Submitted by admin tede (tede@pucgoias.edu.br) on 2018-11-06T20:11:59Z No. of bitstreams: 1 ARTUR JOSE DE OLIVEIRA E SILVA.pdf: 6171200 bytes, checksum: 89b4f4c8b84180ddb3985bfd0fa17df2 (MD5) / Made available in DSpace on 2018-11-06T20:11:59Z (GMT). No. of bitstreams: 1 ARTUR JOSE DE OLIVEIRA E SILVA.pdf: 6171200 bytes, checksum: 89b4f4c8b84180ddb3985bfd0fa17df2 (MD5) Previous issue date: 2018-08-23 / SILVA, Artur José de Oliveira e. Aprendizagem do Conceito Fração: um Experimento de Ensino baseado na Teoria do Ensino Desenvolvimental. Dissertação (Mestrado em Educação) – Pontifícia Universidade Católica de Goiás: Goiânia, 2018. This research, inscribed in the line of research Theories of Education and Pedagogical Processes, starts from an understanding based on the Historical- Cultural theory, according to which the school is the privileged place in the formation of scientific concepts by the students, being the form of learning that best contributes to its development as an integral human being. It seeks to clarify how to organize the Mathematich teaching, based on the the developmental teaching theory, to help the Pedagogy course students to form a fraction concept theoretical thinking. For this, the concepts construction, particularly the mathematical concept of fraction, was approached with theoretical and practical interest in the future teachers formation who will teach mathematics in the Elementary School initial years. The research objectives were: to understand the developmental theory contributions to the formation of the fraction concept, by the licentiate course in Pedagogy students of a public institution of higher education in the Goiás State; To understand in the course of the teaching-learning process of the fraction concept of elements that indicate qualitative and quantitative changes in the development of student thinking; To point out the developmental theory peculiarities of teaching the fraction concept considering the context of the Pedagogy course students formation. To investigate the problem, a teaching experiment was carried out, based on Davydov's assumptions, in a group of 36 undergraduate students in a Pedagogy course. Data collection involved questionnaires application, interviews and audio and video recordings. For the data categorization and systematization, the following moments were delineated (1) Approach with the fraction concept in the search for the universal relation of the studied object (2) Modeling the universal relation (3) Internalization of the fraction concept universal relation (4) Abstraction in the fraction concept formation and the particular tasks construction (5) Control of the mental actions realization in the formation of the fraction concept (6) Evaluation of the assimilation in the fraction concept formation through of problem solving. The data analysis revealed that this research main contribution was to show an alternative way of organizing the Mathematics teaching, specifically the fraction concept, since the experiment showed that, on average, 70.53% (seventy point fifty-three percent) of the students pointed out qualitative changes in the mathematical way of thinking and the fraction concept. / SILVA, Artur José de Oliveira e. Aprendizagem do Conceito Fração: um Experimento de Ensino baseado na Teoria do Ensino Desenvolvimental. Dissertação (Mestrado em Educação) – Pontifícia Universidade Católica de Goiás: Goiânia, 2018. Este trabalho, inscrito na linha de pesquisa Teorias da Educação e Processos Pedagógicos, parte de uma compreensão fundamentada na teoria Histórico-Cultural, segundo a qual a escola é o lugar privilegiado na formação de conceitos científicos pelos estudantes, sendo essa a forma de aprendizagem que melhor contribui para o seu desenvolvimento como ser humano integral. Busca esclarecer como organizar o ensino de matemática, fundamentado na teoria do ensino desenvolvimental, para ajudar os estudantes do curso de Licenciatura em Pedagogia, a formar o pensamento teórico do conceito de fração. Para tanto, abordou-se a formação de conceitos, particularmente do conceito matemático de fração, com interesse teórico e prático voltado para a formação inicial dos futuros professores que vão ensinar matemática nos anos iniciais do Ensino Fundamental. A pesquisa teve como objetivos: Compreender as contribuições da teoria do ensino desenvolvimental para a formação do conceito de fração, por estudantes do curso de licenciatura em Pedagogia de uma instituição pública de ensino superior do Estado de Goiás; apreender no decorrer do processo de ensino-aprendizagem do conceito de fração, elementos que indicam mudanças qualitativas e quantitativas no desenvolvimento do pensamento do estudante; apontar as peculiaridades da teoria do ensino desenvolvimental para organização do ensino do conceito de fração, considerando o contexto da formação dos estudantes do curso de Pedagogia. Para investigar o problema, realizou-se um experimento de ensino, baseado nos pressupostos de Davydov, em uma turma do curso de licenciatura em Pedagogia, com 36 (trinta e seis) estudantes. A coleta de dados envolveu aplicação de questionários, entrevistas e gravações em áudio e vídeo. Para a categorização e sistematização dos dados, foram delineadas os seguintes momentos (1) Aproximação com o conceito de fração na busca da relação universal do objeto estudado; (2) A modelação da relação universal; (3) Interiorização da relação universal do conceito de fração, a partir da transformação do modelo; (4) Abstração na formação do conceito de fração e a construção do sistema de tarefas particulares; (5) Controle da realização das ações mentais na formação do conceito de fração; (6) Avaliação da assimilação na formação do conceito de fração, por meio da resolução de problemas. A análise dos dados revelou que a principal contribuição dessa pesquisa consistiu em mostrar um caminho alternativo de organização do ensino de matemática, especificamente do conceito de fração, pois o experimento permitiu verificar que, em média, 70,53% (setenta vírgula cinquenta e três por cento) dos estudantes tiveram mudanças qualitativas no modo de pensar a matemática e o conceito de fração.

Submitted by Jorge Silva (jorgelmsilva@ufrrj.br) on 2017-08-31T18:21:55Z No. of bitstreams: 1 2014 - Aline Viana Oliveira.pdf: 1958433 bytes, checksum: 7d9ba724e2d3c00412549d70fa0cd73e (MD5) / Made available in DSpace on 2017-08-31T18:21:55Z (GMT). No. of bitstreams: 1 2014 - Aline Viana Oliveira.pdf: 1958433 bytes, checksum: 7d9ba724e2d3c00412549d70fa0cd73e (MD5) Previous issue date: 2014-08-29 / CAPES / Perceiving a deficiency of motivation for to learn mathematic from students of magistery of high school in an Estadual highschool of Nova Igua?u - RJ, came up a desire to perform a differentiated activity, that could to give more significant learning and motivates them to learn in the same time. The Electronics plays of Mangahigh Platform, supplied by SESI Mathematics Program were selected for this work. It was realized a workshop in a class of first year of normal course and the students worked equation of first degree, and the results in the motivation and learning increased after realization of workshop. The level of the motivation of students was measured by Motivation in Mathematics Scale by Gontijo (2007) before and after workshop. The results show a changing of stance from students and this leads to believe in achieving the desired objectives. / Percebendo-se a falta de motiva??o para aprender matem?tica dos alunos do curso de magist?rio em n?vel m?dio em uma escola estadual de Nova Igua?u - RJ, surgiu a vontade de realizar uma atividade diferenciada que pudesse ao mesmo tempo proporcionar aprendizado mais significativo e motiv?-los para aprender. Os jogos eletr?nicos da plataforma Mangahigh, fornecidos pelo programa SESI Matem?tica foram os escolhidos para esta empreitada. Foi realizada uma oficina com uma turma de 1? ano do curso normal onde os alunos trabalharam o conte?do de equa??es do 1? grau atrav?s de jogos, tendo aumentado significativamente os resultados dos testes ap?s a realiza??o da oficina. Tamb?m foi avaliado o n?vel de motiva??o dos alunos atrav?s da Escala de Motiva??o em Matem?tica de Gontijo (2007) antes da oficina e ap?s a sua realiza??o com o question?rio de avalia??o. O comparativo dos resultados dos question?rios mostra uma mudan?a de postura por parte dos alunos que leva a acreditar no alcance dos objetivos desejados.

Submitted by Maicon Juliano Schmidt (maicons) on 2015-04-24T12:12:07Z No. of bitstreams: 1 Marta Cristina Cezar Pozzobon.pdf: 1268473 bytes, checksum: 1871c4af4bb37ff036505e31a125fca6 (MD5) / Made available in DSpace on 2015-04-24T12:12:07Z (GMT). No. of bitstreams: 1 Marta Cristina Cezar Pozzobon.pdf: 1268473 bytes, checksum: 1871c4af4bb37ff036505e31a125fca6 (MD5) Previous issue date: 2012-12-12 / Nenhuma / Esta tese problematiza a formacao de professores que ensinam matematica nos anos iniciais a partir de um Curso de Formacao de Professores de Nivel Medio de uma Escola do interior do Rio Grande do Sul, nas decadas de 1960 a 2000, considerando algumas aproximacoes dos estudos foucaultianos, da area da educacao e da area de educacao matematica. As questoes que orientaram a pesquisa sao: de que forma os saberes matematicos constituiram as praticas de ensino de matematica de nivel medio (Normal/Magisterio) do Curso de Formacao analisado? Que praticas de ensino de matematica operaram na formacao de professores de anos iniciais no periodo analisado? Para dar conta de tais questoes, as ferramentas analiticas ?\praticas discursivas de formacao., ?\regimes de verdade. e ?\jogos de verdade. foram se constituindo juntamente com as analises do material, que consistiu de: um livro de atas de estagio, oito entrevistas com professores que trabalharam no Curso, quatro questionarios com supervisoras de estagio, um caderno de planejamentos, um Programa Experimental de Matematica, duas apostilas de planejamentos e duas propostas de estagio. Do exercicio de analise empreendido, resultaram dois movimentos, nomeados como regimes e jogos de verdade. No primeiro, sao apresentados os regimes de verdade constituidos na producao do desenvolvimento do raciocinio e do comportamento, a partir da alianca entre a psicologia e a pedagogia, no final do seculo XIX e inicio do seculo XX, no sentido de investir em praticas voltadas ao desenvolvimento do raciocinio, a producao de um sujeito inteligente, a aprendizagem de conceitos, ao uso do material concreto, ao raciocinio logico. No segundo movimento, os jogos de verdade e uma politica de verdade enfatizam as praticas de ensino de matematica voltadas aos discursos das pedagogias centradas na crianca, na pedagogia critica, em que a enfase esta em ensinar a partir do interesse da crianca, do tema gerador, da globalizacao e da realidade do aluno. Esses jogos de verdade produzem efeitos na formacao de professores, produzindo outra matematica, que assume a funcao de luta politica e esclarecimento de consciencias, tanto de alunos quanto de professores. Com essas praticas, produzem-se outros modos de ver e de dizer a matematica, o professor e o aluno. Dessa forma, a analise empreendida permitiu argumentar que as praticas de ensino de matematica nos anos iniciais constituem e sao constituidas por jogos de verdade que envolvem as concepcoes de conhecimento cientifico, de matematica, de ensino de cada epoca e de sujeito, articuladas pela razao de um Estado governamentalizado. / From approximations to both Foucauldian studies and investigations in the areas of education and mathematical education, this thesis problematizes the education provided by a Teaching Course from 1960 to 2000 in a countryside high school in Rio Grande do Sul to teachers who teach mathematics to the early grades. The questions that have guided this research are the following: How did mathematical knowledge constitute the mathematics teaching practices of the high school Teaching Course analyzed? Which mathematics teaching practices operated on the education of early grade teachers in the period analyzed? In order to address these questions, the analytical tools of ‘discursive education practices’, ‘regimes of truth’ and ‘games of truth’ were considered along the analysis of the material, which consisted of the following: a training record book, eight interviews with teachers that taught the Course, four questionnaires applied to training supervisors, a planning notebook, a Mathematics Experimental Program, two planning booklets and two training proposals. Two movements resulted from the analysis, and they were named as regimes and games of truth. The first one is related to regimes of truth constituted in the production of the development of reasoning and behavior, from the alliance between psychology and pedagogy in the late nineteenth century and early twentieth century by investing in practices directed to reasoning development, production of intelligent subjects, concept learning, use of concrete material, and logical reasoning. In the second movement, the games of truth and a politics of truth emphasize mathematics teaching practices directed to discourses of pedagogy centered on the child, in the critical pedagogy, in which the emphasis has been put on teaching from the child’s interest, the generating topic, the globalization and the student’s reality. Such games of truth have produced effects on teacher education by producing other kind of mathematics, one that assumes the function of political struggle, of enlightenment of consciences of students and teachers. With these practices, other ways of regarding and talking about mathematics, teachers and students have been produced. The analysis has led to the argument that the mathematics teaching practices of early grades both constitute and are constituted by games of truth, involving the conceptions of scientific knowledge, mathematics knowledge, teaching knowledge and subject in different times, and such conceptions are articulated by the reason of a governmentalized State.

Federal dollars are utilized to develop instructional programs for students not demonstrating mathematical proficiency on state standardized mathematics assessments, but there is a lack of empirical data on the effectiveness of two different approaches that were used in the local context. The purpose of this quantitative, nonexperimental, casual-comparative study was to determine if state achievement test scores of students in fourth grade who received instruction from a Mathematics Specialist (MS) during the 2007-2009 academic years demonstrated a statistically significant difference from the mathematics state achievement test scores of fourth grade students who received instruction from Grades 1-8 credentialed teachers supported by a Math Coach (MC) during the 2012-2014 academic years. The theoretical base includes two components: National Council of Teachers of Mathematics Standards and Federal No Child Left Behind educational policy, which focus on standards-based education, curriculum, assessment, and instruction to meet students' mathematical needs. Data was collected from a census sample of 13,671 students' state scores from school years 2007-2008, 2008-2009 (MS) and 2012-2013, 2013-2014 (MC). The research question was whether there is a difference in MS and MC scores. An independent samples t test was used to compare the means of all the scores. The results show that the MS program produced statistically higher math scores than the MC. This supports the limited literature in favor of MS. Positive social change includes supporting increasing the use of the MS program in the local context to increase mathematics test scores and the potential for redistribution of federal funds to develop MS programs nationwide.

<p>Syftet med avhandlingen är att beskriva och analysera argument för matematik i grundskolan och att förstå varför och hur de officiella argumenten förändras, från de argument som återfinns i styrdokument till de argument som förs fram av undervisande matematiklärare. En utgångspunkt är att skolmatematikens villkor och verklighet kan beskrivas genom analys av officiella argument och av lärarstudenters och lärares personliga argument för matematik i grundskolan. Specifika forskningsfrågor i anslutning till syftet är:</p><p>- Vilka argument för lärarstudenten fram inför yrkesdebuten?</p><p>- Vilka argument för läraren fram under sina första år i yrket?</p><p>- Vilka beskrivningar av skolmatematikens villkor ger lärarna?</p><p>En longitudinell studie har genomförts där en grupp lärarstudenter följts genom utbildningen och under de första åren i yrket. Resultatet visar att lärarstudenter under utbildningen utvecklar en syn på matematik och matematikundervisning som stämmer väl med läroplanen och kursplanen i matematik enligt Lpo 94. De nyblivna lärarna med undervisning i matematik och NO-ämnen upplever i början av yrkeskarriären skilda villkor på olika skolor. Gemensamt för de lärare som undervisar i senare delen av grundskolan är upplevelser av krav på att ”hinna med kursen” inför det nationella provet i årskurs 9. Lärarnas mål med matematikundervisningen i grundskolan blir därför att förbereda eleverna för det nationella provet. En faktor som påverkar är kravet på att elever skall ha betyget godkänd för att vara behöriga till gymnasieskolans nationella program. De nyblivna lärarna upplever en konflikt mellan olika officiella argument för matematik i grundskolan. Faktorer som påverkar lärarnas och matematikämnets villkor och verklighet i grundskolan är bl.a. skolornas organisation i arbetslag och lärarnas kombination av undervisningsämnen.</p> / <p>The aim of this thesis is to describe and analyse arguments for mathematics in compulsory school and to understand why and how the official arguments change, from the arguments written in the national curriculum and course syllabus for mathematics to the arguments presented by mathematics teachers. The point of departure is that the conditions and the reality for school mathematics can be understood through an analysis of official arguments and of personal arguments given by teacher students and teachers. A longitudinal investigation has been carried out; a group of teacher students has been followed during their teacher education and the first three years after their professional debut. The result shows that during their education the teacher students develop a view on mathematics and mathematics education harmonizing with the goals of mathematics in the national syllabus. The novice teachers have mathematics and sciences as their teaching subjects and they experience quite different conditions when they start to work as teachers. Common for those teaching in school years 7–9 is the experience of pressure to “cover the course” before the pupils shall take the national test in school year 9. Preparing the pupils for the national test becomes the most important goal for the novice teachers. A factor influencing the mathematics teacher is the qualification requirement in mathematics from compulsory school to go into the national programs in the upper secondary school. The novice teachers experience a conflict between different goals in the national curriculum and course syllabus for mathematics. Factors that have an influence on mathematics as a school subject are the organization of teachers at the local schools and the teachers’ combination of teaching subjects.</p>

In school algebra, using different methods including factorization to solve quadratic equations is one common teaching and learning topic at upper secondary school level. This study is about analyzing the algebra content related to solving quadratic equations and the method of factorization as presented in Swedish mathematics textbooks with subject matter content knowledge (CK) and pedagogical content knowledge (PCK) as analytical tools. Mathematics textbooks as educational resources and artefacts are widely used in classroom teaching and learning. What is presented in a textbook is often taught by teachers in the classroom. Similarly, what is missing from the textbook may not be presented by the teacher. The study is based on an assumption that pedagogical content knowledge is embedded in the subject content presented in textbooks. Textbooks contain both subject content knowledge and pedagogical content knowledge. The primary aim of the study is to explore what pedagogical content knowledge regarding solving quadratic equations that is embedded in mathematics textbooks. The secondary aim is to analyze the algebra content related to solving quadratic equations from the perspective of mathematics as a discipline in relation to algebra history. It is about what one can find in the textbook rather than how the textbook is used in the classroom. The study concerns a teaching perspective and is intended to contribute to the understanding of the conditions of teaching solving quadratic equations. The theoretical framework is based on Shulman’s concept pedagogical content knowledge and Mishra and Koehler’s concept content knowledge. The general theoretical perspective is based on Wartofsky’s artifact theory. The empirical material used in this study includes twelve mathematics textbooks in the mathematics B course at Swedish upper secondary schools. The study contains four rounds of analyses. The results of the first three rounds have set up a basis for a deep analysis of one selected textbook. The results show that the analyzed Swedish mathematics textbooks reflect the Swedish mathematics syllabus of algebra. It is found that the algebra content related to solving quadratic equations is similar in every investigated textbook. There is an accumulative relationship among all the algebra content with a final goal of presenting how to solve quadratic equations by quadratic formula, which implies that classroom teaching may focus on quadratic formula. Factorization method is presented for solving simple quadratic equations but not the general-formed quadratic equations. The study finds that the presentation of the algebra content related to quadratic equations in the selected textbook is organized by four geometrical models that can be traced back to the history of algebra. These four geometrical models are applied for illustrating algebra rules and construct an overall embedded teaching trajectory with five sub-trajectories. The historically related pedagogy and application of mathematics in both real world and pure mathematics contexts are the pedagogical content knowledge related to quadratic equations.

Syftet med avhandlingen är att beskriva och analysera argument för matematik i grundskolan och att förstå varför och hur de officiella argumenten förändras, från de argument som återfinns i styrdokument till de argument som förs fram av undervisande matematiklärare. En utgångspunkt är att skolmatematikens villkor och verklighet kan beskrivas genom analys av officiella argument och av lärarstudenters och lärares personliga argument för matematik i grundskolan. Specifika forskningsfrågor i anslutning till syftet är: - Vilka argument för lärarstudenten fram inför yrkesdebuten? - Vilka argument för läraren fram under sina första år i yrket? - Vilka beskrivningar av skolmatematikens villkor ger lärarna? En longitudinell studie har genomförts där en grupp lärarstudenter följts genom utbildningen och under de första åren i yrket. Resultatet visar att lärarstudenter under utbildningen utvecklar en syn på matematik och matematikundervisning som stämmer väl med läroplanen och kursplanen i matematik enligt Lpo 94. De nyblivna lärarna med undervisning i matematik och NO-ämnen upplever i början av yrkeskarriären skilda villkor på olika skolor. Gemensamt för de lärare som undervisar i senare delen av grundskolan är upplevelser av krav på att ”hinna med kursen” inför det nationella provet i årskurs 9. Lärarnas mål med matematikundervisningen i grundskolan blir därför att förbereda eleverna för det nationella provet. En faktor som påverkar är kravet på att elever skall ha betyget godkänd för att vara behöriga till gymnasieskolans nationella program. De nyblivna lärarna upplever en konflikt mellan olika officiella argument för matematik i grundskolan. Faktorer som påverkar lärarnas och matematikämnets villkor och verklighet i grundskolan är bl.a. skolornas organisation i arbetslag och lärarnas kombination av undervisningsämnen. / The aim of this thesis is to describe and analyse arguments for mathematics in compulsory school and to understand why and how the official arguments change, from the arguments written in the national curriculum and course syllabus for mathematics to the arguments presented by mathematics teachers. The point of departure is that the conditions and the reality for school mathematics can be understood through an analysis of official arguments and of personal arguments given by teacher students and teachers. A longitudinal investigation has been carried out; a group of teacher students has been followed during their teacher education and the first three years after their professional debut. The result shows that during their education the teacher students develop a view on mathematics and mathematics education harmonizing with the goals of mathematics in the national syllabus. The novice teachers have mathematics and sciences as their teaching subjects and they experience quite different conditions when they start to work as teachers. Common for those teaching in school years 7–9 is the experience of pressure to “cover the course” before the pupils shall take the national test in school year 9. Preparing the pupils for the national test becomes the most important goal for the novice teachers. A factor influencing the mathematics teacher is the qualification requirement in mathematics from compulsory school to go into the national programs in the upper secondary school. The novice teachers experience a conflict between different goals in the national curriculum and course syllabus for mathematics. Factors that have an influence on mathematics as a school subject are the organization of teachers at the local schools and the teachers’ combination of teaching subjects.

The purpose of this study is to examine the effects of a mathematics teaching methods course on pre-service elementary mathematics teachers&rsquo / content knowledge for teaching mathematics (CKTM). In order to accomplish this purpose, pre-service mathematics teachers&rsquo / understanding of basic concepts and procedures in school mathematics, use of mathematical definitions, presentation of mathematical content to students, identification of common errors, misconceptions and solution strategies and evaluation of unusual solution methods were examined with the help of a multiple choice test. The data were collected from 43 senior pre-service mathematics teachers from a teacher education program at a large public university in Ankara. The participants were given an 83-item test to measure their content knowledge for mathematics teaching at the beginning and after the methods course. The purpose of the pre- and post-test assessment was to measure the amount of change in the participants&#039 / knowledge for mathematics teaching. The test was developed and piloted at the University of Michigan in the USA for Learning Mathematics for Teaching (LMT) Project. Quantitative data analysis techniques were used to answer the research questions. The results indicated that there was a significant effect of the mathematics teaching methods course on pre-service teachers&rsquo / content knowledge for teaching mathematics. Moreover, the findings showed that there is no significant mean difference between male and female pre-service teachers, and between the pre-service teachers who have taken at least one mathematics teaching elective course and the ones who have not taken any elective course related to mathematics teaching in terms of their CKTM. Also, the study showed that there is a significant positive relationship between pre-service teachers&rsquo / CKTM and their academic achievement on undergraduate mathematics content courses. The study is expected to make important contributions to the literature by providing information about whether the methods courses significantly contribute to pre-service teachers&rsquo / understanding of knowledge for mathematics teaching. Moreover, the findings of the study is hoped to inform teacher educators and policy makers about the needs and improvements in teacher preparation programs.

Views of teaching: implications for the didactic training of mathematics teachers. School mathematics teaching is an essential learning area in South African schools. Owing to persistent traditional positivist-based views and approaches, it still suffers from a variety of teaching-learning problems. Various national attempts have already been made to develop an effective teaching-learning program for school mathematics. Prominent researchers reveal that the failure of teaching-learning programmes often have to be attributed to the lack of an underlying grounded didactic theory. Therefore this study focused on the development of a grounded teaching-theoretical framework for school mathematics teaching. A further problem regarding school mathematics is that its teaching and learning traditionally are viewed from a narrow school subject disciplinary perspective. Therefore this study departed from a general didactic-theoretical perspective, creating the opportunity to approach and solve problems from a wider angle. A constructivist-based post-positivist view of effective teaching was developed, before entering the field of school mathematics. In this way an integrated ontologicalcontextual view of teaching was developed in terms of six identified ontological essential features, and their contextual coherence, namely: intention, teacher, leamer, interaction, content and context. Contrary to traditional positivist views, no causal relationship between teaching and learning was imposed, and teaching was not qualified in terms of learning products. Instead, teaching was characterised and qualified on ontological grounds, departing from the phenomenon itself. In this way the limitations of positivist process-product views of teaching could be identified, explained and overcome. Alternatively, a dynamic integrated view of teaching as a human act, directed at the facilitation of relevant and meaningful learning, was grounded and developed. Based on this general ontological-contextually based view, a specific ontologicalcontextual view of effective school mathematics teaching was grounded and developed. To this end a variety of prominent contemporary views of and approaches to school mathematics, and its teaching and learning, needed to be analysed in a critical way. According to this analysis school mathematics, and its teaching and learning should be viewed and approached from a constructivist-based dynamic change-and-grow perspective as human acts. In addition, it could have been proved that the perspective concerned can facilitate the treatment and solving of the currently experienced teaching-learning problems. This requires the reconsideration, from a similar perspective, of the current school mathematics curriculum, as well as the preservice didactic training of mathematics teachers. Specific implications of the developed ontological-contextual view of effective school mathematics teaching were identified, and practically tested in the corresponding preservice didactic training situation in the North West Province. Based on this an integrated model for the training concerned was formulated. It was found that the current training largely contributed to the continuation of traditional views of and approaches to school mathematics teaching, and its essential features. From the developed integrated ontological-contextual perspective definitive proposals regarding the transformation of school mathematics teaching and the corresponding didactic training were made and motivated. Further areas for investigation and development, resulting from this study, were identified, as well. This study aimed at investigating, and revealing for further exploration, the specific and broadening interaction between the general teaching and subject didactical fields and research, particularly in the two contexts of effective school mathematics teaching and the corresponding preservice didactical training. A particular attempt was made to accomplish this in a grounded and integrated way, to the benefit of both fields. / Thesis (PhD)--PU for CHE, 1998.

Syftet med studien är att beskriva erfarenheter elever i gymnasiesärskolan har av ämnet matematik. Den teoretiska ansatsen utgår från grunderna i konstruktionismen och Berger och Luckmann's (2008) kunskapssociologiska förhållningssätt. Jag analyserar mina resultat utifrån Hacking (2000) och ett socialkonstruktionistiskt perspektiv. Studien är kvalitativ och gruppintervju används som metod. I gruppintervjun deltog sju elever som går i olika årskurser på gymnasiesärskolan. Eleverna går i Handelsprogrammet, Hotel och Restaurangprogrammet och Naturbruksprogrammet. Fokus i analysen är på vilka konstruktioner av skolämnet matematik, sig själva som matematikelever och nyttan med matematikkunskaper som eleverna gör. Resultatet visar att matematik som skolämne ses som ett nödvändigt ont och något som upplevs som svårt men viktigt. Det upplevs också som onödigt av vissa elever. Men även om relationen till matematik och rollen som matematikelev uppvisar kluvenhet, så var eleverna överens om att matematik var nyttigt att kunna i vardagslivet. Det fanns en stor samstämmighet bland de intervjuade eleverna om att man klarar sig bättre som vuxen om man kan matematik. / The purpose of the study is to describe the experiences students in Upper Secondary Special School have from the subject mathematics. The theoretical approach is based on the fundamentals of constructionism and Berger and Luckmann's (2008) approach to sociological knowledge. I analyse my results through Hacking (2000) and a social constructionistic perspective. The study is qualitative and a qualitative group interview is used as method. In the group interview, seven students in different levels on Upper Secondary Special School, participated. The students attend the Tradeprogram, Hotel and Restaurantprogram and Natural Resources Program. The focus of the analyse is which different constructions of the school matemathic, themselves as mathlearners and the usefulness of mathematics knowledge, that the students do. The result shows that mathematics as a school subject is seen as a necessary trouble and something that is perceived as difficult but important. It is also perceived as unnecessary by some students. But even if the relation to mathematics and the role of mathematics student exhibits ambivalence, the students were agreed that mathematics is useful to everyday life. There was a broad consensus among the interviewed students that you are doing better as an adult if you know mathematics.