I detta 10-poängsarbete går jag igenom hur min egenhändigt producerade kvadratrotsalgoritm fungerar praktiskt och teoretiskt. Med denna algoritm kan man för hand räkna ut kvadratrötter som innehåller 50-60 värdesiffror. Med de tidigare kända algoritmerna för kvadratrötter kan man räkna ut 5-6 värdesiffror. Min algoritm fungerar inte på samma sätt som de tidigare använda kvadratrotsalgoritmerna men den är lika korrekt. Stor tyngdvikt i arbetet har därför lagts på att visa på att det finns flera olika korrekta algoritmer för våra vanliga räknesätt.

This study compares the sample variance of the mean in a simple random sample (SRS) and a systematic sample from a surface. The study also compares the prediction error variance in a SRS and systematic sample from a random field. Recommendations are presented on which method to use in the clearance and exemption process in the nuclear industry. The results indicate that quadratic systematic sampling outperformed SRS in most instances and proved to be especially efficient in the presence of a long-ranged covariance function and high sampling intensity (i.e. short distances between observations).

Syftet med denna rapport är att utreda vad matematik- respektive karaktärsämneslärare på yrkesprogrammen på gymnasiet anser att det finns för för- respektive nackdelar med en ämnesintegrering mellan deras ämnen. Med hjälp av en enkät har de två grupperna fått delge sina för- och nackdelar samt i vilken utsträckning de tillämpar en sådan ämnesintegrering. Enkäten användes också som underlag för en intervju som låg till grund för en beskrivning av hur ett ämnesintegrerat arbete kan gå till. Majoriteten av lärarna var positiva till att ämnesintegrera och ansåg att de tillämpade en sådan undervisning men endast ett fåtal samarbetade med sina kollegor över ämnesgränserna..

This work is about how teachers describe their work with mathematics in a traditional nursery school and a Montessori preschool. Another aim is to study how children mathematise on the two different preschools and to see if there are any differences between the various educational theories and practices mathematising. I have used two methods wich is interviews with preschool teachers, and observation of the children. The results of my study was that differences exist but the biggest difference is the material that Montessori uses. The difference between the teachers' way of teaching mathematics is to Montessori preschool places great emphasis on the material and how it is used, while in the traditional preschool puts the emphasis on learning through interaction with others.

The aim of this study is to fill the gap in mathematics education research concerning the relationship between identity and positioning in mathematical collaboration in groups. This study elaborates on the relationship between how pupils see themselves as math students in sixth grade, how they show their identities as math students, in contrast to how they position themselves reflexively in group collaboration while engaging in mathematical problem solving. The theoretical concepts linked to this study are discourse, identity and positioning. Discourse is used to describe and form the setting and context of the study. Identity is seen as a transient and elusive concept formed by the students own perceptions of self through narratives.

This study is about the above-average pupils? situation in schools and how teachers work to encourage and motivate these pupils' development in mathematics. The purpose of this study is to find out how a group of teachers work with above-average pupils in mathematics. The study addresses previous research on these students' school situation and how teachers should work with them. There have been unstructured interviews with a number of educators to get a personal insight into how they work with above-average pupils.

We have done a qualitative and quantitative study about math problems on second­ary school students. The study is based on the diagnosis, treatment and training of teachers, about students who have math difficulties. The aim of this work is to obtain teachers ?perceptions about students? diagnosis, treatment / improvement and continuing education for students who have math difficulties. By having interviewed various teachers through surveys we have received answers to their concerns about the diagnosis, treatment and the importance of continuous training of teachers on students? mathematics difficulties.

Aim: The study aims to investigate the distribution of grades between students in a practical subject and in a theoretical subject.The problem:What is the grade distribution in physical education and mathematics, with respect to gender, socioeconomic background, parental education, ethnicity, and physical activity?Method:To answer the aim of the study a quantitative method was chosen. As the collection method used was questionnaires to 620 students in the 9th grade in Stockholm. Of the 620 questionnaires, 597 questionnaires were used for the static analysis. The method of analysis used cross tables and logistic regression analysis.

Transition to Non-Compulsory EducationScrutinizing flaws in Students? knowledge in Mathematics.

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.

We derive the equation linking the Weyl tensor with its Lanczos potential, called the Weyl-Lanczos equation, in 1+3 covariant formalism for perfect fluid Bianchi type I spacetime and find an explicit expression for a Lanczos potential of the Weyl tensor in these spacetimes. To achieve this, we first need to derive the covariant decomposition of the Lanczos potential in this formalism. We also study an example by Novello and Velloso and derive their Lanczos potential in shear-free, irrotational perfect fluid spacetimes from a particular ansatz in 1+3 covariant formalism. The existence of the Lanczos potential is in some ways analogous to the vector potential in electromagnetic theory. Therefore, we also derive the electromagnetic potential equation in 1+3 covariant formalism for a general spacetime.

We have done a qualitative and quantitative study about math problems on second­ary school students. The study is based on the diagnosis, treatment and training of teachers, about students who have math difficulties. The aim of this work is to obtain teachers ?perceptions about students? diagnosis, treatment / improvement and continuing education for students who have math difficulties. By having interviewed various teachers through surveys we have received answers to their concerns about the diagnosis, treatment and the importance of continuous training of teachers on students? mathematics difficulties.

Syftet med detta examensarbete är att fördjupa vår förståelse kring matematikspråk och kommunikation som verktyg i matematikundervisningen. Detta har sökts svar på genom att observera och intervjua tre stycken matematiklärare i grundskolans lägre åldrar. Vi har undersökt hur dessa lärare använder och ser på muntlig kommunikation samt infor-mellt och formellt matematikspråk. Vi redogör för tidigare forskning kring språk och kommunikation i matematikundervis-ningen. Studiens utgångspunkt är Vygotskijs syn på språk och kommunikation i ett so-ciokulturellt perspektiv.

The aim of the study was to investigate the students´ attitudes towards mathematics, their knowledge in the subject area they find the least interesting and whether laborative/practical working methods could awaken their interest and curiosity. During our work, we have looked into previous studies regarding girls´ and boys´ attitude and performance in mathematics. We handed out surveys to students in grade 9 at a School with many people from other cultures and nationalities in Malmö in order to find the answers to our questions. The result showed that most of the students thought that the subject area "scaling" was the least interesting. The implemented action program was a laborative/practical task within the "scaling" area.

This analysis is about the fourth basic competence and how you can define it, what it includes and if it is possible to find it in the new curriculum for the Swedish high school; Gymnasiereformen -07. The analysis was focused on the following subjects; Mathematics, Social science and Swedish. The aim with this analysis has been to create a summary in the field of information literacy and to define the fourth basic competence. The analysis were focused on and delimited by the following conceptions; information literacy, digital competence and the information search process. The sources of information has primarily been taken from the field of information literacy and statements from professionals in the fields of information literacy and education.