New: Try it out now Here is a tablet web app with reduced functionality.

With the Calculator app for iOS (iPad and iPhone/iPod Touch) The part-whole concept, which is the basis of the basic operations plus and minus, can be illustrated and explored interactively. The idea for this virtual tool was based on the ideas of Gerster & Schultz (2000) to promote part-whole understanding in children with arithmetic difficulties.

Description of the app

Two (partial) sets together make up a set. This is called addition calculation. And if you take away a part from a set, another part remains. This is called subtraction calculation. With this tool, you can interactively experience and research these relationships between partial sets and the total set.

• Use your fingers to touch the screen to place one or more tiles or to move them from side to side.
• Swipe over a number to hide or show it.
• Tap a number to sort the tiles on the board.
• Ziehe den Rollladen runter und wieder hoch, um eine Tabletthälfte abzudecken. So kannst du Aufgaben für deinen Lernpartner erstellen oder die Aufgabe kontrollieren.
• Drag a tile up to delete it. Shaking the tray will empty it.

Didactic principles and exemplary tasks

The basic operations plus and minus are based on the concept that a set can be broken down into subsets and subsets can be put back together again (part-whole concept). In addition, two subsets are combined to form a total. In subtraction, a subset is removed from a set and another subset remains. Once children have understood these relationships between subsets and total, an important foundation for successful mathematical learning has been laid and the prerequisites for developing effective calculation strategies have been created. This virtual tool is a tool with which the part-whole concept can be illustrated, experienced and explored.

In order for the learning material to effectively promote the understanding of the part and the whole, appropriate tasks are required that encourage experimentation and reflection with the work material. Tasks that encourage the discovery of connections (operational tasks) are particularly suitable. Suitable tasks include:

• How can you place 6 tiles on the tray as quickly as possible with your hands?
• Wie kannst du die Plättchen so anordnen, dass du möglichst schnell ohne Abzählen siehst, wie viele es sind?
• There are 4 tiles on one side and 3 tiles on the other side. How many tiles are there on both sides together? (Addition)
• What happens if I move 1 (2, 3, ...) tiles from one side to the other? (number decomposition, invariance)
• Was passiert mit den Teilmengen und mit der Gesamtmenge, wenn ich ein Plättchen vom Tablett entferne?
• How many different ways are there to distribute 10 tiles on both sides? (Number decomposition)
• Auf der einen Seite liegen 3 Plättchen. Wie viele muss ich auf der anderen Seite dazulegen, damit zusammen 7 Plättchen auf dem Tablett liegen? (Ergänzungsaufgaben)
• There are 10 tiles on the tray. You can only see part of them. How many tiles are hidden? (Adding a quantity, subtraction)
• I put 8 tiles on one half of the tray. I then take 5 of the 8 tiles away and place them on the other side. How many are left? (Subtraction)
• Auf dem Tablett liegt die Aufgabe 9 + 7. Wie kann ich die Plättchen so umlegen, dass ich sofort sehen kann, was herauskommt? (Nachbaraufgaben als Rechenvorteil nutzen)
• The calculation tablet can also be used to introduce number walls or to clarify the relationships when difficulties arise.

literature

Gerster, H.-D. & Schultz, R. (2000): Schwierigkeiten beim Erwerb mathematischer Konzepte im Anfangsunterricht (Forschungsbericht). Im Internet verfügbar unter: http://nbn-resolving.de/urn:nbn:de:bsz:frei129-opus-161