DSpace Communidade:

Ensino de estatística descritiva com Python : uma proposta aplicada ao ensino médio

Fri, 10 Jul 2026 00:00:00 GMT

Título: Ensino de estatística descritiva com Python : uma proposta aplicada ao ensino médio Autor(es): Santana, José Eugênio Andrade Abstract: The teaching of Descriptive Statistics in High School faces challenges related to data interpretation, tables, graphs, and the understanding of measures of central tendency and dispersion, difficulties frequently observed in school practice. Considering the importance attributed by the Brazilian National Common Core Curriculum to the reading, interpretation, and critical analysis of statistical information, this study aimed to propose, apply, describe, analyze, and reflect on a sequence of activities for Descriptive Statistics mediated by the Python programming language, aiming to integrate calculations, graphical representations, and data interpretation. This study is an experience report with a qualitative approach, developed in High School Mathematics classes at Colégio Estadual de Tempo Integral Castro Alves, located in Adustina, Bahia, Brazil. The methodological proposal consisted of integrating conventional instruction of statistical content with computational practices in Python, in which students simulated data, organized information into tables, constructed graphs, and calculated statistical measures, relating these results to the analyzed data sets. The data were analyzed through triangulation involving teacher observations, students' productions, and a feedback questionnaire, aiming to understand the perceptions and reflections emerging from the developed experience. As an educational product, a sequence of activities mediated by Python was developed, aiming at the development of statistical interpretation. The results indicate that the proposed approach has the potential to foster the understanding of Descriptive Statistics concepts and expand the possibilities for data interpretation, in line with the demands of Mathematics Education. It is not intended to claim that the use of Python, by itself, guarantees better learning outcomes, but rather that its use as a mediating tool showed potential to foster statistical interpretation processes, expand possibilities for data analysis, and stimulate students' engagement in the proposed activities.

Uma equação do calor semilinear com uma reação localizada e dados iniciais não contínuos

Tue, 19 May 2026 00:00:00 GMT

Título: Uma equação do calor semilinear com uma reação localizada e dados iniciais não contínuos Autor(es): Santos, Poliano Fagundes dos Abstract: This dissertation studies a semilinear heat equation with a nonlinear term repre senting a concentrated reaction in a closed region of Ω ⊂ Rn, a smooth and bounded domain, or the entire space Rn, with n ≥ 2. The work is based on the article [9], which allows for the consideration of non-continuous initial data. We first present the preliminary concepts and analytical tools required for the development of the theory, including special functions, results from measure theory, and Lebesgue spaces Lr(Ω), with 1 < r < ∞. We then study the linear heat equation and the associated Green’s function, deriving fundamental linear estimates in both the interior of the domain and on the boundary, which are essential for handling the localized nonlinear term. Finally, we establish the main result of the dissertation, proving local-in time existence, uniqueness of solutions, continuous dependence on the initial data, and preservation of positivity by means of Banach’s Fixed Point Theorem.

A importância das metodologias ativas na gamificação de jogos matemáticos com ênfase em análise combinatória no ensino médio

Thu, 28 May 2026 00:00:00 GMT

Título: A importância das metodologias ativas na gamificação de jogos matemáticos com ênfase em análise combinatória no ensino médio Autor(es): Silva, Pedro Fernando da Abstract: The teaching of Combinatorial Analysis in Brazilian high school is often characterized by overly procedural approaches, centered on the memorization of formulas for permutation, arrangement, and combination, without developing students’ understanding of the logical structures underlying counting problems. This didactic gap motivated the present disserta tion, which aims to propose a didactic sequence for teaching Combinatorial Analysis in high school, integrating active methodologies, gamification, and the Wordwall digital platform within the context of Brazilian public schools. The research is bibliographic and propo sitional in nature, with a qualitative approach, grounded in references from mathematics education, active methodologies, and digital technologies in education. Based on an analysis of students’ most common difficulties, three intervention axes were identified: conceptual progression of combinatorial reasoning, intentional use of gamification elements for enga gement and feedback, and integration of Wordwall as a didactic mediation tool offering equivalent interactive and printable formats. The resulting educational product consists of an eight-lesson sequence, including a formative assessment rubric, teacher mediation stra tegies, inclusion adaptations, and alternatives for low-connectivity contexts. The findings indicate that the combination of conceptual progression, intentional gamification, and a fle xible digital platform enables more active, argumentative, and context-sensitive learning. The main contribution of the research lies in providing mathematics teachers in public scho ols with a replicable didactic framework that subordinates technology use to mathematical understanding and pedagogical mediation

Modelo de regressão simbólica informado por física para a temperatura de transição vítrea em vidros alcalino borato

Wed, 25 Feb 2026 00:00:00 GMT

Título: Modelo de regressão simbólica informado por física para a temperatura de transição vítrea em vidros alcalino borato Autor(es): Vitoria, Leonardo dos Santos Abstract: In this thesis, a new analytical model for the glass transition temperature of borate glasses of the form xM2O–(100 − x)B2O3, with M = Li, Na, and K, is proposed. The model was induced through a physics-informed symbolic regression framework. The physical descriptors employed in the induction process were based on the elastic deformation model originally proposed by Makishima and Mackenzie, in which the Young’s modulus of multicomponent glasses is expressed in terms of the average bond dissociation energy of the glass network and the manner in which atoms are structurally arranged, represented by the packing density factor. In addition, a contemporary revision of the original model was considered, introducing a new formulation of the packing factor based on rigid unit packing fraction called RUPF. The validation of the induced model was carried out through three complementary stages designed to ensure both physical and statistical rigor: (i) evaluation of the extrapolation capability to systems chemically distinct from those used in training, specifically glasses containing Rb and Cs; (ii) estimation of bond dissociation energies via error minimization with respect to experimental glass transition temperature data, followed by comparison with reference values from the literature in order to assess physical plausibility; and (iii) knowledge transfer to the prediction of the Young’s modulus of Rband Cs-containing glasses using the model proposed by Shi et al. The results from these three validation stages indicate that the induced model is physically consistent, as the estimated bond dissociation energies fall within physically reasonable ranges, while also exhibiting good statistical accuracy, with mean deviations on the order of 17 K relative to experimental Tg values between 300 and 800K. The limitations of the model were further investigated along two fronts: (i) uncertainty analysis through Monte Carlo uncertainty propagation and (ii) extrapolation to systems containing divalent modifiers, specifically Sr and Ba. A region of increased uncertainty was observed in the compositional range between 20% and 40% alkali addition, which was attributed to the larger uncertainties associated with the dissociation energies of BO4 structural units characteristic of this range. Extrapolation to alkaline-earth modifiers revealed a clear limitation of the model, which systematically underestimated the glass transition temperature by more than 100 K for both systems. Overall, this thesis demonstrates a methodological framework capable of inducing data-driven, physics-informed analytical models that exhibit physical consistency by extrapolating beyond the physical-chemical domain used in training and by transferring knowledge to simillar property models. This approach establishes a promising pathway for the development of interpretable models capable of generating new physical insight from experimental data.