In several scientific and technical educations today we meet mathematical studies in differential- and integral calculus. The classic mechanics is a foundation for the physics and it has made it possible for today's technical developments that we in our everyday life meet and make use of. The intention for this essay is to give a picture of the person behind this discoveries that changed the science and the world. Besides the purpose to bring the reader on a journey through Isaac Newton's life the main intention is to give an understanding of the way he discovered the binomial theorem, the differential- and integral calculus, the numerical methods Newton-Raphson's and Newton's interpolation-polynomial, Newtons identities and his classification of third-degree curves and elliptic curves. A derivation of Kepler's first law is also included..

This study aims to visualize the youngest preschool children matematical learning in the free game. In my study the mathematics will be analyzed  based on the interactions children participate in, and how children experience mathematics through the lived body.I have chosen to undertake a qualitative research in form of observations. Through this research method, I would approach the child's perspective, which means that i analyze the material that the children in the observations reveals to me as a researcher.The results of the study show that children experience mathematics skills both through the lived body, as well as in interaction situations between children. The mathematics are around among us, all the time. This is very important to take into account for children's continued development of mathematical knowledge..

In my study I have chosen to examine the mathematics in children's free play and everyday situations, with focus on sorting and classification. The purpose of the study was to see how children express their mathematical knowledge. I have chosen to use a qualitative method in my examination, here I did observations in a children's group where the children were between three and six years old. I also did interviews with the teacher's on the department to see how they relate to the mathematics and how they formulate the department to achieve as good a learning environment as possible.The result shows that the teacher's approach is incredible important to the children's learning ability and that they are always present to challenge and discuss together with the children. The observation indicates that children use mathematics all the time in their everyday situations and that it is the interaction between individuals and environment that affects children's development. .

This master thesis is the documented work of the construction process and testing of a three hour laboratory session in mathematics aimed at high school level students. The purpose of the thesis was to create an interesting laboratory session for the science education center ?The House of Science? that could be used as a part of their regular program directed to schools. The thesis explores the possibilities for how one can construct a laboratory session on the topic ?molecular symmetry? as well as the underlying pedagogical theories used to describe learning processes in creative contexts.

The purpose of this study is to investigate the children?s mathematics learning through play. The questions to be answered are: how can teachers facilitate children?s mathematics learning through play? How can play affect children?s math learning? Are the children aware of the role of play in their mathematics learning?My method is based on interviews and observations. My informants are three teachers who work in two different preschools.

Syftet med denna empiriska studie är att undersöka hur lärare kan erbjuda möjligheter för 6-åringar att vidga sin förståelse av likhetstecknets innebörd. Undersökningen är inspirerad av Learning Study metoden vilket är en metod som har sin utgångspunkt i variationsteorin. Barnens initiala förmågor analyseras före planeringen av undervisningen och det ger en uppfattning om barnens kunskaper. Utifrån det planeras lektionerna och de aspekter som är de mest kritiska för barnen lyfts och på så sätt utvecklas deras kunskap. Vår slutsats är att det är viktigt att arbeta utifrån ett variationsinriktat lärandeperspektiv.

AbstraktStudien behandlar begreppskunskap inom området positionssystemet hos elever i matematiksvårigheter. Undersökningen har gjorts i årskurs 4 och omfattar naturliga tal avseende tiobassystemet.Studien består av en kvantitativ undersökning och en kvalitativ del med intervjuer.Resultatet av studien har organiserats i tre områden som har betydelse för individens utveckling av matematiska begrepp. Talområdet 1-10, talsystemets uppbyggnad samt förståelsen av stora tal.Av resultatet framgår att förståelse av ett begrepp kan vara mer ytlig än den ser ut att vara. Brister i grundläggande begreppsförståelse kan leda till att räknesvårigheter uppstår. Svårigheter är bland annat begreppen talsort och platsvärde, särskilt i stora tal.Sökord: begrepp, matematiksvårigheter, positionssystemet, schema, specialundervisning, tiobassystemet..

This thesis compares different methods for risk assessment of a creosote contaminated site in Vansbro, Dalarna. In a complementary study the importance of using representative data for calibration and validation of stationary groundwater models is discussed. The time dependency between surface water levels and groundwater levels on the site in Vansbro is evaluated by step response analysis. The results show that the groundwater levels reflect only long-term variation in the surface water levels. Hence the use of such long-term means for calibration and validation of the stationary groundwater models is the only theoretically defendable alternative.As a first step in the comparison of risk assessment methods the degree of contamination is evaluated on the basis of generic guideline values for contaminated soils, developed by the Swedish Environmental Protection Agency.

Syftet med denna studie är att undersöka förekomsten av de matematiska kompetenserna i läroböcker för Matematik A. Centralt i studien är de sex matematiska kompetenser, som Palm et al. (2004) analyserat fram ur de nationella styrdokumenten. Dessa kompetenser är: kommunikationskompetens, modelleringskompetens, resonemangskompetens, begreppskompetens, problemlösningskompetens och algoritmkompetens. För att nå syftet genomfördes en analys av uppgifter i två läroböcker för Matematik A.Undersökningens resultat visar att alla sex matematiska kompetenser finns representerade i läroböckernas uppgifter.

AbstractBy finding out the pupils' choice of strategies for problem solving, we as teachers, can get a better understanding of their way of thinking, and thus also help them develop in their learning of mathematics. In a classroom environment where several different strategies could be found, the pupils' learning is facilitated as they, with the help of classmates, find positive and negative attributes of different kinds of strategies. The pupils are, in other words, each other's resources, rather than competitors. The main point is that the classroom environment, as well as the role of the teacher in the classroom, are both key elements for good mathematics learning.In order to increase the understanding of the pupils' choice of learning strategies, a survey was performed based on two school classes, one third grade and one six grade class at the same school. Both classes received the same mathematical problem to work with, and the strategies observed were analyzed and compared.

At the end of August 1999, the local government council of Malmö city decided thatthe area known as Kvarteret Bilen would be made available for the European HousingExhibition 2001 (Bo01-mässan). Kvarteret Bilen extends over approximately 80hectars and includes the western parts of the Western Harbour area (Västra hamnen)of Malmö.Kvarteret Bilen as a whole, but especially the western sections of this area, the socalledBo01 section, has been the subject of heated discussions. This is mainly due tothe fact that the ground in question has proven to be contaminated to a certain extentby different chemical compounds. Investigations undertaken during 1998 showed sporadically high concentrations forespecially one chemical group: polycyclic aromatic hydrocarbons (PAH).The first part of the paper describes the use of a mathematical equation (Fetter 1994)to calculate the concentration of PAH from a continuous discharge at a given time byemploying Geographical Information System (GIS). Even the constraints of theequation are discussed, as well as the consequences that follow as a result of usingGIS.The second part of the paper focuses on the connections between the content ofcarcinogenic PAH in Kvarteret Bilen and the ground water level and type of fillingmaterial.

With this empirical essay I want to research how and why pedagogues use music in their preschool activities. Music is important to me and in relation to the new educational plan I have cautions about that the esthetic subjects may be less prioritized than before. The purpose with my study is to find out preschool pedagogues perspective in learning and evolving children?s educational matters through music. I base my literature theories in this study on Vygotskij and Fröbels theoretical perspectives.

Detta examensarbete är en studie om matematik i vardagssituationer i en svensk förskola. Syftet med min studie var att undersöka vilken matematik som uppstår i av- och påklädningssituationer. Ytterligare ville jag ta reda på hur pedagoger arbetar för att lyfta fram och stimulera barnen för att upptäcka matematiken i dessa situationer. Jag har valt att göra en kvalitativ studie. I den empiriska undersökningen använder jag ostrukturerade observationer av pedagoger tillsammans med barnen i tamburen, som kompletteras med löpande protokoll.

The purpose of this study is to give a description of how six pedagogues in the third and fourth grade teaches mathematics and which working methods they use. When using the term working methods it is implied that it can for example be outdoors pedagogic, laboratory material, problem solutions et cetera. This material can both be an everyday material or a pedagogical material. The research was carried through by interviews and observations. Six pedagogues were interviewed in two different districts.

This study?s aim is to investigate how multilingual students learn mathematics and teaching strategies used to support the students? development of knowledge. A total of eleven scientific articles were selected for analysis and comparison. The results showed that visual representation, multimodal forms of expression and the students? whole linguistic repertoire constitute central resources for learning.