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Probleme der Entwicklung grundlegender Begriffe der Integralrechnung: Belegarbeit für das Hauptseminar in der Mathematikdidaktik

Probleme der Entwicklung grundlegender Begriffe der Integralrechnung: Belegarbeit für das Hauptseminar in der Mathematikdidaktik

          
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About the Book

Studienarbeit aus dem Jahr 2011 im Fachbereich Didaktik - Mathematik, Universität Rostock (Institut für Mathematik), Veranstaltung: Hauptseminar - Didaktik der Mathematik, Sprache: Deutsch, Abstract: Der Integralbegriff beschäftigt den Menschen schon seit langer Zeit, noch vor dem des Differentials. Die heutige Integralrechnung bildet zusammen mit der Differentialrechnung die Grundlage der Analysis als Teilgebiet der Mathematik. In Abgrenzung zu der Differentialrechnung, in der es darum geht, zu einer gegebenen Funktion eine Ableitung zu bilden und um die Fragen wie man zur Ableitung gelangt und unter welchen Voraussetzungen diese existiert und die Frage nach der lokalen Änderungsrate, betrachtet die Integralrechnung die Problematiken umgekehrt. Das Integrieren tritt also als "Umkehrung" des Differenzierens auf. Allerdings tritt sie oft auch im Zusammenhang mit Flächeninhaltsbestimmungen auf. Man benutzt den Begriff wenn man die Fläche unter einem Funktionsgraphen und bei der Berechnung der Fläche des Kreises, also allgemein von krummlinig begrenzten Flächen. Nicht nur in der Flächenberechnung sondern auch in der Volumenberechnung ist dieser Begriff präsent. So findet er Anwendung bei Volumenberechnungen von Rotationskörpern, bspw. von Zylindern, Kegeln und Kugeln. Diesen Begriff sieht man sich insgesamt in vielen Anwendungsbereichen gegenüber. So folgt, dass der Integralbegriff in die Schulbildung an Gymnasien aufgenommen wurde. Daher ist dieser Begriff für die Fachdidaktik der Wissenschaft Mathematik von enormer Bedeutung. Diese Arbeit beschäftigt sich im Wesentlichen mit dem Begriff des Integrals im Mathematikunterricht. Es wird vorerst ein kurzer historischer Überblick über die Entwicklung des Integralbegriffes gegeben. Neben dieser wird insbesondere auf die formalen und inhaltlichen Aspekte und kurz auf das Wissen und Können zu diesem Begriff vor und nach der Behandlung in der Sekundarstufe II eingegangen. Darüber hinaus sollen im Speziellen die Erarbeitungsmög


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Product Details
  • ISBN-13: 9783656371878
  • Publisher: Grin Publishing
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 4 mm
  • Weight: 95 gr
  • ISBN-10: 3656371873
  • Publisher Date: 15 Feb 2013
  • Height: 210 mm
  • No of Pages: 64
  • Series Title: German
  • Sub Title: Belegarbeit für das Hauptseminar in der Mathematikdidaktik
  • Width: 148 mm


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Probleme der Entwicklung grundlegender Begriffe der Integralrechnung: Belegarbeit für das Hauptseminar in der Mathematikdidaktik
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Probleme der Entwicklung grundlegender Begriffe der Integralrechnung: Belegarbeit für das Hauptseminar in der Mathematikdidaktik
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