. The subjects of this study consisted of six students, and the instruments used were lesson plans, self-directed learning questionnaires, student response questionnaires, and interview guidelines. The result of this research shows that digital literacy with students who have high level for self-directed learning are able to fulfill all of indicators for digital literacy including being able to understand instructions for use and how to use the GeoGebra application, explain the information in the GeoGebra application, do the exercises correctly, participate in exchanging ideas with friends and develop their creativity into a new work in the GeoGebra application, students with moderate self-directed learning are only able to meet five digital literacy indicators including being able to understand instructions for use and explain the information in the GeoGebra application, do the exercises correctly, participate in brainstorming with friends and try to develop their creativity into a new work on the GeoGebra application, and students with low self-directed learning are only able to meet two digital literacy indicators including able to understand the instructions for use and be able to do practice questions correctly.

Application of genetic algorithm to industrial scheduling and problems of parameters evaluation

Genetic algorithms are widely used in various mathematical and real world problems. They are approximate metaheuristic algorithms, commonly used for solving NP-hard problems in combinatorial optimisation. Industrial scheduling is one of the classical NP-hard problems. We analyze three classical industrial scheduling problems: job-shop, flow-shop and open-shop. Canonical genetic algorithm is applied for those problems varying its parameters. We analyze some aspects of parameters such as selecting optimal parameters of algorithm, influence on algorithm performance. Finally, three strategies of algorithm – combination of parameters and new conceptualmodel of genetic algorithm are proposed.

Mathletics software and student attainment in grade 4- a cultural historical analysis

Mathletics is a networked mathematics software package that affords students the opportunity to solve problems. This software is extremely popular in the developed world (Day, 2013) and is gaining popularity in the developing world as a tool that can potentially impact students’ mathematics attainment. 25 years after democracy South Africa continues to lag behind the rest of the world in mathematics and science attainment (Isdale, Reddy, Juan & Arends, 2017). The use of computer-based software packages to meet the needs of developing students’ understanding of mathematics is, therefore, of interest in our context. However, research is clear that it is not technology itself that can lead to learning but rather, how this technology is used; that is, the pedagogical practices underpinning the use of technology serves to develop understanding. This study sought to investigate Mathletics ability to impact positively on student attainment as well as their understanding. Findings indicated that Mathletics software does not build mediation into its programme and, therefore, does not develop conceptual understanding. In relation to student’s attainment, findings indicated that children did not perform better after using Mathletics on a summative test of calculation problems, pointing to the importance of pedagogical underpinnings when using technology.

Postgraduate Mathematics Education Students' Perceptions of Technology-based Tools and Resources: Exploring the Influences of Connectivism and the Three Worlds of Mathematics

As we embrace the Fourth Industrial Revolution, transformations in education necessitate the use of technology-based pedagogy. This study explored postgraduate mathematics education students' perceptions of using technology-based tools and resources. This qualitative and interpretive study was conducted at a university in KwaZulu-Natal, South Africa. The study was framed utilizing the theory of connectivism and the three worlds of mathematics theory. Connectivism is a learning theory that is considered to be strengthened by existing technology-based tools and is founded on the notion that ubiquitous Information Communication Technology impacts teaching and learning. The three worlds of mathematics theory support the view that the development of mathematical thinking is founded on perception, operation and reasoning. Postgraduate mathematics education students engaged in interactive workshops using different online platforms. Subsequently, a sample of participants was interviewed using a semi-structured interview schedule. The interviews were conducted via various online platforms. Data that were generated were analyzed thematically. The results revealed two main themes. These themes focused on the strengths and challenges of using technology-based tools and resources to learn mathematics as perceived by the participants. The results of this study provide evidence that technology-based tools and resources may also be considered by lecturers when teaching mathematics topics that involve drawing complex mathematical diagrams and solving problems based on these complex mathematics diagrams. Also, the results support the view that to alleviate challenges associated with using technology-based tools and resources, lecturers need to ensure that the technology-based tools and resources being used are user-friendly, inexpensive, readily available and data-efficient. Moreover, this study support the view that lecturers need to consider attending professional development workshops and seminars that focus on integrating technology effectively in educational environments. This study has relevance globally and nationally when considering the implications of using technology-based tools and resources for learning mathematics.

Geometry and Division by Zero Calculus

We demonstrate several results in plane geometry derived from division by zero and division by zero calculus. The results show that the two new concepts open an entirely new world of mathematics.

Online mathematics programs and the figured world of primary school mathematics in the digital era

Internet access and the availability of digital devices in classrooms have been growing exponentially. This has led to the development of subscription-based online platforms for mathematics learning, available for purchase by schools and individuals. Currently, research in mathematics education tends to focus on the benefits to teaching and learning of digital technologies, while less attention is given to the use of commercial applications in mathematics, and to the rationale of schools in choosing these resources, or to consideration of how they might fundamentally change the shape of mathematics education in our schools. This paper reports on a survey sent to mathematics leaders of all schools in Aotearoa New Zealand, attaining a 24% response rate. Schools appeared to provide a great variety of learning experiences in mathematics, including the use of online programs. Many different online programs were utilised by schools, and the majority of these operate for business profit within state-funded school systems. The theoretical construct of ‘figured worlds’ was used to understand the school leaders’ rationales for using the programs. Leaders gave contrasting and conflicting reasons for their choices: discourses of neoliberalism, reform teaching, traditionalism and Ed-tech were all evident in their responses. The survey results suggest that in this era of market competition, schools face pressure to provide mathematics programmes that are simultaneously traditional, modern, high-tech and balanced.

A Note on Few Interesting Approaches of Solving Equations to Find the Number of Real Zeros

Be it in the world of mathematics or real life, it is often rewarding to think out-of-the box while solving a problem. Accordingly, in this paper, our aim is to explore the various alternative approaches for solving algebraic equations and finding the number of real zeros. We will further delve deeper into the conceptual part of mathematics and understand how implementation of simple ideas can lead to an acceptable solution, which otherwise would have been tedious by considering the conventional approaches. In the pursuit of achieving the objective of this paper, we will consider few examples with full solutions coupled with precise explanation. It is also intended to leave something meaningful for the readers to explore further on their own. The fundamental objective of this paper is to emphasize on the importance of application of basic mathematical logic, concept of inequality, concept of domain and range of functions, concept of calculus and last but not the least the graphical approach in solving mathematical equations. As a further clarification on the scope of this paper, it is highly pertinent to bring to the understanding of the readers two important aspects - firstly, we will only deal with equations involving real variables; and secondly, this paper does not include topics related to number theory.

Shifts in the Foundation: The Continual Modification and Generalization of Axioms and the Search for the Mathematical Principles that Underlie our Reality

The study shall seek to explore the deep, underlying correspondence between the mathematical world of pure numbers and our physical reality. The study begins by pointing out that while the familiar, one-dimensional real numbers quantify many aspects of our day-to-day reality, complex numbers provide the mathematical foundations of quantum mechanics and also describe the behavior of more complicated quantum networks and multi-party correlations, and quaternions underlie Einsteinian special theory of relativity, and then poses the question whether the octonions could play a similar role in constructing a grander theory of our universe. The study then points out that by increasing the level of abstraction and generalization of axiomatic assumptions, we could construct a more powerful number system based on octonions, the seditions, or even other hypercomplex numbers so that we may more accurately describe the universe in its totality.

Srinivas Ramanujan: An Indigenous Mathematician

The paper undertaken for the deliberation of International stature on December 22, 2020 rivets attention on the topic of THE CONTRIBUTION OF RAMANUJAN in the arena of MATHEMATICS. He is remembered for India’s greatest mathematical genii. He made significant contribution to the analytical theory of numbers elliptical functions, continued fractions and infinite series. Ramanujan left a slew of unpublished note books enfolding theorems that future generation of mathematical world have been exploring continuously. He is an icon of a self-studied, self learnt, self-taught mathematical genius who is a living legend and ennobling soul for the posterity. He is known as child prodigy. Owing to his ingenuous acumen and surprising accomplishments in the field of Mathematics, Indian govt. decided to celebrate his birthday 22nd December as National Mathematics Day.

Symbol sense characteristics for designing mathematics tasks

Symbol sense, an analogy of number sense in the symbolic world of mathematics, is an ability to give meaning to symbols, expressions, and formulas that involves many characteristics, including friendliness with symbols, an ability to examine symbol meanings, and skills to manipulate symbolic expressions. The characteristics of symbol sense are usually used, for instance, for designing symbolic algebra tasks, but are a bit rare for designing mathematics tasks in general. Therefore, this study aims to use symbol sense characteristics for designing mathematics tasks for secondary school students. To do this, using a design research method, we conducted a literature study to collect characteristics of symbol sense and to see possibilities of designing mathematics tasks in general. Next, we designed mathematics tasks according to the symbol sense characteristics. Finally, we provided possible responses of students for the designed tasks. The results of this study included six types of tasks according to the characteristics of symbol sense, including tasks on symbolic problems and word problems—which require translation into symbolic problems. In addition, we provided predicted responses to examples for each type of the tasks and suggestions for use in the learning and teaching process. For further investigation, we recommend to use the set of designed tasks for assessing student symbol sense ability.

From Boolean Valued Analysis to Quantum Set Theory: Mathematical Worldview of Gaisi Takeuti

Gaisi Takeuti introduced Boolean valued analysis around 1974 to provide systematic applications of the Boolean valued models of set theory to analysis. Later, his methods were further developed by his followers, leading to solving several open problems in analysis and algebra. Using the methods of Boolean valued analysis, he further stepped forward to construct set theory that is based on quantum logic, as the first step to construct "quantum mathematics", a mathematics based on quantum logic. While it is known that the distributive law does not apply to quantum logic, and the equality axiom turns out not to hold in quantum set theory, he showed that the real numbers in quantum set theory are in one-to-one correspondence with the self-adjoint operators on a Hilbert space, or equivalently the physical quantities of the corresponding quantum system. As quantum logic is intrinsic and empirical, the results of the quantum set theory can be experimentally verified by quantum mechanics. In this paper, we analyze Takeuti’s mathematical world view underlying his program from two perspectives: set theoretical foundations of modern mathematics and extending the notion of sets to multi-valued logic. We outlook the present status of his program, and envisage the further development of the program, by which we would be able to take a huge step forward toward unraveling the mysteries of quantum mechanics that have persisted for many years.

Новый подход к оценке площади поверхности хвои пихты сибирской

Новый подход к оценке площади поверхности хвои пихты сибирской

Linking Real-Life Situation with Content of School Mathematics at Secondary Level: Exploring Current Practice and Challenge in Bangladesh

Worldwide mathematics is considered as a subject in school curriculum which is intimately connected to students’ daily life. However, it is disheartening that there are some level of disconnection between students’ mathematics learning and the way it is applied to real-world. This study is conducted to explore the current practice and challenges in linking real-life situation with mathematical content at secondary level in Bangladesh, a country in transition from least-developed to developing status. Here multiple case study approach was followed under qualitative framework. Mathematics teachers of Grade 8 and their lessons were selected conveniently to explore how teachers were responding to the issues of practice and challenges in linking real-life situation and eventually promoted mathematical literacy in their lessons. Each teacher was considered as a case. Lesson observations, participant teachers’ interview, FGD with students and document analysis had been used as instruments in the study. Thematic analysis was followed as the data analysis technique. In this paper, we briefly summarized our work in exploring current practice and challenges in Bangladesh in connecting real-world with the world of mathematics. This study finds that teachers emphasize on explaining mathematical concept in ways that make sense to students but practice in specific cases. Occasionally, students struggle with mathematical terminologies while teachers are unaware of it. Moreover, teachers find difficulties to connect some mathematical content with real-life situations because of the nature of content and during the lessons they rely on “teaching textbooks” due to time constraint. Both teachers and students in this study point out that textbook examples and problems are not interesting. Finally, this study finds that Grade 8 mathematics textbook, in limited cases, deals with “real” problems: problems that are typically placed in a “situation”. The present study will thus provide insights to the teachers to improve their practice in order to make mathematics more significant and interesting to the students. This study will also notify the textbook writers to bridge between content and context to increase the effectiveness and quality of mathematics textbook by including more real-life oriented mathematical problems. Along with improved teachers’ practice and quality textbook, this study will eventually provide opportunities for students to be engaged with mathematics in a more meaningful way and to finally develop their mathematical literacy at an expected level. Keywords: Real-life situation, Mathematical literacy, Mathematisation DOI: 10.7176/JEP/12-3-19 Publication date: January 31 st 2021