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Dissertations / Theses on the topic 'Mathematics – History'
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1
Klowss, Jacqui. "Using History to Teach Mathematics." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-80402.
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Students today need to be taught not only the real life context of their mathematics lessons but also the historical context of the theory behind their mathematics lessons. Using history to teach mathematics, makes your lessons not only interesting but more meaningful to a large percentage of your students as they are interested in knowing the who, how and why about certain rules,
theorems, formulas that they use everyday in class. Students are captivated by learning the history behind mathematicians, rules, etc. and therefore can link the lesson to something in history and a concept. Even learning the mathematics behind historical events motivates and interests them. They cannot get enough!
2
Marshall, Gerald L. Rich Beverly Susan. "Using history of mathematics to improve secondary students' attitudes toward mathematics." Normal, Ill. Illinois State University, 2000. http://wwwlib.umi.com/cr/ilstu/fullcit?p9995668.
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Thesis (Ph. D.)--Illinois State University, 2000.Title from title page screen, viewed May 4, 2006. Dissertation Committee: Beverly S. Rich (chair), Michael Marsalli, Edward S. Mooney. Includes bibliographical references (leaves 89-124) and abstract. Also available in print.
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Bell, J. Gregory Dossey John A. "A history of mathematics class for middle school teachers." Normal, Ill. Illinois State University, 1992. http://wwwlib.umi.com/cr/ilstu/fullcit?p9234458.
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Thesis (D.A.)--Illinois State University, 1992.Title from title page screen, viewed January 19, 2006. Dissertation Committee: John A. Dossey (chair), Lynn H. Brown, Franklin G. Lewis, Albert D. Otto, Charles L. VanderEynden. Includes bibliographical references (leaves 644-648) and abstract. Also available in print.
4
Pejlare, Johanna. "On Axioms and Images in the History of Mathematics." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8345.
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This dissertation deals with aspects of axiomatization, intuition and visualization in the history of mathematics. Particular focus is put on the end of the 19th century, before David Hilbert's (1862–1943) work on the axiomatization of Euclidean geometry. The thesis consists of three papers. In the first paper the Swedish mathematician Torsten Brodén (1857–1931) and his work on the foundations of Euclidean geometry from 1890 and 1912, is studied. A thorough analysis of his foundational work is made as well as an investigation into his general view on science and mathematics. Furthermore, his thoughts on geometry and its nature and what consequences his view has for how he proceeds in developing the axiomatic system, is studied. In the second paper different aspects of visualizations in mathematics are investigated. In particular, it is argued that the meaning of a visualization is not revealed by the visualization and that a visualization can be problematic to a person if this person, due to a limited knowledge or limited experience, has a simplified view of what the picture represents. A historical study considers the discussion on the role of intuition in mathematics which followed in the wake of Karl Weierstrass' (1815–1897) construction of a nowhere differentiable function in 1872. In the third paper certain aspects of the thinking of the two scientists Felix Klein (1849–1925) and Heinrich Hertz (1857–1894) are studied. It is investigated how Klein and Hertz related to the idea of naïve images and visual thinking shortly before the development of modern axiomatics. Klein in several of his writings emphasized his belief that intuition plays an important part in mathematics. Hertz argued that we form images in our mind when we experience the world, but these images may contain elements that do not exist in nature.
5
Percival, Irene. "Mathematics in history, integrating the mathematics of ancient civilizations with the Grade 7 social studies curriculum." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0026/MQ51447.pdf.
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Coburn, Noah Nathanael. "Galois theory : the history and theories of mathematics' boy genius /." Lynchburg, VA : Liberty University, 2007. http://digitalcommons.liberty.edu.
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Carter, Mary Donette. "The Role of the History of Mathematics in Middle School." Digital Commons @ East Tennessee State University, 2006. https://dc.etsu.edu/etd/2224.
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It is the author's belief that middle school mathematics is greatly taught in isolation with little or no mention of its origin. Teaching mathematics from a historical perspective will lead to greater understanding, student inspiration, motivation, excitement, varying levels of learning, and appreciation for this subject. This thesis will develop four units that will incorporate original source documents and selected historical topics surrounding computation, numbers, and early calculating devices. Many of the units will center on the Rhind Papyrus and The Treviso Arithmetic. These units will be appropriate to middle school, with an emphasis on 6th grade.
8
Lindström, Jens. "On the origin and early history of functional analysis." Thesis, Uppsala University, Department of Mathematics, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-120527.
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Davies, James Edgar. "Changes of Setting and the History of Mathematics: A New Study of Frege." Thesis, University of Canterbury. Mathematics & Statistics, 2010. http://hdl.handle.net/10092/4330.
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This thesis addresses an issue in the philosophy of Mathematics which is little discussed, and indeed little recognised. This issue is the phenomenon of a ‘change of setting’. Changes of setting are events which involve a change in a scientific framework which is fruitful for answering questions which were, under an old framework, intractable. The formulation of the new setting usually
involves a conceptual re-orientation to the subject matter. In the natural sciences, such re-orientations are arguably unremarkable, inasmuch as it is possible that within the former setting for one’s thinking one was merely in error,
and under the new orientation one is merely getting closer to the truth of the matter. However, when the subject matter is pure mathematics, a problem arises in that mathematical truth is (in appearance) timelessly immutable. The conceptions that had been settled upon previously seem not the sort of thing that could be vitiated. Yet within a change of setting that is just what seems to happen. Changes of setting, in particular in their effects on the truth of individual propositions, pose a problem for how to understand mathematical truth.
Thus this thesis aims to give a philosophical analysis of the phenomenon of changes of setting, in the spirit of the investigations performed in Wilson (1992) and Manders (1987) and (1989). It does so in three stages, each of
which occupies a chapter of the thesis:
1. An analysis of the relationship between mathematical truth and settingchanges, in terms of how the former must be viewed to allow for the latter. This results in a conception of truth in the mathematical sciences which
gives a large role to the notion that a mathematical setting must ‘explain itself’ in terms of the problems it is intended to address.
2. In light of (1), I begin an analysis of the change of setting engendered in mathematical logic by Gottlob Frege. In particular, this chapter will address the question of whether Frege’s innovation constitutes a change of setting, by asking the question of whether he is seeking to answer questions which were present in the frameworks which preceded his innovations. I argue that the answer is yes, in that he is addressing the Kantian question of whether alternative systems of arithmetic are possible. This question arises because it had been shown earlier in the 19th century that Kant’s conclusion, that Euclid’s is the only possible description of space, was incorrect.
3. I conclude with an in-depth look at a specific aspect of the logical system constructed in Frege’s Grundgesetze der Arithmetik. The purpose of this chapter is to find evidence for the conclusions of chapter two in Frege’s technical work (as opposed to the philosophical). This is necessitated
by chapter one’s conclusions regarding the epistemic interdependence of formal systems and informal views of those frameworks.
The overall goal is to give a contemporary account of the possibility of setting-changes; it will turn out that an epistemic grasp of a mathematical system requires that one understand it within a broader, somewhat historical context.
10
Wotley, Susan Elaine 1936. "Immigration and mathematics education over five decades : responses of Australian mathematics educators to the ethnically diverse classroom." Monash University, Faculty of Education, 2001. http://arrow.monash.edu.au/hdl/1959.1/8359.
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Alexander, Anita Nicole. "A HISTORY OF THE PRIME NUMBER THEOREM." Kent State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=kent1416827548.
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Taylor, Katie. "Communicating mathematics through vernacular books in Elizabethan England." Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.607744.
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13
Gefwert, Christoffer. "Wittgenstein on philosophy and mathematics : an essay in the history of philosophy /." Åbo : Åbo akademic Förlag, 1994. http://catalogue.bnf.fr/ark:/12148/cb357214439.
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Hartveit, Marit. "The lesser names : the teachers of the Edinburgh Mathematical Society and other aspects of Scottish mathematics, 1867–1946." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/1700.
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The Edinburgh Mathematical Society started out in 1883 as a society with a large proportion of teachers. Today, the member base is mainly academical and there are only a few teachers left. This thesis explores how and when this change came about, and discusses what this meant for the Society. It argues that the exit of the teachers is related to the rising standard of mathematics, but even more to a change in the Society’s printing policy in the 1920s, that turned the Society’s Proceedings into a pure research publication and led to the death of the ‘teacher journal’, the Mathematical Notes. The thesis also argues that this change, drastic as it may seem, does not represent a change in the Society’s nature. For this aim, the role of the teachers within the Society has been studied and compared to that of the academics, from 1883 to 1946. The mathematical contribution of the teachers to the Proceedings is studied in some detail, in particular the papers by John Watt Butters. A paper in the Mathematical Notes by A. C. Aitken on the Bell numbers is considered in connection with a series of letters on the same topic from 1938–39. These letters, written by Aitken, Sir D’Arcy Thompson, another EMS member, and the Cambridge mathematician G. T. Bennett, explores the relation between the three and gives valuable insight into the status of the Notes. Finally, the role of the first women in the Society is studied. The first woman joined without any official university education, but had received the necessary mathematical background from her studies under the Edinburgh Association for the University Education of Women. The final chapter is largely an assessment of this Association’s mathematical classes.
15
Bushman, Nathan. "Hypercomplex Numbers and Early Vector Systems: A History." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1585666516546138.
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Harouni, Houman. "Purpose and Education: The Case of Mathematics." Thesis, Harvard University, 2015. http://nrs.harvard.edu/urn-3:HUL.InstRepos:16461047.
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Why do schools teach mathematics, and why do they teach the mathematics that they do? In this three-part dissertation, I argue that the justifications offered by national education systems are not convincing, and that students are tested on content whose purpose neither they nor their teachers clearly understand. In the first part of the dissertation, I propose a theoretical framework for understanding the content and pedagogy of school mathematics as a set of practices reflecting socio-political values, particularly in relation to labor and citizenship. Beginning with a critical study of history, I trace the origins of modern mathematics education, in the process unearthing common, unexamined assumptions regarding the place and form of mathematics education in contemporary society.
In the second part of the dissertation I use the above theoretical framework to re-examine the literature on mathematical word problems. Word problems have interested research because they operate at the intersection between mathematics, education, and labor. I argue that scholarly discussions of word problems have so far adopted unexamined assumptions regarding the role of history, the structure of everyday life, and the relationship between mathematics and other disciplines. Through the lens of political economy I examine these assumptions and offer new categories and explanation for understanding word problems.
In the final part of the dissertation, I apply my theoretical framework to practice. Using a dialogical approach, I present a group of undergraduate students and pre-service teachers with artifacts and problems that embody some of the defining tensions of mathematics education. Through twelve weeks of in-depth discussion, fieldwork and exploration, students eventually arrive at a more critical understanding of the social purpose of mathematics and the impact of this purpose on its teaching and learning in various contexts. The results for the students include an expanded vision of the possibilities of mathematics, a radical critique of its place in society, and reports of reduced math anxiety as well as increased curiosity toward mathematics.Culture, Communities, and Education
17
Lipson, Mark (Mark Israel). "New statistical genetic methods for elucidating the history and evolution of human populations." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/89873.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 165-173).
In the last few decades, the study of human history has been fundamentally changed by our ability to detect the signatures left within our genomes by adaptations, migrations, population size changes, and other processes. Rapid advances in DNA sequencing technology have now made it possible to interrogate these signals at unprecedented levels of detail, but extracting more complex information about the past from patterns of genetic variation requires new and more sophisticated models. This thesis presents a suite of sensitive and efficient statistical tools for learning about human history and evolution from large-scale genetic data. We focus first on the problem of admixture inference and describe two new methods for determining the dates, sources, and proportions of ancestral mixtures between diverged populations. These methods have already been applied to a number of important historical questions, in particular that of tracing the course of the Austronesian expansion in Southeast Asia. We also report a new approach for estimating the human mutation rate, a fundamental parameter in evolutionary genetics, and provide evidence that it is higher than has been proposed in recent pedigree-based studies.
by Mark Lipson.
Ph. D.
18
Morris, Kathryn 1970. "Geometrical physics : mathematics in the natural philosophy of Thomas Hobbes." Thesis, McGill University, 2001. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=37789.
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My thesis examines Thomas Hobbes's attempt to develop a mathematical account of nature. I argue that Hobbes's conception of how we should think quantitatively about the world was deeply indebted to the ideas of his ancient and medieval predecessors. These ideas were often amenable to Hobbes's vision of a demonstrative, geometrically-based science. However, he was forced to adapt the ancient and medieval models to the demands of his own thoroughgoing materialism. This hybrid resulted in a distinctive, if only partially successful, approach to the problems of the new mechanical philosophy.
19
Ramineni, Sri Ram. "Hidden History: A Mobile Application for Discovering Surrounding Landscapes." DigitalCommons@USU, 2016. https://digitalcommons.usu.edu/etd/4953.
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This thesis work describes the design, development and evaluation of a mobile application called Hidden History. This application lets users discover and explore three types of landscapes (Historic, Scenic and Cultural) using three different modes of discovery (Route, Explore and Tour).
Before designing Hidden History, the feature set of other applications that help users explore surrounding landscapes were identified and analyzed. Hidden History was then designed to implement the best features of these applications and offer several functionality improvements. Design began with iterative paper prototyping, following which a high fidelity, digital prototype was created. The high fidelity prototype was tested through two rounds of usability testing with target users. All the users found the application useful. User testing revealed many issues and areas of improvements for the application. By iteratively prototyping and testing the Hidden History application with users, researchers created a mobile application that better supports the discovery of landscape history. The thesis concludes with suggestions for future work to further improve the application.
20
Martins, João Carlos Gilli [UNESP]. "Sobre revoluções científicas na matemática." Universidade Estadual Paulista (UNESP), 2005. http://hdl.handle.net/11449/102083.
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Tem sido unanimidade entre os filósofos da Matemática a compreensão de que as revoluções científicas, na forma como são apresentadas em A Estrutura das Revoluções Científicas, de Thomas S. Kuhn, não ocorrem na Matemática. Este trabalho pretende o contrário: fundado no Modelo Teórico dos Campos Semânticos e tendo a história da Matemática como cenário mais especificamente, a história da Álgebra esta tese foi elaborada para mostrar que a obra Kitab al mukhtasar fi hisab al-jabr wa l-muqabalah, de al- Khwarizmi, inaugura o primeiro período de pesquisa normal no desenvolvimento da Álgebra na Europa, um período altamente cumulativo e extraordinariamente bem sucedido em seus objetivos paradigmáticos e que se estendeu até as décadas iniciais do século XIX. Mostramos, ainda, que a demonstração do, hoje denominado, Teorema Fundamental da Álgebra, por Gauss, e a publicação do trabalho Sobre a resolução algébrica de equações, de Abel, trouxe à luz, na forma de um fato, uma anomalia irresolúvel do primeiro paradigma da Álgebra no Velho Continente. A partir daí, abriu-se um período de pesquisa extraordinária no âmbito dessa disciplina um período revolucionário de onde viria emergir um novo período de pesquisa normal, um novo paradigma para a Álgebra os sistemas algébricos abstratos fundado nas realizações matemáticas de Galois, Peacock e Hamilton.
Thus far, all the Mathematical Philosophers have unanimously agreed that the scientific revolutions, as it is presented in The Structures of the Scientific Revolutions, by Thomas S. Kuhn, do not take place in Mathematics. This paper intends to prove just the opposite: founded on The Theoretical Models of the Semantic Fields and considering the History of Mathematics as the scenery in question more precisely, the History of Algebra this thesis was prepared to show that the work Kitab al mukhtasar fi hisab al-jabr wa l muqabalah, by al-Khwarizmi, gives birth to the first period of normal research in the European development of Algebra, a highly cumulative and extraordinarily well succeeded period in its paradigmatic objectives, which extended until the first decades of the Nineteenth Century. We further show that the proof of the so called The Fundamental Theorem of Algebra, by Gauss, and the publication of Abel's work on The Algebraic Solutions of Equations, brought to light, as a fact, an unsolvable anomaly of the first paradigm of Algebra in the Old Continent which, from there on, caused the beginning of an extraordinary research period in this particular field in fact, a revolutionary period from which would surface a new time of normal research, a new algebraic paradigm the abstract algebraic systems based on the mathematical achievements of Galois, Peacock and Hamilton.
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Bråting, Kajsa. "Studies in the Conceptual Development of Mathematical Analysis." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-101349.
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This dissertation deals with the development of mathematical concepts from a historical and didactical perspective. In particular, the development of concepts in mathematical analysis during the 19th century is considered. The thesis consists of a summary and three papers. In the first paper we investigate the Swedish mathematician E.G. Björling's contribution to uniform convergence in connection with Cauchy's sum theorem from 1821. In connection to Björling's convergence theory we discuss some modern interpretations of Cauchy's expression x=1/n. We also consider Björling's convergence conditions in view of Grattan-Guinness distinction between history and heritage. In the second paper we study visualizations in mathematics from historical and didactical perspectives. We consider some historical debates regarding the role of intuition and visual thinking in mathematics. We also consider the problem of what a visualization in mathematics can achieve in learning situations. In an empirical study we investigate what mathematical conclusions university students made on the basis of a visualization. In the third paper we consider Cauchy's theorem on power series expansions of complex valued functions on the basis of a paper written by E.G. Björling in 1852. We discuss Björling's, Lamarle's and Cauchy's different conditions for expanding a complex valued function in a power seris. In the third paper we also discuss the problem of the ambiguites of fundamental concpets that existed during the mid-19th century. We argue that Cauchy's and Lamarle's proofs of Cauchy's theorem on power series expansions of complex valued functions are correct on the basis of their own definitions of the fundamental concepts involved.
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Mintz, Daniel V. "Mathematics for history's sake : a new approach to Ptolemy's Geography." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/2152.
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Almost two thousand years ago, Claudius Ptolemy created a guide to drawing maps of the world, identifying the names and coordinates of over 8,000 settlements and geographical features. Using the coordinates of those cities and landmarks which have been identified with modern locations, a series of best-fit transformations has been applied to several of Ptolemy’s regional maps, those of Britain, Spain, and Italy. The transformations relate Ptolemy’s coordinates to their modern equivalents by rotation and skewed scaling. These reflect the types of error that appear in Ptolemy’s data, namely those of distance and orientation. The mathematical techniques involved in this process are all modern. However, these techniques have been altered in order to deal with the historical difficulties of Ptolemy’s maps. To think of Ptolemy’s data as similar to that collected from a modern random sampling of a population and to apply unbiased statistical methods to it would be erroneous. Ptolemy’s data is biased, and the nature of that bias is going to be informed by the history of the data. Using such methods as cluster analysis, Procrustes analysis, and multidimensional scaling, we aimed to assess numerically the accuracy of Ptolemy’s maps. We also investigated the nature of the errors in the data and whether or not these could be linked to historical developments in the areas mapped.
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Evangelista, AntÃnia DinamÃria Gomes. "Mathematical rules and their justifications: brief history of mathematics education in Brazil and a reflection on the inclusion of demonstrations in teaching practice." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=12596.
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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel SuperiorEsse trabalho apresenta uma reflexÃo acerca do ensino da matemÃtica, bem como as dificuldades inerentes a esse tema que, ao longo da historia de nosso pais, teve seus momentos de gloria e de esquecimento. TambÃm e discutido o papel das demonstraÃÃes nas aulas de matemÃtica onde autores divergem quanto a ser ou nÃo uma ferramenta didÃtica no ensino bÃsico. Sempre existiu a preocupaÃÃo dos professores em tornar a MatemÃtica mais dinÃmica e mais fÃcil para os alunos. Do Brasil ColÃnia aos dias atuais o ensino de MatemÃtica sofreu grandes mudanÃas. Apesar de sua importÃncia e aplicabilidade houve tempos em que, o ensino de ciÃncias (incluindo matemÃtica) era reservado aos cursos de nÃvel superior. No Brasil ColÃnia predominava a escola dos JesuÃtas baseado em um ensino tradicional com pouco destaque para a matemÃtica. No Brasil ImpÃrio, foi criado a ConstituiÃÃo de 1824 e implantadas as primeiras instituiÃÃes culturais e educacionais do pais, caracterizando as primeiras mudanÃas educacionais. No Brasil Republica, aconteceram varias reforma no sistema educacional sob fortes influencia francesa, onde, pela primeira vez a MatemÃtica recebeu destaque. Em consequencia, houve a democratizaÃÃo da escola, favorecendo crianÃas e jovens das classes populares. A dÃcada de 50 foi marcada como o perÃodo de estudos e tentativas de implantaÃÃo do Movimento MatemÃtica Moderna que tinha como caracterÃsticas: precisÃo na linguagem matemÃtica; prioridade nos aspectos lÃgicos e estruturais; importÃncia em demonstraÃÃes; desfavorecimento ao ensino de geometria. Esse movimento surgia na tentativa de solucionar os problemas advindos do ensino tradicional. Hà vÃrios fatores que geram/influenciam as dificuldades no ensino de matemÃtica, tais como: a mà formaÃÃo inicial dos professores; metodologia tradicional com Ãnfase no cÃlculo e memorizaÃÃo de formulas; busca inadequada a novos recursos pedagÃgicos; descontextualizaÃÃo; o simbolismo prÃprio da linguagem matemÃtica, etc. A reintroduÃÃo de doses equilibradas de demonstraÃÃes no ensino de MatemÃtica no Brasil e uma pratica que incentiva a compreensÃo, ajuda no desenvolvimento do raciocÃnio matemÃtico e da lÃgica dedutiva. O ensino de matemÃtica necessita de mudanÃas de posturas, metodologias, mas sem abandonar as tÃcnicas e procedimentos operatÃrios caracterÃsticos da disciplina. Nesse trabalho, ainda sÃo apresentadas algumas âregrinhasâ com sua contextualizaÃÃo histÃrica e justificativa a fim de ajudar o professor a responder questionamentos dos alunos como, âde onde veio isso?â ou âpor que à assim?â.
This paper presents a reflection on the teaching of mathematics as well as the difficulties related to the subject, throughout the history of our country, had his moments of glory and oblivion. It discuss the function of demonstrations in math classes where authors disagree as to whether or not a teaching tool in elementary education. There has always been a concern of teachers to become more dynamic and easier for students to mathematics. From Colonial Brazil to today the teaching of Mathematics has undergone great changes. In spite of its importance and applicability there were times where the teaching of science (including mathematics) was reserved for university courses. In Colonial Brazil predominated the Jesuit school based on a traditional education with little emphasis on mathematics. In Empire Brazil, was created the Constitution of 1824 and implemented the first cultural and educational institutions in the country, featuring the first educational changes. In Republic Brazil, happened several reforms in the educational system under strong French influences, where, for the first time the Mathematics was highlighted. Consequently, there was the democratization of the school, encouraging children and young people of the popular classes.The 50's was marked as the period of studies and attempts to implement the Modern Mathematics Movement which had the following characteristics: precision in mathematical language; priority in logical and structural aspects; importance in demonstrations; disadvantage to teaching geometry. This movement arose in the attempt to solve the problems arising from traditional education. There are several factors that create/influence the difficulties in teaching of mathematics, such as: poor initial training of teachers; traditional methodology with emphasis on calculation and memorization of formulas; inadequate seeks new teaching resources; decontextualization; own symbolism of mathematics language etc.The reintroduction of balanced doses of demonstrations in the teaching of Mathematics in Brazil is a practice that encourages understanding, helps in the development of mathematical reasoning and deductive logic. The teaching of mathematics requires changes in attitudes, methodologies, but without give up the technical characteristics and operative procedures of the discipline. In this work is still displayed some "ground rules" with its historical context and justifications in order to help the teacher to answer questions of students as "where did that come from? " or "why is that?".
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Robson, Eleanor. "Old Babylonian coefficient lists and the wider context of mathematics in ancient Mesopotamia 2100-1600 BC." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.296052.
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Huff, Kendra D. "Women in Mathematics: An Historical Account of Women's Experiences and Achievement." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/cmc_theses/150.
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For a long time, women have struggled to gain complete acceptance in the mathematics field. The purpose of this paper is to explore the history of women in the field of mathematics, the impact and experiences of current female mathematicians, and the common trends for women in the mathematics field, through literature review and personal interviews. This paper looks at the lives of four famous female mathematicians, as well as female mathematicians in the Claremont Colleges who were interviewed for this paper. Specifically this paper examines the discrimination they faced and how they overcame this discrimination, as well as the contributions they have made to the mathematics field. In addition, studies about the effects of gender on mathematics achievement were explored. This paper tries to bring the conclusions of these studies together to present arguments from different perspectives. It also recognizes trends and changes in favor of women in the mathematics field in recent years. In spite of the contributions made by women and the improvements that have come about for women in the field, including the increased number of doctoral recipients, women still face challenges in gaining complete acceptance. Continued change can occur through mentoring and encouraging young women to pursue careers in the mathematics field.
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Rosswog, James. "Improving classification of spatiotemporal data using adaptive history filtering." Diss., Online access via UMI:, 2007.
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Reed, Beverly M. "THE EFFECTS OF STUDYING THE HISTORY OF THE CONCEPT OF FUNCTION ON STUDENT UNDERSTANDING OF THE CONCEPT." Kent State University / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=kent1195713522.
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Alpaslan, Mustafa. "Prospective Elementary Mathematics Teachers'." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613610/index.pdf.
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The aim of this study was to investigate the roles of year in teacher education program and gender on prospective elementary mathematics teachers&rsquoknowledge of history of mathematics and their attitudes and beliefs towards the use of history of mathematics in the teaching and learning of mathematics. Moreover, the relationship between prospective teachers&rsquo
knowledge of history of mathematics and their attitudes and beliefs about the history of mathematics usage was examined. The data of the study were obtained from 1593 prospective teachers who were enrolled in first, second, third, and fourth years of Elementary Mathematics Education undergraduate program of nine universities located in seven geographical regions of Turkey through clustered random sampling. The scales used in the data collection were Knowledge of History of Mathematics (KHM) Test and Attitudes and Beliefs towards the Use of History of Mathematics in Mathematics Education (ABHME) Questionnaire. The two-way ANOVA results clarified that prospective teachers&rsquo
knowledge of history of mathematics improved as the years enrolled in the program increased. Results also revealed that males had significantly higher mean scores on KHM Test than females in the first two years of the program. In the third and fourth years, this situation reversed such that females had higher KHM mean scores, but this difference was not statistically significant. Results also showed that prospective teachers&rsquo
ABHME mean scores increased as years of enrollment in the program increased. More clearly, senior prospective teachers&rsquo
relevant mean scores were significantly higher than that of freshmen and sophomores, and juniors&rsquo
attitudes and beliefs were significantly higher than that of freshmen. In addition, females&rsquo
ABHME mean scores were significantly higher than that of males for all years. Lastly, a positive correlation between prospective elementary mathematics teachers&rsquo
KHM mean scores and ABHME mean scores was found through Pearson product-moment correlation analysis.
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Bonetto, Giácomo Augusto. "Uma constituição historica (1965-1995) de praticas escolares mobilizadoras do objeto cultural "função" na cidade de Campinas (SP)." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/251855.
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Orientador: Antonio MiguelTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Educação
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Resumo: Neste trabalho, temos como propósito realizar uma constituição histórica de algumas práticas escolares mobilizadoras do objeto cultural função, na cidade de Campinas (SP), a partir de meados da década de 1960 até meados da década de 1990, período em que a educação matemática escolar brasileira esteve sob a influência marcante do movimento da matemática moderna. Para isso, constituímos uma base documental composta por entrevistas com professores, livros didáticos de matemática, guias e subsídios curriculares produzidos pela Coordenadoria de Ensino e Normas Pedagógicas (CENP) do Estado de São Paulo. Com base no diálogo que estabelecemos com esta base documental, procuramos enfatizar, nesta história de práticas escolares de mobilização cultural, as características idiossincráticas dessas práticas, bem como os valores que elas transmitiram, os condicionamentos institucionais que as formataram e as relações assimétricas de poder que as envolveram
Abstract: In this study, our purpose is to achieve a historical constitution of some school practices that mobilized the cultural object function, at the city of Campinas (SP), since the middle of 1960 decade until the mid of 1990 decade, a period in which Brazilian school mathematical education was under the remarkable influence of the new math movement. In this sense, we composed a documental support constituted by interviews with teachers, mathematical textbooks, curricular guides and proposals produced by the Coordenadoria de Ensino e Normas Pedagógicas (CENP) of the State of São Paulo. Based on the dialogue that we established with this documental support, we tried to give emphases, in that history of school practices of cultural mobilization, to the idiosyncratic properties of these practices, as to the values these practices transmitted, to the institutional conditional elements that gave form to the same practices and to the asymmetrical power relation that enveloped them
Doutorado
Educação Matematica
Doutor em Educação
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Vu, Tam. "Då som nu för alltid : Att skriva ett kompendium till gymnasielärare med förslag för hur matematikens historia kan integreras i matematikundervisningen." Thesis, KTH, Skolan för teknikvetenskaplig kommunikation och lärande (ECE), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-188869.
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Detta arbete handlar om matematikens historia i matematikundervisningen på gymnasienivå. Huvudsyftet är att undersöka hur matematiklärare kan integrera historiska aspekter i sina lektioner och att ge konkreta förslag för hur detta kan göras. Arbetet belyser framför allt en integrering med hjälp av problemlösning, där problem väljs ut så att de både har relevans för ämnesplanerna och kan kopplas till viktiga matematiker i historien samt hur matematik genom tiderna har utvecklats. Frågor som har besvarats är vilka historiskt kända matematikproblem som kan fungera som diskussionsunderlag i klassrummet och hur den undervisande läraren skulle kunna kommentera dessa problem för att synliggöra de bakomliggande historiska kopplingarna. Förslagen på problem och kopplingarna sammanställs i ett kompendium som är tänkt att läsas av matematiklärare på gymnasiet. Metoderna som använts för att producera kompendiet är dels litteraturstudium av tidigare arbeten om matematik och matematikdidaktik i samband med matematikens historia, dels kvalitativa intervjuer med erfarna matematiklärare på gymnasiet. De intervjuade lärarna fick se valda delar i ett prototypiskt kompendium och ge synpunkter samt förbättringsförslag för att det färdiga kompendiet skulle kunna fungera väl för den tänkta målgruppen. Trots att kompendiet inte är en lärobok har det bearbetats för att hålla en god pedagogisk kvalité. Kompendiet ska förmedla matematikens historia på ett koncist och tydligt sätt, där de involverade matematikproblemen och historiska kopplingarna ska upplevas som både intressanta och betydelsefulla för en matematiklärare.This master thesis deals with the use of the history of mathematics in teaching mathematics in Swedish gymnasium schools. A "gymnasium" in Sweden (not to be confused with a gymnastics school) is a type of school which consists of three years, after nine years of elementary school. The main focus of this thesis is to investigate how mathematics teachers can integrate historical aspects of mathematics into their classes, and to give concrete examples of such integration. This thesis illustrates, above all, an integration of mathematics history with problem solving, where problems are selected so that they are relevant to the syllabus and can be connected to important mathematicians in history as well as how mathematics itself has evolved through the ages. The questions to be answered in this thesis concern which mathematical problems that may serve as a basis for discussion in the classroom and how teachers may illuminate the historical connections contained in each discussed problem. The proposed problems and connections are compiled in a compendium which is meant to be read by mathematics teachers teaching at gymnasiums. The methods which have been used to produce the compendium are partly literature study of earlier works about mathematics and mathematics didactics in relation to mathematical history, partly qualitative interviews with experienced mathematics teachers at gymnasiums. The interviewed teachers read selected parts of the prototypal compendium and gave opinions and suggestions of improvement so that the final compendium would work well for the meant target group. Despite the fact that the compendium is not a textbook, a certain pedagogical quality is to be attained. The compendium should convey the history of mathematics in a clear and concise manner, where the involved mathematical problems and historical connections should be experienced as interesting and meaningful for mathematics teachers.
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Reich, David Emile. "Genetic analysis of human evolutionary history with implications for gene mapping." Thesis, University of Oxford, 1999. http://ora.ox.ac.uk/objects/uuid:9e3a3eb7-3cce-4494-82e8-8616fabed145.
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Genetic variation contains detailed and quantitative evidence about the history of populations. The historical traces of demographic growth and contraction, as well as the history of human disease, have left traces on the patterns of modern variation and can be studied by sampling present-day populations. However, the data sets that are necessary in order to take full advantage of this living archaeological record have not been available until recently. The quality and quantity of data have increased dramatically during the past decade because of the identification of polymorphisms, including SNPs and microsatellites, that are much more amenable to mathematical modeling and efficient genotyping than earlier marker systems. The research in this thesis has been carried out in response to the need to provide new methods of analysis to match the new types of data. Chapter 1 describes multilocus tests of demographic history and their application to real data. Chapter 2 describes how the pattern of linkage disequilibrium around a disease-predisposing mutation can be used to estimate the date of a mutation that is, the age of the most recent common ancestor of a set of modern samples. Finally, Chapter 3 draws several direct connections between human evolutionary history and medical genetics.
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McClain, Nichola Sue. "A study in geometric construction." CSUSB ScholarWorks, 1998. https://scholarworks.lib.csusb.edu/etd-project/1811.
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Tashman, Michael. "The Association Between Film Industry Success and Prior Career History: A Machine Learning Approach." Thesis, Harvard University, 2015. http://nrs.harvard.edu/urn-3:HUL.InstRepos:24078355.
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My thesis project is a means of understanding the conditions associated with success and failure in the American film industry. This is carried out by tracking the careers of several thousand actors and actresses, and the number of votes that their movies have received on IMDb. A fundamental characteristic of film career success is that of influence from prior success or failure—consider that an established “star” will almost certainly receive opportunities denied to an unknown actor, or that a successful actor with a string of poorly received films may stop receiving offers for desirable roles. The goal for this project is to to develop an understanding of how these past events are linked with future success.
The results of this project show a significant difference in career development between actors and actresses—actors’ career trajectories are significantly influenced by a small number of “make or break” films, while actresses’ careers are based on overall lifetime performance, particularly in an ability to avoid poorly-received films. Indeed, negatively received films are shown to have a distinctly greater influence on actresses’ careers than those that were positively received.
These results were obtained from a model using machine learning to find which movies from actors’ and actresses’ pasts tend to have the most predictive information. The parameters for which movies should be included in this set was optimized using a genetic learning algorithm, considering factors such as: film age, whether it was well-received or poorly-received, and if so, to what magnitude, and whether the film fits with the natural periodicity that many actors’ and actresses’ careers exhibit. Results were obtained following an extensive optimization, consisting of approximately 5000 evolutionary steps and 200,000 fitness evaluations, done over 125 hours.
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Toledo, José do Carmo [UNESP]. "Uma história do processo de institucionalização da área de Análise Matemática no Brasil." Universidade Estadual Paulista (UNESP), 2008. http://hdl.handle.net/11449/102136.
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toledo_jc_dr_rcla.pdf: 2561466 bytes, checksum: b6bae6e58494225b01dca9e6ae51e81d (MD5)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Este trabalho - uma investigação inserida no campo da História da Matemática argumenta em favor da existência, no Brasil, de uma tradição em pesquisa na área de Análise Matemática e propõe uma narrativa historiadora sobre o processo de institucionalização dessa área no país. Algumas práticas sociais no âmbito da comunidade de analistas brasileiros são enfatizadas: umas, por terem sido cruciais para os processos locais de constituição e autonomização desse campo científico; outras, por conferirem à Análise, o status de área institucionalizada no país.
This work - an investigation inserted in the field of the History of Mathematics argues in favour of a tradition in research in the area of Mathematical Analysis in Brazil and proposes a narrative history about the process of institutionalization of this area here. Some social practices within the community of brazilian analysts are emphasized: one, because they have been crucial to the constitution and autonomization of this scientific field in Brazil; others, by giving to the Analysis the status of an institutionalized area in this country.
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Martins, João Carlos Gilli. "Sobre revoluções científicas na matemática /." Rio Claro : [s.n.], 2005. http://hdl.handle.net/11449/102083.
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Orientador: Romulo Campos LinsBanca: Antonio Vicente Marafioti Garnica
Banca: Francisco César Polcino Miles
Banca: Ligia Arantes Sad
Banca: Marcos Vieira Teixeira
Resumo: Tem sido unanimidade entre os filósofos da Matemática a compreensão de que as revoluções científicas, na forma como são apresentadas em A Estrutura das Revoluções Científicas, de Thomas S. Kuhn, não ocorrem na Matemática. Este trabalho pretende o contrário: fundado no Modelo Teórico dos Campos Semânticos e tendo a história da Matemática como cenário mais especificamente, a história da Álgebra esta tese foi elaborada para mostrar que a obra Kitab al mukhtasar fi hisab al-jabr wal-muqabalah, de al- Khwarizmi, inaugura o primeiro período de pesquisa normal no desenvolvimento da Álgebra na Europa, um período altamente cumulativo e extraordinariamente bem sucedido em seus objetivos paradigmáticos e que se estendeu até as décadas iniciais do século XIX. Mostramos, ainda, que a demonstração do, hoje denominado, Teorema Fundamental da Álgebra, por Gauss, e a publicação do trabalho Sobre a resolução algébrica de equações, de Abel, trouxe à luz, na forma de um fato, uma anomalia irresolúvel do primeiro paradigma da Álgebra no Velho Continente. A partir daí, abriu-se um período de pesquisa extraordinária no âmbito dessa disciplina um período revolucionário de onde viria emergir um novo período de pesquisa normal, um novo paradigma para a Álgebra os sistemas algébricos abstratos fundado nas realizações matemáticas de Galois, Peacock e Hamilton.
Abstract: Thus far, all the Mathematical Philosophers have unanimously agreed that the scientific revolutions, as it is presented in The Structures of the Scientific Revolutions, by Thomas S. Kuhn, do not take place in Mathematics. This paper intends to prove just the opposite: founded on The Theoretical Models of the Semantic Fields and considering the History of Mathematics as the scenery in question more precisely, the History of Algebra this thesis was prepared to show that the work Kitab al mukhtasar fi hisab al-jabr wal muqabalah, by al-Khwarizmi, gives birth to the first period of normal research in the European development of Algebra, a highly cumulative and extraordinarily well succeeded period in its paradigmatic objectives, which extended until the first decades of the Nineteenth Century. We further show that the proof of the so called The Fundamental Theorem of Algebra, by Gauss, and the publication of Abel's work on The Algebraic Solutions of Equations, brought to light, as a fact, an unsolvable anomaly of the first paradigm of Algebra in the Old Continent which, from there on, caused the beginning of an extraordinary research period in this particular field in fact, a revolutionary period from which would surface a new time of normal research, a new algebraic paradigm the abstract algebraic systems based on the mathematical achievements of Galois, Peacock and Hamilton.
Doutor
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Cury, Fernando Guedes [UNESP]. "Uma história da formação de professores de Matemática e das Instituições formadoras do Estado de Tocantins." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/102115.
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cury_fg_dr_rcla.pdf: 3651153 bytes, checksum: 1ebd318484ac9f94a609fae308cdad37 (MD5)Neste trabalho pretendemos constituir uma história da formação de professores de matemática e dos primeiros cursos que preparavam estes profissionais no Estado do Tocantins. A pesquisa aborda a estrutura física dos estabelecimentos, o perfil de discentes e docentes, as disciplinas ministradas, as motivações políticoadministrativas e sociais que influenciaram a criação e desenvolvimento dos cursos, as principais práticas de formação, dentre outros aspectos. Valendo-se da História Oral como alternativa metodológica central e mobilizando fontes escritas disponíveis, constituímos uma análise narrativa em que se entrelaçam situações particulares do contexto educacional tocantinense, a criação do próprio estado, o processo de migração de professores, as influências políticas, o improviso na condução de cursos, as carências, urgências e transitoriedades que marcam a formação de professores de Matemática no Estado
The goal of this work is to build a history of the undergraduate programs whose main objective is the formation of Math teachers in Tocantins State, Brazil. The research discusses the physical structure of these courses, the academic profile of their students and teachers, the curricular content and approaches, the administrative and political motivations that influenced the creation and development of the first courses, the formative practices, among other elements related to these institutions. The methodological approach was based on Oral History as well in the analysis of written documents available. The data collected allowed us to create a narrative in which some particular events are focused in order to bring to the light the creation of Tocantins, its educational context, the migration of teachers, all sorts of political influences, the improvisation in the process of creating and developing such courses, the urgencies, needs and transitoriness that characterizes the formation of mathematics teachers in that State
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Birca, Alina. "The use of divergent series in history." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2591.
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In this thesis the author presents a history of non-convergent series which, in the past, played an important role in mathematics. Euler's formula, Stirling's series and Poincare's theory are examined to show the development of asymptotic series, a subdivision of divergent series.
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Venturin, Jamur Andre [UNESP]. "O processo de integração em Blaise Pascal." Universidade Estadual Paulista (UNESP), 2007. http://hdl.handle.net/11449/91002.
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O propósito desse trabalho é identificar de que maneira Pascal solucionava problemas matemáticos de integração, fazendo uso dos indivisíveis. Para isso, consultamos em particular três de suas obras: Postestatum Numericarum Summa1, LETTRE DE M. DETTONVILLE A M. DE CARCAVI2 e o Tratado do Triângulo Aritmético. Vimos a estreita relação que existe entre essas obras, a saber, na primeira delas é exibida a regra geral para encontrar áreas sob curvas do tipo y = xn , bem como mostra a relação entre a soma de potências numéricas com grandezas contínuas. Faz a integração das curvas segundo a abordagem dos indivisíveis. Já na segunda, que é associada diretamente com a terceira obra, é apresentada tanto a compreensão do indivisível e do infinitamente pequeno na constituição do contínuo, quanto à relação de soma simples, triangular e piramidal (encontradas a partir do triângulo aritmético) com suas respectivas integrais. Desse modo, a fim de entendermos o que aconteceu no século XVII, e sabermos quais as possíveis influências matemáticas de Pascal, buscamos outros métodos de integração como aqueles utilizados pelos gregos, isto é, o método de exaustão e as técnicas do século XVI. Sendo assim, foi possível observar que seus procedimentos de integração podem ser contemplados em dois aspectos: no primeiro, como contribuição para a história do desenvolvimento do cálculo, em um período em que ele estava na eminência de ser estruturado. No segundo, destacamos a relação existente com o cálculo moderno, contudo seu campo teórico é fundamentado nos indivisíveis.
The intention of this work is to identify of which way Pascal solved mathematical problems of integration, making use of the indivisibles. For this we consulted in particular three of his works: Postestatum Numericarum Summa, Lettre De M. Dettonville A. M. de Carcavi and the Treatise on the Arithmetical Triangule. We saw the close connection that exist between these works, namely, the first of them is showed the general rule to find areas under curves y = x2 , as well as it shows the relation between the sums of numerical potences with continuous magnitudes He makes the integration of curves according to approach of indivisibles. Already on the second, itþs associate directly to the third work, is presented the understanding of indivisible and the infinitive little in the constitution of the continuous, and also in the relation of simple, triangular and piramidal sums (found from the arithmetical triangule) with their respective integrals. In this way, in order to understand what happened in the 17th century and to know the possibles mathematical influences of Pascal, we search others methods of integration like those used by the Greeks, that is to say, the method of exhaustion and the techniques of the 16th century. Such being the case, it was possible to observe that its procedures of integration can be contemplated in two aspects: the first one, as a contribution for the history development calculation, in a period that it was the eminence of being structured. The second one detach the relation existent with the modern calculation, however, its theoretical field is based on indivisibles ones.
39
Venturin, Jamur Andre. "O processo de integração em Blaise Pascal /." Rio Claro : [s.n.], 2007. http://hdl.handle.net/11449/91002.
Full textAbstract:
Orientador: Irineu BicudoBanca: Vanderlei Marcos do Nascimento
Banca: Renata Cristina Geromel Meneghetti
Resumo: O propósito desse trabalho é identificar de que maneira Pascal solucionava problemas matemáticos de integração, fazendo uso dos indivisíveis. Para isso, consultamos em particular três de suas obras: Postestatum Numericarum Summa1, LETTRE DE M. DETTONVILLE A M. DE CARCAVI2 e o Tratado do Triângulo Aritmético. Vimos a estreita relação que existe entre essas obras, a saber, na primeira delas é exibida a regra geral para encontrar áreas sob curvas do tipo y = xn , bem como mostra a relação entre a soma de potências numéricas com grandezas contínuas. Faz a integração das curvas segundo a abordagem dos indivisíveis. Já na segunda, que é associada diretamente com a terceira obra, é apresentada tanto a compreensão do indivisível e do infinitamente pequeno na constituição do contínuo, quanto à relação de soma simples, triangular e piramidal (encontradas a partir do triângulo aritmético) com suas respectivas integrais. Desse modo, a fim de entendermos o que aconteceu no século XVII, e sabermos quais as possíveis influências matemáticas de Pascal, buscamos outros métodos de integração como aqueles utilizados pelos gregos, isto é, o método de exaustão e as técnicas do século XVI. Sendo assim, foi possível observar que seus procedimentos de integração podem ser contemplados em dois aspectos: no primeiro, como contribuição para a história do desenvolvimento do cálculo, em um período em que ele estava na eminência de ser estruturado. No segundo, destacamos a relação existente com o cálculo moderno, contudo seu campo teórico é fundamentado nos indivisíveis.
Abstract: The intention of this work is to identify of which way Pascal solved mathematical problems of integration, making use of the indivisibles. For this we consulted in particular three of his works: Postestatum Numericarum Summa, Lettre De M. Dettonville A. M. de Carcavi and the Treatise on the Arithmetical Triangule. We saw the close connection that exist between these works, namely, the first of them is showed the general rule to find areas under curves y = x2 , as well as it shows the relation between the sums of numerical potences with continuous magnitudes He makes the integration of curves according to approach of indivisibles. Already on the second, itþs associate directly to the third work, is presented the understanding of indivisible and the infinitive little in the constitution of the continuous, and also in the relation of simple, triangular and piramidal sums (found from the arithmetical triangule) with their respective integrals. In this way, in order to understand what happened in the 17th century and to know the possibles mathematical influences of Pascal, we search others methods of integration like those used by the Greeks, that is to say, the method of exhaustion and the techniques of the 16th century. Such being the case, it was possible to observe that its procedures of integration can be contemplated in two aspects: the first one, as a contribution for the history development calculation, in a period that it was the eminence of being structured. The second one detach the relation existent with the modern calculation, however, its theoretical field is based on indivisibles ones.
Mestre
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Bullock, Erika C. "An Archaeological/Genealogical Historical Analysis of the National Council of Teachers of Mathematics Standards Documents." Digital Archive @ GSU, 2013. http://digitalarchive.gsu.edu/msit_diss/110.
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Since the mid-20th century in the United States, there have been several reform movements within mathematics education; each movement has been subject to its own unique socio-cultural and -political forces. The National Council of Teachers of Mathematics’ (NCTM) Standards documents—Curriculum and Evaluation Standards for School Mathematics (1989), Professional Standards for Teaching Mathematics (1991), Assessment Standards for School Mathematics (1995), and Principles and Standards for School Mathematics (2000)—not only represent the most recent of these reform movements but also the most enduring. Collectively, these documents have formed a discourse (cf. Foucault, 1969/1972)—Standards-based mathematics education—that has guided mathematics education through the 1990s and beyond. This study uses Foucaultian archaeological and genealogical methods (cf. Foucault, 1969/1972, 1975/1995) to explore Standards-based mathematics education as a “discursive formation” (Foucault, 1969/1972) and the complex power relations (cf. Foucault, 1976/1990) that made it possible for the formation to become The discourse of school mathematics, making others impossible. Data for the exploration includes the Standards documents, earlier histories of the NCTM Standards moment, scholarly and policy literature surrounding the NCTM documents, and oral history interviews with several of the writers of the NCTM documents. The study presents a historical narrative of mathematics education in the 20th century that both contextualizes Standards-based mathematics education and problematizes NCTM’s efforts; a key focus is the strategy that NCTM deployed to maintain the viability of Standards-based mathematics education as a discourse. Foucault’s (1984) “author function” is used to address the ways that the writers, externalities, and NCTM as an organization “authored” the Standards documents. The study concludes arguing that perpetuating the discursive formation of Standards-based mathematics education is neither good nor bad but only dangerous; therefore, it requires mathematics educators to maintain a sense of pessimistic activism related to present and future reform efforts (cf. Foucault, 1983/1997).
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Moraes, Carlos Roberto de [UNESP]. "Uma história da lógica no Brasil." Universidade Estadual Paulista (UNESP), 2007. http://hdl.handle.net/11449/102163.
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moraes_cr_dr_rcla.pdf: 3736090 bytes, checksum: bff4869f93df679fa3b0a827a8a642f5 (MD5)Pretendemos mostrar o desenvolvimento da lógica matemática no Brasil focando principalmente nos sessenta anos iniciais do século XX apresentando obras e estudiosos que contribuíram para a consolidação e o desenvolvimento da lógica como um campo de pesquisa no Brasil. Abordaremos três obras que acreditamos serem relevantes na história da lógica no Brasil: As Ideas Fundamentaes da Matemática, de Manuel Amoroso Costa, publicada em 1929; Elementos de Lógica Matemática, de Vicente Ferreira da Silva, publicada em 1940 e O Sentido da Nova Lógica, de Willian Van Orman Quine, publicada em 1944. A lógica apresenta um salto qualitativo a partir do final dos anos 50, quando dois centros se destacam: um na Universidade de São Paulo (USP), em São Paulo, com o Prof. Edison Farah e outro na antiga Faculdade Nacional de Filosofia, no Rio de Janeiro. Neste trabalho, dedicaremos especial atenção aos pioneiros do grupo de São Paulo, que, no final da década de 50 reuniam-se sob a liderança do Prof. Edison Farah em um grupo de estudiosos de lógica e fundamentos da matemática do qual fizeram parte os professores Benedito Castrucci, Newton Carneiro Affonso da Costa, Mario Tourasse Teixeira e Leonidas Hegenberg que se reuniam em seminários no Departamento de Matemática da Universidade de São Paulo.
We intend to present the development of mathematical logic in Brazil focusing mainly in the first six decades of the twenty century, presenting studies and researchers who contributed to consolidate and develop the logic as a field of research in Brazil. We will discuss about three books we believe that are more relevant in the History of Logic in Brazil: As Ideas Fundamentais da Matemática, by Manuel Amoroso Costa, published in 1929; Elementos de Lógica Matemática, by Vicente Ferreira da Silva, published in 1940; and O Sentido da Nova Lógica, by Willian Van Orman Quine, published in 1944. The logic presents a qualitative upgrade by the end of the fifties, when two centers obtain a great highlight: one at University of Sao Paulo (USP), in Sao Paulo city, with Professor Edison Farah and the other one at the former National Faculty of Philosophy, in Rio de Janeiro city. In the present study, we will pay special attention to the pioneers of the Sao Paulo group that, in the end of the fifty decade, upon the leadership of Professor Edison Farah, organized a group of researchers in logic and fundamentals of mathematics. Professors Benedito Castrucci, Newton Carneiro Affonso da Costa, Mario Tourasse Teixeira, and Leonidas Hegenberg took part of this group that used to have their meetings and seminars in the Department of Mathematics at University of Sao Paulo.
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Abur, Diana, and Emma Söderberg. "Fem pedagogers tankar kring matematikundervisningens utveckling i relation till styrdokumenten." Thesis, University of Gävle, Department of Education and Psychology, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-6175.
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Syftet var att studera matematikundervisningens utveckling genom att beskriva styrdokumentens, läroplanernas och kursplanernas påverkan på undervisningen. Bakgrunden till detta examensarbete är det faktum att många elever uppfattar skolmatematiken som komplicerad och ointressant och att de inte når de uppsatta målen. Metoden som användes var en litteraturgenomgång där matematikundervisningens utveckling studerades. Genom att även utföra en kvalitativ intervjuundersökning kunde fem yrkeserfarna pedagoger beskriva hur de uppfattar denna utveckling och hur det visar sig i deras matematikundervisning. Studien visar att i takt med att samhället utvecklas och förändras utvecklas också styrdokumenten. Historiskt sett har det visat sig att matematik haft andra ändamål än endast att undervisa och lära. Den har alltid kopplats ihop med något som ska uppfylla samhällets behov såsom att förbereda för fortsatta studier, ge en god grund för studier i andra ämnen och skapa dugliga samhällsmedborgare. De kvalitativa intervjuerna visar att lärarnas arbetsformer och undervisning påverkats av styrdokumentens skiftningar. Skolmatematiken har blivit mer kreativ och konkret och man vill komma utanför matematikboken genom att låta eleverna arbeta med vardagsmatematik och problemlösning. Litteraturgenomgången och intervjuerna visar att det inte finns något enkelt svar på när matematikundervisning utvecklas och hur man kan förändra arbetsmetoder i undervisningen därför att det finns andra faktorer som kan påverka. Det handlar inte bara om införandet av nya läroplaner, utan även om att hitta arbetsätt som anpassas efter elevernas förutsättningar för bästa möjliga resultat för både eleverna och samhället.
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Toledo, José do Carmo. "Uma história do processo de institucionalização da área de Análise Matemática no Brasil /." Rio Claro : [s.n.], 2008. http://hdl.handle.net/11449/102136.
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Orientador: Sergio Roberto NobreBanca: Ligia Arantes Sad
Banca: Simone Mazzini Bruschi
Banca: Carlos Henrique Barbosa Gonçalves
Banca: Antonio Vicente Marafioti Garnica
Possui anexo cd-rom com o Corpus documental da tese
Resumo: Este trabalho - uma investigação inserida no campo da História da Matemática argumenta em favor da existência, no Brasil, de uma tradição em pesquisa na área de Análise Matemática e propõe uma narrativa historiadora sobre o processo de institucionalização dessa área no país. Algumas práticas sociais no âmbito da comunidade de analistas brasileiros são enfatizadas: umas, por terem sido cruciais para os processos locais de constituição e autonomização desse campo científico; outras, por conferirem à Análise, o status de área institucionalizada no país.
Abstract: This work - an investigation inserted in the field of the History of Mathematics argues in favour of a tradition in research in the area of Mathematical Analysis in Brazil and proposes a narrative history about the process of institutionalization of this area here. Some social practices within the community of brazilian analysts are emphasized: one, because they have been crucial to the constitution and autonomization of this scientific field in Brazil; others, by giving to the Analysis the status of an institutionalized area in this country.
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Alqhtani, Manal. "Methods for accurate evaluation of population abundance from ecological data." Thesis, University of Birmingham, 2018. http://etheses.bham.ac.uk//id/eprint/8740/.
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An accurate evaluation of total population density is required in many ecological and biological field. To protect crops from pest attacks, the population density of pests must be evaluated adequately. Accurate information obtained as a result of trapping in ecological monitoring is beneficial for decision-making purposes when implementing a control action. In pest monitoring, a classic technique of evaluating density based on a statistical method may result in poor accuracy. Accuracy can be optimised by applying alternative numerical integration methods to the problem. We explain how insufficient information regarding population density negatively affects the accuracy of estimation. Consequently, a coarse grid problem arises where the numerical integration methods are no longer valid. The evaluation of integration error is now a random variable and the probabilistic approach is used, due to the uncertainty in sampling data. In this thesis several population models have been considered to explain that the value of correlation coefficient on a coarse sampling grid is lost even if the true value is close to one. Phenomenon of ghost synchronization has been observed when the value of correlation coefficient on a coarse sampling grid is close to one but in reality the dynamics are not correlated.
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Ribeiro, Dulcyene Maria. "A Obra "Lógica racional, geométrica e analítica" (1744) de Manoel de Azevedo Fortes (1660-1749) : um estudo das possíveis contribuições para o desenvolvimento educacional luso-brasileiro /." Rio Claro : [s.n.], 2003. http://hdl.handle.net/11449/91126.
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Orientador: Sérgio Roberto NobreBanca: Luís Miguel Nunes Carolino
Banca: Rosa Lucia Sverzut Baroni
Resumo: Este trabalho realiza um estudo histórico-analítico da obra Lógica Racional, Geométrica e Analítica, publicada em Lisboa no ano de 1744, de autoria do engenheiro militar Manoel de Azevedo Fortes (1660-1749), com o objetivo de identificar sua importância para o desenvolvimento da matemática em Portugal e no Brasil, bem como quais foram suas possíveis contribuições para o desenvolvimento educacional luso-brasileiro. A obra apresenta vários aspectos originais, sendo considerada a primeira escrita no idioma português, trazendo concepções da então filosofia moderna e apresentando questões da álgebra e, uma das pioneiras a tratar da geometria. Manoel de Azevedo Fortes teve sua formação em outros países europeus, regressando a Portugal com moral elevada, o que lhe valeu uma cadeira de matemática na Academia Militar da Fortificação da corte portuguesa em 1695. O estudo tem como base uma fonte primária que é a própria obra em si, mas outras fontes também são consideradas, a fim de realizar uma contextualização da época na qual o autor viveu, refinando ainda mais seus dados biográficos.
Abstract: This is a analitic-historical study of the work "Logica Racional, Geometrica e Analitica", published in Lisban in 1744, by the military engineer Manoel de Azevedo Fortes (1660-1749), with the purpose of identifying its importance for the development of mathematics in Portugal and in Brazil as well as wich were its possible contribuitions for the luso-brasilian educational development. The book presents several original aspects, being considered the first written work in Portuguese language, bringing conceptions of the modern philosophy of the time and presenting algebra questions and, one of the pioneers on geometry. Manoel de Azevedo Fortes had his formation in other European countries, returning to Portugal with high moral, which earned him chair of mathematics in the Military Academy of Fortification of the Portuguese court in 1695. The study is based on a primary source which is the boock itself, but other sources also are considered, with the purpose of performing a contextualization of the time in which the author lived, refining even more his biografic informations.
Mestre
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Ілляшенко, Валентина Яківна, and Valentyna Ya Illiashenko. "З історії математики у Волинському національному університеті імені Лесі Українки." Thesis, Інститут математики НАН України, 2012. http://esnuir.eenu.edu.ua/handle/123456789/1472.
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Ілляшенко Валентина Яківна - кандидат фізико-математичних наук, доцент кафедри геометрії і алгебри Східноєвропейського національного університету імені Лесі УкраїнкиДоповідь присвячена розвитку історії математики Волинського національного університету імені Лесі Українки. The report by the example of the development history of mathematics of Lesya Ukrainka Volyn National University.
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Riggs, Laurie Jan. "Polynomial equations and solvability: A historical perspective." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1186.
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Gambera, Artur Rezzieri. "História da Integral de Lebesgue /." Rio Claro, 2017. http://hdl.handle.net/11449/151161.
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Orientador: Henrique LazariBanca: Irineu Bicudo
Banca: Carlos Roberto de Moraes
Resumo: Esse trabalho consiste em um relato histórico do surgimento do conceito de integral proposto por Henri Léon Lebesgue (1875-1941). A pesquisa se insere no campo da História da Matemática e é focada na análise e discussão de duas publicações de Lebesgue: o artigo Sur une généralisation de l'intègrale dèfinie publicado em 1901 e sua tese de doutorado Intégrale, Longueur, Aire publicada em 1902. Na primeira publicação Lebesgue apresenta pela primeira vez sua ideia de integral e na segunda discute mais profundamente suas ideias acerca da noção de medida e integração
Abstract: This work consists in a historical report of the appearance of the concept of integral proposed by Henri Léon Lebesgue (1875-1941). The research is inserted on the History of Mathematics field and is focused on the analysis and discussions of two publications of Lebesgue: the paper Sur une généralisation de l'intègrale dèfinie published in 1901 and his doctoral thesis Intégrale, Longueur, Aire published in 1902. In the first publication Lebesgue presents for the first time his idea about integrals and in the second discuss more deeply his ideas about the notion of measure theory and integration
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Lewis, Elizabeth Faith. "Peter Guthrie Tait : new insights into aspects of his life and work : and associated topics in the history of mathematics." Thesis, University of St Andrews, 2015. http://hdl.handle.net/10023/6330.
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In this thesis I present new insights into aspects of Peter Guthrie Tait's life and work, derived principally from largely-unexplored primary source material: Tait's scrapbook, the Tait–Maxwell school-book and Tait's pocket notebook. By way of associated historical insights, I also come to discuss the innovative and far-reaching mathematics of the elusive Frenchman, C.-V. Mourey. P. G. Tait (1831–1901) F.R.S.E., Professor of Mathematics at the Queen's College, Belfast (1854–1860) and of Natural Philosophy at the University of Edinburgh (1860–1901), was one of the leading physicists and mathematicians in Europe in the nineteenth century. His expertise encompassed the breadth of physical science and mathematics. However, since the nineteenth century he has been unfortunately overlooked—overshadowed, perhaps, by the brilliance of his personal friends, James Clerk Maxwell (1831–1879), Sir William Rowan Hamilton (1805–1865) and William Thomson (1824–1907), later Lord Kelvin. Here I present the results of extensive research into the Tait family history. I explore the spiritual aspect of Tait's life in connection with The Unseen Universe (1875) which Tait co-authored with Balfour Stewart (1828–1887). I also reveal Tait's surprising involvement in statistics and give an account of his introduction to complex numbers, as a schoolboy at the Edinburgh Academy. A highlight of the thesis is a re-evaluation of C.-V. Mourey's 1828 work, La Vraie Théorie des quantités négatives et des quantités prétendues imaginaires, which I consider from the perspective of algebraic reform. The thesis also contains: (i) a transcription of an unpublished paper by Hamilton on the fundamental theorem of algebra which was inspired by Mourey and (ii) new biographical information on Mourey.
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Shenfield, Stephen. "The mathematical-statistical methodology of the contemporary Soviet family budget survey." Thesis, University of Birmingham, 1985. http://etheses.bham.ac.uk//id/eprint/703/.
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The study describes and assesses the mathematical-statistical methodology of the contemporary Soviet Family Budget Survey, both in regard to the sample design and in regard to the processing and analysis of the survey data. A wide range of methodological deficiencies are identified, accounting for the widely recognised unreliability of the data produced. The problems of using the survey data in various fields of policy-making, planning and research are explored. It is shown that Soviet data-users where possible avoid relying on data from this survey. The historical and social factors influencing the methodology of the Family Budget Survey are discussed. The most important causes of the deficient methodology are found to be the neglect of mathematical statistics and sampling theory in Soviet socio-economic statistics, originating in the Stalin period, and the bureaucratic inertia of the Central Statistical Administration.