Historical Development Of Mathematics Research Articles

On a conjectural series of Sun for the mathematical constant β(4)

Let β ( z ) be the Dirichlet beta function. Series for β ( 4 ) are very rare in the historical development of mathematics. With the help of the operator method and a transformation formula for hypergeometric series, we prove a surprising conjectural series of Z.-W Sun for the mathematical constant β ( 4 ) . Furthermore, we find five new series for the same constant in this paper.

Perkembangan Matematika dan Pendidikan Matematika Di Indonesia

This study aims to determine the development of mathematics education in Indonesia. The research method used is descriptive method, by presenting a description, clarification of a phenomenon and facts in mathematics. As well as library research (library research). By collecting several books, articles and opinions from experts regarding the development of mathematics and mathematics education which are then developed with various existing findings. The results showed that the development of mathematics was based on philosophy, because philosophy is the root of all human knowledge, both scientific knowledge and non-scientific knowledge. The historical development of mathematics, Babiliona mathematics refers to all mathematics developed by the Mesopotamians since the beginning of Hellenism. At that time the development of mathematics expanded to several countries such as Egypt, Greece, Arabia and India. The development of Mathematics Education in Indonesia is never separated from the history of the curriculum. The importance of mathematics in life is not surprising if mathematics learning has developed and adapted to the needs of the times. The development of mathematics learning in Indonesia is as traditional mathematics, modern mathematics, and modern mathematics.

History for the Teaching of Mathematics: Transformation and Mobilization of Mathematical Knowledge for School

This article aims to discuss processes of transformation and mobilization of knowledge related to the history of Mathematics as a teaching approach for mathematics at the Basic Education level. The core of the discussion is to highlight ways to explore this theme and point out guidelines to integrate information related the historical development of mathematics and its didactic uses in the classroom, associated with the rigor and naturalness appropriate to the treatment of the mathematical content stipulated in school curricula. In this sense, I highlight some possibilities of offering mathematics teachers in Basic Education and undergraduate courses didactic guidelines that contribute to their teaching practice. I also indicate central aspects to be focused on when inserting the historical dimension in mathematics classes as a thematic and material presentation, a conceptual development built from the exploration of primary or secondary sources in the form of didactic activities that can be used by the teacher to introduce, illustrate, or deepen a concept that is to be taught.

LAUTMAN ON PROBLEMS AS THE CONDITIONS OF EXISTENCE OF SOLUTIONS

Albert Lautman (1908–44) was a philosopher of mathematics whose views on mathematical reality and on the philosophy of mathematics parted with the dominant tendencies of mathematical epistemology of the time. Lautman considered the role of philosophy, and of the philosopher, in relation to mathematics to be quite specific. He writes that “in the development of mathematics, a reality is asserted that mathematical philosophy has as a function to recognize and describe” (Mathematics, Ideas and the Physical Real (London: Bloomsbury, 2011) 87). He goes on to characterise this reality as an “ideal reality” that “governs” the development of mathematics. The relation between mathematical problems as they arise in the historical development of mathematics and the solutions that are provided to these problems by mathematicians, in the form of new mathematical theories, definitions or axioms, are governed by what Lautman characterises as a dialectics of mathematics. The aim of this paper is to give an account of this Lautmanian dialectic and of how it can be understood to govern the development of solutions to mathematical problems.

Mathematics as a Science and Marine Activity Follow Each Other Throughout History

From the earliest beginnings to the present day, there has always been a strong link between mathematics and shipping. Both started developing at about the same time, fulfilling the basic human needs to act and to be creative. The shipping industry has developed throughout the history relatively in line with the development of science, but there have been periods of stagnation in times of great crises and wars. Mathematics, as one of the oldest sciences, is used for various calculations in shipping from shipbuilding to trade, transportation, and management. The safety of navigation, improvement of accuracy in navigation, optimization of costs, higher earnings and profits for ship owners and employees pose only a fraction of maritime affairs, hardly accessible without the knowledge and application of mathematics. Therefore, the aim of this paper is to examine closely the historical development of mathematics and maritime affairs, and to show how the knowledge of mathematics can become a powerful tool in the hands of a seafarer.

TEACHERS VIEWS RELATED TO TEACHING OF MATHEMATICS COURSE SUBJECTS WITH THEIR HISTORICAL DEVELOPMENTS

The mathematical history plays an important role in becoming interesting of mathematics courses, active participation of the students and the meaningful learning of the mathematical concepts together with the historical processes. For this reason, this study was conducted in order to take teachers’ views with respect to what kind of influences giving examples from the history of mathematics, referring to the historical developments of the subjects will leave on students and how they will affect teaching mathematics. The sample of the research is composed of 20 math teachers working in Konya province. The data were collected during the fall semester of the 2016-2017 academic year. Teachers’ views were taken by asking open-ended questions based on sub-problems involving exploiting the historical development of mathematics in teaching mathematics subjects. The analysis results were examined in detail by using descriptive statistics and content analysis in the findings part. As a result of the research, it is clearly seen that teaching mathematics subjects with their historical developments constitutes a more effective and lasting educational environment. It has been observed that a large majority of the participants support lecturing by using mathematics history but there are substantial deficiencies in practice due to the lack of material with regard to mathematics history, and paying no mind to usefulness of this. Article visualizations:

Deep thinking: what mathematics can teach us about the mind

There is more than one way to think. Most people are familiar with the systematic, rule-based thinking that one finds in a mathematical proof or a computer program. But such thinking does not produce breakthroughs in mathematics and science nor is it the kind of thinking that results in significant learning. Deep thinking is a different and more basic way of using the mind. It results in the discontinuous “aha!” experience, which is the essence of creativity. It is at the heart of every paradigm shift or reframing of a problematic situation.The identification of deep thinking as the default state of the mind has the potential to reframe our current approach to technological change, education, and the nature of mathematics and science. For example, there is an unbridgeable gap between deep thinking and computer simulations of thinking. Many people suspect that such a gap exists, but find it difficult to make this intuition precise. This book identifies the way in which the authentic intelligence of deep thinking differs from the artificial intelligence of “big data” and “analytics”.Deep thinking is the essential ingredient in every significant learning experience, which leads to a new way to think about education. It is also essential to the construction of conceptual systems that are at the heart of mathematics and science, and of the technologies that shape the modern world. Deep thinking can be found whenever one conceptual system morphs into another.The sources of this study include the cognitive development of numbers in children, neuropsychology, the study of creativity, and the historical development of mathematics and science. The approach is unusual and original. It comes out of the author's lengthy experience as a mathematician, teacher, and writer of books about mathematics and science, such as How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics and The Blind Spot: Science and the Crisis of Uncertainty.

A História da matemática e os conhecimentos prévios dos professores como subsídios para o planejamento de um curso sobre geometria esférica e hiperbólica

O objetivo desta pesquisa foi estudar como a evolução histórica da Matemática, tendo como pano de fundo a evolução da geometria, pode auxiliar na formação continuada do professor de Matemática. Para tanto, a sugestão é para um planejamento de curso sobre geometria esférica e hiperbólica estruturado a partir de pressupostos teóricos da aprendizagem significativa, direcionado principalmente a professores de Matemática que atuam no ensino médio. O planejamento do curso foi estruturado: em dados sobre a história da geometria, buscando evidenciar como os conceitos elementares de geometria esférica e hiperbólica desenvolveram-se historicamente; nos conhecimentos prévios mais comuns encontrados na literatura, incluindo um breve esboço de noções identificadas em uma amostra de professores de Matemática de ensino médio e em sugestões de leituras de resultados de pesquisas recentes sobre os processos de ensino e aprendizagem de Matemática. Pretende-se fornecer aos professores elementos de reflexão que lhe proporcionem mudança de postura, através do questionamento da visão da Geometria, enquanto processo de construção e sobre sua própria prática de ensino. A metodologia sugerida privilegia o trabalho coletivo, com a realização de debates e sínteses. As atividades mencionadas são acompanhadas de justificativas sobre a escolha do tema e objetivos.

Bridging History of the Concept of Function with Learning of Mathematics: Students’ Meta-Discursive Rules, Concept Formation and Historical Awareness

In this paper we present a matrix-organised implementation of an experimental course in the history of the concept of a function. The course was implemented in a Danish high school. One of the aims was to bridge history of mathematics with the teaching and learning of mathematics. The course was designed using the theoretical frameworks of a multiple perspective approach to history, Sfard’s theory of thinking as communicating, and theories from mathematics education about concept image, concept definition and concept formation. It will be explained how history and extracts of original sources by Euler from 1748 and Dirichlet from 1837 were used to (1) reveal students’ meta-discursive rules in mathematics and make them objects of students’ reflections, (2) support students’ learning of the concept of a function, and (3) develop students’ historical awareness. The results show that it is possible to diagnose (some) of students’ meta-discursive rules, that some of the students acted according to meta-discursive rules that coincide with Euler’s from the 1700s, and that reading a part of a text by Dirichlet from 1837 created obstacles for the students that can be referenced to differences in meta-discursive rules. The experiment revealed that many of the students have a concept image that was in accordance with Euler’s rather than with our modern concept definition and that they have process oriented thinking about functions. The students’ historical awareness was developed through the course with respect to actors’ influence on the formation of mathematical concepts and the notions of internal and external driving forces in the historical development of mathematics.

Writing about the History of Mathematics as a Means for Growth in Understanding

The purpose of this qualitative study is to explore students’ self-reported growth of mathematical understanding resulting from writing about the historical development of a mathematical concept. Using excerpts from undergraduate students’ written reflections about their experiences with the task of writing about mathematics, this study describes three emergent themes concerning how these students explicitly assessed their own learning: selfawareness of initial understanding, learning from the task of writing, and deeper understanding of mathematics. The results indicate that writing about the historical development of mathematics encouraged students to acknowledge their existing mathematical understanding as well as extend or develop new understandings. Furthermore, writing about mathematics can serve as a viable assessment of individual student learning and provide insight into what students understand independent of formal assessment based on procedural skills.

Making Connections with Prime Numbers

Few topics in mathematics present more possibilities for enrichment and lesson extensions than prime numbers. Each year in my fifth-grade class, I discover more and more ideas to add to this already rich subject. The study of prime numbers offers opportunities for enriching students' mathematical language, making connections with related topics, discussing the historical development of mathematics, exploring the Internet, and gaining further understanding of mathematics topics already covered. As a teacher, I approach prime numbers enthusiastically, and my students come away from the study with a wealth of knowledge and understanding and, more important, a desire for further exploration.

Special Issue Article: Preparing for the 21st Century: The Status of Quantitative Literacy in the United States

This article articulates and operationalizes a framework for investigating the level of quantitative literacy in the United States. Quantitative literacy is defined in terms of mathematical content knowledge, mathematical reasoning, understanding of the social impact and utility of mathematics, understanding the nature and historical development of mathematics, and mathematical disposition‐Data from the Third International Mathematics and Science Study are used to document the level of quantitative literacy in the US. Results suggest that, although students in the US seem to possess an awareness of the usefulness of mathematics and have positive dispositions toward mathematics, they fall short in their understanding of the nature of mathematics and an ability to apply their content knowledge to everyday situations. Suggestions for curriculum and instruction that align with the framework for promoting quantitative literacy are offered.

A Brief Historical Dictionary of Mathematical Terms

I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.

Some foundational problems in mathematics suggested by physics

It is largely recognized that physics has represented an important source of suggestions in the historical development of mathematics and, in more recent times, even of logic. At the same time, if we look to the foundational investigations about both sciences in our century, one cannot help but notice that these researches have very rarely inter acted. Further, a number of discussions about the foundations of mathematics seem to go along with a somewhat naive and old fashioned image of physics, whereas foundational investigations about physics often propose an oversimplified image of the world of mathe matics (stressing for instance the characterization of mathematics as a merely analytical science). I would like to discuss in what sense contemporary physics might provide some interesting arguments and theoretical results, which could have a bearing on the foundational studies about mathematics. Let me start with a traditional philosophical question. It is well known that many discussions of the golden period of the foundational studies in mathematics in our century are essentially founded on a somewhat schematic contraposition between a platonistic view according to which, roughly, mathematical objects are described) and a concep tualista view (according to which mathematical objects are invented or constructed). Now, such a contraposition is clearly based on an extrapolation from the theoretical constructs of empirical sciences. Namely, the starting point of the traditional platonist in mathematics seems to be founded on a very uncritical concept of physical object, to which the platonist intends to assimilate even the concept of mathema tical object. In other words (according to the classical platonistic view), the concept of mathematical object should share the same logical and gnoseological characters as the concept of physical object. But what are the relevant properties of the concept of physical object? It is well known that contemporary physics has submitted to a strong criticism the traditional concept of object, developed by classical macrophysics [10]. I would like to recall only four main reasons, which in my opinion confirm the thesis according to which the concept of

The Evolution of Number

Abstract How is the historical development of mathematics to be understood sociologically? The writings of Mannheim and Wittgenstein suggest two contrasting approaches which may be evaluated through a detailed analysis of the development of the number concept. Five main number systems can be distinguished of which the most basic is the system of whole numbers and, given that importance attaches to generalizing power, there can be shown to be a tendency for the number concept to be progressively augmented. This process may be understood by reference to the basic pre-Darwinian evolutionary idea of “unfolding.” Complementing this intrinsic element, in actual historical instances a variety of extrinsic factors may be seen to be operative, facilitating or retarding development. To explain historical change fully an elaborate normative structure must be analyzed incorporating a macroinstitutional level, the “rules of the mathematical game,” notational considerations, and relations internal to mathematics itself...

A Group Theoretic Approach to the Equations of Plasma Physics

AbstractThis paper concerns the interaction between group theory and classical mechanics in general and with the application of this theory to plasma physics in particular.Mechanics has had a profound role in the historical development of mathematics. Leading original thinkers in pure mathematics such as Newton, Euler, Lagrange, Jacobi, Laplace, Cauchy, Gauss, Riemann, Poincaré, Hilbert, Birkhofï, Smale and Arnold were also great original thinkers in various facets of mechanics. The interaction between mechanics and pure mathematics remains one of the most active and flourishing areas of current research. It is this flavor which I hope to convey in this lecture.