Purpose: The purpose of the study is to find out what mathematical content primary school children encounter in their free options at school.Through observation, the study defines mathematical areas that primary school students encounter in their free options at school. We want the study to show the reader the mathematics that students continuously meet without associating it with regular mathematics as taught in school.A number of mathematical areas have been defined in the analysis of the observations. These areas have subsequently been discussed more thoroughly. Finally, the areas have been arranged in a grid system to clarify the results.In our study, we have discovered that mathematics exists in all the observed situations the students participated in.We believe that observation as a method can give teachers a tool for helping students associate practical actions during their free options with the more theoretical aspects of formal teaching of mathematics. We discuss this further in the study..

Empirical research shows that a possible reason why Swedish students mathematical knowledge deteriorates can be a too big focus on imitative reasoning, i.e. recalling solutions or follow algorithms, and a lack of creative mathematical reasoning, i.e. when a student construct his/her own solution and motivates its plausibility with mathematically well-founded arguments. The purpose of this study is therefore to examine if, and in what way, lecturers can provide students an opportunity to learn creative reasoning by simulating creativity in their presentations of examples. Six lectures were observed and 22 task situations were analyzed with respect to three aspects; reflection, plausibility and mathematical foundation, which are to be present in the situation if the reasoning will be seen as simulated creative.

Undersökningen beskriver den matematiska kommunikationen mellan speciallärare och matematiksvaga elever. Den empiriska datan består av två matematiklektioner från år 9 i grundskolan. Datan analyserades för att finna olika typer av kommunikation.Lärarna var i många delar medvetna i sitt sätt att kommunicera med eleverna och undervisningsmiljön kändes trygg. Under lektionerna observerades två parallella språk, ett vardagsanknutet och ett matematiskt språk. Det framkom att ett tydligt förhållningssätt beträffande matematiskt språk kan underlätta för elevens inlärning samt medvetandegöra läraren om den kommunikativa betydelsen i undervisningen med styrdokumentens mål i fokus. .

The objective of this study was to bring further knowledge to the subject as to what influences students motivation and self-esteem. The study had focus on role that the teachers play in these aspects. The study was done by using both a qualitative and quantitative approach. The qualitative method was interviews based on six interviews with two teachers and four students from two different classes. The quantitative method was a questionnaire study that was done in both classes.

 Title:              Not just words, classroom communication about subtraction in year 2Language:      Swedish with summary in English.Keywords:     Communication, mathematics, subtraction, teaching The purpose of this study is to analyze the mathematical communication in a classroom during a lesson in the field subtraction, and to find out how students describe their perception of mathematics that is communicated in the classroom.The study consists of the observations through the videotaping of two lessons in primary school grades 2 and student and teacher interviews related to these lecture occasions.Research indicates that Swedish pupils' mathematical skill continuously deteriorates in a national and international perspective, and that student experiences of mathematics in general are negative. The literature emphasizes the importance of communicating mathematics in various forms to deepen and develop understanding of concepts and mathematical operations. Communication must be generated between teachers and students but also between student and student to have a beneficial impact for the student.Our result demonstrate the different types of communication in the classroom but that communication does not always have a clear mathematical content in spite of teachers' mathematical intentions with teaching. The result also indicates that the mathematical communication that takes place, in essence, is a one-way communication where the teacher has a great opportunity to speak. The teachers perceived as oblivious to their own ways of communicating, but stressed in the interviews with an understanding of the importance of communication learning.

Concrete is a very common construction material. It´s characteristics are strength, durability and formablility. Superplasticizer is a common admixture, which changes the properties of concrete. Today (spring 2007) there are no certian mathematical methods to calculate the required percentage of this admixture needed to give the necessary set slump flow in the overall concrete recipe. Concrete batching companies must therefor experiment with different amount of superplasticizer in order to meet the specified slump and strength. The purpose og this report is to investigate if any mathematical relation can be established between the amount of superplasticizer used and the slump flow achieved. After carrying out some practical experiments using four different superplasticizers a direct relationship can be establish between the percentage of admixture used and the slump/flowability achieved. Unfortunatly at present due to the numerous variables, the calculation of mathematical formula can not be achieved..

The purpose of my study is to examine how four preschool teachers go about using the term play in children's early mathematical development. In order to fulfill the purpose of this study, I have the following questions:How the preschool teachers visualize mathematics in children?s play?What reflections have the preschool teachers about the importance of play for children's mathematical learning in preschool?How do the preschool teachers see on their own role in the children's play?In this study, I have conducted a semi-structured qualitative interviews based on the interviews with four preschool teachers from various departments in a preschool. I have also conducted some observations to complete my study. Whereas in my analysis of the researched material, I have used Vygotsky's theory.The survey shows that the preschool teachers are aware of the use of mathematical language and concepts in children?s different activities which were conducted daily in the preschool.

The starting point of this work has been to get knowledge about teachers working in a mathematical workshop with the students. I also wanted to investigate what students think about math, both within the workshop and in traditional teaching.To achieve this I chose to interview a teacher in charge within the framework of a mathematical workshop, and six students in the 5th grade. I also did a lesson observation with the purpose to see how well the teacher?s tutoring agrees with the results of the interview.In this study I have discovered that the lessons in the mathematical workshop are planned after what the students are working with in the textbook. The teacher opens the lessons with the whole class and then splits it up in groups.

The purpose of this study is to see how some teachers in primary school creates and adapts their mathematics teaching for students with special mathematical abilities. It also aims to identify opportunities and challenges that teachers see in creating a teaching adapted to these students.In this study, qualitative interviews has been done to collect data. The interviews were conducted with five teachers who all are active in the primary school.The study results show that there is great variation in how the interviewed teachers create their mathematics teaching for students with special mathematical abilities. The use of mathematics book proved to be significant for how this adaptation took place. The result also shows that the teachers? explanations for the choice of the adaptations that they make in teaching vary.

Yahtzee is a popular dice game around the world. The complexity makes the game interesting to play and analyze. This report compares the effectiveness of the mathematically optimal strategy with a strategy that can be used for casual play. The rules used are those of the Nordic variant Yatzy, in which a few but important rules are different from the American Yahtzee. To evaluate the everyday strategy 100,000 games was simulated in a java program written specifically for this purpose.

Yahtzee is a popular dice game around the world. The complexity makes the game interesting to play and analyze. This report compares the effectiveness of the mathematically optimal strategy with a strategy that can be used for casual play. The rules used are those of the Nordic variant Yatzy, in which a few but important rules are different from the American Yahtzee. To evaluate the everyday strategy 100,000 games was simulated in a java program written specifically for this purpose.

Dyscalculia and General Mathematical Dificulties.

The aim is to examine how students with attention difficulties may demonstrate their mathematical understanding through visual representations. A curiosity about how students think about mathematics, national tests and Concepts cartoons has also permeated the study. With help of observations combined with interviews and actively work for a week, the study shows an idea of how visual representations can help students with concentration difficulties to stay focused on their tasks. I chose a selection of pupils to do some mathematical tasks from the national tests which they had not been able to solve before. Now in the form of Concepts cartoons, which I designed, they managed to solve the same mathematics data. In my study treatment and interaction reveals as key pillars for a successful educational work with the students with concentration difficulties. Thus, all pupils who previously have been unable to solve these assignments on the National test were now able to show their mathematical understanding supported by visual representations..

My aim with the experience-based essay is that I want to explore the implications of mathematics on children's development. I also want to examine my approach in relation to the various mathematical tasks. Why do we think that mathematics is important for pre-school children? What does the research say about how the teacher is thinking about mathematics? Can the teacher combine playing and learning and create meaningful moments and activities related to mathematics? I also want to explore our policies and the objectives that the teacher should relate to. What is required of me as a teacher in order to meet those goals?My essay is about mine and my boss?s view of the mathematical tasks that I usually perform in the preschool.

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.