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Visualisierung des Newton-Verfahrens mittels Computers zur Unterstützung eines tieferen Verständnisses iterativer Verfahren

Visualisierung des Newton-Verfahrens mittels Computers zur Unterstützung eines tieferen Verständnisses iterativer Verfahren

          
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About the Book

Examensarbeit aus dem Jahr 2002 im Fachbereich Didaktik - Mathematik, Note: 2,0, Zentrum für schulpraktische Lehrerausbildung, Gelsenkirchen; ehem. Studienseminar für Lehrämter an Schulen Gelsenkirchen (-), Sprache: Deutsch, Abstract: Das Thema der vorliegenden Arbeit ist aus meiner unterrichtlichen Praxis in einem Mathematik-Kurs der Jahrgangsstufe 11 am Heinrich-Heine-Gymnasium, Bottrop, erwachsen. In diesem Kurs, der mir im Bereich meines bedarfsdeckenden Unterrichtes zugeteilt war, unterrichtete ich im zweiten Halbjahr des Schuljahres 2001/02 u. a. eine Unterrichtsreihe zum Thema der Kurvendiskussion im Bereich der Analysis, wozu auch das Ermitteln von Nullstellen ganzrationaler (Polynom-)Funktionen gehörte. Hier wurden die unterschiedlichen Methoden wie z.B. Substitution, Polynomdivision usw. eingeführt und eingeübt. Die anschließende Einführung und Herleitung des Newton-Verfahrens als Verfahren zur iterativen Bestimmung von Nullstellen bei Funktionen, die sich nicht mit Hilfe der bereits bekannten Methoden auf ihre Nullstellen hin untersuchen lassen, verlief derart, dass zusammen mit den Schülerinnen und Schülern die geometrischen Hintergründe an der Tafel bzw. auf Folien erarbeitet wurden. Hieraus wurde dann die Rekursionsformel des Newton-Verfahrens hergeleitet. Bei der Korrektur der sich an diese Unterrichtsreihe anschließenden Klausur stellte ich jedoch fest, dass die SuS zwar problemlos die Rekursionsformel behalten hatten und diese auch anwenden konnten, jedoch fehlte den meisten jegliches Verständnis für die geometrische Anschauung bzw. die geometrischen Zusammenhänge. Aus diesem Grunde suchte ich nach einer Methode, den SuS die hinter dem iterativen Newton-Verfahren stehenden geometrischen Zusammenhänge näher zu bringen. Diese Arbeit stellt im Folgenden die Überlegungen und Beweggründe vor, die letztlich zur Entwicklung der Excel-Arbeitsmappe "Newton.xls" geführt haben.


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Product Details
  • ISBN-13: 9783640980574
  • Publisher: Grin Publishing
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 4 mm
  • Width: 148 mm
  • ISBN-10: 3640980573
  • Publisher Date: 30 Aug 2011
  • Height: 210 mm
  • No of Pages: 60
  • Series Title: German
  • Weight: 91 gr


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Visualisierung des Newton-Verfahrens mittels Computers zur Unterstützung eines tieferen Verständnisses iterativer Verfahren
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