Sannolikhet och statistik är ett ämne lärare har svårt att undervisa i. Dels för att ämnet är relativt nytt, dels för att lärare saknar fördjupade kunskaper inom området. Syftet med den här litteraturstudien är att bidra med kunskap om undervisningsaktiviteter i sannolikhet och statistik i grundskolan, år f-6, för lärare. Databaserna ERIC, WoS och DiVA användes för att samla in vetenskapligt underlag till denna systematiska litteraturstudie. Resultatet visar att aktiviteter med konkret material är användbart i alla delar i sannolikhet och statistik samt att det ger bättre resultat för elevers kunskapsinhämtande om aktiviteterna följs upp av diskussioner. I resultatet framkommer även konkreta förslag på hur aktiviteter med konkret material kan användas i en undervisningssituation. Konsekvenser för undervisning samt förslag till vidare forskning avslutar den här studien. / Probability and statistics is a subject that teachers find difficult to teach. Partly because this area is relatively new in the mathematics course, partly because of the lack of deepened knowledge amongst teachers in this subject area. The purpose of this study is to contribute with knowledge about teaching activities in the probability and statistics course in the early years of elementary school, years K–6, for teachers. The databases used to collect scientific foundation to this systematic literature study is ERIC, WoS and DiVA. The result showed that activities with manipulatives are useful in all subareas in probability and statistics and that students’ knowledge acquirement improves if the activities are followed up by discussions. However, the result also brought out tangible suggestions of how activities with concrete materials can be used in a teaching situation. To round up this study is a discussion of consequences for teaching as well as suggestions for further research.

The aim of this study was to assess the strength, durability properties and corrosion resistance of concrete samples using supplementary cementitious blended materials. In this investigation, three supplementary concrete materials (SCMs) were used together with ordinary Portland Cement (OPC) to form cementitious blends at different proportions. The supplementary materials are silica fume (SF), ground granulated blast furnace slag (GGBS) and fly ash (FA). Sixteen (16) different proportions of the cementitious blends were produced. Tests carried out on concrete samples include slump test, compressive strength, oxygen permeability, sorptivity, porosity, chloride conductivity test, resistance to chloride and sulphate attack. The electrode potentials of tested samples were also observed using electrochemical measurements. Concrete specimens prepared with 10%, 20%, 30%, 40%, up to 60% of blended cements replacement levels were evaluated for their compressive strength at, 7, 14, 28, 90 and 120 days while the specimens were evaluated for durability tests at 28, and 90 days respectively. The results were compared with ordinary Portland cement concrete without blended cement. Voltage, and temperature measurements were also carried out to understand the quality of concrete. The corrosion performance of steel in reinforced concrete was studied and evaluated by electrochemical half-cell potential technique in both sodium chloride, and magnesium sulphate solutions respectively. The reinforced concrete specimens with centrally embedded 12mm steel bar were exposed to chloride and sulphate solutions with the 0.5 M NaCl and MgSO4 concentrations respectively. An impressed voltage technique was carried out to evaluate the corrosion resistance of the combination of quaternary cementitious blended cement, so as to get the combination with optimum performance. Improvement of strength, durability, and corrosion resistance properties of blended concrete samples are observed at different optimum percentages for binary, ternary and quaternary samples. The effect of cementitious blends is recognized in limiting the corrosion potential of the tested SCM concrete samples. Generally, the cementitious blends with limited quantity of SF to 10% have the potential to produce satisfactory concrete. These should however be used for low cost construction, where high quality concrete is not required. / Civil and Chemical Engineering / M. Tech. (Chemical Engineering)

<p>Thanks to I have got to explore different teaching ways around the problem solving in a year 3, in a multicultural school which is located south of Stockholm, I have been able to answer my question at issue in my degree work. My question at issue on this investigation and the purpose with my degree work was to explore different teaching ways that promotes pupils with another mother tongue than Swedish, to develop reading comprehension and to get a better understanding of mathematical concepts in problem solving tasks. On this investigation have I chosen to teach these pupils to explore, reach and gain a deeper understanding of what teaching about problem solving promotes these pupils. I have when it concerns choice of method and material collections assumed from a qualitative investigation and gathered the material with help from participation notices and interviews. </p><p>I have in my investigation reached the conclusion that those pupils with another mother tongue than Swedish developed reading comprehension and got a better understanding of mathematical concepts in problem solving tasks by being taught in a creative and varied teaching. A creative and varied teaching as I taught those pupils in contained:</p><ul><li>the pupils had to work with living-related problem tasks</li><li>the pupils had to work in pairs to resolve problem solving</li><li>the pupils had to work in larger groups to resolve problem solving</li><li>the pupils had to work in a creative way, by writing and drawing pictures and do their own mathematical fairy tale in problem solving</li><li>the pupils had to work with manipulatives to resolve problem solving in half classes.</li></ul> / <p>Tack vare att jag fick undersöka olika undervisningssätt runt problemlösning i en årskurs 3, i en mångkulturell skola som ligger söder om Stockholm, har jag kunnat besvara min frågeställning i mitt examensarbete. Syftet med examensarbetet var att undersöka vilken undervisning som gynnar elever med annat modersmål än svenska att utveckla läsförståelsen och få en ökad förståelse för matematiska begrepp i problemlösningsuppgifter. I undersökningen har jag valt att själv undervisa eleverna för att kunna undersöka, komma fram till och få en djupare förståelse om vilken undervisning runt problemlösning som gynnar dessa elever. När det gäller mitt val av metod och materialinsamling har jag valt att utgå från en kvalitativ undersökning, där jag har använt mig av deltagande observationer och intervjuer. </p><p>Jag har i min undersökning kommit fram till att dessa elever med annat modersmål än svenska utvecklade läsförståelsen och fick en ökad förståelse för matematiska begrepp i problemlösningsuppgifter genom att undervisas i en kreativ och varierad undervisning. En kreativ och varierad undervisning som jag undervisade eleverna i bestod av:</p><ul><li>att eleverna fick arbeta med elevnära problemuppgifter</li><li>eleverna fick arbeta med att lösa problemlösning i par</li><li>eleverna fick arbeta med att lösa problemlösning i större grupper</li><li>eleverna fick arbeta kreativt, genom att skriva och rita bilder och egna räknehändelser i problemlösning</li><li>eleverna fick arbeta med laborativt medel för att kunna lösa problemuppgifter i halvklasser.</li></ul>

Thanks to I have got to explore different teaching ways around the problem solving in a year 3, in a multicultural school which is located south of Stockholm, I have been able to answer my question at issue in my degree work. My question at issue on this investigation and the purpose with my degree work was to explore different teaching ways that promotes pupils with another mother tongue than Swedish, to develop reading comprehension and to get a better understanding of mathematical concepts in problem solving tasks. On this investigation have I chosen to teach these pupils to explore, reach and gain a deeper understanding of what teaching about problem solving promotes these pupils. I have when it concerns choice of method and material collections assumed from a qualitative investigation and gathered the material with help from participation notices and interviews.  I have in my investigation reached the conclusion that those pupils with another mother tongue than Swedish developed reading comprehension and got a better understanding of mathematical concepts in problem solving tasks by being taught in a creative and varied teaching. A creative and varied teaching as I taught those pupils in contained: the pupils had to work with living-related problem tasks the pupils had to work in pairs to resolve problem solving the pupils had to work in larger groups to resolve problem solving the pupils had to work in a creative way, by writing and drawing pictures and do their own mathematical fairy tale in problem solving the pupils had to work with manipulatives to resolve problem solving in half classes. / Tack vare att jag fick undersöka olika undervisningssätt runt problemlösning i en årskurs 3, i en mångkulturell skola som ligger söder om Stockholm, har jag kunnat besvara min frågeställning i mitt examensarbete. Syftet med examensarbetet var att undersöka vilken undervisning som gynnar elever med annat modersmål än svenska att utveckla läsförståelsen och få en ökad förståelse för matematiska begrepp i problemlösningsuppgifter. I undersökningen har jag valt att själv undervisa eleverna för att kunna undersöka, komma fram till och få en djupare förståelse om vilken undervisning runt problemlösning som gynnar dessa elever. När det gäller mitt val av metod och materialinsamling har jag valt att utgå från en kvalitativ undersökning, där jag har använt mig av deltagande observationer och intervjuer.  Jag har i min undersökning kommit fram till att dessa elever med annat modersmål än svenska utvecklade läsförståelsen och fick en ökad förståelse för matematiska begrepp i problemlösningsuppgifter genom att undervisas i en kreativ och varierad undervisning. En kreativ och varierad undervisning som jag undervisade eleverna i bestod av: att eleverna fick arbeta med elevnära problemuppgifter eleverna fick arbeta med att lösa problemlösning i par eleverna fick arbeta med att lösa problemlösning i större grupper eleverna fick arbeta kreativt, genom att skriva och rita bilder och egna räknehändelser i problemlösning eleverna fick arbeta med laborativt medel för att kunna lösa problemuppgifter i halvklasser.

Made available in DSpace on 2015-03-03T15:36:13Z (GMT). No. of bitstreams: 1 OdilonJS_DISSERT.pdf: 1624865 bytes, checksum: f08c3087f93d38a7f0eca20c25b43940 (MD5) Previous issue date: 2014-03-31 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / In this paper we analyze the Euler Relation generally using as a means to visualize the fundamental idea presented manipulation of concrete materials, so that there is greater ease of understanding of the content, expanding learning for secondary students and even fundamental. The study is an introduction to the topic and leads the reader to understand that the notorious Euler Relation if inadequately presented, is not sufficient to establish the existence of a polyhedron. For analyzing some examples, the text inserts the idea of doubt, showing cases where it is not fit enough numbers to validate the Euler Relation. The research also highlights a theorem certainly unfamiliar to many students and teachers to research the polyhedra, presenting some very simple inequalities relating the amounts of edges, vertices and faces of any convex polyhedron, which clearly specifies the conditions and sufficient necessary for us to see, without the need of viewing the existence of the solid screen. And so we can see various polyhedra and facilitate understanding of what we are exposed, we will use Geogebra, dynamic application that combines mathematical concepts of algebra and geometry and can be found through the link http://www.geogebra.org / Neste trabalho, analisamos a Rela??o de Euler de uma maneira geral, utilizando, como meios de visualiza??o, a manipula??o de materiais concretos, a fifim de que haja maior facilidade na percep??o do conte?do, expandindo a aprendizagem aos alunos de n?vel m?dio e at? fundamental. O estudo faz uma introdu??o ao tema e leva o leitor a entender que a Rela??o de Euler, se apresentada de maneira inadequada, n?o ? sufificiente para determinar a exist?ncia de um poliedro. Pois, analisando alguns exemplos, o texto insere a id?ia de d?vida, mostrando casos onde n?o ? sufificiente encaixar n?meros que validem a Rela??o de Euler. A pesquisa destaca ainda um teorema, certamente desconhecido de muitos alunos e professores que pesquisam sobre os poliedros, apresentando algumas inequa??es muito simples, relacionando as quantidades de arestas, v?rtices e faces de qualquer poliedro convexo, as quais definem de forma precisa as condi??es sufificientes e necess?rias para que possamos constatar, sem a necessidade da visualiza??o, a exist?ncia do s?lido em tela. E para que possamos visualizar v?rios poliedros e facilitar a compreens?o do que estamos expondo, utilizaremos o Geogebra, aplicativo de matematica din?mica que combina conceitos de geometria e alg?bra e pode ser encontrado por meio do link http://www.geogebra.org

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-07-07T20:02:21Z No. of bitstreams: 1 ricardoferreiraparaizo.pdf: 3940678 bytes, checksum: 5e119e9029a47efd360b90ca2458d7cb (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-07-08T13:21:52Z (GMT) No. of bitstreams: 1 ricardoferreiraparaizo.pdf: 3940678 bytes, checksum: 5e119e9029a47efd360b90ca2458d7cb (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-07-08T13:22:06Z (GMT) No. of bitstreams: 1 ricardoferreiraparaizo.pdf: 3940678 bytes, checksum: 5e119e9029a47efd360b90ca2458d7cb (MD5) / Made available in DSpace on 2016-07-08T13:22:06Z (GMT). No. of bitstreams: 1 ricardoferreiraparaizo.pdf: 3940678 bytes, checksum: 5e119e9029a47efd360b90ca2458d7cb (MD5) Previous issue date: 2012-07-02 / Neste trabalho investigamos as possibilidades e limitações emergentes da utilização integrada de vídeos didáticos e da manipulação de materiais concretos no ensino de geometria no Ensino Médio. A pesquisa, conduzida segundo os critérios da grounded theory, foi realizada com doze participantes do terceiro ano de uma escola pública de Minas Gerais. A coleta e a análise dos dados tiveram como foco os conceitos de área de figuras planas e de volume de sólidos. O estudo descreve as percepções e concepções dos participantes em relação aos conceitos geométricos supra-referidos e à abordagem metodológica utilizada, e sugere que o ludismo, a interação, a contextualização, a etimologia, a qualidade de imagem e som, a concisão e a clareza são os principais elementos a serem observados em vídeoproduções com objetivos similares ao investigado. A pesquisa destaca ainda o papel significativo da manipulação de materiais concretos pelos participantes, assim como o papel mediador do professor, ao longo de todo o processo instrucional. / In this work we investigate the possibilities and limitations arising from the integrated use of educational videos and manipulation of concrete materials in high school geometry. The research was conducted, according to the grounded theory method, with twelve third-year high school participants from a public school of Minas Gerais, Brazil. The data collection and analysis focused on the concept of area of plane figures and on the concept of volume of solids. The study describes the perceptions and conceptions of the participants in relation to the aforementioned geometric concepts as well as to the methodological approach, and suggests that ludic dimension, interaction, context, etymology, image and sound quality, conciseness and clarity are the main elements to be observed in video productions addressing similar goals. The research also highlights as significant the manipulation of concrete materials by the participants as well as the mediator role of the teacher throughout the instructional process.