Experiencing Manipulative Material for the Teaching and Learning of Mathematics

This paper presents some outcomes from research based on classroom experiences. The main themes are the use of mirrors, kaleidoscopes, dynamic geometry software, and manipulative material considering their possibilities for the teaching and learning of Euclidean and non-Euclidean geometries.

GeoPlexo: um material manipulável para o ensino dos números complexos

This study aims to develop a manipulative material to assist the teaching and learning of Complex Numbers. Primarily, It tries to define the status of the current teaching of Complex Numbers, having as guide the bias of the research produced in dissertations and published on the website of Capes and the Virtual Library of Profmat from 2004 to 2014. It presents historical aspects of the theme, a mathematical foundation and a discussion of the use of manipulative materials as teaching resources for the teaching of mathematics. It introduces the manipulative material called GeoPlexo and a sequence of activities of potentiation and settling of complex numbers, explaining its use. It concludes with the importance of manipulative materials as a teaching resource for the teaching of Complex Numbers, especially regarding the geometric visualization of this mathematical object.

Contributos de um ambiente de geometria dinâmica (geogebra) e do geoplano na compreensão das propriedades e relações entre quadriláteros: um estudo com alunos do 4.º ano

O estudo insere-se no âmbito da educação matemática, mais especificamente na área da geometria. Com esta investigação pretende-se compreender qual o contributo do Ambiente de Geometria Dinâmica (AGD), GeoGebra, e do material manipulável (geoplano) na identificação das propriedades e relações entre quadriláteros: trapézio, paralelogramo, retângulo, losango e quadrado. De acordo com o objetivo do estudo formularam-se três questões: Qual o papel das representações na identificação das propriedades dos quadriláteros? Que influência tem a visualização na identificação das propriedades dos quadriláteros? Quais os contributos da utilização do AGD, GeoGebra, e do material manipulável (geoplano) na compreensão das propriedades e relações entre os quadriláteros? Atendendo à problemática em estudo, optou-se por uma metodologia de investigação predominantemente qualitativa, baseada em três estudos de caso. A recolha de dados empíricos foi realizada numa turma de 4.º ano do 1.º ciclo do ensino básico onde se implementou uma experiência de ensino, envolvendo todos os alunos e recorrendo ao geoplano e ao GeoGebra. Essa recolha incidiu na observação participante, em sala de aula, no registo de notas da investigadora, nos documentos produzidos pelos alunos e nos registos áudio e vídeo das discussões nos grupos e no coletivo da turma. Em termos de resultados, salienta-se que a utilização de representações evidenciou a compreensão que os alunos têm dos conceitos, facilitou a identificação das propriedades dos quadriláteros e a compreensão das relações entre eles. Os alunos identificaram as propriedades com base nas representações, no entanto focaram-se em casos particulares, de acordo com a imagem mental que têm da figura, especificamente o protótipo, indiciando a influência da visualização. Dos resultados sobressai também a dificuldade que os alunos sentiram em considerar uma figura como representante de uma classe e em distinguir atributos essenciais e não essenciais. Da análise dos dados ressalta também que tanto o geoplano como o GeoGebra foram uma mais-valia na concretização da experiência de ensino deste estudo. Os dois possuem vantagens e limitações e podem ser usados de maneira que um complemente o outro, podendo dessa forma contribuir, favoravelmente, para a aprendizagem da geometria. - ABSTRACT The study falls within the scope of mathematics education, specifically in the area of geometry. This research aims to understand the contribution of the Dynamic Geometry Environment (GeoGebra) and manipulative material (Geoboard) in the identification of properties and relations of quadrilaterals: trapezium, parallelogram, rectangle, diamond and square. According to the purpose of the study three questions were formulated: What is the role of the representations in the identification of the properties of quadrilaterals? What is the influence of visualization on the identification of the properties of quadrilaterals? What are the contributions on the use of Dynamic Geometry Environment (GeoGebra) and manipulative material (Geoboard) to understand the properties and relationships among quadrilaterals? Given the problem under study, it was chosen a predominantly qualitative research methodology based on three case studies. The empirical data collection was carried out on a fourth primary grade class, where it was implemented a teaching experience, involving all students and the use of Geoboard and GeoGebra. This collection was focused on participant observation in the classroom, in the record of the researcher’s notes, the documents produced by the students and the audio and video recordings of group discussions and collective class. In terms of results, it is noted that the use of representations showed the students understanding of the concepts and that it has facilitated the identification of the properties of quadrilaterals and understanding of the relationships between them. The students identified properties based on representations, however they focused in particular cases, according to the mental image that they have of the figure, specifically the prototype, indicating the influence of visualization. Results also highlights the difficulty that students felt in considering a figure as a representation of a group and distinguishing essential and nonessential attributes. Data analysis also highlights that both Geoboard and GeoGebra have been an asset in the delivery of teaching experience in this study. Both have advantages and limitations and they may be used to complement each other and contribute favorably to the learning of geometry.

Atividades de investigação em Geometria: uma experiência no 2º ano de escolaridade

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ciências da Educação, especialidade Educação Matemática na Educação Pré-Escolar e nos 1.º e 2.º Ciclos do Ensino Básico

Experienciando Materiais Manipulativos para o Ensino e a Aprendizagem da Matemática

This paper presents some outcomes from research based on classroom experiences. The main themes are the use of mirrors, kaleidoscopes, dynamic geometry software, and manipulative material considering their possibilities for the teaching and learning of Euclidean and non-Euclidean geometries.

Um estudo de fractais geométricos na formação de professores de matemática

Pós-graduação em Educação Matemática - IGCE

Pavimentações do plano: um estudo com professores de matemática e arte

Pós-graduação em Educação Matemática - IGCE

Do improviso às possibilidades de ensino: estudo de caso de uma professora de matemática no contexto da inclusão de estudantes cegos

Pós-graduação em Educação Matemática - IGCE

O uso do material manipulativo Tangram e de jogos como estratégias de motivação para a aprendizagem de frações

In this research, we analyzed the use of manipulative materials and games as motivators tools that facilitate the comprehension of fractions content when presented to a class of students from the 9th grade from a public school in Guaratinguetá-SP city. The students are 14 and 17 years old. Initially we presented the benefits that could bring manipulative materials for teaching and learning with understanding, followed by historical accounts of the Tangram material. We show the advantages of the games, when properly used in activities classroom. The game titled Dominoes fractions using the Tangram was applied in order to check if students retook properly the fractions contents. This research was motivated students to participate in math classes and this motivation may have promoted the understanding of the contents worked

Effect Of Platform Connection And Abutment Material On Stress Distribution In Single Anterior Implant-supported Restorations: A Nonlinear 3-dimensional Finite Element Analysis.

Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections.

Improved Selective Cholesterol Adsorption By Molecularly Imprinted Poly(methacrylic Acid)/silica (pmaa-sio₂) Hybrid Material Synthesized With Different Molar Ratios.

The present paper describes the synthesis of molecularly imprinted polymer - poly(methacrylic acid)/silica and reports its performance feasibility with desired adsorption capacity and selectivity for cholesterol extraction. Two imprinted hybrid materials were synthesized at different methacrylic acid (MAA)/tetraethoxysilane (TEOS) molar ratios (6:1 and 1:5) and characterized by FT-IR, TGA, SEM and textural data. Cholesterol adsorption on hybrid materials took place preferably in apolar solvent medium, especially in chloroform. From the kinetic data, the equilibrium time was reached quickly, being 12 and 20 min for the polymers synthesized at MAA/TEOS molar ratio of 6:1 and 1:5, respectively. The pseudo-second-order model provided the best fit for cholesterol adsorption on polymers, confirming the chemical nature of the adsorption process, while the dual-site Langmuir-Freundlich equation presented the best fit to the experimental data, suggesting the existence of two kinds of adsorption sites on both polymers. The maximum adsorption capacities obtained for the polymers synthesized at MAA/TEOS molar ratios of 6:1 and 1:5 were found to be 214.8 and 166.4 mg g(-1), respectively. The results from isotherm data also indicated higher adsorption capacity for both imprinted polymers regarding to corresponding non-imprinted polymers. Nevertheless, taking into account the retention parameters and selectivity of cholesterol in the presence of structurally analogue compounds (5-α-cholestane and 7-dehydrocholesterol), it was observed that the polymer synthesized at the MAA/TEOS molar ratio of 6:1 was much more selective for cholesterol than the one prepared at the ratio of 1:5, thus suggesting that selective binding sites ascribed to the carboxyl group from MAA play a central role in the imprinting effect created on MIP.

Mesenchymal Stromal Cells From Adipose Tissue Attached To Suture Material Enhance The Closure Of Enterocutaneous Fistulas In A Rat Model.

Surgical treatment for enterocutaneous fistulas (EF) frequently fails. Cell therapy may represent a new approach to treatment. Mesenchymal stromal cells (MSCs) have high proliferative and differentiation capacity. This study aimed to investigate whether MSCs could adhere to suture filament (SF), promoting better EF healing. MSCs, 1 × 10(6), from adipose tissue (ATMSCs) were adhered to a Polyvicryl SF by adding a specific fibrin glue formulation. Adhesion was confirmed by confocal and scanning electron microscopy (SEM). A cecal fistula was created in 22 Wistar rats by incising the cecum and suturing the opening to the surgical wound subcutaneously with four separate stitches. The animals were randomly allocated to three groups: control (CG)-five animals, EF performed; injection (IG)-eight animals 1 × 10(6) ATMSCs injected around EF borders; and suture filament (SG): nine animals, sutured with 1 × 10(6) ATMSCs attached to the filaments with fibrin glue. Fistulas were photographed on the operation day and every 3 days until the 21st day and analyzed by two observers using ImageJ Software. Confocal and SEM results demonstrated ATMSCs adhered to SF (ATMSCs-SF). The average reduction size of the fistula area at 21st day was greater for the SG group (90.34%, P < 0.05) than the IG (71.80%) and CG (46.54%) groups. ATMSCs adhered to SF maintain viability and proliferative capacity. EF submitted to ATMSCs-SF procedure showed greater recovery and healing. This approach might be a new and effective tool for EF treatment.

Brazilian Natural Fiber (jute) As Raw Material For Activated Carbon Production.

Jute fiber is the second most common natural cellulose fiber worldwide, especially in recent years, due to its excellent physical, chemical and structural properties. The objective of this paper was to investigate: the thermal degradation of in natura jute fiber, and the production and characterization of the generated activated carbon. The production consisted of carbonization of the jute fiber and activation with steam. During the activation step the amorphous carbon produced in the initial carbonization step reacted with oxidizing gas, forming new pores and opening closed pores, which enhanced the adsorptive capacity of the activated carbon. N2 gas adsorption at 77K was used in order to evaluate the effect of the carbonization and activation steps. The results of the adsorption indicate the possibility of producing a porous material with a combination of microporous and mesoporous structure, depending on the parameters used in the processes, with resulting specific surface area around 470 m2.g-1. The thermal analysis indicates that above 600°C there is no significant mass loss.

Produção de serapilheira e decomposição do material foliar em um cerradão na Estação Ecológica de Jataí, município de Luiz Antônio, SP, Brasil

We estimate litter production and leaf decomposition rate in a cerradão area, physiognomy little studied and very threatened in São Paulo State. During the period of study, litter production was 5646.9 kg.ha-1.year-1, which the 'leaf' fraction corresponded to 4081.2 kg.ha¹.year¹; the 'branch' fraction, to 1066.1 kg.ha-1.year-1; the 'reproductive structures' fraction, to 434.1 kg.ha-1.year-1; and the 'miscellaneous' fraction to 65.5 kg.ha-1.year-1. Litter production was highly seasonal and negatively correlated with relative humidity and air temperature. Leaf production was negatively correlated with relative humidity, rainfall, and air temperature. There was no significant difference between litter production found in this study and those in two other sites with cerradão and semideciduous forest, but these physiognomies differed significantly from the cerrado sensu stricto. Leaf decomposition rate (K) was 0.56. Half-life of the decomposing material was 1.8 years and turnover time was 2.3 years.

Estimulação perceptivo-motora em crianças portadoras de deficiencia visual : proposta de utilização de material pedagogico

Universidade Estadual de Campinas . Faculdade de Educação Física