This study aims to investigate the impact of using stories in pre-school mathematics teaching in Saudi Arabia. An intervention was designed to promote interactive teaching and learning in eight classrooms across three private schools. Integral to the intervention was a series of five stories especially written by the researcher based around the same central characters; reflecting the cultural setting familiar to the children, and with a problem-solving storyline. The stories include a range of mathematical facts, skills and concepts applicable to young learners. Additional resource materials to accompany the stories were also designed and provided for the participating teachers. The researcher adopted a qualitative, constructivist, technical action research approach and three data collection tools were used: a bibliographical questionnaire for the teachers; pre- and post-interventions semi-structured interview schedules, and classroom observations. A thematic analysis of the pre- and post-intervention data was undertaken in order to monitor the impact of using the stories in the pre-school classrooms. The study considers the findings from the data in relation to both the teachers’ and the children's’ experiences pre- and post-intervention. In particular, the impact of the intervention on teachers’ subject knowledge, attitudes, confidence and classroom practice is discussed along with the impact on children’s engagement and enjoyment of mathematics; their mathematical understanding and thinking skills. The study concludes that using stories to teach mathematics had a positive impact on the quality of teaching and learning mathematics. Using the stories prompted a positive change in teacher’s and children’s attitudes and feelings towards mathematics; a greater understanding of key mathematical ideas; and an appreciation of the value and uses of mathematics in everyday life. The implications from the study highlight the importance of providing appropriate training for pre-school teachers (and elsewhere) and the pivotal role that using stories can play in ensuring high quality mathematics teaching and learning.

I den här studien vill jag belysa hur lärare beskriver prevention och intervention, alltså deras förebyggande och ingripande agerande när det gäller undervisningen av elever som presterar lågt i matematik. Det är en kvalitativ studie som bygger på en serie gruppintervjuer av lärare i grundskolan. Det finns fortfarande en traditionellt kompensatoriskt syn på eleverna hos matematiklärarna och de är ofta av uppfattningen att det behövs specialpedagogik för att alla ska få ett godkänt betyg i matematik. I och med fortbildning, främst genom matematiklyftet, har inställningen till att klara av att inkludera elever som presterar lågt i matematik på ett bra sätt dock ökat. Arbetet i skolorna pågår för att förbättra matematikundervisningen men man ser sällan en övergripande gemensam plan från skolans eller lärarnas sida. Det arbete lärarna bedriver preventivt för att kunna inkludera de elever som presterar lågt har en positiv effekt på alla elever. Mycket av förändringen ligger i att lärare och elever talar mer matematik och inte följer läroboken lika slaviskt som tidigare. / In this study I want to illustrate how teachers describe their preventions and interventions when teaching students with low achievement in mathematics. This is a qualitative study based on a series of group interviews of teachers in the Swedish compulsory school. Mathematics teachers still hold a traditional compensatory perspective on students with low achievement thus placing the responsibility for learning with the students. The general opinion is that special pedagogics is necessary to enable support enough to help students with low achievement in mathematics to reach a passing grade. Thanks to further training, primarily through “Matematiklyftet”, the view on the possibility to include low achieving students in the classroom in a good way is more positive. There is an ongoing work in schools to improve the mathematics teaching, but one cannot see a complete or common plan for the schools neither from the school administration nor the teachers. The preventive measures made to include the low achieving students does have a positive effect for all students. Much of the implemented changes have its origin in talking mathematics in the classroom and not following the textbook as slavishly as previously done.

Licentiatavhandlingen riktar blicken mot planeringsarbete i förskolan. Syftet är att beskriva och analysera förskollärares autentiska planering av barns möten med matematik. Studiens teoretiska inramning utgörs av den reflektiva skoldidaktiska teorin som betonar, oavsett skolform, lärares ansvarstagande för undervisning. Med den reflektiva skoldidaktiska teorin beskrivs planeringsprocessen som betydelsefull för undervisning. Planeringsprocessen utgörs av tre pedagogiska aktiviteter: intention – handling – reflektion. I denna studie fokuseras det pedagogiska arbete som sker distanserat från handling vilket gör intention och reflektion till studiens centrala begrepp. Studiens empiriska material har producerats med hjälp av deltagande observation. Fältarbetet har genomförts i en förskola på deltid under två terminer läsåret 2012/13 i ett arbetslags återkommande och autentiska planeringssamtal. Resultatet visar att arbetslaget planerar barns möten med matematik genom att de tar sin utgångspunkt i reflektion över planerade och dokumenterade pedagogiska skeenden. Det finns därmed en koppling mellan intention och reflektion. Resultatet visar att arbetslaget har konstruerat en egen planeringsmodell. Förskollärarna utgår inte från explicit uttryckta målformuleringar som anger vad som ska läras utan resonemang om möjligt lärande kommer in som en del i deras samtal om aktiviteter. Resultatet visar även att arbetslagets planering skapar förutsättningar för möten med en mångfald av matematik. Dock visar resultatdiskussionen att det finns utrymme för att utveckla resonemang kring vilka sätt barn kan få göra övergångar från vardagliga matematiska representationsformer till mer abstrakta. Resultatet visar även att det finns ett behov av att utveckla ett matematikdidaktiskt yrkesspråk i förskolan. / Nyckelord: förskola, planering, didaktik, matematikundervisning  This Licentiate thesis focuses on planning in Swedish preschool. The aim is to describe and analyze pre-school teacher's authentic planning of children's meetings with mathematics. The theoretical framing of the study consists of the reflective school didactic theory emphasizing, regardless of school form, teachers' responsibility for teaching. With the reflective school didactic theory, the planning process is described as important for teaching. The planning process consists of three pedagogical activities: intention – action – reflection. This study focuses on the pedagogical work that takes place away from action, which makes intention and reflection to the central concept of the study. The empirical material of the study has been produced using participatory observation. Field work has been carried out in a preschool on part time for two semesters in the academic year 2012/13 in a regular and authentic planning conversation. The results show that the pre-school teachers do plan children's meetings with mathematics by taking their starting point in reflection on planned and documented pedagogical events. There is thus a link between intention and reflection. The result shows that the team has construct a planning model of their own. The planning is not based on explicit expressed goal formulations about what to learn. The reasoning of possible learning comes in as part of their conversations about activities. The result also shows that planning creates conditions for meetings with a multitude of mathematics. However, the results discussion shows that there is room to develop reasoning about the ways in which children can make transitions from everyday mathematical representations to more abstract. The result also shows that there is a need to develop a mathematics didactic language in preschool. Nyckelord: förskola, planering, didaktik, matematikundervisning  This Licentiate thesis focuses on planning in Swedish preschool. The aim is to describe and analyze pre-school teacher's authentic planning of children's meetings with mathematics. The theoretical framing of the study consists of the reflective school didactic theory emphasizing, regardless of school form, teachers' responsibility for teaching. With the reflective school didactic theory, the planning process is described as important for teaching. The planning process consists of three pedagogical activities: intention – action – reflection. This study focuses on the pedagogical work that takes place away from action, which makes intention and reflection to the central concept of the study. The empirical material of the study has been produced using participatory observation. Field work has been carried out in a preschool on part time for two semesters in the academic year 2012/13 in a regular and authentic planning conversation. The results show that the pre-school teachers do plan children's meetings with mathematics by taking their starting point in reflection on planned and documented pedagogical events. There is thus a link between intention and reflection. The result shows that the team has construct a planning model of their own. The planning is not based on explicit expressed goal formulations about what to learn. The reasoning of possible learning comes in as part of their conversations about activities. The result also shows that planning creates conditions for meetings with a multitude of mathematics. However, the results discussion shows that there is room to develop reasoning about the ways in which children can make transitions from everyday mathematical representations to more abstract. The result also shows that there is a need to develop a mathematics didactic language in preschool.

ABSTRACT This study investigates what and how mathematics (for teaching) is constituted in classroom practice. Specifically mathematical knowledge for teaching fractions in Grade 7. One teacher was studied to gain insight into the mathematical problemsolving the teacher does and the dilemmas he faces as he goes about his work. The analysis of the data show that the mathematical problem-solving that this particular teacher engaged in can be classified as demonstrating, encouraging and working with learner ideas. He appealed to mathematics (rules & empirical), experience (everyday) and the curriculum (tests and exams) to fix meaning. The mathematical problem solving and appeals he made threw up dilemmas of representing the content, competing goals and student thinking. This aided in providing a description of what mathematics for teaching is in this practice. The report concludes with a discussion of what teachers need to know or study in order to become better mathematics teachers and where do they find these courses to accommodate their need to improve as mathematics teachers.

Neste trabalho apresentamos o conceito de desenvolvimento atípico; um texto de referência para o ensino de funções voltado para o 9ª ano, dois modelos didáticos de avaliação formativa, levando em consideração a diversidade do educando e uma palestra motivacional e instrutiva sobre educação inclusiva. Atualmente o ensino da Matemática está voltado para uma apresentação estritamente formal, sem levar em consideração o desenvolvimento do aluno no processo de ensino aprendizagem, quantizando o aprendizado segundo padrões. Nosso objetivo é promover uma aprendizagem significativa pelo aluno, abandonando o uso de fórmulas decoradas, prezando o raciocínio lógico e analisar se o uso de estratégias diferenciadas como: jogos, listas personalizadas, laboratório de matemática são capazes de motivar o aluno, em especial os casos de desenvolvimento atípico, a desejar ser parte da turma e trabalhar em função do seu progresso. / In this work we present the concept of atypical development; a reference text for teaching towards facing the 9th grade, two educational models of formative assessment, taking into consideration the student\'s diversity and motivational and instructive lecture on inclusive education. Currently teaching mathematics is aimed at a strict presentation, regardless of the student\'s development in the teaching and learning process, quantizing the standard learning. Our goal is to promote meaningful learning by the student, abandoning the use of decorated formulas, valuing logical reasoning and examine whether the use of different strategies as games, custom lists, math lab are able to motivate the student with special cases of atypical development, to wish to be part of the class and work according to their progress.

A presente pesquisa objetivou compreender como o conceito de resistência, em relação ao processo de ensino da matemática, se manifesta na voz do professor dos anos iniciais do ensino fundamental no contexto da atividade docente. Para desenvolvimento deste trabalho, foram realizados estudos sobre educação matemática, atividade docente e o conceito de resistência, sendo estes associados à abordagem Histórico-Cultural e princípios da Teoria da Atividade, concepções apoiadas, principalmente nas ideias de Vigotski e Leontiev. A construção metodológica foi norteada pela abordagem qualitativa, e os dados que constituíram a investigação foram obtidos por meio de estudos bibliográficos e documentais, observações, diário de campo e entrevistas em áudio, configurando-se como estudo de caso. O local escolhido para realização deste trabalho foram três escolas públicas da rede estadual de ensino do município de Palmas-TO, que ofertam o 4º e 5º ano do ensino fundamental. Os sujeitos participantes foram as professoras das respectivas turmas escolhidas. A análise dos dados indica que o processo de ensino e aprendizagem é uma atividade consciente e exclusivamente humana, nesse contexto, a atividade se constitui como construção histórica e cultural. No que concerne ao conceito de resistência, a pesquisa observou que este é um elemento evidente no contexto escolar, sendo manifesto nas atitudes e nas contradições docentes, caracterizando a escola como um espaço que concomitantemente pode atuar para reproduzir os interesses da classe dominante como também pode possibilitar a emancipação e a transformação social dos sujeitos. / The present study aims to comprehend how the concept of resistence, regarding the process of teaching mathematics, is manifested in the voice of the teachers who teach in the first years of elementary school at the teaching context. In order to develop this study, a literature review on mathematics education, teaching and the concept of resistence associated with the Historical-Cultural approach and the Activity Theory principles, conceptions supported mainly in the ideas of Vigotski and Leontiev. The methodology was guided by the qualitative approach, specifically a case study, in which the data that compose this investigation was collected through literature review, documentary research, observations, field diaries and audio interviews. The investigation was carried out in three public schools, from the State of Tocantins, in the city of Palmas, these schools offer the 4th and 5th grade of elementary school. The participants were the teachers of the classes chosen. The analysis has shown that the process of teaching and learning is a conscious activity and a solely human one. In this context, the activity becomes a historical and cultural construction. It was observed that, with regard to the concept of resistence, it is an evident element at schools, which manifest itself in the aptitudes and contradictions of their teachers, categorizing schools as spaces that can both work to reproduce the interests of the ruling class and to enable the emancipation and the social transformation of individuals.

Made available in DSpace on 2017-07-21T20:56:28Z (GMT). No. of bitstreams: 1 Rodovlas Santos.pdf: 2016733 bytes, checksum: 6e68081442d6100ecc8c130cb6cb6a1a (MD5) Previous issue date: 2015-10-01 / Music is without any doubt one of the main ways to express culture, gender and personal tastes. Western music in general has the same musical basis which has its core in simple mathematical concepts. This study aims to bring mathematical concepts to high and elementary school students through the history of music. This essay proposes a literature review about the importance and the contributions of Pitagoras in the construction of Diatonic Scale and the influence that pitagorian studies exert in the Equal Tempered Scale, used nowadays. This paper is based in official documents such as PCN and PCNEM (National Curricular Parameters and National Curricular Parameters of High School) and curricular guidelines about the study of Mathematics allying mathematical subjects to daily life concepts, in this case, musical concepts. Activities that can be reproduced by Mathematics teachers even when the teacher does not have advanced musical knowledge are studied in this paper, for example, studying fractions aiming to build a monochord with the program Geogebra exploring sound concepts described by exponential and trigonometric functions. / A música é sem dúvida uma das principais formas de manifestação cultural, de gêneros e gostos diversos a música ocidental tem em geral uma mesma base musical e esta base tem seu cerne em conceitos matemáticos simples. Esse trabalho objetiva trazer esses conceitos matemáticos ao conhecimento de alunos do ensino médio e fundamental através da história da música. Propõe-se uma revisão bibliográfica da importância e das contribuições de Pitágoras na construção da escala Diatônica e da influência que os estudos pitagóricos exerceram na escala Temperada, que é atualmente utilizada. O estudo apresenta-se norteado por documentos oficiais como PCN e PCNEM (Parâmetros Curriculares Nacionais e Parâmetros Curricular Nacionais do Ensino Médio) e diretrizes curriculares a respeito do estudo da matemática, aliando conteúdos matemáticos a conceitos do cotidiano, nesse caso a conceitos musicais. Nesse trabalho, são tratadas atividades que podem ser reproduzidas por professores de matemática sem que o mesmo necessite de conhecimentos avançados sobre música, tais como o estudo de frações na construção de um monocórdio e com auxílio do programa Geogebra é explorado conceitos de sons descritos através de funções exponenciais e trigonométricas.

A partir da Lei de Diretrizes e Bases da Educação Brasileira (LDBEN) do ano de 1996, iniciou-se a produção de diversos documentos, tanto de orientações como de definições em torno da organização de conteúdos, ou ainda, sobre as ideias geradoras dessas bases. Surgem daí os Parâmetros, Diretrizes e Orientações Curriculares Nacionais que, juntamente com as inovações educacionais, o desenvolvimento científico, econômico e social, ou mesmo influenciados pela opção política, subsidiam os processos das reformas ou mudanças curriculares produzidas nos estados. Esta pesquisa trata de compreendermos e discutirmos como se estabelecem as relações de (in)compreensões dos professores de Matemática que dela participaram e que atuam na rede de ensino da Secretaria de Estado da Educação de São Paulo: o engajamento dos professores; os elementos facilitadores e dificultadores percebidos por eles nesse processo, e as possibilidades de resistências na prática da sala de aula. Para tanto, produzimos e aplicamos questionários e entrevistas a dois grupos de professores, em três regiões do Estado de São Paulo. Elaboramos, dessa forma, três eixos principais que nortearam nossa pesquisa: o currículo, a competência e a prática docente. Sobre o currículo, pesquisamos suas concepções, as teorias que o influenciam e as pesquisas em Educação e Educação Matemática que fomentam a produção desses documentos. A competência é elemento inovador nos documentos curriculares; ela invade os currículos, porém, produz pluralidade em seu significado. Quanto à formação dos professores, destacamos tanto o conhecimento profissional destes como a resistência elaborada nos seus discursos. / The 1996 Lei de Diretrizes e Bases da Educação Brasileira (LDBEN) [Brazilian Education Bases and Guidelines Law] paved the way for the production of various strands of literature, involving both guidelines and definitions on the organisation of content and even on the ideas to have generated these bases. The National Curriculum Parameters, Directives and Guidelines soon followed, and, along with innovations in education, scientific, economic and social development and influences from political decisions, have come to subsidise the procedures for curricular reforms or changes produced across each state. This study aims to understand and discuss how (mis)understanding(s) are established on the part of mathematics teachers in the São Paulo state education network by considering teachers engagement, elements which they believe facilitate or complicate the process and practical possibilities for the generation of counterarguments in the classroom. We therefore produced and carried out questionnaires and interviews with two groups of teachers in three regions in the state of São Paulo. This allowed us to develop three strands of focus for our study: the curriculum, teaching competence and teaching practice. In terms of the curriculum, we researched the concepts behind it, the theories to have influenced it and the research into Education and Mathematics Education to have fed the production of the literature. Competence is an innovative element in literature on curricula; it dominates curricula, and yet there is plurality inherent to its meaning. In terms of teacher training, we highlight both professional knowledge and the counterarguments developed in the teachers discourse.

Avec plus d'un tiers de professeurs pratiquants dans l'académie de Toulouse, les enquêtes ont constaté que, désormais, le recours informatique est un phénomène historique irréversible dans l'enseignement des mathématiques au collège dû : premièrement, à la généralisation des équipements (vidéoprojecteurs en classe) ; à l'engagement des professeurs qui a compensé les défaillances de l'institution dans leurs administrations ; deuxièmement, aux incitations et obligations institutionnelles des nouveaux programmes et des inspections ; troisièmement, à la disponibilité des logiciels gratuits qui ont suppléé les carences budgétaires ; à l'abondance des activités diffusées en ligne par les sites académiques, les IREM et l'association Sésamath ; quatrièmement, au rôle éminent de la formation continue volontaire qui a mobilisé 40 % des professeurs en douze ans ; cinquièmement, à l'enclenchement d'un cercle vertueux de reconnaissance de la valeur du recours informatique. L'étude pragmatique et théorique a révélé que les diverses activités informatiques d'enseignement-apprentissage (AIEA) pratiquées (apprenticiel, imagiciel, exerciseur, didacticiel, praticiel), en utilisant les apports spécifiques de l'informatique (concrétisation, expérimentation intensifiée, individualisation, interaction, motivation), ont apporté des situations instrumentées nouvelles de transposition interne offrant des champs conceptuels féconds qui sous l'effet de schèmes opératoires sont capables d'améliorer l'enseignement-apprentissage des notions et méthodes mathématiques. Un résultat qui dépend de la qualité de ses composantes praxéologiques (intégration, pertinence, performance, supériorité, scénario, mise en scène, durée) et du respect de règles pratiques qui déterminent conjointement les valeurs éducologiques de l'AIEA (propre, efficace et d'usage, professionnelle et institutionnelle) susceptibles de donner un meilleur rendement et une plus grande productivité à l'enseignement des mathématiques. / With more than a third of practicing teachers in the Academy of Toulouse, surveys found the computer use is now, an irreversible historical phenomenon in the teaching of mathematics at the college due to : 1st, the generalization of equipment (video projectors in the classroom); the commitment of teachers has offset the institution failures; 2nd, the incentives and institutional obligations of new programs and inspections; 3rd, the availability of free software who have deputized budgetary deficiencies; the abundance of broadcast activities online by academic sites, the IREM and the association Sésamath; 4th, the prominent role of continuing education who has mobilized 40% of teachers in twelve years; 5th, the engagement of a virtuous circle of recognition of the value of the computer use. The pragmatic and theoretical study revealed that activities computer teaching-learning (ACTL) carried out (learnial, imagicial, exerciser, tutorial, practical), using the specific contributions of computing (implementation, testing intensified, individualization, interaction, motivation), brought new instrumented situations of internal transposition offering fertile conceptual fields which, under the effect of operative schemes, are able to improve the teaching-learning of concepts and mathematical methods. A result that depends on the quality of its components praxiological (integration, relevance, performance, superiority, scenario, staging, duration) and respect of practical rules that jointly determine the training values of ACTL (intrinsic, efficient, to use, professional and institutional) able to give better performance and higher productivity in the teaching of mathematics.

Thesis (Ed.D.)--University of Delaware, 2006. / Principal faculty advisor: Frank B. Murray, School of Education. Includes bibliographical references.