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Leibniz Institute for Science and Mathematics Education, Kiel

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  • 1
    Type of Medium: Book
    Pages: XXIII, 377 S.
    ISBN: 9783319732527 , 9783319732534 , 9783319892450
    Series Statement: ICME-13 Monographs
    Language: German
    Note: This book focuses on issues related to mathematics teaching and learning resources, including mathematics textbooks, teacher guides, student learning and assessment materials, and online resources. The book highlights various theoretical and methodological approaches used to study teaching and learning resources, and addresses the areas of resources, teachers, and students at an international level. As for the resources, the book examines the role textbooks and other curricular or learning resources play in mathematics teaching, learning, and assessment. It asks questions such as: Could we consider different types of textbooks and roles they play in teaching and learning? How does the digitalization of information and communication affect these roles? What are defining features of e-textbooks, and how could we characterize the differences between the traditional textbooks and e-textbooks? As for the teachers, the book discusses the relationships between teachers’ individual and collective resources, and the way in which we could model such relationships. Specific questions addressed are: What is the role of teachers in developing textbooks and other teaching and learning materials? What are the relationships between resource designers and users? What are the consequences of these changing roles and relationships for the teaching of mathematics, and for teacher knowledge and professional development? As for the students, the book explores how students, as well as their teachers, interact through resources. It raises and addresses questions such as: What are the effects of modern ICT (particularly internet) on students’ use and the design of resources? How do changing patterns of use and design affect student behaviour, learning, and relationships to the subject of mathematics?
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  • 2
    Type of Medium: Unknown
    Pages: XX, 363 S.
    ISBN: 9789400719651
    Series Statement: Mathematics Teacher Education
    Language: German
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  • 3
    ISSN: 1573-0816
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper concerns the problems of conceptualization of the function limit in technological environments (principally graphic calculators today, symbolic calculators tomorrow) that are gradually being adopting in precalculus teaching. In France, such teaching takes place in the scientific stream during the last year of high school (18-year-old pupils). This paper shows out how the instrumentation process and the conceptualization process are dependent on each other and stresses especially: the importance of the notion of scheme analysing the instrumented action where act and thought are linked; the importance of the notion of metaknowledge analyzing different pupil behaviours. A typology of pupil behaviours and a list of schemes are set out. The relationships between this typology and these schemes provide information about the influence of calculating tools and provide some ways of controlling their integration in mathematics lessons. Résumé. L' article concerne les problèmes de conceptualisation de la notion de limite de fonctions, au niveau de la classe terminale scientifique des lycées français (élèves de 18 ans), en relation avec les environnements technologiques dans lesquells l'enseignement des débuts de l'analyse tend progressivement à s'inscrire (principalement les calculatrices ‘graphiques’ aujourd'hui, ‘symboliques’ demain). L'article met en évidence l'interdépendance des processus d'instrumentation et de conceptualisation. Il insiste en particulier sur deux points: l'importance de la notion de schème pour analyser l'action instrumentée, pour mettre en relation le geste et la pensèe; l'importance de la notion de métaconnaissance pour analyser les différences de comportements des élèves. Une typologie des comportements est établie, un répertoire de schèmes est dressé. La mise en relation de cette typologie et de ce répertoire donne quelques informations sur l'influence des outils de calcul dans le processus d'apprentissage et fournit quelques pistes pour contrôler leur intégration dans le cours de mathématiques.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1573-1766
    Keywords: instrumentation process ; instrumental genesis ; graphic and symbolic calculators ; student behaviour ; conceptualisation process ; limits ; classroom practice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Transforming any tool into a mathematical instrument for students involves a complex ‘instrumentation’ process and does not necessarily lead to better mathematical understanding. Analysis of the constraints and potential of the artefact are necessary in order to point out the mathematical knowledge involved in using a calculator. Results of this analysis have an influence on the design of problem situations. Observations of students using graphic and symbolic calculators were analysed and categorised into profiles, illustrating that transforming the calculator into an efficient mathematical instrument varies from student to student, a factor which has to be included in the teaching process.
    Type of Medium: Electronic Resource
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  • 5
    Keywords: Wissen ; Forschung ; Lehrer ; Lehrerbildung ; Individualisierung ; Geometrie ; Mathematik ; Training ; Beruf ; Online
    In: ZDM : the international journal on mathematics education, Bd. 44 (2012) H. 6, S. 717-731, 1863-9690
    In: 1863-9704
    Description / Table of Contents: This paper considers the work carried out by online teacher educators and their professional development. We use the theoretical perspective of the documentational approach that focuses, in this case, on the interaction between teacher educators and the resources they use for their online training work. We thus study the following issues: (1) What kinds of resources do online teacher educators need, and how are such resources modified according to the educators' specific skills and needs? (2) What specific skills are needed for setting up online training for mathematics teachers and how do these skills evolve as teacher education resources are used? We consider both questions simultaneously, while presenting results from a study within a specific teacher training programme in France that proposes "training paths" on a national platform. These "paths" are resources designed for teacher educators. We follow the appropriation of two training paths by two educator teams. The ways in which these educator teams were able to appropriate the paths give insights into the teacher educators' skills and, as well, into the resources they need. By looking at their use of resources (as online mathematics teacher educators), we observe and analyse professional geneses, leading to the development of new skills.
    Type of Medium: Article
    ISSN: 1863-9690 , 1863-9704
    Language: English
    FIS Link: 999115
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  • 6
    Keywords: Lehr-Lern-Prozess ; Computer ; Fachdidaktik ; Computer-Algebra-System ; Mathematik ; Mathematikunterricht
    In: Zentralblatt für Didaktik der Mathematik, Bd. 34 (2002) H. 5, S. 204-211, 0044-4103
    In: 1615-679X
    Description / Table of Contents: In diesem Beitrag werden didaktische Phaenomene diskutiert, die bei der Integration von CAS (implementiert in Taschenrechnern) in den Unterricht auftreten. Basierend auf diesen Untersuchungen wird der Nutzen eines instrumentalen Zugangs fuer das Verstaendnis des Einflusses von Werkzeugen auf mathematische Zugaenge und fuer den Aufbau von SchuelerInnenwissen gezeigt: durch einen Prozess - instrumentale Genese - wird ein Taschenrechner zu einem mathematischen Werkzeug; dieser Prozess ist abhaengig von den Grenzen und Potenzialen dieses Werkzeugs, vom Wissen der SchuelerInnen und von den Arbeitssituationen im Unterricht. Fuer die Analyse von Unterschieden in der instrumentalen Genese wird dann das Verhalten von SchuelerInnen untersucht und eine Methode vorgeschlagen, die es ermoeglicht, eine Typologie extremer Arbeitsweisen in Umgebungen symbolischer Rechner anzugeben. Eine Beruecksichtigung der unterschiedlichen instrumentalen Genesen erfordert vom Lehrer bzw. der Lehrerin eine besondere Organisation von Raum und Zeit der Arbeit im Unterricht. Es wird vorgeschlagen diese Organisation als instrumentale Orchestrierung zu bezeichnen. In der Folge wird gezeigt, wie eine solche Vorstellung eine bessere Definition der Ziele, der Strukturen und der Umsetzungsformen verschiedener Anordnungen ermoeglicht, die darauf abzielen, fuer jede/n SchuelerIn kohaerente Systeme von Instrumenten zu schaffen.
    Type of Medium: Online Resource
    ISSN: 0044-4103 , 1615-679X
    Language: English
    FIS Link: 621303
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  • 7
    Keywords: Bildungsgeschichte ; Semiotik ; Geschichte (Histor) ; Mathematikunterricht ; Mathematische Bildung ; Technologie ; Instrumentalisierung
    In: ZDM : the international journal on mathematics education, Bd. 42 (2010) H. 1, S. 33-47, 1863-9690
    In: 1863-9704
    Description / Table of Contents: In our research work, we have looked at the way in which artefacts become, for teachers as well as for students, instruments of their mathematical activity. The issues related to the use of tools and technologies in mathematical education are now widely considered. A look to history highlights the different ways in which the same questions have been studied at different times and in different places. This suggests that the contribution of artefacts to mathematics learning should be considered in terms of various contexts. Our "visits" to these contexts will be guided by the coordination of two main theoretical frameworks, the instrumental approach and the semiotic mediation approach from the perspective of mathematics laboratory. This journey through history and schooling represents a good occasion to address some questions: Are there "good" contexts in which to develop mathematical instruments? Are there "good" teaching practices which assist students' instrumental geneses and construct mathematical meanings? How is it possible to promote such teaching practices? Some study cases are discussed.
    Type of Medium: Article
    ISSN: 1863-9690 , 1863-9704
    Language: English
    FIS Link: 912800
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  • 8
    Keywords: Mathematikunterricht ; Instrumentierung ; Orchestration ; Technologie ; Mobilität ; Effekt
    In: ZDM : the international journal on mathematics education, Bd. 42 (2010) H. 7, S. 667-681, 1863-9690
    In: 1863-9704
    Description / Table of Contents: In the 1990s, handheld technology allowed overcoming infrastructural limitations that had hindered until then the integration of ICT in mathematics education. In this paper, we reflect on this integration of handheld technology from a personal perspective, as well as on the lessons to be learnt from it. The main lesson in our opinion concerns the growing awareness that students' mathematical thinking is deeply affected by their work with technology in a complex and subtle way. Theories on instrumentation and orchestration make explicit this subtlety and help to design and realise technology-rich mathematics education. As a conclusion, extrapolation of these lessons to a future with mobile multi-functional handheld technology leads to the issues of connectivity and in- and out-of-school collaborative work as major issues for future research.
    Type of Medium: Article
    ISSN: 1863-9690 , 1863-9704
    Language: English
    FIS Link: 944114
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  • 9
    Keywords: Lehrer ; Lehrerbildung ; Lernen ; Lehren ; Geometrie ; Mathematikunterricht ; Training ; Austausch ; Praxis ; Dokumentation
    In: ZDM : the international journal on mathematics education, Bd. 43 (2011) H. 3, S. 399-411, 1863-9690
    In: 1863-9704
    Description / Table of Contents: We present a research work about an innovative national teacher training program in France: the Pairformance program, designed to sustain ICT integration. We study here training for secondary school teachers, whose objective is to foster the development of an inquiry-based approach in the teaching of mathematics, using investigative potentialities of dynamic geometry environments. We adopt the theoretical background of the documentational approach to didactics. We focus on the interactions between teachers and 'resources': teachers' professional knowledge influences these interactions, which at the same time yield knowledge evolutions, a twofold process that we conceptualise as a documentational genesis. We followed in particular the work of a team of trainees; drawing on the data collected, we analyse their professional development, related with the training. We observe intertwined evolutions and stabilities, consistent with ongoing geneses.
    Type of Medium: Article
    ISSN: 1863-9690 , 1863-9704
    Language: English
    FIS Link: 964022
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