O desenvolvimento do conceito de área: um estudo com alunos do 3.º ano de escolaridade

O objetivo desta investigação é compreender como é que alunos do 3.º ano de escolaridade desenvolvem o conceito de área com ênfase em conhecimentos sobre figuras e propriedades geométricas. Para melhor objetivar o estudo, formulei três questões que orientaram a investigação. Pretendo (1) compreender como é que os alunos mobilizam conhecimentos sobre as propriedades das figuras geométricas no estudo da área de uma figura plana? A que estratégias recorrem? Que dificuldades sentem? (2) que compreensão é que os alunos têm sobre o processo de medição? e (3) que ideias e/ou experiências são relevantes no desenvolvimento do conceito de área? Este é um estudo que se insere no paradigma interpretativo e que segue uma abordagem qualitativa, pelo que não visa generalização de resultados, mas uma descrição compreensiva dos processos vivenciados, tendo em conta os contextos pessoais e sociais. Optei por realizar dois Estudos de Caso. Os dados foram recolhidos através de fontes diversificadas, donde se destacam a observação participante e a análise de registos audiovisuais e escritos dos alunos. A análise dos dados teve por referência categorias criadas com base em contributos da literatura de referência. As conclusões desta investigação centram-se numa análise acerca das estratégias a que os alunos em estudo tendencialmente mais recorrem, visando também algumas das suas dificuldades mais relevantes e sobre as quais importa refletir. Destaca-se que ambos os alunos foram capazes de recorrer a raciocínios baseados e não baseados na medida, embora seja evidente uma tendência para raciocínios baseados na medida. É igualmente importante referir que os dois alunos revelaram um bom conhecimento acerca do processo de medição, mesmo quando ele implicava a definição de uma unidade de medida adequada e/ou mudança de unidade. É dado, também, destaque às experiências matemáticas que devem ser proporcionadas aos alunos no sentido do desenvolvimento de um conhecimento amplo e flexível do conceito de área. - Abstract The purpose of this investigation is to understand the development of 3rd year students’ concept of area based on their knowledge of geometrical properties and figures. As means to orientate the present study, the following investigation questions were formulated: 1) how do students use their knowledge about geometrical properties in order to understand geometrical shape’s areas? Which strategies do they use? What do they struggle with? (2) What is their understanding about measurement? And (3) what are the most relevant mathematical reasonings and classroom tasks in the development of the concept of area? This is a study that follows a qualitative approach: it does not intend to be a generalization, but a fully comprehensive description of the witnessed learning processes, bearing in mind the social and personal contexts. As such, two study-cases were developed. The data were collected through various sources, such as direct observation and analysis of audiovisual records or written worksheets. The scrutiny of the generated data was undertaken following criteria based on the literature of reference. The conclusions of this investigation are centered on the most used strategies as well as the students’ difficulties upon which it is important to discuss. It was noticed that the two students were able to use both measurement and non measurement thinking – although, preferably, they tend to use the first one. On the other hand, it is equally demonstrated that the two students have shown good acquaintance about measurement, even if obliged to the establishment of a suitable unit of measurement and/or change of units. At last, it is also referred which mathematical classroom tasks are important to develop a sustained and comprehensive concept of area.

Decomposing complete tripartite graphs into cycles of lengths 3 and 4

Necessary and sufficient conditions are given for the edge-disjoint decomposition of a complete tripartite graph K-r,K-s,K-t into exactly alpha 3-cycles and beta 4-cycles. (C) 1999 Elsevier Science B.V. All rights reserved.

Conceptual model for decomposing the value for the customer

Value has been defined in different theoretical contexts as need, desire, interest, standard /criteria, beliefs, attitudes, and preferences. The creation of value is key to any business, and any business activity is about exchanging some tangible and/or intangible good or service and having its value accepted and rewarded by customers or clients, either inside the enterprise or collaborative network or outside. “Perhaps surprising then is that firms often do not know how to define value, or how to measure it” (Anderson and Narus, 1998 cited by [1]). Woodruff echoed that we need “richer customer value theory” for providing an “important tool for locking onto the critical things that managers need to know”. In addition, he emphasized, “we need customer value theory that delves deeply into customer’s world of product use in their situations” [2]. In this sense, we proposed and validated a novel “Conceptual Model for Decomposing the Value for the Customer”. To this end, we were aware that time has a direct impact on customer perceived value, and the suppliers’ and customers’ perceptions change from the pre-purchase to the post-purchase phases, causing some uncertainty and doubts.We wanted to break down value into all its components, as well as every built and used assets (both endogenous and/or exogenous perspectives). This component analysis was then transposed into a mathematical formulation using the Fuzzy Analytic Hierarchy Process (AHP), so that the uncertainty and vagueness of value perceptions could be embedded in this model that relates used and built assets in the tangible and intangible deliverable exchange among the involved parties, with their actual value perceptions.

A Quantitative Model for Decomposing & Assessing the Value for the Customer

The research presented in this paper proposes a novel quantitative model for decomposing and assessing the Value for the Customer. The proposed approach builds on the different dimensions of the Value Network analysis proposed by Verna Allee having as background the concept of Value for the Customer proposed by Woodall. In this context, the Value for the Customer is modelled as a relationship established between the exchanged deliverables and a combination of tangible and intangible assets projected into their endogenous or exogenous dimensions. The Value Network Analysis of the deliverables exchange enables an in-depth understanding of this frontier and the implicit modelling of co-creation scenarios. The proposed Conceptual Model for Decomposing Value for the Customer combines several concepts: from the marketing area we have the concept of Value for the Customer; from the area of intellectual capital the concept of Value Network Analysis; from the collaborative networks area we have the perspective of the enterprise life cycle and the endogenous and exogenous perspectives; at last, the proposed model is supported by a mathematical formal description that stems from the area of Multi-Criteria Decision Making. The whole concept is illustrated in the context of a case study of an enterprise in the footwear industry (Pontechem). The merits of this approach seem evident from the contact with Pontechem as it provides a structured approach for the enterprises to assess the adequacy of their value proposition to the client/customer needs and how these relate to their endogenous and/or exogenous tangible or intangible assets. The proposed model, as a tool, may therefore be a useful instrument in supporting the commercialisation of new products and/or services.

Analysis of exploratory eye movements in patients with schizophrenia during visual scanning of projective tests' figures

OBJECTIVE: Compare pattern of exploratory eye movements during visual scanning of the Rorschach and TAT test cards in people with schizophrenia and controls. METHOD: 10 participants with schizophrenia and 10 controls matched by age, schooling and intellectual level participated in the study. Severity of symptoms was evaluated with the Positive and Negative Syndrome Scale. Test cards were divided into three groups: TAT cards with scenes content, TAT cards with interaction content (TAT-faces), and Rorschach cards with abstract images. Eye movements were analyzed for: total number, duration and location of fixation; and length of saccadic movements. RESULTS: Different pattern of eye movement was found, with schizophrenia participants showing lower number of fixations but longer fixation duration in Rorschach cards and TAT-faces. The biggest difference was observed in Rorschach, followed by TAT-faces and TAT-scene cards. CONCLUSIONS: Results suggest alteration in visual exploration mechanisms possibly related to integration of abstract visual information.

Icones plantarum Indiae Orientalis :or figures of Indian plants /by Robert Wight.

v.1 (1840)

Icones plantarum Indiae Orientalis :or figures of Indian plants /by Robert Wight.

v.2 (1843)

Icones plantarum Indiae Orientalis :or figures of Indian plants /by Robert Wight.

v.3 (1846)

Icones plantarum Indiae Orientalis :or figures of Indian plants /by Robert Wight.

v.4 (1850)

Icones plantarum Indiae Orientalis :or figures of Indian plants /by Robert Wight.

v.5 (1852)

Icones plantarum Indiae Orientalis :or figures of Indian plants /by Robert Wight.

v.6 (1853)

The London journal of botany : containing figures and descriptions of such plants as recommend themselves by their novelty, rarity, history, or uses : together with botanical notices and information and and occasional portraits and memoirs of eminent botanists.

v.2 (1843)

The London journal of botany : containing figures and descriptions of such plants as recommend themselves by their novelty, rarity, history, or uses : together with botanical notices and information and and occasional portraits and memoirs of eminent botanists.

v.3 (1844)

The London journal of botany : containing figures and descriptions of such plants as recommend themselves by their novelty, rarity, history, or uses : together with botanical notices and information and and occasional portraits and memoirs of eminent botanists.

v.4 (1845)

The London journal of botany : containing figures and descriptions of such plants as recommend themselves by their novelty, rarity, history, or uses : together with botanical notices and information and and occasional portraits and memoirs of eminent botanists.

v.5 (1846)