The goal of working with mathildr is to internalize the quantity pictures and to be able to recall them in the mind’s eye. For mental arithmetic, the quantity pictures are modified by mentally adding or taking away cherries.

Here, especially the verbalization of the quantity pictures plays a major role.

Internalization through verbalization

Internalizing the quantity pictures usually happens in a three-step process:

1. concretely: The quantity pictures are counted.

2. explicit-verbal: The quantity pictures are recognized at a glance. Their structure is verbalized step by step.

3. purely mental: The quantity pictures can be evoked in the mind’s eye without aids by building them up step by step.

In mathildr a single cherry is called a cherry, a pair of cherries is called a pair. In the second step of the internalization process, the quantity pictures are verbalized in a building manner. This encourages the children to imagine the pictures in their mind’s eye in a building way as well. 

3pair, cherry
4pair, pair
5pair, pair, cherry
6pair, pair, pair
7pair, pair, pair, cherry
8pair, pair, pair, pair
9pair, pair, pair, pair, cherry
10pair, pair, pair, pair, pair

Three-step process for internalizing the quantity pictures based on Klafki, W. (2007). Neue Studien zur Bildungstheorie und Didaktik. Zeitgemäße Allgemeinbildung und kritisch-konstruktive Didaktik (6. Auflage). Weinheim: Beltz, S. 193 f.