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  • MPI Ethno. Forsch.  (18)
  • MPI-MMG
  • Dordrecht : Springer Netherlands  (9)
  • Wiesbaden : Springer Fachmedien Wiesbaden  (9)
  • Education  (14)
  • Hochschulschrift  (7)
  • Mathematics  (18)
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  • 1
    Online Resource
    Online Resource
    Wiesbaden : Springer Fachmedien Wiesbaden | Cham : Springer International Publishing AG
    ISBN: 9783658309527 , 3658309520
    Language: German
    Pages: 1 Online-Ressource (XXIII, 296 Seiten) , 129 Abb.
    Edition: 1st ed. 2020
    Series Statement: Essener Beiträge zur Mathematikdidaktik
    Parallel Title: Erscheint auch als Schulte-Wißing, Eva-Maria Kinder deuten Zahlenmuster
    DDC: 301
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    Keywords: Zahl ; Muster ; Epistemische Logik ; Arithmetik ; Mathematikunterricht ; Grundschule ; Sociology ; Mathematics Study and teaching  ; Mathematics ; Sociology ; Mathematics Education ; Mathematics ; Hochschulschrift
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  • 2
    ISBN: 9783658236625
    Language: German
    Pages: Online-Ressource (XIX, 203 S, online resource)
    Series Statement: Dortmunder Beiträge zur Entwicklung und Erforschung des Mathematikunterrichts 38
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Erscheint auch als Mayer, Carolin, 1989 - Zum algebraischen Gleichheitsverständnis von Grundschulkindern
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    Keywords: Mathematics ; Mathematics Education ; Mathematics ; Mathematics—Study and teaching . ; Hochschulschrift ; Grundschulkind ; Mathematikunterricht ; Algebra ; Gleichung ; Lernumwelt
    Abstract: Carolin Mayer zeigt, dass Gleichungen im Arithmetikunterricht der Grundschule für das weitere Lernen in der Primar- und Sekundarstufe, insbesondere unter algebraischer Perspektive, eine zentrale Rolle spielen. Sie konzentriert sich hierzu auf das Gleichheitsverständnis von Kindern, das sich beim Erkennen, Beschreiben und Begründen der Gleichheit bzw. Ungleichheit von arithmetischen Termen zeigt. Die Autorin arbeitet Charakteristika des Verstehens von Gleichheiten bei Viertklässlern heraus und stellt Lernumgebungen zur Anregung eines algebraischen Gleichheitsverständnisses vor. Der Inhalt Gleichheiten und Argumentationsprozesse im Mathematikunterricht der Grundschule Methode und Design: Fachdidaktische Entwicklungsforschung im Dortmunder Modell Argumentationsanalysen zur Charakterisierung eines algebraischen Gleichheitsverständnisses Interpretative Analysen zur Charakterisierung der Lernumgebungen Die Zielgruppen Dozierende und Studierende der Mathematikdidaktik Lehrerinnen und Lehrer an Grundschulen und ihre Aus- und Fortbildenden Die Autorin Carolin Mayer promovierte als Stipendiatin und später als wissenschaftliche Mitarbeiterin am Institut für Entwicklung und Erforschung des Mathematikunterrichts der TU Dortmund und arbeitet zurzeit als Lehrerin an einer Grundschule. Die Herausgeberinnen und Herausgeber Die Reihe Dortmunder Beiträge zur Entwicklung und Erforschung des Mathematikunterrichts wird herausgegeben von Stephan Hußmann, Marcus Nührenbörger, Susanne Prediger und Christoph Selter
    Abstract: Gleichheiten und Argumentationsprozesse im Mathematikunterricht der Grundschule -- Methode und Design: Fachdidaktische Entwicklungsforschung im Dortmunder Modell -- Argumentationsanalysen zur Charakterisierung eines algebraischen Gleichheitsverständnisses -- Interpretative Analysen zur Charakterisierung der Lernumgebungen
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  • 3
    ISBN: 9783658213756
    Language: German
    Pages: 1 Online-Ressource
    Edition: Springer eBook Collection. Social Science and Law
    Series Statement: Dortmunder Beiträge zur Entwicklung und Erforschung des Mathematikunterrichts 35
    Series Statement: SpringerLink
    Series Statement: Bücher
    Series Statement: Dortmunder Beiträge zur Entwicklung und Erforschung des Mathematikunterrichts
    Parallel Title: Erscheint auch als
    Dissertation note: Dissertation Technische Universität Dortmund 2017
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    Keywords: Education ; Mathematics Study and teaching
    Abstract: Birte Pöhler (verh. Friedrich) präsentiert ein theoretisch fundiertes und empirisch erprobtes fach- und sprachintegriertes Lehr-Lern-Arrangement zur alltagsrelevanten Thematik der Prozente, das der Förderung insbesondere von sprachlich schwachen Lernenden dient und sich auch für den Erstzugang im Unterricht zweier Klassen als wirksam erwiesen hat. Das Konzept zeichnet sich dadurch aus, dass ein fachlicher und ein sprachlicher Lernpfad strukturiert und mithilfe eines graphischen Darstellungsmittels systematisch verknüpft werden. Die Autorin illustriert die damit initiierbaren individuellen Lernwege und rekonstruiert detailliert, inwiefern Lernende schriftlich oder mündlich angebotene Sprachmittel tatsächlich aufnehmen oder eigene finden, um die mathematischen Zusammenhänge auszudrücken. Der Inhalt Typische konzeptuelle Hürden und Lesehürden im Umgang mit Prozenten Sprachförderung im Mathematikunterricht Konzeption eines fach- und sprachintegrierten Konzepts am Beispiel der Thematik der Prozente Methode der Spurenanalyse zur Rekonstruktion lexikalischer Lernwege Die Zielgruppen Dozierende und Studierende der Mathematikdidaktik Lehrerinnen und Lehrer und ihre Aus- und Fortbildenden Die Autorin Birte Pöhler promovierte als wissenschaftliche Mitarbeiterin bei Prof. Dr. Susanne Prediger am Institut für Entwicklung und Erforschung des Mathematikunterrichts der Technischen Universität Dortmund. Die Herausgeberinnen und Herausgeber Die Reihe Dortmunder Beiträge zur Entwicklung und Erforschung des Mathematikunterrichts wird herausgegeben von Stephan Hußmann, Marcus Nührenbörger, Susanne Prediger und Christoph Selter
    Abstract: Typische konzeptuelle Hürden und Lesehürden im Umgang mit Prozenten -- Sprachförderung im Mathematikunterricht -- Konzeption eines fach- und sprachintegrierten Konzepts am Beispiel der Thematik der Prozente -- Methode der Spurenanalyse zur Rekonstruktion lexikalischer Lernwege
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  • 4
    ISBN: 9783658229085
    Language: German
    Pages: Online-Ressource (XV, 363 S. 50 Abb, online resource)
    Edition: Springer eBook Collection. Social Science and Law
    Series Statement: Perspektiven der Mathematikdidaktik
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Erscheint auch als Cramer, Jenny Mathematisches Argumentieren als Diskurs
    Parallel Title: Erscheint auch als Cramer, Jenny Mathematisches Argumentieren als Diskurs
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    Keywords: Education ; Education ; Mathematics Study and teaching ; Mathematics Study and teaching ; Hochschulschrift ; Mathematikunterricht ; Bildungsförderung ; Migrationshintergrund ; Argumentation
    Abstract: Mathematisches Argumentieren ist bedeutsam für die Entwicklung eines mathematischen Verständnisses, doch für viele Lernende scheint diese unterrichtliche Tätigkeit nur schwer zugänglich zu sein. Ausgehend von einem auf Habermas zurückgehenden Diskursbegriff dokumentiert Jenny Cramer die Entwicklung eines Modells, das die Rekonstruktion potentieller und tatsächlich entstehender Hindernisse im mathematischen Argumentationsdiskurs ermöglicht. Mittels einer theoretisch und empirisch erarbeiteten Typologie liefert sie Erklärungsansätze für die Entstehung von Hindernissen aus den Perspektiven Bildungssprache, Rationalität und Diskursethik. Der Inhalt Argumentieren als bedeutsame mathematische Tätigkeit Argumentieren als Herausforderung für Lernende Habermas’sche Zugänge zum Argumentieren Empirisch fundierte Beschreibung der Hinderniskategorien Hindernisse im mathematischen Argumentationsdiskurs Die Zielgruppen Forschende, Dozierende und Studierende der Mathematikdidaktik Lehrerinnen und Lehrer und ihre Aus- und Fortbildenden Die Autorin Jenny Cramer promovierte bei Prof. Dr. Christine Knipping an der Universität Bremen und ist derzeit als Lehrerin an einem Bremer Gymnasium tätig
    Abstract: Argumentieren als bedeutsame mathematische Tätigkeit -- Argumentieren als Herausforderung für Lernende -- Habermas’sche Zugänge zum Argumentieren -- Empirisch fundierte Beschreibung der Hinderniskategorien -- Hindernisse im mathematischen Argumentationsdiskurs
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  • 5
    ISBN: 9783658225674
    Language: German
    Pages: Online-Ressource (XX, 346 S. 29 Abb., 13 Abb. in Farbe, online resource)
    Edition: Springer eBook Collection. Social Science and Law
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Erscheint auch als
    Parallel Title: Printed edition
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    Keywords: Education ; Education ; Mathematics Study and teaching ; Mathematics Study and teaching
    Abstract: Helmut Hofbauer analysiert und vergleicht bestehende fachwissenschaftliche, fachdidaktische und pädagogische Unterschiede hinsichtlich des Argumentierens und Begründens mit dem Fokus auf den Inhaltsbereich Geometrie. Im Rahmen einer empirischen Querschnittsuntersuchung mit 21 berufserfahrenen Lehrkräften und 4 Experten werden berufsrelevante Kompetenzen und Einstellungen von Mathematiklehrkräften mit unterschiedlichen Hochschulabschlüssen für die Sekundarstufe 1 erforscht. Es gelingt dem Autor, die daraus resultierenden Vorschläge zusammenzuführen und zu einer Verbesserung des Lehramtsstudiums beizutragen. Der Inhalt Theoretische Analyse des Kompetenz- und Einstellungsbegriffs Auswirkung und Bedeutung von Kompetenzen und Einstellungen im Lehrberuf Kompetenz- und Einstellungserwerb in der präuniversitären, universitären und postuniversitären Phase Kompetenz- und Einstellungsunterschiede bei Lehrkräften der Sekundarstufe 1 Überlegungen über Veränderungen in der Lehrerausbildung Die Zielgruppen Dozierende und Studierende aus den Bereichen Didaktik der Mathematik, Pädagogik, Hochschulforschung Professoren in der Lehramtsausbildung, Lehrkräfte in der Sekundarstufe 1, Akteure im Schul- und Universitätsbetrieb Der Autor Prof. Mag. Dr. Helmut Hofbauer lehrt Angewandte Mathematik und Physik an der HTL Paul-Hahn-Straße in Linz, Österreich
    Abstract: Theoretische Analyse des Kompetenz- und Einstellungsbegriffs -- Auswirkung und Bedeutung von Kompetenzen und Einstellungen im Lehrberuf -- Kompetenz- und Einstellungserwerb in der präuniversitären, universitären und postuniversitären Phase -- Kompetenz- und Einstellungsunterschiede bei Lehrkräften der Sekundarstufe 1 -- Überlegungen über Veränderungen in der Lehrerausbildung
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  • 6
    ISBN: 9783658225872
    Language: German
    Pages: Online-Ressource (XXI, 323 S. 51 Abb., 15 Abb. in Farbe, online resource)
    Edition: Springer eBook Collection. Social Science and Law
    Series Statement: Freiburger Empirische Forschung in der Mathematikdidaktik
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Erscheint auch als Bernack-Schüler, Carola Die Entwicklung von Mathematikbildern bei Lehramtsstudierenden
    Parallel Title: Printed edition
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    Keywords: Education ; Education ; Mathematics Study and teaching ; Mathematics Study and teaching ; Hochschulschrift ; Einstellung ; Bewusstsein ; Mathematikunterricht ; Lehrerbildung ; Mathematik
    Abstract: Carola Bernack-Schüler geht der Frage der Veränderung von mathematikbezogenen Beliefs Studierender durch ein qualitatives Vorgehen in Form von Prä-Post-Interviews nach. Dabei wird die Änderung von Mathematikbildern durch ein Problemlöseseminar für Lehramtsstudierende aus unterschiedlichen Perspektiven und auf verschiedenen Ebenen in Einzelfallanalysen und fallübergreifend herausgearbeitet. Die Autorin identifiziert verschiedene Typen der Beliefänderung und zeigt die Kontextbezogenheit von Beliefs und die teilweise schwach ausfallende Argumentation bei deren Verbalisierung auf. Die Arbeit liefert Erkenntnisse zur Ausbildung eines reflektierten Beliefsystems zukünftiger Mathematiklehrerinnen und -lehrer sowie erste Anhaltspunkte zu Ursachen der Beliefänderung durch ein Problemlöseseminar. Der Inhalt Die Rolle von Beliefs zur Mathematik in der Lehrerbildung und die Anbindung an das Forschungsprojekt FORMAT Qualitative Datenaufbereitung und -auswertung Einzelfallanalysen und fallübergreifende Auswertung der Beliefänderung Die Zielgruppen Dozierende und Studierende der Mathematikdidaktik Lehrerinnen und Lehrer und ihre Aus- und Fortbildenden Die Autorin Carola Bernack-Schüler promovierte als wissenschaftliche Mitarbeiterin in Forschung und Lehre am Institut für Mathematische Bildung (IMBF) der Pädagogischen Hochschule Freiburg. Derzeit ist sie im Schuldienst an einer Realschule in Baden-Württemberg tätig. Die Herausgeberinnen und Herausgeber Die Reihe Freiburger Empirische Forschung in der Mathematikdidaktik wird herausgegeben von Lars Holzäpfel, Timo Leuders, Katja Maaß, Gerald Wittmann und Andreas Eichler
    Abstract: Die Rolle von Beliefs zur Mathematik in der Lehrerbildung und die Anbindung an das Forschungsprojekt FORMAT -- Qualitative Datenaufbereitung und -auswertung -- Einzelfallanalysen und fallübergreifende Auswertung der Beliefänderung
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  • 7
    ISBN: 9783658118075
    Language: German
    Pages: 1 Online-Ressource (XXIII, 391 Seiten) , Illustrationen, Diagramme
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Erscheint auch als Scherrmann, Alexandra Lernen mit Lösungsbeispielen im Mathematikunterricht
    Parallel Title: Erscheint auch als Scherrmann, Alexandra Lernen mit Lösungsbeispielen im Mathematikunterricht
    Dissertation note: Dissertation Pädagogische Hochschule Ludwigsburg 2015
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    Keywords: Education ; Mathematics Study and teaching ; Educational psychology ; Education—Psychology. ; Education ; Mathematics Study and teaching ; Educational psychology ; Education Psychology ; Hochschulschrift ; Mathematikunterricht ; Sekundarstufe 1 ; Datenauswertung ; Lösung ; Beispiel
    Abstract: Lehren und Lernen zwischen Instruktion und Konstruktion -- Cognitive Apprenticeship -- Lernen und Wirkungen des Lernens mit verschiedenen Lösungsbeispieltypen -- Die Unterrichtseinheit „Auswerten von Daten“ -- Die Intervention aus Sicht von Schülerinnen und Schülern – Analyse subjektiver Perspektiven.
    Abstract: Alexandra Scherrmann setzt sich mit der Lernmethode „Lernen mit Lösungsbeispielen“ unter der Prämisse eines konstruktivistisch orientierten Unterrichts auseinander. Um zu untersuchen, ob sich auch Lösungsbeispiele mit Lücken oder Fehlern im regulären Mathematikunterricht – außerhalb von Laborsettings – bewähren, setzt sie verschiedene Lösungsbeispieltypen (vollständig, unvollständig, fehlerhaft) in einer Unterrichtseinheit zum „Auswerten von Daten“ in der Sekundarstufe I ein. Die quantitativen Analysen zeigen günstige Auswirkungen auf fachlicher sowie motivational-affektiver Ebene. Die qualitativen Analysen der Schülerinterviews geben Aufschlüsse über eingesetzte Lernwege und -strategien. Der Inhalt Lehren und Lernen zwischen Instruktion und Konstruktion Cognitive Apprenticeship Lernen und Wirkungen des Lernens mit verschiedenen Lösungsbeispieltypen Die Unterrichtseinheit „Auswerten von Daten“ Die Intervention aus Sicht von Schülerinnen und Schülern – Analyse subjektiver Perspektiven Die Zielgruppen Dozierende und Studierende der Pädagogischen Psychologie und der Erziehungswissenschaften, insbesondere Mathematikdidaktik Mathematiklehrerinnen und Mathematiklehrer Die Autorin Alexandra Scherrmann ist Akademische Mitarbeiterin und Dozentin für Mathematikdidaktik für die Lehrämter Sekundarstufe I, Primarstufe und Sonderpädagogik am Institut für Mathematik und Informatik (Abteilung Mathematik) der Pädagogischen Hochschule Ludwigsburg.
    Description / Table of Contents: Lehren und Lernen zwischen Instruktion und KonstruktionCognitive Apprenticeship -- Lernen und Wirkungen des Lernens mit verschiedenen Lösungsbeispieltypen -- Die Unterrichtseinheit „Auswerten von Daten“ -- Die Intervention aus Sicht von Schülerinnen und Schülern - Analyse subjektiver Perspektiven.
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  • 8
    ISBN: 9783658136918 , 9783658136901
    Language: German
    Pages: 1 online resource (316 pages)
    Parallel Title: Erscheint auch als Kaganova, Ekaterina Was uns Lehrtexte lehren : Eine empirische Untersuchung von Schulbuchlehrtexten im Fach Mathematik
    DDC: 370
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    Keywords: Hochschulschrift
    Note: Description based on publisher supplied metadata and other sources
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  • 9
    ISBN: 9789400727151
    Language: English
    Pages: Online-Ressource (XIII, 215 p. 103 illus, online resource)
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Druckausg. Brousseau, Guy Teaching Fractions through Situations: A Fundamental Experiment
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    Keywords: Mathematics ; Education ; Education ; Mathematics
    Abstract: This work presents one of the original and fundamental experiments of Didactique, a research program whose underlying tenet is that Mathematics Education research should be solidly based on scientific observation. Here the observations are of a series of adventures that were astonishing for both the students and the teachers: the reinvention of fractions and of decimal numbers in a sequence of lessons and situations that permitted the students to construct the concepts for themselves. The book leads the reader through the highlights of the sequence's structure and some of the reasoning behind the lesson choices. It then presents explanations of some of the principal concepts of the Theory of Situations. In the process, it offers the reader the opportunity to join a lively set of fifth graders as they experience a particularly attractive set of lessons and master a topic that baffles many of their contemporaries
    Description / Table of Contents: 1. The Adventure of the Students2. Viewing the Adventure from the Perspective of Teachers and Researchers -- 3. Some Key Concepts and Terms from the Theory of Situations -- 4. The Setting for the Adventure -- 5. Description of the Center for Observation for Research in Mathematics Education -- 6. Conclusions and future directions.
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  • 10
    ISBN: 9789400775312
    Language: English
    Pages: Online-Ressource (VIII, 176 p, online resource)
    Series Statement: Archimedes, New Studies in the History and Philosophy of Science and Technology 33
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Druckausg. Goeing, Anja-Silvia, 1966 - Summus mathematicus et omnis humanitatis pater
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    Keywords: Humanities ; History ; Regional planning ; Humanities / Arts ; Humanities ; History ; Regional planning ; Hochschulschrift ; Biografie ; Victorinus Feltrensis 1378-1446 ; Victorinus Feltrensis 1378-1446 ; Biografie ; Geschichte 1444 - 1470
    Abstract: This book revises the picture of the teacher and educator of princes, Vittorino Rambaldoni da Feltre (c. 1378, Feltre -- 1446, Mantua), taking a completely new approach to show his work and life from the individual perspectives created by his students and contemporaries. From 1423 to 1446, Vittorino da Feltre was in charge of a school in Mantua, where his students included not only the offspring of Italy’s princes, but also the first generation of authors dealing with books in print. Among his students were historians like Bartolomeo Sacchi (named Platina), who wrote an extensive history of the popes, and mathematicians like Jacopo Cassiano (Cremonensis), who translated the work of Archimedes from Greek into Latin. Vittorino is still regarded as the educationalist of Italian Renaissance humanism per sé. This work not only contributes to the study of the history of Italian humanist institutions, it also uses available sources to demonstrate the development of a new attitude to education in Italy
    Description / Table of Contents: Acknowledgements1 Introduction -- 2 The Sources on Vittorino da Feltre -- 3 Sassolo da Prato's Correspondence with Leonardo Dati, ca. 1443-1444 -- 4 The Concept of Education in the Second Generation of Vitae and Portraits of Vittorino Da Feltre -- 5 Between History and Praise: Approaches on Understanding Humanist Biographie -- 6 Appendix: The Letter Of Sassolo Da Prato About Vittorino; Translated into English by James Astorga -- References -- Index.
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  • 11
    ISBN: 9783658036720
    Language: English
    Pages: Online-Ressource (XXI, 179 p. 23 illus, online resource)
    Series Statement: Perspektiven der Mathematikdidaktik
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Druckausg. Huang, Rongjin Prospective mathematics teachers’ knowledge of algebra
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    Keywords: Mathematics ; Education ; Education ; Mathematics ; USA ; China ; Mathematiklehrer ; Algebra ; Fachwissen
    Abstract: Rongjin Huang examines teachers’ knowledge of algebra for teaching, with a particular focus on teaching the concept of function and quadratic relations in China and the United States. 376 Chinese and 115 U.S.A. prospective middle and high school mathematics teachers participated in this survey. Based on an extensive quantitative and qualitative data analysis the author comes to the following conclusions: The Chinese participants demonstrate a stronger knowledge of algebra for teaching and their structure of knowledge of algebra for teaching is much more interconnected. They show flexibility in choosing appropriate perspectives of the function concept and in selecting multiple representations. Finally, the number of college mathematics and mathematics education courses taken impacts the teachers’ knowledge of algebra for teaching. Contents · Knowledge Needed for Teaching · Mathematics Teacher Education in China and the U.S.A. · Instrumentation, Data Collection, and Data Analysis · Comparison of Knowledge of Algebra for Teaching (KAT) between China and the U.S.A. · Relationship among Different Components of KAT · Comparison of KTCF between China and the U.S.A. Target Groups · Researchers, academics, and scholars of mathematics and didactics · Teachers The Author Dr. Rongjin Huang works as an associate Professor at the Middle Tennessee State University, U.S.A
    Description / Table of Contents: Foreword; Acknowledgments; Table of Contents; Figures; Tables; Nomenclature; 1 Chapter One: Introduction; 1.1 Background; 1.2 Statement of Purpose; 1.3 Research Questions; 1.4 Delimitations; 2 Chapter Two: Literature Review; 2.1 Knowledge Needed for Teaching; 2.2 Mathematics Knowledge for Teaching; 2.3 Teachers' Knowledge of Algebra for Teaching; 2.4 Mathematics Knowledge for Teaching Some Key Concepts in Algebra; 2.4.1 Teaching and Learning of the Concept of Function; 2.4.2 Teaching and Learning of Expressions and Equations Expressions.
    Description / Table of Contents: 2.4.3 Two Perspectives about the Concept of Function: A Case Study of Quadratic Function2.4.4 Flexibility in Learning the Concept of Function: A Case Study of Quadratic Function.; 2.5 Mathematics Teacher Education Systems in China and the U.S.; 2.5.1 Mathematics Teacher Education in China; 2.5.2 Mathematics Teacher Education in the U.S.; 2.6 Comparative Studies on Teachers' Knowledge for Teaching between China and the U.S.; 2.7 Conclusion; 3 Chapter Three: Methodology; 3.1 Instrumentation; 3.1.1 Content Appropriateness; 3.1.2 Translation Equivalence
    Description / Table of Contents: 3.1.3 Appropriateness of the Survey from Teachers' Perspectives3.1.4 Measuring Knowledge for Teaching the Concept of Function; 3.2 Data Collection; 3.2.1 Chinese Data Collection; 3.2.2 U.S. Data Collection; 3.2.3 Interview of the Selected U.S. Participants; 3.3 Data Analysis; 3.3.1 Quantifying the Data; 3.3.2 Inter-Rater Reliability; 3.3.3 Developing Categories of Different Strategies of Solving OpenendedItems; 3.3.4 Quantitative Analysis; 3.3.5 Interview Data Analysis; 3.4 Framework for Data Analysis; 3.5 Conclusion; 4 Chapter Four: Results; 4.1 Comparison of KAT between China and the U.S.
    Description / Table of Contents: 4.1.1 Reliability of the Instrument4.1.2 The Mean Differences of Items and Components between China and the U.S.; 4.1.3 Analysis of Selected Multiple Choice Items; 4.2 Relationship among Components of KAT in China and the U.S.; 4.2.1 Path Model Analysis; 4.3 Comparisons of KTCF between China and the U.S.; 4.3.1 Logical Reasoning in Matrix System; 4.3.2 Flexibility in Adopting Perspectives of Function Concept; 4.3.3 Flexibility in Using and Shifting Different Representations; 4.4 An Analysis of Correlation between Flexibility and Other Variables; 4.5 Summary of the Findings
    Description / Table of Contents: 4.5.1 The Differences and Similarities of KAT in Chinese and U.S. Prospective Teachers4.5.2 The Relationship between Different Components of KAT; 4.5.3 Difference and Similarities of Knowledge for Teaching the Concept of functions; 4.5.4 The Relationship between KAT and Courses Taken; 5 Chapter Five: Conclusion and Discussion; 5.1 Conclusion; 5.1.1 Knowledge of Algebra for Teaching in China and the U.S.; 5.1.2 The Relationship between Different Components of KAT; 5.1.3 The Difference and Similarities of Knowledge for Teaching the Concept of Functions
    Description / Table of Contents: 5.1.4 The Relationship between Prospective Teachers' KAT and Their Course Taking
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  • 12
    ISBN: 9789400765405
    Language: English
    Pages: Online-Ressource (XVI, 627 p. 193 illus., 59 illus. in color, online resource)
    Series Statement: International Perspectives on the Teaching and Learning of Mathematical Modelling
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Druckausg. Teaching mathematical modelling
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    Keywords: Mathematics ; Education ; Education ; Mathematics ; Mathematisches Modell ; Mathematisches Modell
    Abstract: This book provides readers with an overview of recent international research and developments in the teaching and learning of modelling and applications from a variety of theoretical and practical perspectives. There is a strong focus on pedagogical issues for teaching and learning of modelling as well as research into teaching and practice. The teaching of applications of mathematics and mathematical modelling from the early years through primary and secondary school and at tertiary level is rising in prominence in many parts of the world commensurate with an ever-increasing usage of mathematics in business, the environment, industry and everyday life. The authors are all members of the International Community of Teachers of Mathematical Modelling and Applications and important researchers in mathematics education and mathematics. The book will be of interest to teachers, practitioners and researchers in universities, polytechnics, teacher education, curriculum and policy.?
    Description / Table of Contents: part I. Innovative practices in modelling education research and teachingpart II. Research into, or evaluation of, teaching practice -- part III. Pedagogical issues for teaching and learning -- part Ivolume Influences of technologies -- part volume Assessment in schools -- part VI. Applicability at different levels of schooling, vocational education, and in tertiary education -- part VII. Modelling and applications in business and the lived environment.
    Note: Includes bibliographical references and index
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  • 13
    Online Resource
    Online Resource
    Dordrecht : Springer Netherlands
    ISBN: 9789400764408
    Language: English
    Pages: 1 Online-Ressource (viii, 329 Seiten) , Illustrationen
    Series Statement: Advances in Mathematics Education
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Erscheint auch als Reconceptualizing early mathematics learning
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    Keywords: Curriculum planning ; Mathematics ; Science Study and teaching ; Early childhood education ; Education ; Education ; Curriculum planning ; Mathematics ; Science Study and teaching ; Early childhood education ; Mathematics ; Study and teaching (Elementary)
    Abstract: This book emanated primarily from concerns that the mathematical capabilities of young children continue to receive inadequate attention in both the research and instructional arenas. Research over many years has revealed that young children have sophisticated mathematical minds and a natural eagerness to engage in a range of mathematical activities. As the chapters in this book attest, current research is showing that young children are developing complex mathematical knowledge and abstract reasoning a good deal earlier than previously thought. A range of studies in prior to school and earl
    Description / Table of Contents: Reconceptualizing Early Mathematics Learning; Series Preface; Contents; Perspectives on Reconceptualizing Early Mathematics Learning; References; Early Mathematics Learning in Perspective: Eras and Forces of Change; Era of Experiential Learning (1900-1920); Influential Personages; Views of Children and the Teaching of Mathematics; Competing Views; Era of Childhood Readiness (1920-1940); Personages; Views of Children and the Teaching of Mathematics; Competing Views; Era of Cognitive Development (1940-1960); Personages; Views of Children and the Teaching of Mathematics; Competing Views
    Description / Table of Contents: Era of Socially-Scaffolded Development (1960-1980)Personages; Views of Children and the Teaching of Mathematics; Competing Views; Era of Culturally-Nested Learning (1980-2000); Personages; Views of Children and the Teaching of Mathematics; Competing Views; Emerging Era of Embodied Learning (2000-present); Conclusions; References; Early Awareness of Mathematical Pattern and Structure; Introduction; Pattern and Structure in Early Mathematical Development; Spatial Structuring; Numerical Structuring; Patterning and Data Representation; The Pattern and Structure Project
    Description / Table of Contents: Studies on Multiplicative StructureStructural Development of the Base Ten System; Awareness of Mathematical Pattern and Structure (AMPS); Examples of Structural Development; Structuring a Clock Face; Structuring Rectangular Grids; Structuring Area; Structuring a Triangular Array; Structuring Length; Structuring Data; Discussion; Conclusion; References; Reconceptualizing Early Mathematics Learning: The Fundamental Role of Pattern and Structure; Classroom-Based PASMAP Studies; Preschoolers' Patterning; An Intervention Study with Kindergarten Students; Summary of Early Research Findings
    Description / Table of Contents: The Reconceptualizing Early Mathematics Learning ProjectThe Sample; Procedure; The PASMAP Components; Assessment Interviews and Classroom Data; Results; Quantitative Outcome Analysis; Rasch Scale Analysis; Structural Outcomes Analysis; Discussion; Conclusions and Implications for Further Research and Teaching; References; Reconceptualizing Statistical Learning in the Early Years; Introduction; Data Modelling; Structuring and Representing Data; Metarepresentational and Conceptual Competence; Informal Inference: Making Predictions; The Role of Context; A Longitudinal Study of Data Modelling
    Description / Table of Contents: Activities and ProceduresData Collection and Analysis; Selection of Findings; Grade Two Children's Predictions for Baxter Brown's Picnic; Children's Questions and Representations for Planning a Picnic; Sharing Models for Planning a Picnic; Children's Conceptual and Metarepresentational Competence in Investigating and Planning Playgrounds; Discussion and Concluding Points; References; Cognitive Guidelines for the Design and Evaluation of Early Mathematics Software: The Example of MathemAntics; Introduction; Cognitive Principles for the Design of Software
    Description / Table of Contents: Engage Children in Cognitively and Mathematically Appropriate Activities
    Note: Includes bibliographical references and index
    URL: Cover
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  • 14
    ISBN: 9789400762718
    Language: English
    Pages: Online-Ressource (XIV, 651 p. 134 illus, digital)
    Series Statement: International Perspectives on the Teaching and Learning of Mathematical Modelling
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Buchausg. u.d.T.
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    RVK:
    Keywords: Mathematics ; Education ; Education ; Mathematics
    Abstract: Modeling Students Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects.
    Abstract: Modeling Students' Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects
    Description / Table of Contents: Modeling Students' Mathematical Modeling Competencies; Contents; Contributors; Chapter 1: Introduction: ICTMA and the Teaching of Modeling and Applications; Part I: The Nature of Models & Modeling; Chapter 2: Introduction to Part I Modeling: What Is It? Why Do It?; References; Section 1: What Are Models?; Chapter 3: Modeling Theory for Math and Science Education; 3.1 Introduction; 3.2 Origins of Modeling Theory; 3.3 Models and Concepts; 3.4 Imagination and Intuition; 3.5 Mathematical Versus Physical Intuition; 3.6 Modeling Instruction; 3.7 Conclusions
    Description / Table of Contents: 3.8 Epilogue: A New Generation of Mathematical ToolsReferences; Chapter 4: Modeling a Crucial Aspect of Students' Mathematical Modeling; 4.1 Introduction; 4.2 Three Examples; 4.3 The Intricacies of Mathematization; 4.4 Modeling Students' Mathematizations; References; Chapter 5: Modeling Perspectives in Math Education Research; 5.1 Introduction; 5.2 Spesier and Walter on Models; 5.3 Harel on Models; 5.4 Larson on Models; 5.5 Oehrtman on Models; 5.6 Rasmussen and Zandieh on Models; References; Section 2: Where Are Models & Modelers Found?
    Description / Table of Contents: Chapter 6: Modeling to Address Techno-Mathematical Literacies in Work6.1 Introduction; 6.2 Methodology; 6.3 Findings; 6.4 Results; 6.4.1 Two Examples: Manufacturing and Statistical Process Control; 6.5 Conclusions; References; Chapter 7: Mathematical Modeling in Engineering Design Projects; 7.1 Introduction; 7.2 Methodology; 7.2.1 Industrial Engineering Undergraduates; 7.2.2 Mechanical Engineering Graduate Students; 7.3 Discussion; 7.4 Conclusion; References; Chapter 8: The Mathematical Expertise of Mechanical Engineers - The Case of Mechanism Design; 8.1 Introduction
    Description / Table of Contents: 8.2 Method of Investigation8.3 The Task: Design of Part of a Cutting Device; 8.4 Results and Discussion; 8.5 Conclusions; References; Section 3: What Do Modeling Processes Look Like?; Chapter 9: Modeling and Quantitative Reasoning: The Summer Jobs Problem; 9.1 Theoretical Framework; 9.2 Methods; 9.3 Results; 9.3.1 What Is the Students' Model?; 9.3.2 What Is the Role of Quantities in Students' Models?; 9.3.3 What Is the Role of Quantitative Reasoning in Students' Models?; 9.3.4 What Is the Relationship Between Quantitative Reasoning and Model Development?; 9.4 Discussion; References
    Description / Table of Contents: Chapter 10: Tracing Students' Modeling Processes in School10.1 Introduction; 10.2 Theoretical Framework; 10.3 The Present Study; 10.3.1 The Purpose of the Study; 10.3.2 Participants, Modelling Activity, and Procedures; 10.3.3 Data Sources and Analysis; 10.4 Results; 10.4.1 Modelling Processes; 10.4.2 Mathematical Developments; 10.5 Discussion; References; Section 4: What Creates "The Need For Modeling"; Chapter 11: Turning Ideas into Modeling Problems; 11.1 Introduction; 11.2 Approaches to Mathematical Modeling; 11.2.1 Modeling as Vehicle; 11.2.2 Modeling as Content
    Description / Table of Contents: 11.3 Educational Rationale
    Note: Includes bibliographical references and index
    URL: Cover
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  • 15
    Online Resource
    Online Resource
    Dordrecht : Springer Netherlands
    ISBN: 9789400729841
    Language: English
    Pages: Online-Ressource (VIII, 188p. 1 illus, digital)
    Series Statement: Mathematics Education Library 56
    Series Statement: SpringerLink
    Series Statement: Bücher
    Series Statement: Springer eBook Collection
    Series Statement: Humanities, Social Science and Law
    Parallel Title: Buchausg. u.d.T. Wood, Leigh N. Becoming a mathematician
    RVK:
    Keywords: Mathematics ; Education ; Mathematiker ; Berufsbild ; Berufslaufbahn ; Mathematikunterricht ; Mathematiker ; Berufsbild ; Berufslaufbahn ; Mathematikunterricht
    URL: Cover
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  • 16
    Online Resource
    Online Resource
    Dordrecht : Springer Netherlands
    ISBN: 9789400721296
    Language: English
    Pages: Online-Ressource (XII, 475 p. 120 illus, digital)
    Series Statement: New ICMI Study Series 15
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Buchausg. u.d.T.
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    Keywords: Mathematics ; Education ; Education ; Mathematics ; Mathematics—Study and teaching .
    Abstract: 1. Aspects of proof in mathematics education: Gila Hanna and Michael de Villiers -- Part I: Proof and cognition -- 2. Cognitive development of proof: David Tall, Oleksiy Yevdokimov, Boris Koichu, Walter Whiteley, Margo Kondratieva, and Ying-Hao Cheng -- 3. Theorems as constructive visions: Giuseppe Longo -- Part II: Experimentation: Challenges and opportunities -- 4. Exploratory experimentation: Digitally-assisted discovery and proof: Jonathan M. Borwein -- 5. Experimental approaches to theoretical thinking: Artefacts and proofs -- Ferdinando Arzarello, Maria Giuseppina Bartolini Bussi, Allen Leung, Maria Alessandra Mariotti, and Ian Stevenson (With response by J. Borwein and J. Osborn) -- Part III: Historical and educational perspectives of proof -- 6. Why proof? A historian’s perspective: Judith V. Grabiner -- 7. Conceptions of proof – in research and in teaching: Richard Cabassut, AnnaMarie Conner, Filyet Asli Ersoz, Fulvia Furinghetti, Hans Niels Jahnke, and Francesca Morselli -- 8. Forms of proof and proving in the classroom: Tommy Dreyfus, Elena Nardi, and Roza Leikin -- 9. The need for proof and proving: mathematical and pedagogical perspectives: Orit Zaslavsky, Susan D. Nickerson, Andreas Stylianides, Ivy Kidron, and Greisy Winicki -- 10. Contemporary proofs for mathematics education: Frank Quinn -- Part IV: Proof in the school curriculum -- 11. Proof, Proving, and teacher-student interaction: Theories and contexts: Keith Jones and Patricio Herbst -- 12. From exploration to proof production: Feng-Jui Hsieh, Wang-Shian Horng, and Haw-Yaw Shy -- 13. Principles of task design for conjecturing and proving: Fou-Lai Lin, Kyeong-Hwa Lee, Kai-Lin Yang, Michal Tabach, and Gabriel Stylianides -- 14. Teachers’ professional learning of teaching proof and proving: Fou-Lai Lin, Kai-Lin Yang, Jane-Jane Lo, Pessia Tsamir, Dina Tirosh, and Gabriel Stylianides -- Part V: Argumentation and transition to tertiary level -- 15. Argumentation and proof in the mathematics classroom: Viviane Durand-Guerrier, Paolo Boero, Nadia Douek, Susanna Epp, and Denis Tanguay -- 16. Examining the role of logic in teaching proof: Viviane Durand-Guerrier, Paolo Boero, Nadia Douek, Susanna Epp, and Denis Tanguay -- 17. Transitions and proof and proving at tertiary level: Annie Selden -- Part VI: Lessons from the Eastern cultural traditions -- 18. Using documents from ancient China to teach mathematical proof: Karine Chemla -- 19. Proof in the Western and Eastern traditions: Implications for mathematics education: Man Keung Siu -- Acknowledgements -- Appendix 1: Discussion Document -- Appendix 2: Conference Proceedings: Table of contents -- Author Index -- Subject Index.
    Abstract: One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.
    Description / Table of Contents: Proof and Provingin Mathematics Education; Contents; Contributors; Chapter 1: Aspects of Proof in Mathematics Education; 1 ICMI Study 19; 2 Contents of the Volume; 3 Conclusion; Part1: Proof and Cognition; Chapter 2: Cognitive Development of Proof; 1 Introduction; 2 Perceptions of Proof; 2.1 What Is Proof for Mathematicians?; 2.2 What Is Proof for Growing Individuals?; 3 Theoretical Framework; 3.1 Theories of Cognitive Growth; 3.2 Crystalline Concepts; 3.3 A Global Framework for the Development of Mathematical Thinking; 4 The Development of Proof from Embodiment
    Description / Table of Contents: 4.1 From Embodiment to Verbalisation4.2 From Embodiment and Verbalisation to Pictorial and Symbolic Representations; 4.3 From Embodiment, Verbalisation and Symbolism to Deduction; 5 Euclidean and Non-Euclidean Proof; 5.1 The Development of Euclidean Geometry; 5.2 The Beginnings of Spherical and Non-Euclidean Geometries; 6 Symbolic Proof in Arithmetic and Algebra; 6.1 The Increasing Sophistication of Proof in Arithmetic and Algebra; 6.2 Proof by Contradiction and the Development of Aesthetic Criteria; 7 Axiomatic Formal Proof; 7.1 Student Development of Formal Proof
    Description / Table of Contents: 7.2 Structure Theorems and New Forms of Embodiment and Symbolism in Research Mathematics8 Summary; References*; Chapter 3: Theorems as Constructive Visions; 1 The Constructive Content of Euclid's Axioms; 2 From Axioms to Theorems; 3 On Intuition; 4 Little Gauss' Proof; 4.1 Arithmetic Induction and the Foundation of Mathematical Proof; 4.2 Prototype Proofs; 5 Induction vs. Well-Ordering in Concrete Incompleteness Theorems; 6 The Origin of Logic; 7 Conclusion; References; Part2: Experimentation: Challenges and Opportunities
    Description / Table of Contents: Chapter 4: Exploratory Experimentation: Digitally-Assisted Discovery and Proof1 Digitally-Assisted Discovery and Proof; 1.1 Exploratory Experimentation; 1.2 Digitally Mediated Mathematics; 1.3 Experimental Mathodology; 1.3.1 What Is Experimental Mathematics?; 1.4 Cognitive Challenges; 1.5 Paradigm Shifts; 2 Mathematical Examples; Example I: What Did the Computer Do?; Example II: What Is That Number?; Example III: From Discovery to Proof; Example IV: From Concrete to Abstract; Example V: A Dynamic Discovery and Partial Proof; Example VI: Knowledge Without Proof
    Description / Table of Contents: Example VII. A Mathematical Physics LimitExample VIII: Apéry's Formula; Example IX: When Is Easy Bad?; 3 Concluding Remarks; References; Chapter 5: Experimental Approaches to Theoretical Thinking: Artefacts and Proofs; 1 Introduction; 2 Part 1: From Straight-Edge and Compass to Dynamic Geometry Software; 2.1 Classical European Geometry; 2.2 The Modern Age in Europe; 2.3 Constructions with Straight-Edge and Compass in the Mathematics Classroom; 2.4 Constructions in a DGS; 2.5 DGS Constructions in the Classroom; 2.6 Experiments and Proofs with the Computer
    Description / Table of Contents: 2.7 Implementation in Mathematics Classrooms
    Note: Description based upon print version of record
    URL: Volltext  (kostenfrei)
    URL: Volltext  (lizenzpflichtig)
    URL: Cover
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  • 17
    ISBN: 9781402083839
    Language: English
    Pages: Online-Ressource (digital)
    Series Statement: SpringerLink
    Series Statement: Bücher
    Series Statement: Springer eBook Collection
    Series Statement: Humanities, Social Science and Law
    Parallel Title: Buchausg. u.d.T. Garfield, Joan B. Developing Students' Statistical Reasoning
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    Keywords: Mathematics ; Education, Higher ; Statistics ; Consciousness ; Education
    URL: Volltext  (lizenzpflichtig)
    URL: Cover
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  • 18
    ISBN: 9780306472237
    Language: English
    Pages: 1 Online-Ressource(VII, 278 p.)
    Edition: 1st ed. 2002.
    Series Statement: Mathematics Education Library 22
    Parallel Title: Erscheint auch als
    Parallel Title: Erscheint auch als
    Parallel Title: Erscheint auch als
    RVK:
    Keywords: Learning. ; Instruction. ; Mathematics—Study and teaching . ; Artificial intelligence. ; Mathematics. ; History. ; Learning, Psychology of. ; Education ; Artificial intelligence ; Mathematics_$xHistory ; Mathematics ; Algebra ; Mathematikunterricht
    Abstract: Approaches to Algebra -- The Historical Origins of Algebraic Thinking -- The Production of Meaning for Algebra: A Perspective Based on a Theoretical Model of Semantic Fields -- A Model for Analysing Algebraic Processes of Thinking -- The Structural Algebra Option Revisited -- Transformation and Anticipation as Key Processes in Algebraic Problem Solving -- Historical-Epistemological Analysis in Mathematics Education: Two Works in Didactics of Algebra -- Curriculum Reform and Approaches to Algebra -- Propositions Concerning the Resolution of Arithmetical-Algebraic Problems -- Beyond Unknowns and Variables - Parameters and Dummy Variables in High School Algebra -- From Arithmetic to Algebraic Thinking by Using a Spreadsheet -- General Methods: A Way of Entering the World of Algebra -- Reflections on the Role of the Computer in the Development of Algebraic Thinking -- Symbolic Arithmetic vs Algebra the Core of a Didactical Dilemma.
    Abstract: This book confronts the issue of how young people can find a way into the world of algebra. The contributions represent multiple perspectives which include an analysis of situations in which algebra is an efficient problem-solving tool, the use of computer-based technologies, and a consideration of the historical evolution of algebra. The book emphasises the situated nature of algebraic activity as opposed to being concerned with identifying students' conceptions in isolation from problem-solving activity. The chapters emerged from a working group of the International Group for the Psychology of Mathematics Education. The authors are drawn from an international community and the work highlights the differences in school algebra around the world. The group invited Nicolas Balacheff to write a provocative postscript and he suggests that `there is no possible entrance to the world of algebra without a strong push or guidance from the teacher, because there is no natural passage from the problématique accessible from the child's world to the mathematical problématique'.
    Note: Includes bibliographical references and index
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