[pt] A determinação automática e ótima de uma topologia é um passo muito importante dentro do processo da otimização de estruturas. Normalmente, a busca da topologia ótima é o primeiro passo para a definição da configuração da estrutura, pois é nela que é encontrada uma distribuição ótima de material dentro de um domínio pré-estabelecido. Esta dissertação tem como objetivo apresentar uma metodologia simples de otimização topológica, dado um sistema estrutural, definido por suas condições de apoio, carregamento e um domínio de projeto. Tipicamente, um problema de otimização topológica procura obter uma conectividade ótima da estrutura em um domínio de projeto visando minimizar a flexibilidade (ou maximizar a rigidez) com restrição no volume total da estrutura. Desde a introdução dos métodos de homogeneização o campo de pesquisa na área de otimização topológica aumentou e novos critérios estão sendo desenvolvidos. Nesta dissertação é apresentada uma metodologia para a solução de problemas de otimização topológica de estruturas no meio contínuo. A parametrização do tensor constitutivo é feita através de materiais do tipo SIMP (Solid Isotropic Microstruture with Penalty). O problema matemático proposto é o de minimização do volume total da estrutura com restrição no trabalho externo, além de obedecer implicitamente às restrições de equilíbrio e conectividade da estrutura. A análise estática da estrutura é realizada pelo Métodos dos Elementos Finitos utilizando o programa FEMOOP (Finit Element Method - Object Oriented Program) desenvolvido pelo grupo de pesquisa em computação gráfica do DEC/PUC-Rio. Vários métodos são sugeridos para a resolução do problema matemático de otimização topológica. Entre eles encontram-se métodos puramente heurísticos e métodos amparados por uma base matemática sólida. Nesta dissertação, o problema de otimização topológica é resolvido através de técnicas de programação matemática e é resolvido através da técnica de programação seqüencial convexa, utilizando o algoritmo do Método das Assíntotas Móveis (MMA). O desenvolvimento de um programa de computador em otimização topológica, permitiu determinar de maneira automática uma topologia ótima, bem como o estudo de algoritmos de solução e critérios de otimização topológica foi de grande importância para uma maior compreensão de modelos estruturais. / [en] Automatic and optimal determination of a topology is a crucial step in the process of structural optimization. Usually, the search for an optimal topology is the first step for the definition of the structure layout, found as an optimal distribution of material inside of a pre- established domain. This dissertation has as an objective to present a simple methodology for topology optimization, given a structural system, defined by support conditions, load and a design domain.Typically, a problem of topology optimization tries to obtain an optimum connectivity of the structure in a design domain, seeking to minimize the compliance (or maximize the stiffness) with constraints over the total volume of the structure. Since the introduction of homogenization methods,the research field in the area of topology optimization increased and new criteria are being developed.In this dissertation a methodology is presented for the solution of problems of topology optimization of structures in a continuum medium. The parametrization of the constitutive tensor is made through materials of the type SIMP (Solid Isotropic Microstruture with Penalty). The proposed mathematical problem is of minimization of the total volume of the structure with constraint to the external work while obeying implicitly the equilibrium constraints and connectivity of the structure. The static analysis of the structure is accomplished by the Finite Elements Method using the program FEMOOP (Finite Element Method - Object Oriented Program) developed by the research group in computer graphics of DEC/PUC-Rio.Several methods are suggested for the resolution of the mathematical problem of topology optimization. Among them there are some purely heuristic and others aided by a solid mathematical base. In this dissertation, the problem of topology optimization is solved through techniques of mathematical programming, applying the technique of convex sequential programming, using the algorithm of the Method of Moving Asymptots (MMA).The development of a computer program in topology optimization allowed us to determine automatically an optimal topology, and the study of solution algorithms and criteria of topology optimization were of great importance to a larger understanding of structural models.

Thesis advisor: Marina Vasilyeva / Motivated by the underrepresentation of women in math-related majors and occupations, the present dissertation explored the possibility that disparities in frequency of classroom participation—a measure of engagement prone to gender differences—could be partially responsible for gender differences in belonging and identity in math contexts. Via the introduction of a novel psychological construct, class participation confidence threshold, and the adoption of a Regulatory Focus Theory framework, the present work aimed to investigate mechanisms underlying gender differences in math classroom participation, as well as how these disparities might contribute to more distal outcomes.The dissertation consisted of two studies conducted with undergraduate students. Both studies tested a theoretical model that posited potential predictors and outcomes of gender differences in classroom participation. Study 1 (N = 161) was a cross-sectional investigation of students’ participation frequency, reported based on their general experience in current math and social science classes. Study 2 (N = 269) investigated the same associations using a daily diary methodology, including pre- and post-measures of relevant constructs. Results indicated that, when considering opportunities for participation, women participated less than men—both in math and the comparison domain of social science. In addition to less frequent participation, women generally displayed higher stereotype threat susceptibility and confidence thresholds in both domains. Women also demonstrated higher levels of a prevention focus in math compared to social science, while men’s regulatory orientation was similar across domains. With respect to the proposed outcomes of participation (i.e., belonging, identity, and career interest), women exhibited lower levels than men in math and equal or higher levels in social science. Path analyses revealed that students’ regulatory focus predicted their classroom participation and that this relation was mediated by their confidence threshold. Importantly, these results persisted even when controlling for motivational variables traditionally regarded as predictors of classroom participation according to Expectancy-Value Theory. The results suggest that an increased prevention focus in the math domain may lead women to set higher confidence thresholds and participate less frequently. / Thesis (PhD) — Boston College, 2022. / Submitted to: Boston College. Lynch School of Education. / Discipline: Counseling, Developmental and Educational Psychology.

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This study explores the impact of incorporating Food-away-from-Home (FAFH) into the Thrifty Food Plan (TFP). The new model of this study, FLEX, uses similar sets of datasets on prices, nutrition and average consumption pattern as those used in the TFP model. The 2001-2002 National Health and Nutrition Examination Survey (NHANES) data is used to generate average consumption and nutrient profiles. The relative price ratio of FAFH to FAH is assumed and fixed at 1.77. We compared nutrient intake, food intake and food expenditure amount across the FLEX, TFP, and the current low-income consumers' consumption pattern. The overall finding is that moderate amount of FAFH can be a part of a balanced and nutritious diet and allowing FAFH as another food sources makes the diet recommendations relatively easier to follow. With the relative price assumption used in this study, considering FAFH does not make the diet plan unaffordable. / Master of Science

Recently, there has been a big surge of research and public interest in increasing the math capabilities and skills of American children. This paper serves as a literature review examining how the home environment, specifically parents, can help with that. This meta-analysis delves into the factors of maternal math talk, a parent’s own math anxiety, and the relationship between a parent and child in the context of a parent’s gender stereotypes and a parent’s perception on his or her child’s math abilities. Interventions, suggestions, and future implications are also discussed. This paper will hopefully bring needed awareness to parents about their roles in their child’s math development, abilities, and achievement.

Student test scores related to mathematical word problems have been declining in a rural school district in western Louisiana. Word problems constitute a major component of the Algebra 1 End of Course examination, which students must be able to pass to graduate. Mathematics teachers have struggled to find appropriate strategies to teach students to answer constructed response questions (CRQs) effectively. The purpose of this study was to investigate the perceptions of math teachers about effective teaching strategies for improving student performance on CRQs. Guided by Piaget's constructivist theory, which is characterized by an emphasis on learner control of the learning process through active engagement and activation of prior knowledge, this study investigated teachers' perceptions and practices in relation to teaching the skills needed for CRQs. The research questions focused on math teachers' perceptions of current teaching practices, instructional effectiveness, and professional development needs. A case study design was used to capture the insights of 8 participants through semistructured interviews and observations. Emergent themes were identified from the data through a code-recode approach, and findings were developed and validated through triangulation and member checking. The key results were that math teachers expressed a need to collaborate with their colleagues to develop effective strategies that would incorporate literacy and hands-on learning. A project was designed to engage teachers in collaboration and planning to prepare students to think critically and problem solve. This study may promote positive social change by providing teachers with the tools necessary to improve students' thinking skills, problem-solving skills, and learning strategies.

Outlets for students to develop mathematical ideas and skills to solve real-life problems and applicable situations have been neglected in secondary classrooms (Gainsburg, 2008). Designing curricula that applies real-life situations has been promoted by the National Council of Teachers of Mathematics (2000), the National Research Council (1998), and the Commission on Behavioral and Social Sciences and Education (2000) and also is an expectation of state standards for student learning (Texas Education Agency, 2009). Contrary, evidence has shown low benefits to classroom real-life examples perceived by students. This study served dual purposes: 1) Determine the relationship between place-based education and mathematics learning, and 2) Investigate teacher conceptions of place-based education opportunities in high school, mathematics curriculum. This study employed two methodologies. A mixed-methods approach was employed for the meta-analysis of place-based programs and the second employed qualitative methods of structured interviewing to determine teachers’ conceptions of place-based pedagogy. Upon completion of the study, I concluded: 1) Place-based pedagogies align toward more foundational mathematic skills (e.g. measurement, number sense) when implemented, and 2) Teachers’ conceive place-based as a general effective tool for student engagement and real-world context of how mathematics functions in society.

As a result of low student scores on math assessments and teachers' seeming inability to raise those scores, professional development (PD) interventions were developed to address teachers' knowledge and understanding of math instruction. The purpose of this case study was to gain a deeper understanding of teachers' experiences with the math staff development training and how those experiences influence their teaching and students' learning. Guided by constructivist theory, the key research questions addressed the math teachers' experiences with the math PD and what teachers perceive to be their needs for effective math PD. Data for this case study were collected through interviews and observations of 25 secondary math teachers at 3 high schools. The data were coded using an analytic method to discern themes and patterns. The findings indicated that PD should have a focus on strategies that are relevant, include team collaboration and time to observe demonstration lessons. As a result, a 3-day PD was designed to focus on specific course content taught by teachers, opportunities to observe lessons, and team collaboration to design lessons. This project study affects positive social change via a PD training program with consistent, pertinent and content-specific support for math teachers in the classroom. Teachers will be more engaged in the process, students will be more engaged in their learning, and the community will benefit from increased student success. Effective PD has the potential to improve teacher practice, thus student learning, enabling student success in school and beyond. Successful students make successful adults who live independent, constructive and fulfilled lives.

Math to Mastery (MTM) is a multi-component math intervention that has demonstrated effective results in building math fluency and skill acquisition. Few studies have explored the use of brief experimental analysis (BEA) procedures to create an individualized, abbreviated MTM intervention to address skill deficits in basic math. The purpose of this current study is to analyze the utility of randomizing BEA procedures to effectively identify necessary mathematic components to create a more efficient intervention that will yield the highest math gains among participants. Researchers used an alternating treatment design with an extended analysis phase to address basic math skills. Participants included three grade school students with difficulty across different core math skills including addition, subtraction, multiplication, and division. Overall, this study yielded mixed results. Results indicated an abbreviated MTM intervention was effective for 1 out of 3 participants. Results, limitations, implications, and future research are also discussed.

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