Rock groundwater has always caused major problems when tunnelling. Water leaking into tunnels can cause large problems, not only on the construction itself but also on the environment. A continuous water leakage can lead to a declining water supply, and geotechnical problems can occur as subsidence in the ground. Therefore it is of great importance to predict the consequences that can appear in the surroundings due to a declining groundwater surface.The aim of the study was to investigate different methods for predicting leakage and changes in groundwater level due to tunnelling excavations in rock. This thesis was performed by comparing mathematical methods, actual groundwater changes and results from preliminary investigations.Investigations were made for three railway tunnels planned by Botniabanan AB.

Syftet med detta arbete är att jämföra International Baccalaureate Diploma Programme (IB), med svenska SP och NV program. Detta görs genom att besvara frågan hur innehållen i matematikkurserna på IB programmet skiljer sig från matematikkurser som ges i de svenska programmen. Inte enbart innehållet i kurserna jämförs utan även timplanen granskas för att undersöka om arbetsbördan i programmen skiljer sig åt. Den lättaste matematikkursen som undervisas i IB programmet, Mathematical Studies är mest lik de svenska Matematik A-C kurserna. Den andra IB kursen, Mathematical Methods täcker framförallt Matematik A-E kurserna medan den tredje kursen, Mathematics Higher Level stämmer bäst överens med Matematik kurserna A-F och Matematik-diskret.

During my time as a student of education I have learnt that it is my responsibility, as a teacher, to adjust the ways in which I teach to the needs, abilities, experiences, and thoughts of each individual child. What I have not yet gained much knowledge on is how to go about finding the children?s thoughts.In this thesis I investigate the interview as a method of finding out how sixth graders think about their mathematics education. Four children were interviewed. In addition to these inter-views, as a means of giving a broader perspective to and a greater understanding of the chil-dren?s answers, one math lesson was filmed and the math teacher was interview on two sepa-rate occasions.What I found was that a number of factors seemed to influence the children?s thoughts and answers, and that their answers were most likely not always a mirror of their thoughts.

Gravitational lenses are unlike ordinary optical lenses, a phenomenon corrupting our optical view of the cosmos. When we look out intospace we see celestial bodies lying with astronomical distance from Earth. There is no guarantee that what we see out there in space is actually there where we are observing it, and it may be that we see multiple images of the same star! Studies have shown that thenumber of distorted images of an n-mass (n > 1) plane lens can not exceed 5(n -1) for lighter lenses or 5n for more massive lens. This mathematical thesis covers gravitational lensing and their properties that distort light rays coming towards us from distant celestial bodies. In addition of gravitational lensing, its properties and the proof of the maximum number of distorted images, a bigger part of this work even cover two very interesting mathematical tools - the so-called Schwarz function and Bezout theorem..

The Squares Family is a game developed as a learning aid in mathematics. With its graphical representation of the decimal system, the four basic arithmetic operations and positive and negative numbers together with a learning agent as pedagogical approach, the game?s primary purpose is to motivate students in their learning of mathematics. Although the game is strictly based on mathematical rules it attempts to encourage students to play and work with math without experiencing it as mathematics as this is initially not obvious. The game being internationally tested on normal performing students, this project introduced the game to six Swedish students who experience low motivation for and/or difficulties in mathematics.

This study investigates the difficulties that may arise for students as a consequence of differences that exist in mathematics education between different educational systems. The questions asked are when and why difficulties as a consequence of differences in writing or types of student problems may arise and in which way teachers and students attend to these difficulties. The focus is thus on the written parts of mathematics education and the questions are asked within the frame of general upper secondary education.In order to answer these questions, a sociocultural perspective based mainly on Sfard?s (2006) participationist theories together with Vygotsky?s (1999) general theories on development and learning is used. An important analytic tool is the discourse concept which in this context means a type of communication that brings some people together while excluding others from the communication.

From autumn 2008 Sweden has reinstalled the Special Education Needs teacher education. For future special education teachers and active teachers in the field, it is important to know the history and be aware of future visions to create a good role for the Special Education Needs teachers. This study examines attitudes towards special education and Special Education Needs teachers amongst school principals and classroom teachers at seven schools in Umeå municipality. School principals were interviewed, and a survey was handed out amongst the selected General Education teachers. From this it appears that school principals have a picture of special needs education and Special Education Needs teachers' work that corresponds well with the objectives of the school's governing documents.

The concept of function represents a major part of mathematics and becomes more significant in school during high school. Throughout history, it has been a difficult concept to define and may create challenges for contemporary students. This literature study aims to identify students' difficulties with the concept of function, as well as to account for how the definition of a function has evolved historically. The literature study has been conducted through database searches in ERIC, Education Research Complete and MathSciNet via EBSCOhost, as well as through chain searching. The study results in identifying that students' difficulties with the concept of function primarily include the graphical and algebraic forms of representation.

At the department of Electronic Warfare Assessments at the Swedish Defence Research Agency in Linköping one of the activities is modelling and simulation of the duel between a robot and a target. The aim with this Master's thesis is to develop a simulation model of an hovering helicopter. First a theoretical description of the forces and moments acting on an helicopter is given. Then the equations of motion are derived. These equations are simplified to be valid only for a hovering helicopter and the result is a mathematical model.

The purpose of this study was to gain a deeper understanding of teacher´s motives to engage in outdoor education in their teaching. A qualitative approach through interviews was used and a total of eight teachers were interviewed. The result showed that there were several motives to engage in outdoor education. These motives were divided into three main categories which were: to engage in outdoor education from teacher`s interest, to engage in outdoor education based on teacher`s perceptions of children's needs and to engage in outdoor education based on external factors..

Being able to reflect, evaluate and justify your views is an important part of adult life. Moral education can be a path to develop this knowl-edge; however, it is possible that the moral education gets more obscure when it is not a separate subject. The purpose with this essay is to examine the need of moral education and the presence and the framing of moral education of seven teachers in religion. The purpose is also to analyse where and how the moral education should be included in the curriculum. The survey was conducted through qualitative interviews with a hermeneutic approach.

Being able to reflect, evaluate and justify your views is an important part of adult life. Moral education can be a path to develop this knowl-edge; however, it is possible that the moral education gets more obscure when it is not a separate subject. The purpose with this essay is to examine the need of moral education and the presence and the framing of moral education of seven teachers in religion. The purpose is also to analyse where and how the moral education should be included in the curriculum. The survey was conducted through qualitative interviews with a hermeneutic approach.

The overall aim with this study is to elucidate outdoor education as an education method and on the basis of that illustration to examine active educators vision on it as a way to motivate students' learning. This study is based on a literature component and a qualitative study through interviews five teachers.The results of the interviews show how to interpret the motivation and how to work with students' motivation. As well as outdoor education as part of the activity.  The interviews show the importance of outdoor education can be to increase students'motivation for learning. They also show the importance of outdoor education is for student learning and test scores have shown the effectiveness of student learning through outdoor education.

The overall aim with this study is to elucidate outdoor education as an education method and on the basis of that illustration to examine active educators vision on it as a way to motivate students' learning. This study is based on a literature component and a qualitative study through interviews five teachers.The results of the interviews show how to interpret the motivation and how to work with students' motivation. As well as outdoor education as part of the activity.  The interviews show the importance of outdoor education can be to increase students'motivation for learning. They also show the importance of outdoor education is for student learning and test scores have shown the effectiveness of student learning through outdoor education.

The aim of my study is to investigate how last year students in upper secondary schoolunderstand certain mathematical concepts, in particular the unit circle and its trigonometry.I have used intentional analysis to interpret student?s actions when they solve certain tasks onthe basis of a cognitive, situated and cultural context.Interviews with four university teachers in mathematics about the unit circle, trigonometry,and mathematical understanding, serve both as background for the study and as basis for adiscussion, where I relate students understanding to what the teachers want new students toknow about these concepts when they begin university studies in mathematics.The students were arranged in three groups with three students in each group. Each group waspresented with two tasks, one in which they were asked to calculate the cosine values for onepointed, one blunt and one straight angle, each located in a separate triangle. They were alsoasked to decide whether the points (0,71; 0,71) and d (1 2 , 3 2 ) are located on the unit circleor not.My conclusion is that students mainly have an operational conception of the unit circle andtrigonometry. The lack of structural conceptions result in difficulties in seeing connectionsbetween the concepts in unfamiliar situations.