Página 9 dos resultados de 228881 itens digitais encontrados em 0.156 segundos

Juros em livros didaticos de matematica no Maranhão do Seculo XIX; Interest in textbooks of mathematics in Maranhão in the Nineteenth century

Waleria de Jesus Barbosa Soares
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 14/12/2009 Português
Relevância na Pesquisa
35.44%
O presente trabalho investiga os livros didáticos de matemática, produzidos no Maranhão ou publicados por maranhenses, durante o século XIX. Para tal pesquisa, considera as produções que tratavam de juros, visto ser este conteúdo parte integrante do ensino da matemática que preparava os alunos já no ensino primário, para o ofício de comerciante. Toma por base então, a obra ?Primeiras Noções de Arithmética para o uso dos alunos das escolas de ensino primário", de Ayres de Vasconcellos Cardoso Homem, considerada a mais antiga, tendo como norte a pergunta: como era tratado o estudo de juros no livro e em outras produções maranhenses? A metodologia qualitativa analisa a partir de aportes teóricos de Marc Bloch, Gert Schubring, André Chervel, Roger Chartier e Allan Chopin, documentos de fontes primárias do século XIX, da província do Maranhão (pesquisa in loco) e de Portugal (via e-mail). Considera o contexto histórico na qual a obra foi escrita; dados biográficos de Ayres de Vasconcellos Cardoso Homem e a aritmética por ele apresentada no livro; além de um esboço histórico sobre os juros com enfoque em Nicolo Fontana de Brescia, o Tartaglia; Alexis Clairaut; e, Leonhard Paul Euler. Compara a obra de Homem com outros didáticos publicados no Maranhão ou escritos por maranhenses...

Impacto do Programa de Formação Contínua em Matemática para professores de 1º ciclo do ensino básico no seu conhecimento didático; The impact of the Lifelong Training Program in Mathematics on the didactic knowledge of elementary school teachers

Alves, Maria Palmira; Fernandes, José António; Silva, Nuno Miguel
Fonte: Unisinos Publicador: Unisinos
Tipo: Artigo de Revista Científica
Publicado em //2014 Português
Relevância na Pesquisa
35.44%
Em Portugal, o Programa de Formação Contínua de Matemática para professores do 1º ciclo (do 1º ao 4º ano de escolaridade) tem por meta principal promover o conhecimento didático dos professores, tendo em vista o sucesso escolar dos alunos em matemática. No presente estudo, inquiriram-se 197 professores generalistas do 1º ciclo do ensino básico, que participaram no programa durante o ano letivo de 2007/2008, sobre as suas percepções acerca de várias dimensões do ensino e da aprendizagem da matemática e da sua participação no programa. Em termos de resultados, salientam-se, do antes para o depois da formação, algumas mudanças que vão no sentido das recomendações atuais para o ensino da matemática, que parecem requerer um maior tempo de formação tendo em vista o aprofundamento do conhecimento didático.; In Portugal, the Lifelong Training Program in Mathematics for elementary school teachers (from the 1st to the 4th grade) is primarily designed to promote the teachers’ didactic knowledge in order to improve the pupils’ performances in mathematics. In the present study, 197 generalist elementary school teachers who had participated in the program during the 2007/2008 school year were inquired about their perceptions concerning various dimensions of the teaching and learning of mathematics and about their participation in the program. Concerning results...

Existence in a way : resolving a tension in Aristotle’s philosophy of mathematics

Cadavid, Eva Maria (1968 - ); Modrak, Deborah K. W.
Fonte: University of Rochester Publicador: University of Rochester
Tipo: Tese de Doutorado Formato: Number of Pages:ix, 171 leaves
Português
Relevância na Pesquisa
35.44%
Thesis (Ph. D.)--University of Rochester. Dept. of Philosophy, 2010.; There is no one Aristotelian text devoted to mathematics. Instead, Aristotle’s view can be found in Posterior Analytics, Metaphysics, De Anima, and Physics. These texts show that Aristotle believed we could have mathematical knowledge and that mathematics is an ideal science. Aristotle’s views on the ontology of mathematical objects are less clear. He says in Metaphysics XIII.2 that mathematical objects exist neither separately from nor in sensible objects. He concludes that they either do not exist or have a qualified existence. Aristotle’s comments on mathematical objects have given rise to different interpretations. These include accusations of naïveté about mathematics, incoherence, and even a Platonic ontology about mathematics. In the past 30 years, the work of scholars such as Ian Mueller, Julia Annas, and Jonathan Lear have challenged these interpretations. Their work calls attention to the need to clarify Aristotle’s comments on the existence of mathematical objects. This dissertation analyzes the interpretations of Mueller, Annas, and Lear, and building from them, defends a fictionalist account of mathematical objects in Aristotle. There is an apparent inconsistency in Aristotle that arises from his claim that there is mathematical knowledge...

A Expressão da Compreensão de Alunos com Dificuldades de Aprendizagem em Matemática ao Trabalhar com o Material Cuisenaire; Expressive comprehensions students with learning dificulties im mathematics teaching with the cuisenaire material

LEITE, Lusitonia da Silva
Fonte: Universidade Federal de Goiás; BR; UFG; Mestrado em Educação em Ciências e Matemática; Ciências Exatas e da Terra Publicador: Universidade Federal de Goiás; BR; UFG; Mestrado em Educação em Ciências e Matemática; Ciências Exatas e da Terra
Tipo: Dissertação Formato: application/pdf
Português
Relevância na Pesquisa
35.44%
Concrete materials are part in the searching of learning methods that allow a better understanding in the learning of mathematics. In this work, I research how do students with difficulties in learning express Mathematics comprehension when they deal with the Cuisenaire Material in a learning situation, and what do they understand from it? The investigation basis was the Experiencing Mathematics in Elementary School project developed in CEPAE (Center of Teaching and Research Applied in the Education of UFG). The data collection happened in five meetings/classes performing activities on the basic arithmetic operations. The participants are twelve students from 5º e 6º grades who have a low learning performance, according to their mathematics teachers. In terms of procedure, we used the qualitative research on the perspective of the phenomenological approach. Once a contact was established among the students speech, my interpretations on their speeches and the theories used to support my interpretations, I think this material revealed itself significant and the students demonstrated comprehension on the basic arithmetic operations. Seeing, thinking, combining parts to the numbers, comparing them, putting them in order, compounding and decompounding them...

Redes académicas generadas por las tesis doctorales de educación matemática en España; Academic networks generated by spanish phd theses on mathematics education

Maz-Machado, Alexander; Bracho-López, Rafael; Torralbo-Rodríguez, Manuel; Gutiérrez-Arenas, Mª Pilar; Jiménez-Fanjul, Noelia; Adamuz-Povedano, Natividad
Fonte: Universidade de Múrcia Publicador: Universidade de Múrcia
Tipo: Artigo de Revista Científica Formato: application/pdf
Português
Relevância na Pesquisa
35.44%
Introducción. Se presenta un estudio sobre las redes académicas generadas por las tesis doctorales de Educación Matemática leídas en España desde el año 1976 hasta el 2009. Propósito y objetivos. El propósito es identificar los posibles colegios invisibles de colaboración académica en la disciplina de Educación Matemática.Metodología. Se ha recuperado información de 328 tesis listadas en trabajos previos, la base de datos de tesis doctorales TESEO, las páginas web de los departamentos de Educación Matemática y los boletines de la Sociedad Española de Investigación en Educación Matemática (SEIEM), así como consulta a doctores del área. Mediante técnicas bibliométricas, se realiza un análisis de redes de colaboración.Resultados. El estudio revela sesgo en el género de los directores y que la participación en los tribunales de tesis no tiene correlación con las tesis dirigidas. También se observan cambios producidos en las direcciones de tesis respecto a trabajos anteriores sobre el mismo tema además de aportar información más actualizada.; Introduction. We present a study of the academic networks generated by PhD theses on mathematics education read in Spain from 1976 until 2009. Objectives. The main purpose is to identify "invisible colleges" for academic collaboration in Educational Mathematics. Method. Data has been recovered from 328 theses listed in previuos studies...

Rendimiento en matemáticas y actitud hacia la materia en centros inclusivos: estudio en la comunidad de Madrid; Mathematics performance and attitude towards mathematics in inclusive schools: a study in the region of Madrid

García-García, Mercedes; Biencinto-López, Chantal; Carpintero-Molina, Mª Elvira; Núñez-del-Río, María Cristina; Arteaga Martínez, Blanca
Fonte: Universidade de Múrcia Publicador: Universidade de Múrcia
Tipo: Artigo de Revista Científica Formato: application/pdf
Português
Relevância na Pesquisa
35.44%
This article deals with the problem of low achievement in instrumental subjects such as Mathematics from the perspective of Adaptive Theory. It was assumed that schools, aware of diversity in their classrooms, would plan educational strategies accordingly in order to cater for different students, thus achieving better results than schools which focus on groups as a whole. Using a quasi-experimental research design, three types of interventions were compared in terms of the degree of inclusiveness of their projects. The sample comprised 437 second year Compulsory Secondary Education students from different schools in Madrid. Mathematics performance and attitude towards the subject were measured. Contrastive analyses were carried out before and after the intervention. Results show differences in mathematics performance in favour of inclusive schools; however, no improvement in the attitude toward the subject was observed.; Este artículo aborda el problema del bajo rendimiento en matemáticas desde la Teoría Adaptativa. Se parte del supuesto de que una escuela consciente de la diversidad en las aulas planificará estrategias educativas adaptadas a las diferencias de los estudiantes, logrando mejores resultados que los centros que proyectan únicamente para el grupo. Mediante un diseño de investigación cuasiexperimental...

A review of research trends in mathematics teacher education

S??nchez, Mario
Fonte: Universidade de Granada Publicador: Universidade de Granada
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
35.44%
This article presents a literature review in the field of mathematics teacher education research. The review focuses on identifying the main research trends in this field, that is, the main research topics that the mathematics teacher educators??? community is currently addressing, and the main theoretical concepts used to study these topics. One of the contributions of the review is that it identifies new research trends that have not been previously reported. Some of these trends are online mathematics teacher education, and the design and role of tasks in mathematics teacher education.; Este art??culo presenta una revisi??n de la literatura en el campo de la investigaci??n en formaci??n de profesores de matem??ticas. La revisi??n se centra en identificar las principales tendencias de investigaci??n en este campo, es decir, los principales temas de investigaci??n que la comunidad de formadores de profesores est?? abordando actualmente, as?? como los principales conceptos te??ricos usados para estudiar esos temas. Una de las contribuciones de esta revisi??n es que se identifican tendencias de investigaci??n que no han sido reportadas previamente. Algunas de estas tendencias son la formaci??n online de profesores de matem??ticas y el dise??o y rol de las tareas en la formaci??n de profesores de matem??ticas.

Mathematics, computers in mathematics, and gender: public perceptions in context

Forgasz, Helen J.; Leder, Gilah C.
Fonte: Grupo de Investigaci??n Did??ctica de la Matem??tica: Pensamiento Num??rico, (FQM-193) Publicador: Grupo de Investigaci??n Did??ctica de la Matem??tica: Pensamiento Num??rico, (FQM-193)
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
35.44%
In Australia, national tests of mathematics achievement continue show-ing small but consistent gender differences in favor of boys. Societal views and pressures are among the factors invoked to explain such subtle but persistent differences. In this paper we focus directly on the beliefs of the general public about students??? learning of mathematics and the role played by computers, and then we compare the findings with data previously gathered from students. Although many considered it inappropriate to differentiate between boys and girls, gender based stereotyping was still evident.; En Australia, los test nacionales del logro matem??tico contin??an mos-trando peque??as pero consistentes diferencias de g??nero en favor de los chicos. Las presiones y visiones sociales est??n entre los factores invocados para explicar tales diferencias sutiles pero persistentes. En este trabajo nos centramos directamente en las creencias del p??blico en general acerca del aprendizaje matem??tico de los estudiantes y del papel desempe??ado por los ordenadores, y despu??s comparamos las conclusiones con datos previamente obtenidos de los estudiantes. Aunque muchos consideran inapropiado diferenciar entre ni??os y ni??as, todav??a son evidentes estereotipos basados en el g??nero.

The impact of standards -based practices in mathematics on the achievement of low -performing students

Anglin, Marcus V
Fonte: FIU Digital Commons Publicador: FIU Digital Commons
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
35.44%
This study examined standards-based mathematics reform initiatives to determine if they would improve student achievement on the part of low-performing students. New curricula, the Carnegie Learning Cognitive Tutor®, were provided for algebra and geometry students. The new instructional strategy relied on both the teacher-led instruction and the use of computers to differentiate instruction for individual students. Mathematics teachers received ongoing professional development to help them implement the new curricula. In addition, teachers were provided with ongoing support to assist them with the transformation of the learning environments for students using standards-based practices. This quasi-experimental (nonrandomized) study involved teachers in two matched urban high schools. ^ Analyses (ANCOVAs) revealed that the experimental group with an appropriately implemented program had significantly higher learning gains than the comparison group as determined by the students' 2007 mathematics Developmental Scale Score (DSS). In addition, the experimental group's adjusted mean for the second interim mathematics assessment was significantly higher than the comparison group's mean. The findings support the idea that if the traditional curriculum is replaced with standards-based curriculum...

The effectiveness of an intelligent tutoring system on the attitude and achievement of developmental mathematics students in a community college

Burton, Linda Kramer
Fonte: FIU Digital Commons Publicador: FIU Digital Commons
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
35.44%
This study examined the effectiveness of intelligent tutoring system instruction, grounded in John Anderson's ACT theory of cognition, on the achievement and attitude of developmental mathematics students in the community college setting. The quasi-experimental research used a pretest-posttest control group design. The dependent variables were problem solving achievement, overall achievement, and attitude towards mathematics. The independent variable was instructional method.^ Four intact classes and two instructors participated in the study for one semester. Two classes (n = 35) served as experimental groups; they received six lessons with real-world problems using intelligent tutoring system instruction. The other two classes (n = 24) served as control groups; they received six lessons with real-world problems using traditional instruction including graphing calculator support. It was hypothesized that students taught problem solving using the intelligent tutoring system would achieve more on the dependent variables than students taught without the intelligent tutoring system.^ Posttest mean scores for one teacher produced a significant difference in overall achievement for the experimental group. The same teacher had higher means...

Teachers' professional learning within communities of mathematics-for-teaching practice

Fleming, Glynnis
Fonte: Brock University Publicador: Brock University
Português
Relevância na Pesquisa
35.44%
Ontario bansho is an emergent mathematics instructional strategy used by teachers working within communities of practice that has been deemed to have a transformational effect on teachers' professional learning of mathematics. This study sought to answer the following question: How does teachers' implementation of Ontario bansho within their communities of practice inform their professional learning process concerning mathematics-for-teaching? Two other key questions also guided the study: What processes support teachers' professional learning of content-for-teaching? What conditions support teachers' professional learning of content-for-teaching? The study followed an interpretive phenomenological approach to collect data using a purposive sampling of teachers as participants. The researcher conducted interviews and followed an interpretive approach to data analysis to investigate how teachers construct meaning and create interpretations through their social interactions. The study developed a model of professional learning made up of 3 processes, informing with resources, engaging with students, and visualizing and schematizing in which the participants engaged and 2 conditions, ownership and community that supported the 3 processes. The 3 processes occur in ways that are complex...

Inovação e Resistência: Uma análise do ensino da Matemática em uma escola pública; Innovation and Resistance: An analysis of mathematics teaching in a public school

RIBEIRO, Dilson Ferreira
Fonte: Universidade Federal de Pelotas; Educação; Programa de Pós-Graduação em Ensino de Ciências e Matemática; UFPel; BR Publicador: Universidade Federal de Pelotas; Educação; Programa de Pós-Graduação em Ensino de Ciências e Matemática; UFPel; BR
Tipo: Dissertação Formato: application/pdf
Português
Relevância na Pesquisa
35.44%
This thesis aims to develop a study that allows understanding why some math teachers are tough on the possibilities of changes that occur in their area of expertise. Changes that establish a relation between innovation and teaching methodology, through the possibility of diversifying its evaluation instruments. It's made a study of factors considered responsible for teachers' attitudes, contrary to innovation in teaching mathematics as their working conditions or their experience of the classroom throughout his career, beginning even in their basic training. For this, we made an approach relating the strength and innovation, Teaching Traditional and Innovative Education, through the study of Organizations National Curriculum of Secondary Education, from the changes proposed by the state government of Rio Grande do Sul in relation to basic education. The field research was empirically chosen the College Municipal Pelotense, place of work of the author, with the participation of seven mathematics teachers of high school. Respondents discussed the possibilities of change in mathematics education from meetings that provided activities. These meetings were offered in the second half of 2012 with its height at the beginning of the school year of 2013 with the implementation of a teaching methodology different from that used by teachers and stood as the final product of this dissertation. Amid the conclusions is possible to highlight some factors that lead to resistance changes in the teaching of mathematics...

O Intuitivo e o Lógico no Conhecimento Matemático: análise de uma proposta pedagógica em relação a abordagens filosóficas atuais e ao contexto educacional da matemática; The Intuitive and the Logical in Mathematical Knowledge: analysis of a pedagogical proposal from a viewpoint of new philosophical approaches and in the educational context of mathematics

MENEGHETTI, Renata Cristina Geromel
Fonte: UNESP-DEPT MATHEMATICA Publicador: UNESP-DEPT MATHEMATICA
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
35.44%
In this paper, we consider Meneghetti & Bicudo's proposal (2003) regarding the constitution of mathematical knowledge and analyze it with respect to the following two focuses: in relation to conceptions of mathematical knowledge following the fundamentalist crisis in mathematics; and in the educational context of mathematics. The investigation of the first focus is done analyzing new claims in mathematical philosophy. The investigation of the second focus is done firstly via a theoretical reflection followed by an examination of the implementation of the proposal in the process of development of didactic materials for teaching and learning Mathematics. Finally, we present the main results of the application of one of those materials.

Professoras das séries iniciais do ensino fundamental e as orientações curriculares oficiais para o ensino de matemática: um estudo dessa relação; Teachers of the initial grades of elementary school and the official curriculum guidelines for the teaching of Mathematics: a study of this relationship

Poggetti, Liane Geyer
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 20/05/2014 Português
Relevância na Pesquisa
35.44%
O presente estudo, de natureza qualitativa, foi desenvolvido entre 2012 e 2013, com professoras das séries iniciais do Ensino Fundamental, de uma escola da rede estadual de ensino de São Paulo. Adotando como referência o ponto de vista das professoras, buscou-se discutir o papel, em sua prática de ensino da Matemática, das concepções e do modo de ensinar sugeridos pelos programas curriculares oficiais, e dos saberes e concepções decorrentes de sua própria história, englobando sua formação inicial e sua experiência docente; discutiu-se, também, o papel da formação continuada, que recebem na instituição em que lecionam, cujo propósito principal é prepará-las para lidar com as orientações oficiais para o ensino de Matemática. O desenvolvimento da pesquisa teve como referência estudos como os de Fiorentini (1995, 2003), Abreu (1995, 2000), Curi (2005), Garcia Blanco (2003), Ponte (1992, 1999, 2012), Nacarato, Mengali e Passos (2009), Canavarro (2003), Tardif (2010, 2012), Nóvoa (2012), Chacon (2003) e Sacristán (1998), dentre outros, e a utilização de questionários, entrevistas e aplicação de um caso de ensino. Esses instrumentos de coleta de dados tiveram como objetivo captar as concepções e ideias dos sujeitos sobre a Matemática e seu ensino...

Perscrutando diários de aulas de matemática do estágio supervisionado da licenciatura em matemática : reorientando histórias e investigações; Peering into class diaries about a student teaching course in a preparation of mathematics teachers program : reorienting stories and investigations

Marcos Antonio Gonçalves Júnior
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 23/03/2015 Português
Relevância na Pesquisa
35.44%
De 2008 a 2010, recebi, em minhas aulas de matemática, alunos de um curso de licenciatura que cursavam o Estágio Supervisionado II. Supervisionei-os em seu estágio e orientei-os em seu Trabalho Final de Curso. Tal processo me levou a desenvolver com eles um trabalho conjunto, olhando nossas aulas numa perspectiva de investigação-ação e colaboração. Assim, juntos, escrevemos um diário de aula descritivo e reflexivo sobre as aulas em todas as etapas do estágio: observação, semirregência e regência. Passados alguns anos, passei a perscrutar esses diários de aula, procurando investigar esse processo de formação, narrando-o, contando sobre o processo de constituição identitária dos futuros professores, descrevendo o trivial simples do dia a dia da sala de aula, bem como as tensões da prática de colaborar e investigar a própria prática. Em certa altura, por figurar como personagem nas histórias que contava, dei-me conta de que não investigava os estagiários, mas, sim, a mim mesmo, minhas contradições, minhas identidades no papel de professor de matemática, de supervisor (formador de professores) e de pesquisador em Educação Matemática. Desse modo, desenvolvi uma investigação sobre mim mesmo, por meio de uma pesquisa narrativa em que meus "eus" são objeto de estudo. Por meio de uma conversa comigo mesmo...

Open-ended tasks in the promotion of classroom communication in mathematics

Viseu, Floriano; Oliveira, Inês Bernardo
Fonte: Universidade do Minho Publicador: Universidade do Minho
Tipo: Artigo de Revista Científica
Publicado em //2012 Português
Relevância na Pesquisa
35.44%
Mathematics programmes in basic education are currently undergoing reform in Portugal. This paper sets out to see how teachers are putting the new guidelines for the teaching of mathematics into practice, with particular emphasis on maths communication in the classroom. To achieve this, an experiment in teaching the topic 'Sequences and Regularities' with open-ended tasks, using a qualitative and interpretative approach, is reported. Data were collected during two class observations, from two interviews and by analysing the activities of the students. An exploratory task was chosen in the first lesson and a investigative one in the second. One month separated the two lessons, and during this time the teacher read and discussed texts on mathematics communication. Observation of the first lesson showed that the communication in the classroom was mostly focused on the teacher, which provided little student-student and student-class interaction. In the second observed lesson, the teacher changed the attention she paid to what each student said and did, encouraging the students to ask each other and encouraged student-class and the student-student communication.

Teachers' and students' views and attitudes towards a new mathematics curriculum: A case study

Ponte, João Pedro da; Matos, João Filipe; Guimarães, Henrique Manuel; Leal, Leonor Cunha; Canavarro, Ana Paula
Fonte: Universidade de Lisboa Publicador: Universidade de Lisboa
Tipo: Artigo de Revista Científica
Publicado em //1994 Português
Relevância na Pesquisa
35.44%
The education system in Portugal is in the midst of a period of intensive reform. This paper describes the findings of a qualitative case study focusing on the views and attitudes of teachers and students participating in a pilot curriculum development programme stressing active methodologies and group work, conducted by the Ministry of Education In particular it discusses their views and attitudes about mathematics, mathematics teaching and curriculum innovation. The teachers were found to struggle with a contradiction: whilst they approved the new orientations, which were seen as adequate and innovative, they complained strongly about the design and implementation of the programme Students had a generally positive attitude towards mathematics, although there were differences among them. The 7th graders were satisfied with their mathematics classes and with the new curriculum. The 10th graders did not consider the changes as significant in themselves, but expressed concern for their academic progress.

Idempotent (Asymptotic) Mathematics and the Representation Theory

Litvinov, Grigori; Maslov, Viktor; Shpiz, Grigori
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/06/2002 Português
Relevância na Pesquisa
35.44%
A brief survey of some basic ideas of the so-called Idempotent Mathematics is presented; an "idempotent" version of the representation theory is discussed. The Idempotent Mathematics can be treated as a result of a dequantization of the traditional mathematics over numerical fields in the limit of the vanishing "imaginary Planck constant"; there is a correspondence, in the spirit of N. Bohr's correspondence principle, between constructions and results in traditional mathematics over the fields of real and complex numbers and similar constructions and results over idempotent semirings. In particular, there is an "idempotent" version of the theory of linear representations of groups. Some basic concepts and results of the "idempotent" representation theory are presented. In the framework of this theory the well-known Legendre transform can be treated as an idempotent version of the traditional Fourier transform. Some unexpected versions of the Engel theorem are given.; Comment: 10 pages

The Deeper Roles of Mathematics in Physical Laws

Knuth, Kevin H.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
35.44%
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as exemplified by the laws of physics. In this essay, I claim that much of the utility of mathematics arises from our choice of description of the physical world coupled with our desire to quantify it. This will be demonstrated in a practical sense by considering one of the most fundamental concepts of mathematics: additivity. This example will be used to show how many physical laws can be derived as constraint equations enforcing relevant symmetries in a sense that is far more fundamental than commonly appreciated.; Comment: This essay placed Third in the FQXi 2015 Essay Contest "Trick or Truth: the Mysterious Connection between Physics and Mathematics". 12 Pages, 2 Figures, 1 Table

Mathematics Education in Russia and Mathematical Circles

Bartolomé, Daniel Grilo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/12/2015 Português
Relevância na Pesquisa
35.44%
This Master's Thesis analyzes thoroughly the topic of the Mathematics Education in Russia and Mathematical Circles. It deals with the historical context of the Mathematics Education in Russia in the XVIIIth, XIXth and XXth centuries; the programs of the Mathematics Education which were developed between 1930 and 1985 in the Soviet Union, including the Mathematical Circles for its particularly importance and influence on the rest of the Programs and on the way of understanding the Mathematics Education; the objectives and the organization of practical cases nowadays, legacy of the Russian Mathematical Circles; and the way of establishing the didactic process of the Mathematical Circles. Finally it is attached an appendix with a practical proposal in order to develop a session following the Mathematic Circle manner within the current framework of the Spanish Middle and High School education.; Comment: 91 pages, in Spanish