The aim of this study is to investigate into the use of discussions in the classroom to help the pupils develop a deeper understanding of Mathematical concepts and operations. The empirical data contain interviews with two teachers and observations from their lessons. The purpose of the interviews was to find out what importance the teachers ascribed to the ability of their pupils to talk about mathematics, and how they organised their classes to encourage mathematical discussions. With the observations, I was able to see the interaction in the classroom and hear discussions between the teacher and the pupils, as well as between the pupils themselves.The interviewed teachers proved to share my own belief in the results of researchers like Malmer (1999) and Löwing (2006) about the importance of verbal discussion, argumentation and reflection during mathematics classes. But convictions derived from the research of others are one thing, the practical application of the wisdom in the classroom another.

This paper investigates the methods used by teachers when teaching elementary mathematics to children with Swedish as their second language. The original mathematical terminology derives from Latin, Greek and Arabic, this terminology is not of great importance in this paper, the everyday language spoken in elementary classes when teaching Mathematical concepts and calculations to younger children is. The use of everyday language is an advantage for children with Swedish as their second language as mathematical problems presented in a more plain language is easier to comprehend and solve than problems in mere numerals. Special teachers in home language classes often have the task of clarifying the Mathematical concepts, introduced to the children during mathematical lessons, in the pupils first acquired language. A qualitative method was used in this study.

The aim of this study is to investigate into the use of discussions in the classroom to help the pupils develop a deeper understanding of Mathematical concepts and operations. The empirical data contain interviews with two teachers and observations from their lessons. The purpose of the interviews was to find out what importance the teachers ascribed to the ability of their pupils to talk about mathematics, and how they organised their classes to encourage mathematical discussions. With the observations, I was able to see the interaction in the classroom and hear discussions between the teacher and the pupils, as well as between the pupils themselves.The interviewed teachers proved to share my own belief in the results of researchers like Malmer (1999) and Löwing (2006) about the importance of verbal discussion, argumentation and reflection during mathematics classes. But convictions derived from the research of others are one thing, the practical application of the wisdom in the classroom another.

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.

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 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.

In this thesis we study four groups of students in grade 8, 9 and 10 when they try to solve a classical mathematical problem: Which rectangle with given circumference has the largest area? The aim of the study was too see how the students did to solve a mathematichal problem?The survey shows that students have rather poor strategies to solve mathematical problems. The most common mistake is that students don?t put much energy to understand the problem before trying to solve it. They have no strategies.

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 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..

AbstractMy essay is about pupils with difficulties in mathematics. I have choosed to do a literaturestudy and interviews of teachers to get some answers to my framing of the questions.· What is mathematical difficulties?· How do we discover pupils with mathematical difficulties?· What can a teather do to facilitate for pupils with mathematical difficulties?· What resources is there to help pupils with mathematical difficulties?I have done my investigationin two schools to be abel to see if the schools are working in the same way and have the same prerequisite of pupils with mathematical difficulties.By doing an interview with both teachers and remedial teachers I have got a better insight how to help pupils in the best way. Both of this schools are putting the pupils in the middle and give them wath they need to get to the destinations that claims. The procedure are not the same between the schools.

 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.

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.

The Swedish curriculum points out mathematical communication as one of the importantabilities that students need to develop. Previous studies show that students have not been given the right conditions to develop this ability sufficiently. The purpose of this study is to investigate how some Swedish teachers interpret mathematical communication and how the work with this takes place in their classrooms.The investigation consists of qualitative interviews with six teachers in the grades of Fk-3. The interviews have been focused around the teacher's interpretation regarding mathematical communication, how this is reflected in their work in the classroom and also if they see any advantages or difficulties in working with mathematical communication with their pupils.The result of the study shows that the teachers are well aware of the importance of communication and they have a will and an intention to let the pupils communicate mathematically. Mathematical communication is emphasized mainly as important for the pupil's learning and understanding.