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Mathematikunterricht Im 7.-10. Schuljahr Der Lehrplan Und Seine

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Mathematikunterricht Im 7.-10. Schuljahr Der Lehrplan Und Seine Mathematikunterricht im 7.-10. Schuljahr Der Lehrplan und seine Inhalte Sammlung von Materialien zur Vorlesung R.Deißler WS 2003/2004 DER LEHRPLAN UND SEINE INHALTE i DEISSLER WS 03/04 Skript-LP-04-Master.doc INHALTSVERZEICHNIS 1 ZIELE DES MATHEMATIKUNTERRICHTS...................................................................................................................1 1.1 TIMS-STUDIE: MATHEMATISCH-NATURWISSENSCHAFTLICHER UNTERRICHT IM INTERNATIONALEN VERGLEICH............1 1.2 INTERNATIONALE LEISTUNGSVERGLEICHSSTUDIE PISA....................................................................................................2 1.3 MATHEMATIK ALS HILFSMITTEL IM PRIVATEN UND BERUFLICHEN ALLTAG ......................................................................4 1.4 EIN SZENARIO FÜR DEN KÜNFTIGEN MATHEMATIKUNTERRICHT?......................................................................................6 2 ARITHMETIK IM 7.SCHULJAHR: RATIONALE ZAHLEN .........................................................................................7 2.1 EIN SPIEL ZUR EINFÜHRUNG: SALDIX ................................................................................................................................7 2.2 EIN SPIEL ZU NEGATIVEN ZAHLEN MIT DEM TASCHENRECHNER: KATZ UND MAUS ..........................................................9 2.3 EIN SPIEL ZUR ADDITION UND SUBTRAKTION: DAS KONTOSPIEL ....................................................................................10 2.4 AUS DER GESCHICHTE DER NEGATIVEN ZAHLEN: ............................................................................................................10 2.5 DIE NEGATIVEN ZAHLEN IM UNTERRICHT DES 7.SCHULJAHRES.......................................................................................11 2.5.1 Vorkenntnisse ..........................................................................................................................................................11 2.5.2 Modelle zur Einführung und zum Rechnen mit negativen Zahlen ...........................................................................11 2.5.3 Schülerfehler beim Rechnen mit negativen Zahlen..................................................................................................12 2.5.4 Verwendung von negativen Zahlen in späteren Schuljahren...................................................................................12 2.6 EIN UNGEWÖHNLICHES MODELL......................................................................................................................................13 3 ALGEBRA .............................................................................................................................................................................14 3.1 ALGEBRA IM ÜBERBLICK: FACHLICHE GRUNDLAGEN .....................................................................................................14 3.1.1 Zentrale Leitbegriffe................................................................................................................................................14 3.1.2 Fachwissenschaftliche Grundlagen: .......................................................................................................................14 3.2 VARIABLEN UND VARIABLENASPEKTE.............................................................................................................................16 3.3 EIN SPIEL ZU TERMEN: RATE MEINE REGEL.....................................................................................................................17 3.4 ALGEBRA VOM 7.-10.SCHULJAHR: INHALTE UND FACHLICHER HINTERGRUND ...............................................................18 3.4.1 Terme und lineare Gleichungen (7.Schuljahr) ........................................................................................................18 3.4.2 Terme mit Klammern (8. Schuljahr)........................................................................................................................18 3.4.3 Bruchterme und Bruchgleichungen (8. Schuljahr)..................................................................................................18 3.4.4 Der Funktionsbegriff (ab 8. Schuljahr.) ..................................................................................................................18 3.4.5 Koordinatensysteme ................................................................................................................................................19 3.4.6 Lineare Funktionen (8.Schuljahr) ...........................................................................................................................19 3.4.7 Lineare Gleichungssysteme mit 2 Variablen (8.Schuljahr) .....................................................................................19 3.4.8 Potenzen und Wurzeln (9.Schuljahr) .......................................................................................................................20 3.4.9 Quadratische Funktionen und quadratische Gleichungen (9. und 10. Schuljahr) ..................................................20 3.4.10 Verschieben und Strecken/Stauchen von Funktionsgraphen:..................................................................................21 3.5 GLEICHUNGEN IM 7.SCHULJAHR: MODELLE ....................................................................................................................24 3.6 EIN SPIEL ZU BRUCHTERMEN: HINDERNISRENNEN ..........................................................................................................25 3.7 ÜBUNGSPROGRAMME ZUR ALGEBRA: BEISPIEL TERMUMFORMUNG (KLETT SOFTWARE).................................................26 3.8 EIN PAKET VON ÜBUNGS- UND TESTPROGRAMMEN ZUR ALGEBRA IN DER SI: SMILE....................................................27 3.9 FUNKTIONALES DENKEN..................................................................................................................................................29 4 SACHRECHNEN..................................................................................................................................................................31 4.1 SACHRECHNEN: ÜBERSICHT............................................................................................................................................31 4.2 SINNVOLLES RUNDEN, GENAUIGKEIT BEIM RECHNEN VON SACHAUFGABEN. .................................................................32 4.3 PROPORTIONALE UND ANTIPROPORTIONALE ZUORDNUNGEN..........................................................................................33 4.4 PROZENTRECHNUNG ........................................................................................................................................................40 DER LEHRPLAN UND SEINE INHALTE ii DEISSLER WS 03/04 Skript-LP-04-Master.doc 4.4.1 Inhalte der einzelnen Schuljahre im Prozentrechnen ..............................................................................................40 4.4.2 Modelle zum Prozentbegriff.....................................................................................................................................40 4.4.3 Mögliche Zugänge zur Prozentrechnung.................................................................................................................40 4.4.4 Diagramme..............................................................................................................................................................41 4.4.5 Prozentrechnen: Grundaufgaben ............................................................................................................................41 4.4.6 Verminderter und vermehrter Grundwert (8.Schuljahr) ........................................................................................43 4.4.7 Verknüpfen von Prozentsätzen (9.Schuljahr) ..........................................................................................................44 4.5 ZINSRECHNEN (AB 8. SCHULJAHR)...................................................................................................................................44 4.6 SPEZIELLE BEGRIFFE ZUM PROZENT- UND ZINSRECHNEN................................................................................................46 4.7 AUFGABEN ZUM SACHRECHNEN: PROZENT UND ZINS......................................................................................................47 5 GEOMETRIE........................................................................................................................................................................49 5.1 ÜBERSICHT.......................................................................................................................................................................49 5.2 GRUNDLEGENDE KONZEPTE UND ZIELE DES GEOMETRIEUNTERRICHTS, MATERIALIEN ..................................................51 5.2.1 Ziele des Geometrieunterrichts ...............................................................................................................................51 5.2.2 Geometrische Grundkonzepte..................................................................................................................................51 5.2.3 Beweisen im Geometrieunterricht ...........................................................................................................................52 5.2.4 Materialien und Modelle, Aktivitäten......................................................................................................................53
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