Dificuldades de aprendizagem da álgebra: Análise de manuais do 7º e 8º anos de escolaridade

Dissertação de Mestrado apresentada ao Instituto Superior de Psicologia Aplicada para obtenção de grau de Mestre na especialidade de Psicologia Educacional.

THERE GOES THE ELECTORAL NEIGHBORHOOD: LOCAL NETWORKS, ATTRIBUTION OF RESPONSIBILITY, AND THE (UN) FAIRNESS OF ELECTIONS

During the last two decades there have been but a handful of recorded cases of electoral fraud in Latin America. However, survey research consistently shows that often citizens do not trust the integrity of the electoral process. This dissertation addresses the puzzle by explaining the mismatch between how elections are conducted and how the process is perceived. My theoretical contribution provides a double-folded argument. First, voters’ trust in their community members (“the local experience”) impacts their level of confidence in the electoral process. Since voters often find their peers working at polling stations, negative opinions about them translate into negative opinions about the election. Second, perceptions of unfairness of the system (“the global effect”) negatively impact the way people perceive the transparency of the electoral process. When the political system fails to account for social injustice, citizens lose faith in the mechanism designed to elect representatives -and ultimately a set of policies. The fact that certain groups are systematically disregarded by the system triggers the notion that the electoral process is flawed. This is motivated by either egotropic or sociotropic considerations. To test these hypotheses, I employ a survey conducted in Costa Rica, El Salvador, Honduras, and Guatemala during May/June 2014, which includes a population-based experiment. I show that Voters who trust their peers consistently have higher confidence in the electoral process. Whereas respondents who were primed about social unfairness (treatment) expressed less confidence in the quality of the election. Finally, I find that the local experience is predominant over the global effect. The treatment has a statistically significant effect only for respondents who trust their community. Attribution of responsibility for voters who are skeptics of their peers is clear and simple, leaving no room for a more diffuse mechanism, the unfairness of the political system. Finally, now I extend analysis to the Latin America region. Using data from LAPOP that comprises four waves of surveys in 22 countries, I confirm the influence of the “local experience” and the “global effect” as determinants of the level of confidence in the electoral process.

INVESTIGATING THE POSTWAR DECLINE OF RACE IN SCIENCE

Race as a biological category has a long and troubling history as a central ordering concept in the life and human sciences. The mid-twentieth century has been marked as the point where biological concepts of race began to disappear from science. However, biological definitions of race continue to penetrate scientific understandings and uses of racial concepts. Using the theoretical frameworks of critical race theory and science and technology studies and an in-depth case study of the discipline of immunology, this dissertation explores the appearance of a mid-century decline of concepts of biological race in science. I argue that biological concepts of race did not disappear in the middle of the twentieth century but were reconfigured into genetic language. In this dissertation I offer a periodization of biological concepts of race. Focusing on continuities and the effects of contingent events, I compare how biological concepts of race articulate with racisms in each period. The discipline of immunology serves as a case study that demonstrates how biological concepts of race did not decline in the postwar era, but were translated into the language of genetics and populations. I argue that the appearance of a decline was due to events both internal and external to the science of immunology. By framing the mid-twentieth century disappearance of race in science as the triumph of an antiracist racial project of science, it allows us to more clearly see the more recent resurgence of race in science as a recycling of older themes and tactics from the racist science projects of the past.

POSITIVE FILTERED P_N METHOD FOR LINEAR TRANSPORT EQUATIONS AND THE ASSOCIATED OPTIMIZATION ALGORITHM

We propose a positive, accurate moment closure for linear kinetic transport equations based on a filtered spherical harmonic (FP_N) expansion in the angular variable. The FP_N moment equations are accurate approximations to linear kinetic equations, but they are known to suffer from the occurrence of unphysical, negative particle concentrations. The new positive filtered P_N (FP_N+) closure is developed to address this issue. The FP_N+ closure approximates the kinetic distribution by a spherical harmonic expansion that is non-negative on a finite, predetermined set of quadrature points. With an appropriate numerical PDE solver, the FP_N+ closure generates particle concentrations that are guaranteed to be non-negative. Under an additional, mild regularity assumption, we prove that as the moment order tends to infinity, the FP_N+ approximation converges, in the L2 sense, at the same rate as the FP_N approximation; numerical tests suggest that this assumption may not be necessary. By numerical experiments on the challenging line source benchmark problem, we confirm that the FP_N+ method indeed produces accurate and non-negative solutions. To apply the FP_N+ closure on problems at large temporal-spatial scales, we develop a positive asymptotic preserving (AP) numerical PDE solver. We prove that the propose AP scheme maintains stability and accuracy with standard mesh sizes at large temporal-spatial scales, while, for generic numerical schemes, excessive refinements on temporal-spatial meshes are required. We also show that the proposed scheme preserves positivity of the particle concentration, under some time step restriction. Numerical results confirm that the proposed AP scheme is capable for solving linear transport equations at large temporal-spatial scales, for which a generic scheme could fail. Constrained optimization problems are involved in the formulation of the FP_N+ closure to enforce non-negativity of the FP_N+ approximation on the set of quadrature points. These optimization problems can be written as strictly convex quadratic programs (CQPs) with a large number of inequality constraints. To efficiently solve the CQPs, we propose a constraint-reduced variant of a Mehrotra-predictor-corrector algorithm, with a novel constraint selection rule. We prove that, under appropriate assumptions, the proposed optimization algorithm converges globally to the solution at a locally q-quadratic rate. We test the algorithm on randomly generated problems, and the numerical results indicate that the combination of the proposed algorithm and the constraint selection rule outperforms other compared constraint-reduced algorithms, especially for problems with many more inequality constraints than variables.

Multiscale Modeling and Simulation of Stepped Crystal Surfaces

A primary goal of this dissertation is to understand the links between mathematical models that describe crystal surfaces at three fundamental length scales: The scale of individual atoms, the scale of collections of atoms forming crystal defects, and macroscopic scale. Characterizing connections between different classes of models is a critical task for gaining insight into the physics they describe, a long-standing objective in applied analysis, and also highly relevant in engineering applications. The key concept I use in each problem addressed in this thesis is coarse graining, which is a strategy for connecting fine representations or models with coarser representations. Often this idea is invoked to reduce a large discrete system to an appropriate continuum description, e.g. individual particles are represented by a continuous density. While there is no general theory of coarse graining, one closely related mathematical approach is asymptotic analysis, i.e. the description of limiting behavior as some parameter becomes very large or very small. In the case of crystalline solids, it is natural to consider cases where the number of particles is large or where the lattice spacing is small. Limits such as these often make explicit the nature of links between models capturing different scales, and, once established, provide a means of improving our understanding, or the models themselves. Finding appropriate variables whose limits illustrate the important connections between models is no easy task, however. This is one area where computer simulation is extremely helpful, as it allows us to see the results of complex dynamics and gather clues regarding the roles of different physical quantities. On the other hand, connections between models enable the development of novel multiscale computational schemes, so understanding can assist computation and vice versa. Some of these ideas are demonstrated in this thesis. The important outcomes of this thesis include: (1) a systematic derivation of the step-flow model of Burton, Cabrera, and Frank, with corrections, from an atomistic solid-on-solid-type models in 1+1 dimensions; (2) the inclusion of an atomistically motivated transport mechanism in an island dynamics model allowing for a more detailed account of mound evolution; and (3) the development of a hybrid discrete-continuum scheme for simulating the relaxation of a faceted crystal mound. Central to all of these modeling and simulation efforts is the presence of steps composed of individual layers of atoms on vicinal crystal surfaces. Consequently, a recurring theme in this research is the observation that mesoscale defects play a crucial role in crystal morphological evolution.