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.

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..

This study investigates the teaching strategies of four teachers, and determines which teaching strategies give better results in mathematics at the middle school level? Result here means the knowledge level of the students. The result has been measured through leave out a mathematical test, which I leave out designed. Teaching strategies have been assessed through interviews with teachers and observations of their lessons.My study shows that to go through the lessons thoroughly in the traditional way, and open discussions with the whole class are best for students achievements.The information available, however, is too limited to draw some general conclusions, but my study can be seen more like a counter-example to the general praxis that is short lectures and individual assessment with one to one communication when teaching mathematics..

This report documents the process of designing a laboratory exercise in Fourier analysis at Vetenskapens Hus (House of Science) in Stockholm. The lab is designed for high school students studying science or technical education. It focuses on the physicalunderstanding and mathematical description of sound, in particular music. A model of such a lab is presented in this work; containing a review of the mathematical theory, summary of educational research in the field, descriptions of the design process and of the investigativework that led to the final result. The designed material for the lab includes developed computer programs, visit leader tutorial and description for teachers. .

Swedish students' knowledge of both mathematics and reading comprehension has deteriorated in recent years. Scientists are discussing whether there is a connection between these areas and that the pupils deteriorating math skills may have something to do with their increasingly lower results in terms of reading comprehension. To investigate this possible connection, I conducted a survey among students in ninth grade and have come to the conclusion that the scientists are right: this connection absolutely exist. Students who received a high score on tasks designed to test students' mathematical problem-solving skills, also received high results on the reading comprehension test. And students who received a poor performance on the problem-solving tasks, were also low performers in the reading comprehension test.

In this thesis, the four types of math problems that occur in the digital educational math game Zcooly Affären 2 have been analyzed. Focus has been aimed at how the problems mediate instructions and mathematical concepts to players, and how the mathematical content is supported by the context within the game. The result shows both positive and negative aspects of the math problems, based on the theories for math education used in this thesis. Apart from the analysis of the game, this thesis also presents earlier research regarding what possibilities digital games possess as tools for learning. Researchers have partly different views on how digital games should be designed to enhance learning, and whether or not games are efficient to use for learning purposes..

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 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.

The aim of this Master of Science Thesis is to develop guidelines and improvementsuggestions of RiNOVA Traffic AB?s dynamic speed bump. The project started with athorough pre study of the design and its function to find out how passing vehiclesaffects the dynamic speed bump. The majority part of the pre study was to createnecessary mathematical models to explain the arisen forces and strains.The results of the mathematical models gave necessary information about the designregarding weaknesses and flaws. The most critical ones where those which interferedwith the design?s performance and reliability, and therefore needed to be corrected.These problems where more thorough analysed and discussed with experts before thefinal guidelines and improvement suggestions where developed.The parts of the design that had to be redesigned were the extension springs and thebearing that enables the dynamic properties.

This survey is a case study with the purpose to find out the teacher´s perceptions about students´ motivation to mathematics. Further this study aims for the teacher´s vision on how they consider students´ motivation in mathematics in secondary school. To collect research data I have used semi structured interviews with four secondary school teachers. The result constructs according to categories that depict the purpose of the study. These categories define students? motivation like achieving different goals, students? basic knowledge, abilities and perceptions of mathematics and external factors that affect students? motivation.

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.

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.

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.

Lärare planerar undervisning och väljer vad eleverna ska arbeta med. Denna studie syftar till att undersöka lärares tankar om vilket matematiskt innehåll elever möter samt vilka förmågor elever tränar i arbetet med en uppgift i matematik. Studien genomfördes genom intervjuer med fem lärare som fick svara på frågor kring en uppgift i matematik. De övergripande frågorna handlade om matematiskt innehåll och förmågor, men även uppgiftens koppling till Lgr11 efterfrågades. Lärarnas svar kopplades till de specifika kunskaper som behövs för att undervisa i matematik.Studien visade att lärarna i hög utsträckning sorterade in uppgiften inom området kombinatorik och att de framförallt såg uppgiften som en problemlösningsuppgift.

Objective: The aim of the study is to describe pupils' understanding of the mathematical concept of function. How do pupils define the concept of function? What images of the concept of function evoke when they solve tasks, which involve identifying and constructing functions?Theory: A student's thinking about a mathematical concept depends on more than just the formal definition of the concept; therefore Tall and Vinner introduce the term concept image to describe the role cognitive structures play when students learn about concepts. The cognitive structure includes all mental images, associated properties and processes that an individual associates with a given concept. According to Sfard, an individual's understanding of mathematical concepts may have different character: an operational conception, where a concept is conceived as a process and a structural conception, where the given concept is conceived as an object, that is, as a whole.Method: 16 pupils at the Science Program at two different upper secondary schools inSweden answered a questionnaire on the mathematical concept of function.