An increasing number of students leave the Swedish compulsory school without having a satisfactory grade in mathematics. Causes why students risk ending up with difficulties in the subject of mathematics are debated but one explanation might be that more and more students are diagnosed with dyscalculia. The purpose of this study is to investigate how educationalists identify and organize their teaching in order to help students with difficulties in mathematics to reach the schools requirement and long-term goals that are defined in advance. It is vital to detect learning difficulties at an early stage. Accordingly, it can be avoided that the student starts to develop a negative self-image due to repeated failures and in the same time provide relevant help. Educationalists working actively with teaching possess valuable knowledge that is presently well managed. However, there are many indications that the schools steadily reducing amount of resources will limit their efforts. My contribution is an attempt to elucidate this complex of problems that are part of the daily rounds of an educationalist and that have been debated profoundly during the last years. The studie is based in qualitative iterviews with teachers in compulsory shool and one special educationalist and the interwiews are, after compilation, compared with earlier research of difficulties in mathematics.

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. The results of the interviews show that it is the pupils’ experiences of the maths that affects how well they comprehend the subject. Furthermore factors such as reading and writing difficulties can cause problems with regards to understanding tasks in maths. Educationalists in this study regard a varied education with an element of group work, communication and experimental material as being beneficial for pupils with mathematical learning difficulties. How the education of pupils is organised depends on the extent of the learning difficulties of each pupil. The needs of pupils with mild learning difficulties can be met by the form teacher whereas pupils with more severe difficulties require assistance from special teachers.

The aim is to find out how teachers apply the knowledge they get from mathematics pilots in preschool and from mathematics developer in the municipality, as well as how they work further towards the children with mathematics. The study is based on qualitative interviews with two teachers, one mathematic pilot and one mathematic developer. I used the semi-structured interview questions. The results show that teachers believe that mathematics pilots will inspire the teachers in their work with mathematics in preschool. One of the teachers who were interviewed said: “Mathematics pilots should be those that have the strongest glasses and coming up with new ideas and they push the rest of the teachers in their work with mathematics in relation to children in preschool”. The teachers use the correct terms for mathematical concepts with the children. They also stressed how important it is to point out to the kids that it is mathematics that they are doing. The conclusion of the study is that the teachers agree that it is their approach towards the children that is important and how they can lead the children’s interest of mathematics forward. To get into the mathematics of everyday life is something that teachers feel is important. The teachers all agree that math is everywhere in daily life and does not always has to be a planned activity. / Syftet är att ta reda på hur pedagogerna omsätter kunskapen från matematikpiloterna i förskolan och från matematikutvecklaren i kommunen samt hur pedagogerna arbetar vidare gentemot barnen med matematik. Studien bygger på kvalitativa intervjuer med två pedagoger, en matematikpilot och en matematikutvecklare. Jag använde mig av halvstrukturerade intervjufrågor. Av resultaten framgår att pedagogerna anser att matematikpiloterna ska inspirera pedagogerna i deras arbete med matematik i förskolan. En av pedagogerna som intervjuades sa: ”Matematikpiloterna ska vara de som har de starkare glasögonen på sig och som kommer med nya idéer och pushar på de övriga pedagogerna i deras arbete med matematik gentemot barnen i förskolan”. Pedagogerna använder de rätta benämningarna för de matematiska begreppen till barnen. De betonar också hur viktigt det är att poängtera för barnen att det är matematik som de håller på med. Slutsatsen av studien är att pedagogerna är ense om att det är deras förhållningssätt till barnen som är viktig och hur de kan leda barnens intresse framåt för matematik. Att få in matematik i vardagen var något som pedagogerna ansåg viktigt. Att matematik finns överallt i vardagen och inte alltid behöver vara en planerad aktivitet, var pedagogerna överrens om.

Educators strive to improve student learning outcomes and there are numerous theories suggesting how this is best achieved. However, application of these theories to the coal face of a classroom is often fraught with obstacles resulting in poor outcomes. Constraints imposed by educational policy, school systems, structures and the individual students themselves, realistically require adaptation of theoretical techniques if genuine learning is to be imparted to students. This paper discusses some of the issues surrounding the practical implementation of new methodologies into the classroom and identifies important factors that affect teenagers in their learning of mathematics. Working within the constraints, constantly confronted with obstacles, can be frustrating and demoralising. This paper reflects on twenty years of classroom teaching of mathematics to students with relatively poor socio-economic backgrounds and the lessons learnt from them that may assist teachers to remain enthusiastic and creative with the energy to truly improve mathematics education. Key issues explored in the paper include: ‘Realities of a teacher’s working day’, ‘The learning of mathematics within a government secondary system’, and ‘What can be done to ensure mathematical learning takes place?’

The importance of family involvement is highlighted by findings that parents’ behaviours, beliefs and attitudes affect children’s behaviour in a major way. The Family Maths programme, which is the focus of this study, provides support for the transformative education practices targeted by the South African Department of Education by offering an intervention which includes teachers, learners and their families in an affirming learning community. In this study participating parents were interviewed to investigate their perceptions of the Family Maths programme mainly in terms of their engagement, enjoyment and confidence levels. The major themes and ideas that were generated in this study include the development of positive attitudes, parents and children working and talking together, and the skills exhibited by Family Maths facilitators. These findings are analysed within the parameters of complexity science and the pre-requisite conditions for developing a complex learning community, viz. internal diversity, redundancy, decentralized control, organised randomness and neighbour interactions.

Neste trabalho discutimos a inserção de tópicos básicos de Programação Linear em duas variáveis no ensino médio e apresentamos os resultados da aplicação de uma sequência didática abordando este tema. A aplicação da sequência foi realizada ao longo de oito encontros semanais no Centro de Ensino Médio Pastor Dohms – Unidade Camaquã – na modalidade de oficinas no turno inverso às aulas. Nossa sequência didática priorizou atividades que objetivaram levar os alunos a interpretar resultados e estabelecer conjecturas em detrimento à resolução mecanizada de exercícios. Elaboramos, para a aplicação da sequência, cinco problemas e através deles, desenvolvemos toda a teoria necessária para o entendimento e resolução das atividades. Usamos o software GeoGebra como meio facilitador para que os alunos conjecturassem sobre o teorema básico da Programação Linear. A elaboração e as análises dos resultados da aplicação da sequência didática basearam-se na Teoria de Registros de Representação Semióticas, de Raymond Duval, que trata dos aspectos cognitivos relacionados às representações semióticas e à aquisição de conhecimentos matemáticos. A coleta de dados foi feita através de anotações, filmagens dos encontros e do material produzido pelos alunos durante as aulas. Ao final, da pesquisa concluímos que a abordagem do conteúdo Programação Linear na educação básica pode dar significado a conteúdos que, para os estudantes parecem desconexos, além de aumentar o espectro de problemas passíveis de resolução pelos alunos do ensino médio. / In this paper we discuss the integration of basic topics of Linear Programming in two variables in to high school and we present the results of applying a sequence of didactic addressing this theme. The Mathematics application of the sequence was accomplished with eight weekly meetings at the Pastor Dohms High School in Camaquã, in workshops dummy the opposite shift. Our didactic sequence prioritized activities that were designed to take the student to interpret results, and not merely through mechanic exercises. To apply the sequence, we developed five exercises and through them develop all necessary theory for solving the problems. We used the GeoGebra software to facilitate the learning of the basic linear programming theorem. This program was based on the theory of representation registers due to Raymond Duval the addresses he cognitive aspects of knowledge acquisition. The data was collected from notes, filmed meetings and work produced by students in class. At the end of the study conclude that the linear programming approach of content in basic education can give meaning to the contents that seem unconnected to students in addition to increasing the range of problems solvable by students.

Neste trabalho discutimos a inserção de tópicos básicos de Programação Linear em duas variáveis no ensino médio e apresentamos os resultados da aplicação de uma sequência didática abordando este tema. A aplicação da sequência foi realizada ao longo de oito encontros semanais no Centro de Ensino Médio Pastor Dohms – Unidade Camaquã – na modalidade de oficinas no turno inverso às aulas. Nossa sequência didática priorizou atividades que objetivaram levar os alunos a interpretar resultados e estabelecer conjecturas em detrimento à resolução mecanizada de exercícios. Elaboramos, para a aplicação da sequência, cinco problemas e através deles, desenvolvemos toda a teoria necessária para o entendimento e resolução das atividades. Usamos o software GeoGebra como meio facilitador para que os alunos conjecturassem sobre o teorema básico da Programação Linear. A elaboração e as análises dos resultados da aplicação da sequência didática basearam-se na Teoria de Registros de Representação Semióticas, de Raymond Duval, que trata dos aspectos cognitivos relacionados às representações semióticas e à aquisição de conhecimentos matemáticos. A coleta de dados foi feita através de anotações, filmagens dos encontros e do material produzido pelos alunos durante as aulas. Ao final, da pesquisa concluímos que a abordagem do conteúdo Programação Linear na educação básica pode dar significado a conteúdos que, para os estudantes parecem desconexos, além de aumentar o espectro de problemas passíveis de resolução pelos alunos do ensino médio. / In this paper we discuss the integration of basic topics of Linear Programming in two variables in to high school and we present the results of applying a sequence of didactic addressing this theme. The Mathematics application of the sequence was accomplished with eight weekly meetings at the Pastor Dohms High School in Camaquã, in workshops dummy the opposite shift. Our didactic sequence prioritized activities that were designed to take the student to interpret results, and not merely through mechanic exercises. To apply the sequence, we developed five exercises and through them develop all necessary theory for solving the problems. We used the GeoGebra software to facilitate the learning of the basic linear programming theorem. This program was based on the theory of representation registers due to Raymond Duval the addresses he cognitive aspects of knowledge acquisition. The data was collected from notes, filmed meetings and work produced by students in class. At the end of the study conclude that the linear programming approach of content in basic education can give meaning to the contents that seem unconnected to students in addition to increasing the range of problems solvable by students.

Neste trabalho discutimos a inserção de tópicos básicos de Programação Linear em duas variáveis no ensino médio e apresentamos os resultados da aplicação de uma sequência didática abordando este tema. A aplicação da sequência foi realizada ao longo de oito encontros semanais no Centro de Ensino Médio Pastor Dohms – Unidade Camaquã – na modalidade de oficinas no turno inverso às aulas. Nossa sequência didática priorizou atividades que objetivaram levar os alunos a interpretar resultados e estabelecer conjecturas em detrimento à resolução mecanizada de exercícios. Elaboramos, para a aplicação da sequência, cinco problemas e através deles, desenvolvemos toda a teoria necessária para o entendimento e resolução das atividades. Usamos o software GeoGebra como meio facilitador para que os alunos conjecturassem sobre o teorema básico da Programação Linear. A elaboração e as análises dos resultados da aplicação da sequência didática basearam-se na Teoria de Registros de Representação Semióticas, de Raymond Duval, que trata dos aspectos cognitivos relacionados às representações semióticas e à aquisição de conhecimentos matemáticos. A coleta de dados foi feita através de anotações, filmagens dos encontros e do material produzido pelos alunos durante as aulas. Ao final, da pesquisa concluímos que a abordagem do conteúdo Programação Linear na educação básica pode dar significado a conteúdos que, para os estudantes parecem desconexos, além de aumentar o espectro de problemas passíveis de resolução pelos alunos do ensino médio. / In this paper we discuss the integration of basic topics of Linear Programming in two variables in to high school and we present the results of applying a sequence of didactic addressing this theme. The Mathematics application of the sequence was accomplished with eight weekly meetings at the Pastor Dohms High School in Camaquã, in workshops dummy the opposite shift. Our didactic sequence prioritized activities that were designed to take the student to interpret results, and not merely through mechanic exercises. To apply the sequence, we developed five exercises and through them develop all necessary theory for solving the problems. We used the GeoGebra software to facilitate the learning of the basic linear programming theorem. This program was based on the theory of representation registers due to Raymond Duval the addresses he cognitive aspects of knowledge acquisition. The data was collected from notes, filmed meetings and work produced by students in class. At the end of the study conclude that the linear programming approach of content in basic education can give meaning to the contents that seem unconnected to students in addition to increasing the range of problems solvable by students.

This diploma thesis deals with CLIL which stands for Content and Language Integrated Learning, to be more precise it deals with the integration of Mathematics and English for lower secondary pupils. To realize this method I have chosen the topics of congruent figures in the plane and reflective symmetry. The aim of my thesis was to check whether the chosen topics are suitable for CLIL lessons, whether CLIL method is not an obstacle for the activity of pupils in the lesson or if it does not create any problems with understanding of the subject matter in Mathematics. The theoretical part is focused on describing the CLIL method in general, then I summarize the preparation of the educational experiment and describe the project of the lessons in English and in Czech language. The last part is dedicated to the realization of the experiment with three different groups of pupils of the 6th grade of elementary school. The gained data have been processed on the basis of observation and analysis of the final individual work and the questionnaire. The results of observation and analysis confirm that it is possible to integrate the teaching of Mathematics and foreign language successfully. The thesis includes English and Czech worksheets together with methodology for the topics of congruent figures and...

Educators strive to improve student learning outcomes and there are numerous theories suggesting how this is best achieved. However, application of these theories to the coal face of a classroom is often fraught with obstacles resulting in poor outcomes. Constraints imposed by educational policy, school systems, structures and the individual students themselves, realistically require adaptation of theoretical techniques if genuine learning is to be imparted to students. This paper discusses some of the issues surrounding the practical implementation of new methodologies into the classroom and identifies important factors that affect teenagers in their learning of mathematics. Working within the constraints, constantly confronted with obstacles, can be frustrating and demoralising. This paper reflects on twenty years of classroom teaching of mathematics to students with relatively poor socio-economic backgrounds and the lessons learnt from them that may assist teachers to remain enthusiastic and creative with the energy to truly improve mathematics education. Key issues explored in the paper include: ‘Realities of a teacher’s working day’, ‘The learning of mathematics within a government secondary system’, and ‘What can be done to ensure mathematical learning takes place?’