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Teaching methodologies and open source software: empirical application to econometrics and mathematics

Nunes, Alcina; Balsa, Carlos
Fonte: International Association for Scientific Knowledge Publicador: International Association for Scientific Knowledge
Tipo: Conferência ou Objeto de Conferência
Português
Relevância na Pesquisa
35.38%
Nowadays, the software open source represents an important teaching resource. However, it is not sufficiently explored as an higher education teaching methodology. In subjects with a very specific goal, applied contents and attended by a small number of students, the commercial software is still preferred to the open source software. Aware of this reality, this paper presents a reflection about the use of open source software in Applied Econometrics and Mathematics. The adoption of two different software programmes – Gretl and Octave – allows the discussion about a comprehensive set of pedagogical, economical and technical advantages and some observed practical limitations. In practice, the refereed advantages are stressed when the students’ results are analysed. Their academic results benefit from the adoption of software which is executed, distributed and improved freely.

Continuous training in Mathematics: influence on the professional knowledge of elementary school teachers

Martins, Cristina; Santos, Leonor
Fonte: International Group for the Psychology of Mathematics Education Publicador: International Group for the Psychology of Mathematics Education
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
35.38%
Short oral communication; This report is based on an ongoing investigation, aiming to study the contribution of participating in a Continuous Training Program in Mathematics for the professional development of elementary school teachers, specifically regarding professional knowledge.

Professional development of 1st cycle: basic education teachers: contribution of participating in a continuous programme of mathematics training

Martins, Cristina
Fonte: European Society for Research in Mathematics Education Publicador: European Society for Research in Mathematics Education
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
35.38%
In this investigation, my aim is to study the professional development of 1st cycle teachers in the context of the Program for Continuous Education in Mathematics for 1st Cycle of Basic Education Teachers program. Knowing that, on the one hand, professional development involves a number of dimensions and that, on the other, the context of the performance has particular characteristics, namely the kind of sessions foreseen and the form of evaluation, I have devised the following questions for investigation: ─ How does the professional development of the teacher take place through participating in the training program? ─ Which is the contribution of the portfolio usage in the training program towards the professional development of the teacher?

Teaching methodologies and open source software: empirical application to econometrics and mathematics

Nunes, Alcina; Balsa, Carlos
Fonte: Mario Muñoz, Ivan Jelìnek, Fernando Ferreira Publicador: Mario Muñoz, Ivan Jelìnek, Fernando Ferreira
Tipo: Conferência ou Objeto de Conferência
Português
Relevância na Pesquisa
35.38%
Em co-autoria com Alcina Nunes do Departamento de Economia e Gestão.; Nowadays, the software open source represents an important teaching resource. However, it is not sufficiently explored as an higher education teaching methodology. In subjects with a very specific goal, applied contents and attended by a small number of students, the commercial software is still preferred to the open source software. Aware of this reality, this paper presents a reflection about the use of open source software in Applied Econometrics and Mathematics. The adoption of two different software programmes – Gretl and Octave – allows the discussion about a comprehensive set of pedagogical, economical and technical advantages and some observed practical limitations. In practice, the refereed advantages are stressed when the students’ results are analysed. Their academic results benefit from the adoption of software which is executed, distributed and improved freely.

Continuous training in Mathematics: influence on the professional knowledge of elementary school teachers

Martins, Cristina; Santos, Leonor
Fonte: International Group for the Psychology of Mathematics Education Publicador: International Group for the Psychology of Mathematics Education
Tipo: Conferência ou Objeto de Conferência
Português
Relevância na Pesquisa
35.38%
Short oral communication; This report is based on an ongoing investigation, aiming to study the contribution of participating in a Continuous Training Program in Mathematics for the professional development of elementary school teachers, specifically regarding professional knowledge.

Problem-based learning and teacher training in mathematics

Cazzola, Marina
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
35.41%
Problem-based learning (PBL) is a constructivist learner-centered instructional approach based on the analysis, resolution and discussion of a given problem. It can be applied to any subject, indeed it is especially useful for the teaching of mathematics. When compared to "traditional" teaching, the PBL approach requires increased responsibility for the teachers (in addition to the presentation of mathematical knowledge, they need to engage students in gathering information and using their knowledge to solve given problems). It thus become crucial that the future teachers become aware of its effectiveness. One of the main obstacle to this awareness lies usually on the fact that future teachers did not find this methodology in their own pre-service training. In this paper we will describe the attempt to introduce PBL in University courses so to have future maths teacher "experience mathematics" themselves.; Comment: This paper has been withdrawn by the author as it needs substantial revision

Quotient completion for the foundation of constructive mathematics

Maietti, Maria Emilia; Rosolini, Giuseppe
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
35.41%
We apply some tools developed in categorical logic to give an abstract description of constructions used to formalize constructive mathematics in foundations based on intensional type theory. The key concept we employ is that of a Lawvere hyperdoctrine for which we describe a notion of quotient completion. That notion includes the exact completion on a category with weak finite limits as an instance as well as examples from type theory that fall apart from this.; Comment: 32 pages

More than bargained for in Reverse Mathematics

Sanders, Sam
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
35.41%
Reverse Mathematics (RM for short) is a program in the foundations of mathematics with the aim of finding the minimal axioms required for proving theorems about countable and separable objects. RM usually takes place in second-order arithmetic and due to this choice of framework, continuous real-valued functions have to be represented by so-called codes. Kohlenbach has shown that the RM-definition of continuity-via-codes constitutes a slight constructive enrichment of the epsilon-delta definition, namely in the form of a modulus of continuity. In this paper, we show that the RM-definition of continuity also gives rise to a `nonstandard' enrichment in the form of nonstandard continuity from Nonstandard Analysis. This observation allows us to (i) establish that RM-theorems related to continuity are implicitly higher-order statements, (ii) prove equivalences between RM-theorems concerning continuity and their associated higher-order versions, and (iii) obtain explicit equivalences between higher-order theorems from the equivalence between the corresponding RM-theorems. Moreover, we show that it is exactly the RM-definition of continuity-via-codes which gives rise to these higher-order phenomena. In conclusion, we establish that the practice of coding in RM...

Interval orders and reverse mathematics

Marcone, Alberto
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
35.41%
We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the characterization theorem for interval orders: a partial order is an interval order if and only if it does not contain $2 \oplus 2$. We also study proper interval orders and their characterization theorem: a partial order is a proper interval order if and only if it contains neither $2 \oplus 2$ nor $3 \oplus 1$.; Comment: 21 pages; to appear in Notre Dame Journal of Formal Logic; minor changes from the previous version

On Wittgenstein's philosophy of mathematics

Merker, Joel
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/01/2008 Português
Relevância na Pesquisa
35.41%
Mathematics cannot anymore be assimilated to a linguistic game, where formal proofs are strongly differentiated with conjectural thinking, without building any category of knowledge to understand the passage (Wittgenstein's gist). Nowadays, philosophy has to face with the growing, exponential ramified tree of speculative mathematical thinking. Our main (problematical) theses are: 1. In mathematics, there is no empirical automatism, and no separate, physical-like motricity. 2: The irreversible-synthetical must force to complexify the exegetical game of philosophy; numerical experiments in algebra and in number theory are a kind of letting blow up all possible problems; 4. The nature of mathematical questioning still remains in question.; Comment: Written in French

The Infinite as Method in Set Theory and Mathematics

Kanamori, Akihiro
Fonte: Universidade Autônoma de Barcelona Publicador: Universidade Autônoma de Barcelona
Tipo: Artigo de Revista Científica Formato: application/pdf
Publicado em //2009 Português
Relevância na Pesquisa
35.41%
Este artículo da cuenta de la aparición histórica de lo infinito en la teoría de conjuntos, y de cómo lo tratamos dentro y fuera de las matemáticas. La primera sección analiza el surgimiento de lo infinito como una cuestión de método en la teoría de conjuntos. La segunda sección analiza el infinito dentro y fuera de las matemáticas, y cómo deben adoptarse.; This article address the historical emergence of the infinite in set theory, and how we are to take the infinite in and out of mathematics.The first section discusses the emergence of the infinite as a matter of method in set theory. The second section discusses the infinite in and out of mathematics, and how it is to be taken.

Teaching natural philosophy and mathematics at Oxford and Cambridge 1500-1570

Hannam, James
Fonte: University of Cambridge; Department of History and Philosophy of Science Publicador: University of Cambridge; Department of History and Philosophy of Science
Tipo: Thesis; Doctoral
Português
Relevância na Pesquisa
35.41%
The syllabus in natural philosophy and mathematics was radically changed in the course of the sixteenth century with new subjects, textbooks and methods introduced. Education became more practical and less dependent on medieval antecedents. Printing technology improved textbooks and made it possible to replace them with newer versions. Following sweeping syllabus reform around 1500, the Cambridge Master of Arts course was heavily slanted towards humanism. The old scholastic textbooks were rejected and replaced with modern authors. The purpose of natural philosophy was explicitly to illuminate the providential work of the creator, especially through natural history (a newly developing subject in the sixteenth century thanks to newly translated and promulgated Greek texts) where examples of God?s work were there for all to see. Oxford remained wedded to scholastic texts although the trivium was reformed along humanistic lines. Cromwell?s visitors in 1535 outlawed scholasticism by decree but gave little indication of the alternative (their white list stipulating only Aristotle). The solution adopted by the Oxford masters was to import the Cambridge syllabus and textbooks wholesale. When the evangelical regime of Edward VI reformed the universities in 1549...

Unthinkable: Mathematics and the Rise of the West

Welsh, Whitney
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2011 Português
Relevância na Pesquisa
35.41%

This dissertation explores the ideational underpinnings of the rise of the west through a comparison of ancient Greek geometry, medieval Arabic algebra, and early modern European calculus. Blending insights from Thomas Kuhn, Michel Foucault, and William H. Sewell, I assert that there is an underlying logic, however clouded, to the unfolding of a given civilization, governed by a cultural episteme that delineates the boundaries of rational thought and the accepted domain of human endeavor. Amid a certain conceptual configuration, the rise of the west happens; under other circumstances, it does not. Mathematics, as an explicit exhibition of logic premised on culturally determined axioms, presents an outward manifestation of the lens through which a civilization surveys the world, and as such offers a window on the fundamental assumptions from which a civilization's trajectory proceeds. To identify the epistemological conditions favorable to the rise of the west, I focus specifically on three mathematical divergences that were integral to the development of calculus, namely analytic geometry, trigonometry, and the fundamental theorem of calculus. Through a comparative/historical analysis of original source documents in mathematics...

Strategies for the development of the creativity in Mathematics; Estrategias para el desarrollo de la creatividad en Matemática; Estratégias para o desenvolvimento da criatividade em Matemática

Gontijo, Cleyton
Fonte: Linhas Críticas; Critical Lines Publicador: Linhas Críticas; Critical Lines
Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion; ; Formato: application/pdf
Publicado em 20/12/2010 Português
Relevância na Pesquisa
35.41%
Modern society requires more creative persons capable to present innovative solutions for the problems found in the several contexts in which they live. To cope with such social demands, the development of creativity was included as one of the educational goals at all educational levels. Thus, in the education- al context, the need for implementing strategies and actions that stimulate and foment people's creative potential has increasingly been acknowledged. In this regard, this article aims to contribute with reflec- tions about these strategies in one of the areas of the school curriculum, Mathematics. In this area, the studies have privileged problem solving, the formulation of problems and the redefinition of didactic and methodological strategies that make possible the development of creativity. Thus, an attempt is made to discuss, in this study, the relations between creativity and Mathematics, describing such strategies. ; El desarrollo de la creatividad fue incluso entre los objetivos educacionales en los diversos niveles de enseñanza como una de las estrategias para contestar las demandas sociales que necesitan de personas más creativas y con capacidad de presentar soluciones innovadoras para problemas encontrados en los diversos contextos  donde están inseridas. Con eso...

The problem with integer programming

Williams, H. Paul
Fonte: Oxford University Press on behalf of the Institute of Mathematics and its Applications Publicador: Oxford University Press on behalf of the Institute of Mathematics and its Applications
Tipo: Article; PeerReviewed Formato: application/pdf
Publicado em //2011 Português
Relevância na Pesquisa
35.41%
Integer programming (IP), also known as discrete optimization, is a way of modelling a very wide range of problems involving indivisibilities (e.g. yes/no investment decisions) and non-convexities (e.g. economies of scale and fixed cost allocation). Such problems arise in many areas; these are mentioned in the paper. However, IP demands ingenuity in both building models and in their solution. Much is still not properly understood. This paper investigates the question: ‘Is IP like Linear Programming (LP)? ’ The mathematical and economic properties of IP will be contrasted with LP. It will be suggested that the mathematics and economics of IP are still not properly understood. Many of the results which apply to LP do not apply to IP. It will be asserted that this lack of understanding reveals inadequacies in both the mathematics and economics. Published online October 5th, 2010.

Addressing mathematics & statistics anxiety

Kotecha, Meena
Fonte: London School of Economics and Political Science Research Publicador: London School of Economics and Political Science Research
Tipo: Conference or Workshop Item; NonPeerReviewed Formato: application/pdf
Publicado em //2015 Português
Relevância na Pesquisa
35.41%
This paper should be of interest to mathematics and statistics educators ranging from pre-university to university education sectors. It will discuss some features of the author’s teaching model developed over her longitudinal study conducted to understand and address mathematics and statistics anxiety, which is one of the main barriers to engaging with these subjects especially in non-specialist undergraduates. It will demonstrate how a range of formative assessments are used to kindle, as well as maintain, interest in teaching rooms and their impact on students’ engagement with these subjects.

The use of workbooks in South African grade 3 mathematics classrooms

Mathews,Corin; Mdluli,Manono; Ramsingh,Valerie
Fonte: South African Journal of Childhood Education Publicador: South African Journal of Childhood Education
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2014 Português
Relevância na Pesquisa
35.41%
The poor performance of South African learners on national and international benchmark tests in mathematics and literacy has prompted the South African Department of Basic Education (DBE) to devise intervention strategies, one of which is the provision of workbooks for learners. This paper is based on a case study of six grade 3 teachers' use of DBE workbooks. Data from classroom observations and interviews are reported and analysed in relation to literature on mathematical and pedagogical resources. The key finding is that teachers use the workbooks in disparate ways as a resource and that the majority of the teachers in the case study use the workbooks in ways that do not resonate with the DBE's intentions. We argue that the provision of resources alone may not lead to improved teaching and learning in primary school mathematics classrooms and that pre-service and in-service teacher education programmes need to include a focus on how resources such as workbooks can be utilised optimally.

University-school partnerships for social justice in mathematics and science education: the case of the SMILES project at IMSTUS

Ndlovu,Mdutshekelwa C
Fonte: South African Journal of Education Publicador: South African Journal of Education
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2011 Português
Relevância na Pesquisa
35.41%
My purpose in this paper is to situate a university-school mathematics and science education partnership within a social justice perspective in education. The focus of the systemic intervention endeavour was school-based teacher professional development in which university-based facilitators embarked on class visits with the aim of identifying teacher needs, co-teaching and offering professional support over a three-year period. This was in contrast to evaluation (inspection visits) often undertaken by the subject advisors under the auspices of the Department of Education which, for historical reasons, tend to be viewed with suspicion by teachers and teacher unions. Five historically disadvantaged secondary schools and their 10 feeder primary schools were involved in this study with a view to providing equal opportunities to learners from marginalized communities in the Cape Winelands district of the Western Cape. Initial results suggest that an intervention programme that is responsive to local needs can go a long way in bringing about collaborative teacher professional development that leads to reflective practice in professional learning communities and can add value to the quality of student achievement in the gateway subjects of mathematics and science.

An investigation into the opportunity to learn that is available to Grade 12 mathematics learners

Stols,Gerrit
Fonte: South African Journal of Education Publicador: South African Journal of Education
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2013 Português
Relevância na Pesquisa
35.41%
This study investigated the opportunity to learn (OTL) that is available to Grade 12 mathematics learners. Learner workbooks were analysed in terms of time on task, curriculum coverage, curriculum coherence, and cognitive demand. Based on these elements, experienced mathematics teachers judged the opportunity that the learners have to achieve more than 60% for each topic. According to the workbooks, the average number of active learning days in this sample was 54.1 days per annum. This resulted in limited curriculum coverage in almost all sections in 16 of the 18 under-performing schools. In these schools, learners spent most of their time practising routine procedures. The high correlation of 0.95 (p < 0.001) between the experts'prediction about the opportunity to learn in the different schools (based on the learner workbooks) and learners' actual performance in the Grade 12 exam shows that the number, the coverage, the cognitive level, and the coherence of activities play a major role in understanding learner performance.

MATHEMATICS AND LOGIC: RESPONSE TO MARK WILSON

Chateaubriand, Oswaldo
Fonte: UNICAMP-CLE-Publicações Publicador: UNICAMP-CLE-Publicações
Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion; Artigo Avaliado pelos Pares; Formato: application/pdf
Publicado em 11/12/2015 Português
Relevância na Pesquisa
35.41%
Mark Wilson argues that in order to make physical first-order properties suitable for inclusion in the bottom levels of a logical hierarchy of properties, their proper treatment must take into account the methods of applied mathematics. I agree that the methods of applied mathematics are essential for studying physical properties, and in my response focus on the nature of the logical hierarchy and on the requirements of classical logic. Resumo: Mark Wilson argumenta que um tratamento adequado para tornar as propriedades físicas de primeira ordem apropriadas para inclusão nos níveis inferiores de uma hierarquia de propriedades lógicas deve levar em consideração os métodos da matemática aplicada. Concordo que os métodos da matemática aplicada são essenciais para estudar as propriedades físicas, e em minha réplica enfoco a natureza da hierarquia lógica e os requisitos da lógica clássica.Palavras chave: Formas lógicas. Matemática aplicada. Propriedades de primeira ordem.