Die Habilitationsschrift beschäftigt sich mit der Einbeziehung von Elementen der 3D-Computergrafik in den Unterricht der analytischen Geometrie in der Sekundarstufe II. Vorrangiges Ziel dabei ist, den Unterricht praxisnäher, anschaulicher und attraktiver zu gestalten. Im Bereich des Computereinsatzes im Mathematikunterricht weist die 3D-Computergrafik die Besonderheit auf, dass sie sowohl als Unterrichtsgegenstand als auch als Hilfsmittel für die Visualisierung und für experimentelles Arbeiten von Bedeutung ist. Grundlagen der in der vorliegenden Arbeit angestellten Überlegungen und unterbreiteten Vorschläge bilden einerseits eine Analyse der analytischen Geometrie als schulischer Lerninhalt einschließlich der dabei verfolgten Ziele (Kapitel 1) sowie andererseits die mathematischen Grundlagen der 3D-Computergrafik und ihrer Anwendungen (Kapitel 2). Basierend auf diesen beiden Aspekten werden in Kapitel 3 Potenzen und Ziele des Einsatzes dreidimensionaler Grafiksoftware und der Thematisierung mathematischer Grundlagen der Computergrafik im Stoffgebiet Analytische Geometrie herausgearbeitet. Es wird begründet, dass die Einbeziehung von Elementen der 3D-Computergrafik wesentlich dazu beitragen kann, den Intentionen des Unterrichts in analytischer Geometrie gerecht zu werden und den oft formalen Charakter der Behandlung dieses Themas zu überwinden sowie geometrische Betrachtungsweisen in den Vordergrund zu rücken. In Kapitel 4 erfolgt eine Konkretisierung dieser Überlegungen zu Unterrichtsvorschlägen für die Einbeziehung von Elementen der 3D-Computergrafik in das Stoffgebiet anhand einer Reihe von Gegenstandsbereichen. Erfahrungen aus Unterrichtsprojekten, die auf der Grundlage einiger der in Kapitel 4 entwickelten Konzepte durchgeführt wurden, sind Gegenstand von Kapitel 5. / The book is concerned with possibilities for using the potential of 3D computer graphics in mathematics education in grammar schools, especially in the subject analytic geometry, to improve student''s understanding and motivation. Computer graphics can be used as a tool for visualization of ideas and thoughts and can be also considered as a teaching subject because its mathematical foundations are closely related to the classical contents of mathematics education in grammar schools. Proposals, which are developed in the book, are based both on an analysis of history, aims and problems of teaching analytic geometry (chapter 1) and mathematical foundations of 3D computer graphics and its applications (chapter 2). Based on both aspects potencies and goals of the use of three-dimensional graphics software and the treatment of mathematically based working principles of computer graphics in mathematics education are worked out in chapter 3. It is justified that the inclusion of elements of 3D computer graphics can essentially contribute to the intentions of the instruction in analytic geometry and to overcome the often formal character of the treatment of this topic as well as moving geometrical approaches into the foreground. In chapter 4, these considerations are substantiated and concepts and suggestions for the inclusion of elements of computer graphics into a variety of subject areas are developed. Experiences from instruction projects in analytic geometry classes, that were carried out some of the concepts developed in chapter 4 on the basis, are object of chapter 5.

Idén till denna studie uppkom i samband med den förändring i styrdokumenten gällande digitalisering av ämnet Matematik som trädde i kraft 2017. Syftet med studien är att undersöka hur lärare använder och motiverar användandet av digitala verktyg i matematikundervisningen, samt i vilken utsträckning de har förändrat sin undervisning i samband med digitaliseringen av läroplanen. Fem gymnasielärare i matematik deltog i semi-strukturerade intervjuer och fyra matematiklektioner observerades strukturellt. Resultatet visar att lärare använder digitala verktyg både som ett medel för att ge eleverna matematisk kunskap, men också som ett mål för att eleverna ska lära sig de digitala verktygen. Lärarna motiverar användningen av digitala verktyg med att det sparar tid, förenklar representationer av olika koncept, och att de i vissa fall underlättar undervisningen. Lärarna menar också att digitala verktyg kan bidra med att införa nya metoder för lärande, att de förbereder eleverna för nationella prov och för ett liv i det digitala samhället. Lärarna gjorde små eller inga ändringar i sin undervisningspraktik i samband med förändringen i läroplanen, och i de fallet en förändring skedde hade läraren ”öppnat upp” för utökad användning av digitala verktyg. / The idea for the study appeared as a result of the change related to the digitalization of the subject Mathematics in the Swedish senior high school that took effect in 2017. The purpose of the study is to investigate how teachers use and motivate the use of digital tools in the Mathematical education, and if and how the teachers say that they have made changes in their teaching due to the curriculum change. Five mathematics teachers working at senior high schools took part in semi-structured interviews and four mathematics classes were observed structurally. The result has been interpreted by using the framework RAT, Curriculum theory and ATD. The result shows that teachers use digital tools both as an equipment to reach the pupils mathematical understanding, but also as a goal for the pupils to learn the tools. The teachers motivate the use of digital tools by saying that it saves time, makes representations of concepts easier to show, and that it in some cases makes the teaching easier. They also say that digital tools can help introduce new ways of learning, that they prepare the pupils for national tests where they must be able to use digital tools, and that they prepare the pupils for a life in the world of digitalization. The teachers did none or a small change to their ways of teaching due to the curriculum change, and in that case, they said that they “opened up” more for the use of digital tools.

Dans cette thèse, nous étudions l’impact du P.I.B.I.D. (Programa Institucional de Bolsas de Iniciação à Docência), programme de formation des professeurs au Brésil, créé en 2007, sur la formation des enseignants de mathématiques.Notre problématique est double : le P.I.B.I.D. apporte-t-il une amélioration conséquente à la formation des enseignants ?, et pour les professeurs de mathématiques : est-ce que la didactique des mathématiques, telle qu’elle est enseignée dans les Instituts d’Enseignement Supérieur, est liée réellement à la pratique de classe des enseignants formés par ce programme ?L’impact de la pensée française dans la sphère éducative brésilienne est indéniable. Ce sont de grands chercheurs français qui ont dirigé la construction des curriculums de formation des enseignants brésiliens. Il est donc naturel de comparer la formation donnée par le P.I.B.I.D. avec celle donnée dans les E.S.P.E. en France. Quatre parties composent cette thèse. Dans la première nous traçons le cadre général dans lequel se place la formation des enseignants en faisant une brève comparaison des systèmes scolaires brésilien et français au Chapitre I. Dans le suivant après avoir présenté succinctement le système d’enseignement supérieur brésilien, nous faisons un historique de la formation des professeurs au Brésil depuis 1 827, puis nous présentons le PIBID, sa création et son évolution jusqu’à nos jours où il va être remplacé par le Programme de Résidence Pédagogique.Dans la deuxième partie, nous abordons un point technique essentiel pour comprendre le PIBID : le système statistique complexe utilisé au Brésil pour piloter le système éducatif et repérer les écoles ayant le plus d’élèves en difficulté afin de les encourager à participer à ce programme en accueillant des boursiers. Au chapitre III, nous décrivons le Recensement Scolaire et son organisation. Nous explicitons certains concepts statistiques comme le flux scolaire et le taux de performance. Pour trouver des comparaisons pertinentes entre le Brésil et de la France, nous portons notre attention sur le redoublement et le décrochage scolaire en France. Au chapitre IV nous approfondissons ces concepts en détaillant le fonctionnement du S.A.E.B. (Système National d’Évaluation de l’Éducation de Base) et le calcul de l’I.D.E.B. (Indice de Développement de l’Éducation de Base) qui est crucial pour le P.I.B.I.D.Dans la troisième partie au chapitre V, nous analysons les réponses aux questions que nous avons posées lors des entretiens menés auprès de 34 acteurs du P.I.B.I.D. L’intégralité des échanges traduits en français figure à l’Annexe A. V. La transcription représente plus de 3 700 tours de parole.Enfin la quatrième partie est consacrée au point central de notre réflexion sur la formation des enseignants de mathématiques au Brésil, c’est-à-dire l’apport des théories pédagogiques et didactiques à cette formation.Nous décrivons brièvement au chapitre VI, l’influence au Brésil des recherches françaises en pédagogie et en didactique des mathématiques, en prenant en considération les travaux de Gaston Bachelard et Jean Piaget pour la pédagogie et de Guy Brousseau, Gérard Vergnaud, Yves Chevallard et Michèle Artigue, Gérard Sensevy et Rémi Brissiaud pour la didactique. Dans le chapitre VII, après un bref rappel des dispositifs de formation des enseignants en France nous portons un regard personnel sur cette formation dans les E.S.P.E. à travers des comptes rendus de séances d’observation que nous a pu effectuer à Nice. Enfin concernant le P.I.B.I.D., nous concluons que c’est un programme innovant qui a apporté beaucoup de progrès dans la formation des enseignants, et nous suggérons quelques améliorations sur la nature des stages dans les écoles et en retour quelques améliorations à apporter en France dans le choix des écoles où se déroulent les stages de formation des futurs enseignants.Cette recherche est complétée par une bibliographie de 180 références. / In this thesis, we study the impact of the P.I.B.I.D. (Programa Institucional of Bolsas de Iniciação in Docência), training program of teachers in Brazil, created in 2007, on the formation of the teachers of mathematics.Our problem is twofold: does the P.I.B.I.D. provide a significant improvement in teacher training ?, and for mathematics teachers: is the didactic of mathematics, as taught in Higher Education Institutes, really linked to the class practice of teachers trained by this program?The impact of French thought in the Brazilian educational sphere is undeniable. These are great French researchers who led the construction of Brazilian teacher training curricula. It is therefore natural to compare the training given by P.I.B.I.D. with that given in the E.S.P.E. in France.Four parts compose this thesis. In the first we draw the general framework in which teacher training takes place by doing a brief comparison of the Brazilian and French school systems in Chapter I. In the following chapter, after presenting briefly the Brazilian higher education system, we write a historical of the training of teachers in Brazil since 1827, next we present the P.I.B.I.D., its creation and its evolution until our days when it will be replaced by the Pedagogical Residence Program.In the second part, we address an essential technical point to understand the P.I.B.I.D.: the complex statistical system used in Brazil to steer the education system and identify the schools with the most students in difficulty, to encourage them to participate in this program, welcoming fellows future teachers. In Chapter III, we describe the School Census and its organization. We explain some statistical concepts such as school flow and performance rate. To find relevant comparisons between Brazil and France, we turn our attention to repetition and drop out of school in France. In Chapter IV we delve deeper into these concepts by detailing the functioning of the National Basic Education Assessment System (S.A.E.B.) and the calculation of the I.D.E.B. (Basic Education Development Index) which is crucial for the P.I.B.I.D.In the third part, in Chapter V, we analyze the answers to the questions we asked in interviews with 34 stakeholders in the P.I.B.I.D. All the exchanges translated into French are given in Appendix A. V. The transcript represents more than 3,700 speaking slots.Finally, the fourth part is devoted to the central point of our reflection on the training of mathematics teachers in Brazil, that is to say the contribution of pedagogical and didactic theories to this training. We briefly describe in Chapter VI, the influence in Brazil of French researches in pedagogy and didactics of mathematics, taking into account the work of Gaston Bachelard and Jean Piaget for pedagogy and Guy Brousseau, Gérard Vergnaud, Yves Chevallard, Michèle Artigue, Gérard Sensevy and Rémi Brissiaud for didactics.In Chapter VII, after a brief review of teacher training schemes in France, we take a personal look at this training in the E.S.P.E. through reports of observation sessions that we have done in Nice.Finally, concerning the P.I.B.I.D., we conclude that it is an innovative program that has made a lot of progress in the training of teachers, and we suggest some improvements on the nature of internships in schools and in return some improvement to be made in France in the choice of schools where the training courses for future teachers take place.This research is completed by a bibliography of 180 references.

Orientador: Lourdes de la Rosa Onuchic / Banca: Adair Mendes Nacarato / Banca: Kátia Cristina Stocco Smole / Banca: Norma Suely Gomes Allevato / Banca: Rosana Giaretta Sguerra Miskulin / Resumo: Toda pesquisa começa com uma curiosidade do pesquisador e se apresenta como um ponto de partida para uma investigação. Assim, esta pesquisa tem como fenômeno de interesse trabalhar a Geometria Euclidiana, numa abordagem dinâmica, com alunos, futuros professores, do curso de Licenciatura em Matemática da Universidade do Estado da Bahia - UNEB, Campus X. Seu objetivo é o de investigar, compreender e evidenciar as potencialidades didático-matemáticas da Metodologia de Ensino-Aprendizagem-Avaliação de Matemática através da Resolução de Problemas nos processos de ensinar e aprender Geometria. É uma pesquisa de natureza qualitativa que foi desenvolvida seguindo orientações metodológicas de Thomas A. Romberg. Usou-se como procedimentos metodológicos na coleta de dados: a observação, o material escrito pelos alunos, questionários, filmagens, gravações e diário de campo. Dois projetos de ensino foram criados e aplicados nas disciplinas Didática da Matemática e Laboratório de Ensino de Matemática II, respectivamente. Na junção desses dois projetos, depois de aplicados, concluiu-se que essa é mais uma pesquisa no contexto da Educação Matemática que une as disciplinas trabalhadas como uma dupla necessária para a formação de professores. Ademais, sugere um trabalho feito com professores em formação inicial visando a sua própria formação e propicia momentos de reflexão e análise sobre as potencialidades que a Metodologia de Ensino- Aprendizagem-Avaliação de Matemática através da Resolução de Problemas oferece no sentido de incrementar a aprendizagem e melhorar os processos de ensino de Matemática, sobretudo o de Geometria. / Abstract: Every search begins with a curiosity of the researcher and it is presented as a starting point for an investigation. This research has the phenomenon of interest to work Euclidean geometry, a dynamic approach, with students, future teachers, the Degree in Mathematics at the University of Bahia - UNEB, Campus X. Its goal is to investigate, understand and highlight the potential of teaching math-Teaching Methodology-Evaluation of Learning Mathematics through Problem Solving in the processes of teaching and learning geometry. . It is a qualitative research that was developed following methodological guidelines of Thomas A. Romberg. It used as instruments to collect data: observation, material was written by students, quizzes, films, recordings and field diary. Two education projects were created and applied in the disciplines of Didactics of Mathematics and Laboratory of Mathematics II, respectively. At the junction of these two projects, once implemented, it was concluded that this is another research in the context of mathematics education that unites the disciplines worked as a dual need for teacher training. Moreover, it suggests a work that was done with teachers in training to become self-training and provides moments of reflection and analysis on the potential that the methodology of Teaching-Learning-Evaluation of Mathematics through Problem Solving offers to enhance their learning and improve the processes of teaching mathematics, especially in geometry. / Doutor

Made available in DSpace on 2016-04-27T16:58:19Z (GMT). No. of bitstreams: 1 eugenio.pdf: 984600 bytes, checksum: e418bb88c201ea98edc58db64ac89cd4 (MD5) Previous issue date: 2001-11-06 / The purpose of this work is to study the process by which students following a university-level course in the exact sciences acquire/construct the notion of average rate of change. An understanding of this notion could assist students in interpreting the meaning of the derivative as the average rate of change of a point. A didactic sequence was elaborated, inspired by Vergnaud (1994), who considers that the teaching and learning of mathematical notions and concepts should be approached by an exploration of problems, that is, by developing problem situations which favour new conceptualisations in their resolution. Eighteen pairs of students from a first year chemistry course worked on the sequence which lasted 1.440 minutes. The results indicated that the students advanced their understandings of average rate of change, as well as their ability to interpret graphs, for example, identifying intervals in which the function increases or decreases and describing the meaning of points where the function intersects the axes of the graph / Este trabalho tem por objetivo estudar o processo de aquisição/construção da noção de taxa de variação média de uma função, por alunos que ingressaram em um curso superior na área de exatas. A compreensão dessa noção pode favorecer a interpretação do significado da derivada como taxa de variação num ponto. Para tanto, foi elaborada uma seqüência didática inspirada nas concepções de Vergnaud (1994), que considera que o processo de ensino e aprendizagem de noções e conceitos matemáticos devem ser abordados mediante a exploração de problemas, ou seja, de situações em que os alunos precisem desenvolver algum tipo de estratégia para resolvê-las. Essa seqüência foi desenvolvida por 18 duplas de alunos do 1° ano de um curso de Química, ao longo de 1.440 minutos. Os resultados obtidos revelam que houve bom aproveitamento destes alunos na construção da taxa de variação média e também no desenvolvimento de competências para a interpretação de gráficos, como a identificação de intervalos de crescimento e decrescimento e na atribuição de significados aos pontos de intersecção com os eixos coordenados

Made available in DSpace on 2014-06-11T19:31:43Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-03-03Bitstream added on 2014-06-13T18:06:49Z : No. of bitstreams: 1 nunes_cb_dr_rcla.pdf: 3789615 bytes, checksum: dcaee776ef4788b9aa3cd4ba26eefddb (MD5) / Toda pesquisa começa com uma curiosidade do pesquisador e se apresenta como um ponto de partida para uma investigação. Assim, esta pesquisa tem como fenômeno de interesse trabalhar a Geometria Euclidiana, numa abordagem dinâmica, com alunos, futuros professores, do curso de Licenciatura em Matemática da Universidade do Estado da Bahia – UNEB, Campus X. Seu objetivo é o de investigar, compreender e evidenciar as potencialidades didático-matemáticas da Metodologia de Ensino-Aprendizagem-Avaliação de Matemática através da Resolução de Problemas nos processos de ensinar e aprender Geometria. É uma pesquisa de natureza qualitativa que foi desenvolvida seguindo orientações metodológicas de Thomas A. Romberg. Usou-se como procedimentos metodológicos na coleta de dados: a observação, o material escrito pelos alunos, questionários, filmagens, gravações e diário de campo. Dois projetos de ensino foram criados e aplicados nas disciplinas Didática da Matemática e Laboratório de Ensino de Matemática II, respectivamente. Na junção desses dois projetos, depois de aplicados, concluiu-se que essa é mais uma pesquisa no contexto da Educação Matemática que une as disciplinas trabalhadas como uma dupla necessária para a formação de professores. Ademais, sugere um trabalho feito com professores em formação inicial visando a sua própria formação e propicia momentos de reflexão e análise sobre as potencialidades que a Metodologia de Ensino- Aprendizagem-Avaliação de Matemática através da Resolução de Problemas oferece no sentido de incrementar a aprendizagem e melhorar os processos de ensino de Matemática, sobretudo o de Geometria. / Every search begins with a curiosity of the researcher and it is presented as a starting point for an investigation. This research has the phenomenon of interest to work Euclidean geometry, a dynamic approach, with students, future teachers, the Degree in Mathematics at the University of Bahia - UNEB, Campus X. Its goal is to investigate, understand and highlight the potential of teaching math-Teaching Methodology-Evaluation of Learning Mathematics through Problem Solving in the processes of teaching and learning geometry. . It is a qualitative research that was developed following methodological guidelines of Thomas A. Romberg. It used as instruments to collect data: observation, material was written by students, quizzes, films, recordings and field diary. Two education projects were created and applied in the disciplines of Didactics of Mathematics and Laboratory of Mathematics II, respectively. At the junction of these two projects, once implemented, it was concluded that this is another research in the context of mathematics education that unites the disciplines worked as a dual need for teacher training. Moreover, it suggests a work that was done with teachers in training to become self-training and provides moments of reflection and analysis on the potential that the methodology of Teaching-Learning-Evaluation of Mathematics through Problem Solving offers to enhance their learning and improve the processes of teaching mathematics, especially in geometry.

Pavlína Panáčková Učitelství pro první stupeň ZŠ 5. ročník ABSTRACT (MOTIVATION OF PUPILS FOR LEARNING AT PRIMARY SCHOOL) The master thesis deals with motivational quality of semantic support during teaching at first grade at primary school. The theory section consists of four parts. The first part concerns motivation and its sources and motivational problems at school and at the same time it is about communication. The specifics of learning pupils at primary schoo are in chapter 2. The last part deals with the didactic justification of the evocative and motivational function of semantic support for learning. At the same time we are looking for an answer to the question. Does semantics have more meaning in some subjects depending on the type of learning? The aim of the practical part is to find the answer to the question: How does the using of semantic supports influence the pupils' knowledge and their relation to learning? The research contains interviews of the teachers with main topic of semantics and its application during teaching. At the same time, the questionnaire survey is applied to pupils of the third class which compares three types of Mathematics - classical mathematics, Hejny method with semantic focus and Hejny method focused structurally. The thesis contains results evaluation of...

Several years of my experiences in the use of real-time experiments are now upgraded in order to enhance also the teaching of mathematics. The motion sensor device enables us to get real time x(t) and v(t) graphs of a moving object or person. We can productively use these graphs to introduce differentiation on visual level as well as to show the integration procedure. The students are fully involved in the teaching as they are invited to walk in front of the sensor. This approach motivates them by the realistic aspects of mathematical structures. The method could help to fulfill the credo of teaching: comprehension before computation. The steps of such an approach are explained and discussed in further detail below.

Syftet med den här ämnesdidaktiska studien är att undersöka framställningen av multiplikationens olika egenskaper och dess likheter och skillnader mellan två läroboksserier. Detta för att undersöka och förstå vilka möjligheter elever i årskurs 3 ges via läroböcker. Studiens två frågeställningar lyder: Hur framställs multiplikation och dess olika egenskaper i matematikläroböcker för årskurs 3? och Vilka likheter och skillnader avseende multiplikation och dess egenskaper förekommer i två läroboksserier? Ett teoretiskt ämnesdidaktiskt ramverk har konstruerats som utgör en matematisk modell utifrån multiplikationens olika egenskaper. Dessa egenskaper är: upprepad addition, rektangelformation, förlängning, kartesisk produkt, den kommutativa lagen, den associativa lagen, den distributiva lagen samt teorin om multiplikationstabellen. De metoder som användes för att sammanställa resultatet av undersökningen har skett genom en innehållsmässig aspekt av fyra läroböcker. Denna analys utfördes djupgående med fokus på strukturen och karaktären hos innehållet. Dessutom skedde en jämförelse utifrån en mätbar aspekt för att undersöka likheter och skillnader mellan de två läroboksserierna. Resultatet visade att ingen lärobok framställer samtliga av multiplikationens egenskaper i linje med studiens teoretiska ramverk. Däremot förekom de flesta aspekterna av multiplikation i samtliga läroböcker, men med vissa skillnader.

<p>The driving force of conducting the two studies presented in this thesis is to examine ways that conceptual understanding and problem solving could be part of mathematics teaching, and through that, part of students' mathematical knowledge. The specific aims of the thesis are: 1) to characterize the classroom discourse of two, apparently similar, problem solving courses in teacher education and 2) to discuss the possibilities of developing two analytical approaches - the communicational approach to cognition and the dialogical approach - used for studying mathematical discourse. The two aims are elaborated on by means of data collected through audiotaped recordings and field notes from observations of problem-solving activities in engineering and teacher education. In relation to the first aim, the analysis of the classroom discourse within the two courses makes it clear that both courses displayed different kinds of discourse that could be broadly categorized in terms of: subject-oriented, didactically oriented, and problem solving oriented discourses. However, the comparisons between the two courses reveal a marked difference in the distribution of these categories of discourse. It is suggested that the introduction of explicit conceptual frameworks in teaching is of crucial importance for the topical focus of the classroom discourse, and for prospective teachers' opportunity to engage in mathematical productive discourse. The analyses of the two approaches for studying mathematical discourse reveal that the two frameworks can be further developed and the study also indicates ways in which such development can be achieved using a theory of contextualization and theories of mathematical learning. Finally, the thesis discusses theoretical and practical implications of the results, foregrounding issues of importance for the research on mathematical discourse, and for teachers and teacher educators involved in designing instructions for mathematical problem solving.</p>