Steps to success : family-friendly guide for fourth grade : mathematics

This document is designed to: provide examples of the standards, skills, and knowledge your child will learn in mathematics and should be able to do upon exiting fourth grade ; suggest activities on how you can help your child at home ; offer additional resources for information and help.

Steps to success : family-friendly guide for third grade : mathematics

This document is designed to: provide examples of the standards, skills, and knowledge your child will learn in mathematics and should be able to do upon exiting third grade ; suggest activities on how you can help your child at home ; offer additional resources for information and help.

Steps to success : family-friendly guide for fifth grade : mathematics

This document is designed to: provide examples of the standards, skills, and knowledge your child will learn in mathematics and should be able to do upon exiting fifth grade ; suggest activities on how you can help your child at home ; offer additional resources for information and help.

On polynomials with given Hilbert function and applications

Using Macaulay's correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an application we give a new lower bound for the dimension of cactus varieties of the third Veronese embedding. We discuss the case of cubic surfaces, where interesting phenomena occur.

Competencies Required in Education Research and Teaching Systematization according to Students from the Preschool, Primary and Secondary Education Programs of the University of Costa Rica

The purpose of this paper is to present the results of two online forums carried out with the participation of 42 students of the Licenciaturas  in Preschool Education, Primary Education and Secondary Education of the University of Costa Rica. The main purpose of the forums was to determine the insights of the participant students about the competencies they have achieved in the field of education research, and which have been the essential tools for them to systematize their own teaching practices. The discussion forums were part of the course FD5091 Métodos de Investigación Educativa [Education Research Methods] of the School of Teacher Education, delivered from March-April 2010.  Of the sample, 60 percent were students of the Preschool teaching program, 35 percent were from the Primary Education teaching program and 5 percent were from the Secondary Education teaching program in the fields of Science, Mathematics and Social Studies. According to the insights and beliefs showed by the participants –both, the future teachers and the profession practitioners–, there are no opportunities for research or systematization of their own teaching mediation, in the current work situation.(1) Translator’s Note: In Costa Rica, the “Licenciatura” is a one-year post-Bachelor study program, usually including thesis. “Primary Education” refers to students from the 1st to 6th grades, and “Secondary Education” refers to students from the 7th to 11th grades.

Teaching informatics to novices: big ideas and the necessity of optimal guidance

This thesis reports on the two main areas of our research: introductory programming as the traditional way of accessing informatics and cultural teaching informatics through unconventional pathways. The research on introductory programming aims to overcome challenges in traditional programming education, thus increasing participation in informatics. Improving access to informatics enables individuals to pursue more and better professional opportunities and contribute to informatics advancements. We aimed to balance active, student-centered activities and provide optimal support to novices at their level. Inspired by Productive Failure and exploring the concept of notional machine, our work focused on developing Necessity Learning Design, a design to help novices tackle new programming concepts. Using this design, we implemented a learning sequence to introduce arrays and evaluated it in a real high-school context. The subsequent chapters discuss our experiences teaching CS1 in a remote-only scenario during the COVID-19 pandemic and our collaborative effort with primary school teachers to develop a learning module for teaching iteration using a visual programming environment. The research on teaching informatics principles through unconventional pathways, such as cryptography, aims to introduce informatics to a broader audience, particularly younger individuals that are less technical and professional-oriented. It emphasizes the importance of understanding informatics's cultural and scientific aspects to focus on the informatics societal value and its principles for active citizenship. After reflecting on computational thinking and inspired by the big ideas of science and informatics, we describe our hands-on approach to teaching cryptography in high school, which leverages its key scientific elements to emphasize its social aspects. Additionally, we present an activity for teaching public-key cryptography using graphs to explore fundamental concepts and methods in informatics and mathematics and their interdisciplinarity. In broadening the understanding of informatics, these research initiatives also aim to foster motivation and prime for more professional learning of informatics.

Poset associahedra as sections of graph associahedra

Poset associahedra are a family of convex polytopes recently introduced by Pavel Galashin in 2021. The associahedron An is an (n-2)-dimensional convex polytope whose facial structure encodes the ways of parenthesizing an n-letter word (among several equivalent combinatorial objects). Associahedra are deeply studied polytopes that appear naturally in many areas of mathematics: algebra, combinatorics, geometry, topology... They have many presentations and generalizations. One of their incarnations is as a compactification of the configuration space of n points on a line. Similarly, the P-associahedron of a poset P is a compactification of the configuration space of order preserving maps from P to R. Galashin presents poset associahedra as combinatorial objects and shows that they can be realized as convex polytopes. However, his proof is not constructive, in the sense that no explicit coordinates are provided. The main goal of this thesis is to provide an explicit construction of poset associahedra as sections of graph associahedra, thus solving the open problem stated in Remark 1.5 of Galashin's paper.

Sociedade, cultura, matemática e seu ensino

One of the effects of the globalized world is a strong tendency to eliminate differences, promoting a planetary culture. Education systems are particularly affected, undergoing strong pressure from international studies and evaluations, inevitably comparative, and sadly competitive. As a result, one observes the gradual elimination of cultural components in the definition of education systems. The constitution of new social imaginaries becomes clear; imaginaries empty of historical, geographical and temporal referents, characterized by a strong presence of the culture of the image. The criteria of classification establish an inappropriate reference that has as its consequence the definition of practices and even of education systems. On the other hand, resistance mechanisms, often unconscious, are activated seeking to safeguard and recover the identifying features of a culture, such as its traditions, cuisine, languages, artistic manifestations in general, and, in doing so, to contribute to cultural diversity, an essential factor to encourage creativity. In this article, the sociocultural basis of mathematics and of its teaching are examined, and also the consequences of globalization and its effects on multicultural education. The concept of culture is discussed, as well as issues related to culture dynamics, resulting in the proposition of a theory of transdisciplinar and transcultural knowledge. Upon such basis the Ethnomathematics Program is presented. A critique is also made of the curriculum presently used, which is in its conception and detailing, obsolete, uninteresting and of little use. A different concept of curriculum is proposed, based on the communicative (literacy), analytical (matheracy), and material (technoracy) instruments.

Metodologia para a suavização de dados biomecanicos por função não parametrica ponderada local robusta

Universidade Estadual de Campinas. Faculdade de Educação Física

Histopathological evaluation of root canal filling materials for primary teeth

This study aimed to assess the response of apical and periapical tissues of dogs' teeth after root canal filling with different materials. Forty roots from dogs' premolars were prepared biomechanically and assigned to 4 groups filled with: Group I: commercial calcium hydroxide and polyethylene glycol-based paste (Calen®) thickened with zinc oxide; Group II: paste composed of iodoform, Rifocort® and camphorated paramonochlorophenol; Group III: zinc oxide-eugenol cement; Group IV: sterile saline. After 30 days, the samples were subjected to histological processing. The histopathological findings revealed that in Groups I and IV the apical and periapical regions exhibited normal appearance, with large number of fibers and cells and no resorption of mineralized tissues. In Group II, mild inflammatory infiltrate and mild edema were observed, with discrete fibrogenesis and bone resorption. Group III showed altered periapical region and thickened periodontal ligament with presence of inflammatory cells and edema. It may be concluded that the Calen paste thickened with zinc oxide yielded the best tissue response, being the most indicated material for root canal filling of primary teeth with pulp vitality.

Subcutaneous tissue response of isogenic mice to calcium hydroxide-based pastes with chlorhexidine

This study was evaluated the response of subcutaneous connective tissue of isogenic mice to calcium hydroxide-based pastes with chlorhexidine digluconate (CHX). Seventy isogenic male BALB/c mice aged 6-8 weeks and weighing 15-20 g were randomly assigned to 8 groups. The animals received polyethylene tube implants as follows: Groups I, II, and III (n=10) - Calen® paste mixed with 0.4% CHX (experimental paste; Calen/CHX) for 7, 21, and 63 days, respectively; Groups IV, V, and VI (n=10) - UltraCal™ paste mixed with 2% CHX (experimental paste supplied by Ultradent Products Inc.; Ultracal/CHX) for 7, 21, and 63 days, respectively; and Groups VII and VIII (n=5): empty tube for 7 and 21 days, respectively. At the end of the experimental periods, the implants were removed together with the surrounding tissues (skin and subcutaneous connective tissue). The biopsied tissues were subjected to routine processing for histological analysis. Using a descriptive analysis and a four-point (0-3) scoring system, the following criteria were considered for qualitative and quantitative analysis of the tissue around the implanted materials: collagen fiber formation, tissue thickness and inflammatory infiltrate. A quantitative analysis was performed by measuring the thickness (µm), area (µm²) and perimeter (µm) of the reactionary granulomatous tissue formed at the tube ends. Data were analyzed statistically by the Kruskal-Wallis test and Dunn's post-test (α=0.05). Calen/CHX showed biocompatibility with the subcutaneous and reactionary tissues, with areas of discrete fibrosis and normal conjunctive fibrous tissue, though without statistically significant difference (p>0.05) from the control groups. In Groups I to III, there was a predominance of score 1, while in Groups IV to VI scores 2 and 3 predominated for all analyzed parameters. UltraCal/CHX, on the other hand, induced the formation of an inflammatory infiltrate and abundant exudate, suggesting a persistent residual aggression from the material, even 63 days after implant placement. In conclusion, the Calen paste mixed with 0.4% CHX allowed an adequate tissue response, whereas the UltraCal paste mixed with 2% CHX showed unsatisfactory results.

A Análise Matemática no Ensino Universitário Brasileiro: a contribuição de Omar Catunda

The goal of this paper is to show the diffusion, reception, and utilization of Omar Catunda's book Course of Mathematical Analysis for mathematics and engineering teaching in Brazilian universities, e. g., University of Sao Paulo and the University of Bahia from 1950 to 1976. We used interviews of some ex-alumni or users of his book. We also present some signs of the influence of his book and of Catunda himself at University of Rio Grande do Sul. We argue that Catunda and his book were important agents of process of modernizing the teaching of calculus and analysis, through his classes as well as his book.

O Intuitivo e o Lógico no Conhecimento Matemático: análise de uma proposta pedagógica em relação a abordagens filosóficas atuais e ao contexto educacional da matemática

In this paper, we consider Meneghetti & Bicudo's proposal (2003) regarding the constitution of mathematical knowledge and analyze it with respect to the following two focuses: in relation to conceptions of mathematical knowledge following the fundamentalist crisis in mathematics; and in the educational context of mathematics. The investigation of the first focus is done analyzing new claims in mathematical philosophy. The investigation of the second focus is done firstly via a theoretical reflection followed by an examination of the implementation of the proposal in the process of development of didactic materials for teaching and learning Mathematics. Finally, we present the main results of the application of one of those materials.

Multicriteria analysis in decision making under information uncertainty

This paper presents results of research related to multicriteria decision making under information uncertainty. The Bell-man-Zadeh approach to decision making in a fuzzy environment is utilized for analyzing multicriteria optimization models (< X, M > models) under deterministic information. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. This circumstance permits one to generalize the classic approach to considering the uncertainty of quantitative information (based on constructing and analyzing payoff matrices reflecting effects which can be obtained for different combinations of solution alternatives and the so-called states of nature) in monocriteria decision making to multicriteria problems. Considering that the uncertainty of information can produce considerable decision uncertainty regions, the resolving capacity of this generalization does not always permit one to obtain unique solutions. Taking this into account, a proposed general scheme of multicriteria decision making under information uncertainty also includes the construction and analysis of the so-called < X, R > models (which contain fuzzy preference relations as criteria of optimality) as a means for the subsequent contraction of the decision uncertainty regions. The paper results are of a universal character and are illustrated by a simple example. (c) 2007 Elsevier Inc. All rights reserved.

The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes

The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP`s) taking values in a general Borel space and with compact action space depending on the state variable. In order to do that we first derive some important properties for a pseudo-Poisson equation associated to the problem. In the sequence it is shown that the convergence of the PIA to a solution satisfying the optimality equation holds under some classical hypotheses and that this optimal solution yields to an optimal control strategy for the average control problem for the continuous-time PDMP in a feedback form.