Faszination Mathematik
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Faszination Mathematik
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Author : Reinhold Goldmann
language : de
Publisher: tredition
Release Date : 2024-02-16
Faszination Mathematik written by Reinhold Goldmann and has been published by tredition this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-16 with Mathematics categories.
Viele Wissenschaften können veranschaulicht werden. In den Naturwissenschaften führen spannende Experimente zu leichterem Verständnis und Aufmerksamkeit. Zu den Gesellschaftswissenschaften können Beispiele aus der Geschichte oder der täglichen Praxis das Erfassen des Sachverhalts ebnen. In der Mathematik ist jedoch die Beschreibung ihrer Objekte nicht immer einfach, da sie häufig Abstraktionen der realen Welt sind. Aber dieses Abheben von der Wirklichkeit ist häufig nötig, um Begriffe zu ordnen und erfassbar zu machen. Mathematische Modellierungen und Berechnungen sind auch in anderen Wissenschaften von großer Bedeutung. Dabei handelt es sich um abstrakte Beschreibungen eines Sachverhalts mit mathematischen Begriffen, Formeln, Gleichungssystemen und vor allem um die Aufstellung von Modellen mit der Untersuchung ihrer Eigenschaften. Die Mathematik ermöglicht die exakte Vorhersage von astronomischen Ereignissen oder das Steuern von Raumfahrzeugen zu anderen Himmelskörpern. Ingenieure benötigen mathematische Berechnungen zur Konstruktion und Entwicklung funktionsfähiger Maschinen, von Gebäuden, Brücken, Aufzügen usw. Anwender können durch Optimierungsberechnungen Material einsparen und Fehlkonstruktionen vermeiden. Computertomographie-Geräte können aus Messungen mittels Algorithmen berechnen, ob im Körper von Lebewesen Verletzungen oder Veränderungen vorliegen und dadurch chirurgische Eingriffe zu steuern oder gar vermeiden zu helfen. Mit der Übersetzung von Informationen in Zahlen sind Computer in der Lage sehr viele Informationen immer schneller zu übertragen. Damit weisen elektronische Rechner, Fernsehgeräte, Mobiltelefone, Alarmanlagen und viele andere Apparate Leistungen auf, die noch vor wenigen Jahren undenkbar waren. Die Chaostheorie ermöglicht Vorausberechnungen komplexer Vorgänge, wie zum Beispiel beim Wetter. Bereits in Urzeiten mussten die Menschen Mathematik aus praktischen Bedürfnissen entwickeln, was in diesem Buch thematisiert werden wird. Bis in die Gegenwart haben stets neue gesellschaftliche Aufgaben die Entwicklung der Mathematik immer weiter angeregt und vorangebracht. Mathematische Aussagen lassen sich jedoch leichter verstehen, wenn Beispiele gesucht werden, auf die sie anwendbar sind. Erfahrungsgemäß kann eine schwierige mathematische Lösung auch dadurch gefunden werden, indem man nach einiger Wartezeit veränderte Lösungswege einschlägt. "Vieles erledigt sich durch Warten." Leider hat auch die exakte mathematische Wissenschaft ihre Grenzen. Dann müssen Näherungsverfahren angewandt werden, die insbesondere bei Integralen oder Differentialgleichungen unerlässlich sind.
Faszination Mathematik
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Author : Serge Lang
language : de
Publisher: Springer-Verlag
Release Date : 2013-07-02
Faszination Mathematik written by Serge Lang and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-02 with Mathematics categories.
Faszination Mathematik
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Author :
language : de
Publisher: Spektrum Akademischer Verlag
Release Date : 2003-04-10
Faszination Mathematik written by and has been published by Spektrum Akademischer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-10 with Science categories.
Anregend, umfassend und fundiert erschließt das Werk in über 50 ausführlichen Essaybeiträgen das ganze Spektrum der modernen Mathematik. Renommierte Mathematikerinnen und Mathematiker vernetzen in ihren Beiträgen die Teilgebiete der Disziplin mit den "Highlights" spannender und charakteristischer Forschungsschwerpunkte sowie mit ausführlichen Artikeln zur Geschichte des Faches und seiner herausragenden Vertreterinnen und Vertreter. Der inhaltliche Bogen spannt sich dabei von den antiken Kieselsteinrechnern bis hin zur Technomathematik, von der Fermatschen Vermutung bis zur Zahlentheorie. Das Werk wendet sich an Studierende und Lehrende der Mathematik und ihrer Nachbardisziplinen und an alle, die fasziniert sind von der "Wissenschaft der formalen Systeme" (David Hilbert).
In Mathe War Ich Immer Schlecht
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Author : Albrecht Beutelspacher
language : de
Publisher: Springer-Verlag
Release Date : 2009-11-27
In Mathe War Ich Immer Schlecht written by Albrecht Beutelspacher and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-27 with Mathematics categories.
Das Buch öffnet ein Fenster, durch das man einen Einblick in die Mathematik erhält. Der Autor bringt das Kunststück fertig, den scheinbar undurchdringlichen Schleier von der Mathematik wegzuziehen und ihre Geheimnisse zu entschlüsseln. Er zeichnet ein buntes Bild von Mathematik und Mathematikern, das Nichtmathematiker genießen, aus dem aber auch Mathematiker viel über ihresgleichen erfahren können. Zusammen mit vielen witzigen Illustrationen von Andrea Best ist das Buch ein wahres Lesevergnügen. "Mathematiker können auch anders. Das beweist Beutelspacher mit diesem Büchlein, das unterhaltsam und leicht zu lesen ist." (Die Zeit) Der Text der 4. Auflage wurde überarbeitet und neu gestaltet, ein Abschnitt über Strichcodes wurde hinzugefügt.
Mathe
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Author : Serge Lang
language : de
Publisher: Springer-Verlag
Release Date : 2013-03-08
Mathe written by Serge Lang and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-08 with Technology & Engineering categories.
Dieses Buch enthält eine Sammlung von Dialogen des bekannten Mathematikers Serge Lang mit Schülern. Serge Lang behandelt die Schüler als seinesgleichen und zeigt ihnen mit dem ihm eigenen lebendigen Stil etwas vom Wesen des mathematischen Denkens. Die Begegnungen zwischen Lang und den Schülern sind nach Bandaufnahmen aufgezeichnet worden und daher authentisch und lebendig. Das Buch stellt einen frischen und neuartigen Ansatz für Lehren, Lernen und Genuß von Mathematik vor. Das Buch ist von großem Interesse für Lehrer und Schüler.
Mathematik
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Author : STEWART
language : de
Publisher: Springer-Verlag
Release Date : 2013-11-11
Mathematik written by STEWART and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
Teubner Taschenbuch Der Mathematik
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Author : Eberhard Zeidler
language : de
Publisher: Springer-Verlag
Release Date : 2013-10-05
Teubner Taschenbuch Der Mathematik written by Eberhard Zeidler and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-05 with Mathematics categories.
Das Teubner-Taschenbuch der Mathematik erfüllt aktuell, umfassend und kompakt alle Erwartungen, die an ein mathematisches Nachschlagewerk gestellt werden. Es vermittelt ein lebendiges und modernes Bild der heutigen Mathematik. Als Handbuch begleitet es die Studierenden vom ersten Semester bis zur letzten Prüfung und der Praktiker nutzt es als ständiges und unentbehrliches Nachschlagewerk in seinem Berufsalltag.
Abenteuer Mathematik
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Author : Pierre Basieux
language : de
Publisher: Springer-Verlag
Release Date : 2012-01-21
Abenteuer Mathematik written by Pierre Basieux and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-21 with Mathematics categories.
Nicht Mathematik zu betreiben, sondern zu erfahren ist das Abenteuer, das dieses Buch bietet – Denkexpeditionen, deren Ausgangspunkt Fragen sind: Was steckt hinter mathematischen Fiktionen wie den unendlich vielen Stufen des Unendlichen oder dem Letzten Fermatschen Satz? Worin liegt ihre Schönheit, worin ihr Bezug zur Realität? Welchen Köpfen sind solche Ideen entsprungen, welche Schicksale mit ihnen verbunden? Das Buch wurde für die vorliegende 5. Auflage vollständig durchgesehen und aktualisiert.
Implementation Research On Problem Solving In School Settings
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Author : Inga Gebel
language : en
Publisher: WTM-Verlag Münster
Release Date : 2019
Implementation Research On Problem Solving In School Settings written by Inga Gebel and has been published by WTM-Verlag Münster this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Education categories.
Content of the Book The University of Potsdam hosted the 25th ProMath and the 5th WG Problem Solving conference. Both groups met for the second time in this constellation which contributed to profound discussions on problem solving in each country taking cultural particularities into account. The joint conference took place from 29th to 31st August 2018, with participants from Finland, Germany, Greece, Hungary, Israel, Sweden, and Turkey. The conference revolved around the theme “Implementation research on problem solving in school settings”. These proceedings contain 14 peer-reviewed research and practical articles including a plenary paper from our distinguished colleague Anu Laine. In addition, the proceedings include three workshop reports which likewise focused on the conference theme. As such, these proceedings provide an overview of different research approaches and methods in implementation research on problem solving in school settings which may help close the gap between research and practice, and consequently make a step forward toward making problem solving an integral part of school mathematics on a large-scale. Content PLENARY REPORT Anu Laine: How to promote learning in problem-solving? pp 3 – 18 This article is based on my plenary talk at the joint conference of ProMath and the GDM working group on problem-solving in 2018. The aim of this article is to consider teaching and learning problem-solving from different perspectives taking into account the connection between 1) teacher’s actions and pupils’ solutions and 2) teacher’s actions and pupils’ affective reactions. Safe and supportive emotional atmosphere is base for students’ learning and attitudes towards mathematics. Teacher has a central role both in constructing emotional atmosphere and in offering cognitive support that pupils need in order to reach higher-level solutions. Teachers need to use activating guidance, i.e., ask good questions based on pupils’ solutions. Balancing between too much and too little guidance is not easy. https://doi.org/10.37626/GA9783959871167.0.01 RESEARCH REPORTS AND ORAL COMMUNICATIONS Lukas Baumanns and Benjamin Rott: Is problem posing about posing “problems”? A terminological framework for researching problem posing and problem solving pp 21 – 31 In this literature review, we critically compare different problem-posing situations used in research studies. This review reveals that the term “problem posing” is used for many different situations that differ substantially from each other. For some situations, it is debatable whether they provoke a posing activity at all. For other situations, we propose a terminological differentiation between posing routine tasks and posing non-routine problems. To reinforce our terminological specification and to empirically verify our theoretical considerations, we conducted some task-based interviews with students. https://doi.org/10.37626/GA9783959871167.0.02 Kerstin Bräuning: Long-term study on the development of approaches for a combinatorial task pp 33 – 50 In a longitudinal research project over two years, we interviewed children up to 6 times individually to trace their developmental trajectories when they solve several times the same tasks from different mathematical areas. As a case study, I will present the combinatorial task and analyze how two children, a girl and a boy, over two years approached it. As a result of the case studies we can see that the analysis of the data product-oriented or process-oriented provides different results. It is also observable that the developmental trajectory of the girl is a more continuous learning process, which we cannot identify for the boy. https://doi.org/10.37626/GA9783959871167.0.03 Lars Burman: Developing students’ problem-solving skills using problem sequences: Student perspectives on collaborative work pp 51 – 59 Using problem solving in mathematics classrooms has been the object of research for several decades. However, it is still necessary to focus on the development of problem-solving skills, and in line with the recent PISA assessment, more attention is given to collaborative problem solving. This article addresses students’ collaborative work with problem sequences as a means to systematically develop students’ problem-solving skills. The article offers student perspectives on challenges concerning the social atmosphere, differentiation on teaching, and learning in cooperation. In spite of the challenges, the students’ experiences indicate that the use of problem sequences and group problem solving can be fruitful in mathematics education. https://doi.org/10.37626/GA9783959871167.0.04 Alex Friedlander: Learning algebraic procedures through problem solving pp 61 – 69 In this paper, I attempt to present several examples of tasks and some relevant findings that investigate the possibility of basing a part of the practice-oriented tasks on higher-level thinking skills, that are usually associated with processes of problem solving. The tasks presented and analysed here integrate problem solving-components – namely, reversed thinking, expressing and analysing patterns, and employing multiple solution methods, into the learning and practicing of algebraic procedures – such as creating equivalent expressions and solving equations. https://doi.org/10.37626/GA9783959871167.0.05 Thomas Gawlick and Gerrit Welzel: Backwards or forwards? Direction of working and success in problem solving pp 71 – 89 We pose ourselves the question: What can one infer from the direction of working when solvers work on the same task for a second time? This is discussed on the basis of 44 problem solving processes of the TIMSS task K10. A natural hypothesis is that working forwards can be taken as evidence that the task is recognized and a solution path is recalled. This can be confirmed by our analysis. A surprising observation is that when working backwards, pivotal for success is (in case of K10) to change to working forwards soon after reaching the barrier. https://doi.org/10.37626/GA9783959871167.0.06 Inga Gebel: Challenges in teaching problem solving: Presentation of a project in progress by using an extended tetrahedron model pp 91 – 109 In order to implement mathematical problem solving in class, it is necessary to consider many different dimensions: the students, the teacher, the theoretical demands and adequate methods and materials. In this paper, an implementation process is presented that considers the above dimensions as well as the research perspective by using an extended tetrahedron model as a structural framework. In concrete terms, the development and initial evaluation of a task format and a new teaching concept are presented that focus on differentiated problem-solving learning in primary school. The pilot results show initial tendencies towards possible core aspects that enable differentiated problem solving in mathematics teaching. https://doi.org/10.37626/GA9783959871167.0.07 Heike Hagelgans: Why does problem-oriented mathematics education not succeed in an eighth grade? An insight in an empirical study pp 111 – 119 Based on current research findings on the possibilities of integration of problem solving into mathematics teaching, the difficulties of pupils with problem solving tasks and of teachers to get started in problem solving, this article would like to show which concrete difficulties delayed the start of the implementation of a generally problem-oriented mathematics lesson in an eighth grade of a grammar school. The article briefly describes the research method of this qualitative study and identifies and discusses the difficulties of problem solving in the examined school class. In a next step, the results of this study are used to conceive a precise teaching concept for this specific class for the introduction into problem-oriented mathematics teaching. https://doi.org/10.37626/GA9783959871167.0.08 Zoltán Kovács and Eszter Kónya: Implementing problem solving in mathematics classes pp 121 – 128 There is little evidence of teachers are using challenging problems in their mathematics classes in Hungary. At the University of Debrecen and University of Nyíregyháza, we elaborated a professional development program for inservice teachers in order to help them implementing problem solving in their classes. The basis of our program is the teacher and researcher collaboration in the lessonplanning and evaluation. In this paper we report some preliminary findings concerning this program. https://doi.org/10.37626/GA9783959871167.0.09 Ana Kuzle: Campus school project as an example of cooperation between the University of Potsdam and schools pp 129 – 141 The “Campus School Project” is a part of the “Qualitätsoffensive Lehrerbildung” project, whose aim is to improve and implement new structures in the university teacher training by bringing all the essential protagonists, namely university stuff, preservice teachers, and in-service teachers – together, and having them work jointly on a common goal. The department of primary mathematics education at the University of Potsdam has been a part of the Campus School Project since 2017. Thus far several cooperations emerged focusing on different aspects of problem solving in primary education. Here, I give an overview of selected cooperations, and the first results with respect to problem-solving research in different school settings. https://doi.org/10.37626/GA9783959871167.0.10 Ioannis Papadopoulos and Aikaterini Diakidou: Does collaborative problem-solving matter in primary school? The issue of control actions pp 143 – 157 In this paper we follow three Grade 6 students trying to solve (at first individually, and then in a group) arithmetical and geometrical problems. The focus of the study is to identify and compare the various types of control actions taken during individual and collaborative problem-solving to show how the collective work enhances the range of the available control actions. At the same time the analysis of the findings give evidence about the impact of the collaborative problemsolving on the way the students can benefit in terms of aspects of social metacognition. https://doi.org/10.37626/GA9783959871167.0.11 Sarina Scharnberg: Adaptive teaching interventions in collaborative problem-solving processes pp 159 – 171 Even though there exists limited knowledge on how exactly students acquire problem-solving competences, researchers agree that adaptive teaching interventions have the potential to support students‘ autonomous problem-solving processes. However, most recent research aims at analyzing the characteristics of teaching interventions rather than the interventions’ effects on the students’ problem-solving process. The study in this paper addresses this research gap by focusing not only on the teaching interventions themselves, but also on the students’ collaborative problem-solving processes just before and just after the interventions. The aim of the study is to analyze the interventions‘ effect on the learners’ integrated problem-solving processes. https://doi.org/10.37626/GA9783959871167.0.12 Nina Sturm: Self-generated representations as heuristic tools for solving word problems pp 173 – 192 Solving non-routine word problems is a challenge for many primary school students. A training program was therefore developed to help third-grade students to find solutions to word problems by constructing external representations (e.g., sketches, tables) and to specifically use them. The objective was to find out whether the program positively influences students’ problemsolving success and problem-solving skills. The findings revealed significant differences between trained and untrained classes. Therefore, it can be assumed that self-generated representations are heuristic tools that help students solve word problems. This paper presents the results on the impact of the training program on the learning outcome of students. https://doi.org/10.37626/GA9783959871167.0.13 Kinga Szűcs: Problem solving teaching with hearing and hearing-impaired students pp 193 – 203 In the last decade the concept of inclusion has become more and more prevalent in mathematics education, especially in Germany. Accordingly, teachers in mathematics classrooms have to face a wide range of heterogeneity, which includes physical, sensory and mental disabilities. At the Friedrich-Schiller-University of Jena, within the framework of the project “Media in mathematics education” it is examined how new technologies can support teaching in inclusive mathematics classrooms. In the academic year 2017/18, the heterogeneity regarding hearing impairment was mainly focussed on. Based on a small case study with hearing and hearing-impaired students a problem-solving unit about tangent lines was worked out according to Pólya, which is presented in the paper. https://doi.org/10.37626/GA9783959871167.0.14 WORKSHOP REPORTS Ana Kuzle and Inga Gebel: Implementation research on problem solving in school settings: A workshop report 207 On the last day of the conference, we organized a 90-minute workshop. The workshop focused on the conference theme “Implementation research on problem solving in school settings”. Throughout the conference, the participants were invited to write down their questions and/or comments as a response to held presentations. https://doi.org/10.37626/GA9783959871167.0.15 Ana Kuzle, Inga Gebel and Anu Laine: Methodology in implementation research on problem solving in school settings pp 209 – 211 In this report, a summary is given on the contents of the workshop. In particular, the methodology and some ethical questions in implementation research on problem solving in school settings are discussed. The discussion showed how complex this theme is so that many additional questions emerged. https://doi.org/10.37626/GA9783959871167.0.16 Lukas Baumanns and Sarina Scharnberg: The role of protagonists in implementing research on problem solving in school practice pp 213 – 214 Based on seminal works of Pólya (1945) and Schoenfeld (1985), problem solving has become a major focus of mathematics education research. Even though there exists a variety of recent research on problem solving in schools, the research results do not have a direct impact on problem solving in school practice. Instead, a dissemination of research results by integrating different protagonists is necessary. Within our working group, the roles of three different protagonists involved in implementing research on problem solving in school practice were discussed, namely researchers, pre-service, and in-service teachers, by examining the following discussion question: To what extent do the different protagonists enable implementation of research findings on problem solving in school practice? https://doi.org/10.37626/GA9783959871167.0.17 Benjamin Rott and Ioannis Papadopoulos: The role of problem solving in school mathematics pp 215 – 217 In this report of a workshop held at the 2018 ProMath conference, a summary is given of the contents of the workshop. In particular, the role of problem solving in regular mathematics teaching was discussed (problem solving as a goal vs. as a method of teaching), with implications regarding the selection of problems, its implementation into (written) exams as well as teacher proficiency that is needed for implementing problem solving into mathematics teaching. https://doi.org/10.37626/GA9783959871167.0.18
Mathematik Im Reich Der T Ne
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Author :
language : de
Publisher: Springer-Verlag
Release Date : 2013-12-18
Mathematik Im Reich Der T Ne written by and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-18 with Technology & Engineering categories.
Zentrales Anliegen dieses Buches ist es, einen Überblick über den mathematischen Aufbau der Tonleitern nach dem pythagore ischen, dem diatonischen und dem temperierten Stimmungs prinzip zu geben. Die Tonleitern werden in der Reihenfolge ihrer historischen Entwicklung behandelt. Im Zusammenhang mit der pythagoreischen Tonleiter wird auf die philosophischen Lehrmeinungen der Pythagoreer einge gangen und die ideelle Krise aufgezeigt, die in dieser Philo sophenschule als Folge der Widerlegung ihrer Lehren auftrat. Vorzüge und Nachteile der pythagoreischen und diatonischen Tonleitern werden gegeneinander abgewogen. In neuerer Zeit erwuchs aus den Forderungen der musikalischen Praxis nach Modulationsfähigkeit von Instrumenten mit fester Stimmlage das erstmalig von M. Mersenne ausgearbeitete Prinzip der temperierten Stimmung. Nach Durchsetzung der temperierten Tonskala wurde in der Mitte des 19. Jahrhunderts mit der Festlegung der absoluten Schwingungszahlen eine weitere Vor aussetzung für die Internationalisierung des Musiklebens er füllt. Dieses Buch weist auf zahlreiche Querverbindungen zwischen dem mathematischen Aufbau der Tonleitern und der Gestaltung bzw. Konstruktion von Musikinstrumenten hin. Die Begriffe harmonische Schwingung, Resonanz, Schwebung und harmo nische Analyse einer periodischen Schwingung sind gleichfalls Gegenstände der Betrachtung. Die geometrische Schallreflexion an einigen gekrümmten Flächen und die Resonanz werden im Hinblick auf die Raumakustik behandelt. Mit der Erläuterung sowohl des Weber-Fechnerschen Gesetzes als auch des Ohm sehen Gesetzes an Hand von Beispielen und mit der Gegenüber stellung der Verhältniszahlen von Dur-und Moll-Akkord wer den physikalisch-psychische Wechselbeziehungen in die Be trachtungen einbezogen.