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 this study is to show the importance of task texts for students in grades 5 when solving mathematical problems. It was conducted in a class 5 (where the children are 11 years old). The pupils were assigned two different tests with mathematical problems; one where the problems were described in text and one where the problems were presented with numbers and mathematical signs. Previously done research, done on bilingual children, (Bernardo, 2002) shows that pupils tend to do better on mathematical tests when no text is presented. My research supports that theory even though the correlation is not that strong.

AbstractMy purpose with this essey is to study how they work in preschool whir language- stimulation. I will try a way to work with this trough intervjus whit teacher at preschool. My main questions are: Way dose teachers use language- stimulation? How dose teachers use language- stimulation when it comes to there way of working and methods? Do the teachers think that language- stimulation help the childrens development?To answer these questions I interviewed 6 teachers I central Sweden and used this as data. I have written about language, language- development in a biologik and theoretical aspect, teachers plan, language- stimulation, playing by language sounds and TRAS (early registration of language development) in my literary review.My result shows that working whit language- stimulation helps children in there language- development, it also develops there self-image and identity.

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 purpose of this study is to find out teachers view on manipulatives as a way to concretize a certain mathematical content and to highlight knowledge and experiences within the range of using manipulatives to concretize. By answering the questions below different approaches a teacher may have towards the manipulatives and how that may impact on student?s learning will also be discussed in comparison to mainly traditional and socially constructive theories of learning.What is the teachers view on manipulatives as a way to concretize?What purpose do they have when using manipulatives?According to the teachers, what does it mean to concretize a certain mathematical content?According to the teachers, what connection is there between manipulatives and concretizing?Through interviews and observations conclusions can be made that the teachers are in general positive towards using manipulatives as a way to concretize a certain mathematical content although the definition of what a manipulative is differ somewhat between the teachers. The teachers working with manipulatives do it in a well thought out fashion but more research is needed to furthermore define the purpose of using manipulatives. Few countries spend so much time concretizing and working with manipulatives as Sweden do, but still Sweden score below the OECD-average on the mathematical PISA-tests.

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.

This study illuminates one part of the mathematic teaching in school, which is mathematical problem solving in groups. It examines teacher?s and student?s ideas about what conditions it takes to be able to learn in groups. Further on, it studies the importance of group structure when it comes to working with mathematical problem solving in groups from a process focused and/or a product focused learning. Through observations of student groups and interviews with the students and the mathematic teachers, the material has been compiled and analysed under three different headings: conditions for learning in a mathematical problem solving situation, importance of group structure in a mathematical problem solving situation and process versus product.

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 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 this study was to investigate which factors teachers and special needs education teachers view as being the main causes of mathematical learning difficulties and from these choose how to educate pupils with these difficulties. The aim was also to investigate how this education is organised at two different schools. An interview based investigation addressed these objectives by using three comprehensive questions:Which factors do the teachers and special needs teachers view as being the main reasons for mathematical learning difficulties?How do teachers and special needs teachers educate pupils with mathematical learning difficulties?How is the education organised for pupils with mathematical learning difficulties at two different schools?This study is based on four interviews of three teachers and one special needs teacher. The people interviewed work at two different primary schools in the same local authority.

This is an empirical study of how the mathematical talk of adult learners constructs/reconstructs different mathematical discourses. The study is to be regarded as an attempt to develop a discursive approach within the field of mathematics education and to complicate the status of mathematics in education and in society in general. My theoretical underpinnings consist of three possible mathematical discourses ? coercive, regulative and emancipative mathematics. From a discursive psychology perspective, I let these discourses function as analytical interpretive repertoires in relation to the adult learners? rhetorical use of mathematics and their claiming of mathematical subject-positions, named the coerced, the self-regulating and the responsible mathematician.

The purpose of this study is to examine senior high school students? strategies and reasoning when solving mathematical problems and make a review of the concept problem solving. The purpose is also to examine if the students? choice of strategies are influenced when their mathematical knowledge is improved.The study was conducted in two science classes at a senior high school. All the students were asked to individually solve two mathematical problems.

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.

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.