Content:

1. Image of natural numbers (state, magnitude, address, operator). Different semantic types of addition/subtraction.

2. Conceptualisation of process, procept. Perception of number. Big numbers. Rhythm. Regularities.

3. Additive operations. Mental characteristics of drill. Automatisation. Mental calculations, written algorithms, semantic models.

4. Solving and posing word problems. Anti-signal. Pupils' mistakes.

The course is focused on the preparation of students for their teaching practice in the domain of teaching mathematics. The students get various non-traditional mathematical environments in which they develop not only mathematical but also didactic abilities, formulating new problems, discussing difficulties of problems for pupils, creating cascades of problems and new mathematical environments.