Most people do not have to count quantities up to 4. A glance is enough to be able to name the number correctly. The reason is that the brain can process four things at the same time. For quantities above 4, the power of five is used in elementary school. In this system, quantities are divided into single dots and rows of five dots.

The 5 is processed as one row, 6 as a row and one dot, 7 as a row and two dots, 8 as a row and three dots, and 10 as two rows. With the exception of 9, all quantities up to 10 can be recreated in this way in the mind’s eye. In learning materials, different colored dots are used to represent addition tasks. This is how the task 4 + 4 is represented:

The sum 8 can be identified at a glance. And such calculation tasks can also be performed in the mind’s eye. This is how children learn mental calculation.

However, not all people can process four things at once. A representative study at the University of Hamburg showed that people with trisomy 21, Down syndrome, process only 2 to 3 things at the same time. Click here to read the study for free. For them, and for many other people with math learning difficulties, the power of five is not suitable.

mathildr system
We created mathildr as an alternative to the power of five. The system allows children to learn mental arithmetic who process less than four things at a time. It consists of memorable quantity pictures that can be easily captured. After they have been learned, they can be recalled and changed in mind. With mathildr learners can deal with counting and with quantity concepts. The quantity pictures can help to solve arithmetical problems in the mind. The quantity pictures are based on the distinction between 0 and 1. 0 is represented as a ring, 1 as a cherry. Two cherries are bundled together. This ensures that even children with special attention can learn with mathildr.

The bundles of two are arranged in a special way that is reminiscent of dice pictures. This structure makes it possible to recognize the quantity pictures without counting and to reproduce them mentally. The cherry stems support the distinction between even and odd numbers.
The cherries must be placed in a fixed order so that the quantity pictures always remain recognizable.

Just like the power of five, different colour combinations are used to represent addition. This illustration shows the addition 4 + 2. People who have already internalised the quantity pictures recognise the result 6 at a glance.

Numbers up to twenty
To represent quantities from 11 to 20, two ten-slot fields are combined. Children who have already learned the quantity pictures 0 to 10 can draw on existing knowledge when working with the twenty-slot field. The following illustration shows the quantity picture of 15, which is made up of the 10 and the 5.