Structuring representations of continuous data through investigations in grade 1

The study of data modelling with elementary students involves the analysis of a developmental process beginning with children’s investigations of meaningful contexts: visualising, structuring, and representing data and displaying data in simple graphs (English, 2012; Lehrer & Schauble, 2005; Makar, Bakker, & Ben-Zvi, 2011). A 3-year longitudinal study investigated young children’s data modelling, integrating mathematical and scientific investigations. One aspect of this study involved a researcher-led teaching experiment with 21 mathematically able Grade 1 students. The study aimed to describe explicit developmental features of students’ representations of continuous data...

Identification and doing without it, V: A formal mathematical analysis for a case of mix-up of individuals, and of recovery from failure to attain identification

Identification, when sought, is not necessarily obtained. Operational guidance that is normatively acceptable may be necessary for such cases. We proceed to formalize and illustrate modes of exchanges of individual identity, and provide procedures of recovery strategies in specific prescriptions from an ancient body of law for such situations when, for given types of purposes, individuals of some relevant kind had become intermixed and were undistinguishable. Rules were devised, in a variety of domains, for coping with situations that occur if and when the goal of identification was frustrated. We propose or discuss mathematical representations of such recovery procedures.

A mathematical approach to chemical equilibrium theory for gaseous systems—I: theory

Equilibrium theory occupies an important position in chemistry and it is traditionally based on thermodynamics. A novel mathematical approach to chemical equilibrium theory for gaseous systems at constant temperature and pressure is developed. Six theorems are presented logically which illustrate the power of mathematics to explain chemical observations and these are combined logically to create a coherent system. This mathematical treatment provides more insight into chemical equilibrium and creates more tools that can be used to investigate complex situations. Although some of the issues covered have previously been given in the literature, new mathematical representations are provided. Compared to traditional treatments, the new approach relies on straightforward mathematics and less on thermodynamics, thus, giving a new and complementary perspective on equilibrium theory. It provides a new theoretical basis for a thorough and deep presentation of traditional chemical equilibrium. This work demonstrates that new research in a traditional field such as equilibrium theory, generally thought to have been completed many years ago, can still offer new insights and that more efficient ways to present the contents can be established. The work presented here can be considered appropriate as part of a mathematical chemistry course at University level.

Statistics at play

Three core components in developing children’s understanding and appreciation of data — establish a context, pose and answer statistical questions, represent and interpret data — lay the foundation for the fourth component: use data to enhance existing context.

Stability analysis of STATCOM in distribution networks

This chapter presents the stability analysis based on bifurcation theory of the distribution static compensator (DSTATCOM) operating both in current control mode as in voltage control mode. The bifurcation analysis allows delimiting the operating zones of nonlinear power systems and hence the computation of these boundaries is of interest for practical design and planning purposes. Suitable mathematical representations of the DSTATCOM are proposed to carry out the bifurcation analyses efficiently. The stability regions in the Thevenin equivalent plane are computed for different power factors at the Point of Common Coupling (PCC). In addition, the stability regions in the control gain space are computed, and the DC capacitor and AC capacitor impact on the stability are analyzed in detail. It is shown through bifurcation analysis that the loss of stability in the DSTATCOM is in general due to the emergence of oscillatory dynamics. The observations are verified through detailed simulation studies.

O quadro interativo como mediador do desenvolvimento da comunicação matemática no 1º ciclo do ensino básico

Trabalho de projeto de mestrado, Educação (Educação e Tecnologias Digitais), Universidade de Lisboa, Instituto de Educação, 2015

Prática de ensino supervisionado no 1.º e 2.º ciclo do ensino básico: a comunicação (em) matemática em contexto de sala de aula

Relatório de Estágio apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1.º e 2.º ciclo do Ensino Básico

Comunicação matemática - representações utilizadas pelos alunos

Relatório de Estágio apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1.º e do 2.º Ciclo do Ensino Básico

Determination of displacement, stress- and strain-distribution in the human heart: a FE-model on the basis of MR imaging.

The determination of characteristic cardiac parameters, such as displacement, stress and strain distribution are essential for an understanding of the mechanics of the heart. The calculation of these parameters has been limited until recently by the use of idealised mathematical representations of biventricular geometries and by applying simple material laws. On the basis of 20 short axis heart slices and in consideration of linear and nonlinear material behaviour we have developed a FE model with about 100,000 degrees of freedom. Marching Cubes and Phong's incremental shading technique were used to visualise the three dimensional geometry. In a quasistatic FE analysis continuous distribution of regional stress and strain corresponding to the endsystolic state were calculated. Substantial regional variation of the Von Mises stress and the total strain energy were observed at all levels of the heart model. The results of both the linear elastic model and the model with a nonlinear material description (Mooney-Rivlin) were compared. While the stress distribution and peak stress values were found to be comparable, the displacement vectors obtained with the nonlinear model were generally higher in comparison with the linear elastic case indicating the need to include nonlinear effects.

Root growth models: towards a new generation of continuous approaches

Models of root system growth emerged in the early 1970s, and were based on mathematical representations of root length distribution in soil. The last decade has seen the development of more complex architectural models and the use of computer-intensive approaches to study developmental and environmental processes in greater detail. There is a pressing need for predictive technologies that can integrate root system knowledge, scaling from molecular to ensembles of plants. This paper makes the case for more widespread use of simpler models of root systems based on continuous descriptions of their structure. A new theoretical framework is presented that describes the dynamics of root density distributions as a function of individual root developmental parameters such as rates of lateral root initiation, elongation, mortality, and gravitropsm. The simulations resulting from such equations can be performed most efficiently in discretized domains that deform as a result of growth, and that can be used to model the growth of many interacting root systems. The modelling principles described help to bridge the gap between continuum and architectural approaches, and enhance our understanding of the spatial development of root systems. Our simulations suggest that root systems develop in travelling wave patterns of meristems, revealing order in otherwise spatially complex and heterogeneous systems. Such knowledge should assist physiologists and geneticists to appreciate how meristem dynamics contribute to the pattern of growth and functioning of root systems in the field.

As representações matemáticas mediadas por softwares educativos em uma perspectiva semiótica: uma contribuição para o conhecimento do futuro professor de matemática

Pós-graduação em Educação Matemática - IGCE

Matemática e cultura amazônica: representações do brinquedo de miriti

No Município de Abaetetuba-Pará existe uma prática socioeconômica de produção de um artesanato local que vem se consolidando como mais uma cultura dos povos amazônicos. Os "brinquedos de miriti‟, como são popularmente conhecidos, são produzidos a partir de uma palmeira nativa da Amazônia, o miritizeiro (Mauritia flexuosa). As peças artesanais manufaturadas tiveram sua origem perdida no tempo, mas têm sua tradição mantida com o passar dos anos pelos artesãos que produzem e comercializam esse artesanato, cujos picos de venda ocorrem, primeiro em junho depois em outubro, por ocasião do Festival do Miriti, em Abaetetuba, e do Círio de Nazaré, na capital Belém, respectivamente. Esses artesãos, além de reproduzirem no brinquedo o cenário Amazônico no qual convivem cotidianamente, demonstram intenções, inventam e reinventam saberes aqui entendidos como Representações Sociais. Deste modo, este trabalho tem por objetivo analisar representações matemáticas e patrimoniais presentes no artesanato de miriti de Abaetetuba; analisar peças, identificando conhecimentos escolares e não escolares; analisar elementos do contexto cultural e socioambiental que contemplem a educação patrimonial ambiental sob o ponto de vista etnográfico, aproximando aspectos sociais, culturais e ambientais das relações matemáticas presentes no brinquedo de miriti. A fundamentação teórico-metodológica dessa pesquisa baseia-se na Teoria das Representações Sociais, com características de cunho etnográfico. Os dados foram analisados com base no discurso dos artesãos do brinquedo de miriti. A partir das Representações e do convívio com dois grupos de artesãos – ASAMAB e MIRITONG- foi percebida preocupação e respeito ao meio ambiente pelos artesãos em todas as fases do processo de produção do artesanato, faltando poucos ajustes para tornar essa prática sustentável. O saber fazer dos artesãos está recheado de Cultura e conhecimentos repassados de maneira informal e bastante peculiar característicos da Educação Patrimonial Ambiental. Elementos matemáticos identificados nas peças, nos procedimentos e nas representações, estão em alguns casos, coerentes com discussões em etnomatemática.

Estimação de parâmetros de linhas de transmissão utilizando técnicas de decomposição modal: Aplicação em linhas com plano de simetria vertical

Pós-graduação em Engenharia Elétrica - FEIS

Mapping Dynamics into Graphs. The Visibility Algorithm

Si no tenemos en cuenta posibles procesos subyacentes con significado físico, químico, económico, etc., podemos considerar una serie temporal como un mero conjunto ordenado de valores y jugar con él algún inocente juego matemático como transformar dicho conjunto en otro objeto con la ayuda de una operación matemática para ver qué sucede: qué propiedades del conjunto original se conservan, cuáles se transforman y cómo, qué podemos decir de alguna de las dos representaciones matemáticas del objeto con sólo atender a la otra... Este ejercicio sería de cierto interés matemático por sí solo. Ocurre, además, que las series temporales son un método universal de extraer información de sistemas dinámicos en cualquier campo de la ciencia. Esto hace ganar un inesperado interés práctico al juego matemático anteriormente descrito, ya que abre la posibilidad de analizar las series temporales (vistas ahora como evolución temporal de procesos dinámicos) desde una nueva perspectiva. Hemos para esto de asumir la hipótesis de que la información codificada en la serie original se conserva de algún modo en la transformación (al menos una parte de ella). El interés resulta completo cuando la nueva representación del objeto pertencece a un campo de la matemáticas relativamente maduro, en el cual la información codificada en dicha representación puede ser descodificada y procesada de manera efectiva. ABSTRACT Disregarding any underlying process (and therefore any physical, chemical, economical or whichever meaning of its mere numeric values), we can consider a time series just as an ordered set of values and play the naive mathematical game of turning this set into a different mathematical object with the aids of an abstract mapping, and see what happens: which properties of the original set are conserved, which are transformed and how, what can we say about one of the mathematical representations just by looking at the other... This exercise is of mathematical interest by itself. In addition, it turns out that time series or signals is a universal method of extracting information from dynamical systems in any field of science. Therefore, the preceding mathematical game gains some unexpected practical interest as it opens the possibility of analyzing a time series (i.e. the outcome of a dynamical process) from an alternative angle. Of course, the information stored in the original time series should be somehow conserved in the mapping. The motivation is completed when the new representation belongs to a relatively mature mathematical field, where information encoded in such a representation can be effectively disentangled and processed. This is, in a nutshell, a first motivation to map time series into networks.

Process systems modelling and applications in granulation: A review

Granulation is one of the fundamental operations in particulate processing and has a very ancient history and widespread use. Much fundamental particle science has occurred in the last two decades to help understand the underlying phenomena. Yet, until recently the development of granulation systems was mostly based on popular practice. The use of process systems approaches to the integrated understanding of these operations is providing improved insight into the complex nature of the processes. Improved mathematical representations, new solution techniques and the application of the models to industrial processes are yielding better designs, improved optimisation and tighter control of these systems. The parallel development of advanced instrumentation and the use of inferential approaches provide real-time access to system parameters necessary for improvements in operation. The use of advanced models to help develop real-time plant diagnostic systems provides further evidence of the utility of process system approaches to granulation processes. This paper highlights some of those aspects of granulation. (c) 2005 Elsevier Ltd. All rights reserved.