Fehlerstrategien bei Addition

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 Präsentation transkript:

Fehlerstrategien bei Addition Z+Z durch N+N HN richtig, aber ursprüngliche Zähler addiert Multiplikation statt Addition Fehler bei nat. Zahl + Bruch

Vorbeugung und Therapie Anschauliche Grundvorstellungen Quasikardinale Schreibweise Nat. Zahl + Bruch ernster nehmen Sematisch einfache Rechnungen mit dem gesunden Menschenverstand lösen Überschlagsrechnungen Herstellen kognitiver Konflikte

Beispiel für kognitiven Konflikt (Mack) I: When you add fractions, how do you add them? Tony: Across. Add the top numbers across and the bottom numbers across. I: I want you to think of the answer to this problem on your head. If you had 3/8 of a pizza and I gave you 2/8 more of a pizza, how much pizza would you have?

Forts.: Tony: Five-eights. … I don´t think that´s right. I think this just might be 16. I think this´d be 5/16. I: Let´s use our pieces to figure this out. .. Now, how much do you have. Tony: Five eights. Its seems like it would be sixteenths. … This is hard.

Mack: …it was necessary to spend a great deal of time solving real-world problems, then modeling the problems with concrete materials, and finally, recording the problems symbolically.

Subtraktion Vorkenntnisse nach Padberg sehr gering (siehe dort)

Vorgehensweise Wie bei Addition etwa mit Pizzas Anderer Vorschlag von Streefland mit Geschwindigkeiten (siehe Padberg). Ansonsten gilt alles analog zur Addition

Lösungsquoten bei der Subtraktion

Multiplikation Vorkenntnisse sehr gering. Beispiel: Wie viel sind zwei drittel von 36 Äpfeln? Lösungsquote unter 10%. Fazit von Padberg: Anschaulicher Grundlage muss erst erarbeitet werden.

Einführung der Multiplikation Von-Ansatz Multiplikation von Größen (meist Längen) Beide Ansätze müssen natürlich behandelt werden. Weniger empfehlenswert aber möglich: Permanenzprinzip proportionale Funktionen, Dreisatz

Vorschlag von Zech Erst Multiplikation mit ganzen Zahlen, Division durch ganze Zahlen. Dann von-Ansatz Begründen, warum das als Multiplikation aufgefasst werden kann.

Lösungsquoten (Padberg)

Vorbeugung und Therapie Siehe Padberg 6.7 (kritisch lesen)