Reasoning and proof in classroom (9th grade)

This paper is research oriented and pretends to contribute toward giving empirical evidence about how students develop their reasoning and how they achieved to a proof construction in school context. Its main theme is epistemology. It describes the way in which four students in 9th Grade explored a task related with the discovery of symmetry axes in various geometric figures. The proof constructed by students had essentially an explaining function and it was related with the symmetry axes of regular polygons. The teacher’s role in meaning negotiation of the proof and its need is described through illustrative episodes. The paper presents part of a study which purpose is to analyse the nature of mathematical proof in classroom, its role and the nature of the relationship between the construction of a proof and the social interactions. Assuming a social perspective, attention is focussed on the social construction of knowledge and on the structuring resources that shape mathematical experience. The study’s methodology has an interpretative nature. One outcome of the study discussed here is that students develop first a practical understanding with no awareness of the reasons founding mathematical statements and after a theoretical one leading them to a proof elaboration.

Chaos and crises in a model for cooperative hunting: A symbolic dynamics approach

In this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction sigma of predators cooperates in prey's hunting, while the rest of the population 1-sigma hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K, C-0) and (K, sigma) which separates two scenarios: (i) all-species coexistence and (ii) predator's extinction via chaotic crisis. We show that the crisis value of the carrying capacity K-c decreases at increasing sigma, indicating that predator's populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.

Water quality in lakes and reservoirs in China

Dissertation elaborated for the partial fulfilment of the requirements of the Master Degree in Civil Engineering in the Speciality Area of Hydarulics

Occupational exposure to fungi and particles in animal feed industry

Background: Very few studies regarding fungal and particulate matter (PM) exposure in feed industry have been reported, although such contaminants are likely to be a significant contributing factor to several symptoms reported among workers. The purpose of this study has been to characterize fungal and dust exposure in one Portuguese feed industry. Material and Methods: Air and surface samples were collected and subject to further macro- and microscopic observations. In addition we collected other air samples in order to perform real-time quantitative polymerase chain reaction (PCR) amplification of genes from Aspergillus fumigatus and Aspergillus flavus complexes as well as Stachybotrys chartarum. Additionally, two exposure metrics were considered – particle mass concentration (PMC), measured in 5 different sizes (PM0.5, PM1, PM2.5, PM5, PM10), and particle number concentration (PNC) based on results given in 6 different sizes in terms of diameter (0.3 μm, 0.5 μm, 1 μm, 2.5 μm, 5 μm and 10 μm). Results: Species from the Aspergillus fumigatus complex were the most abundant in air (46.6%) and in surfaces, Penicillium genus was the most frequently found (32%). The only DNA was detected from A. fumigatus complex. The most prevalent in dust samples were smaller particles which may reach deep into the respiratory system and trigger not only local effects but also the systemic ones. Conclusions: Future research work must be developed aiming at assessing the real health effects of these co-exposures.