# Sachrechnen

(also application-oriented mathematics education) is an important component of holistic learning. The goal is to prepare students for life so that they can find their way in the world and accordingly become mature. The focus is on the recognition and understanding of mathematical models, which are applied in a concrete situation. Furthermore, factual arithmetic contributes to a gain in knowledge of the concretely processed matter. In doing so, one must proceed according to plan when working on a matter or a problem. In comparison to the often confused text tasks that are clothed in mathematical topics, they are characterized by the fact that factual tasks open up factual contexts from the students' environment or area of interest in a factual and mathematical way Factual tasks should prepare students for life and make an important contribution to their maturity. They learn to put on mathematical glasses in factual situations in everyday life and to clarify the matter with mathematical means. The lessons teach the students how to mathematize the environment. This means, for example, how they can obtain data from the environment, develop factual questions, simplify real phenomena appropriately and interpret mathematical results and concepts into reality.

The starting point of instruction for the development of mathematical models and procedures is the students' prior knowledge. Furthermore, the acquired knowledge, skills and abilities are used to solve everyday problems and to explore the world by mathematical means (application orientation). Factual arithmetic tries incidentally to prevent the problem of captain syndrome

Fears that such complex factual tasks will overtax students with learning difficulties are common. However, if we make a comparison with the complex everyday life in which these students have to find their way around, we can see the opportunity of the factual tasks precisely in this. In many cases, it is precisely these students who are unable to fill the didactically reduced and simple tasks with meaning. In this case, the tasks are perceived as meaningless and what they have learned is quickly forgotten.^{[1]}

Las tareas capitán son tareas irresolubles que, sin embargo, pueden ser aparentemente "resueltas" por el
sin embargo, parecen ser "resueltos" por los alumnos.
En 1989, Stella Baruk propuso a 97 alumnos de segundo y tercer grado lo siguiente
Tarea:
"Hay 26 ovejas y 10 cabras en un barco. ¿Qué edad tiene el
¿Capitán?" (Æ de ahí la expresión comúnmente utilizada en la literatura técnica
"El 80% de los alumnos calculó la edad así: 26 + 10;
El capitán tiene 36 años.
Hendrik Radatz hizo que 333 niños resolvieran tareas de capitán similares en 1983. Ellos
podría hacerse por
- aproximadamente el 10 % de los alumnos de primer grado
- aproximadamente el 30 % de los alumnos de segundo grado
- Aproximadamente el 60% de los alumnos de tercer y cuarto grado
- aproximadamente el 45 % de los alumnos de quinto grado
¡podría ser "resuelto"! (cf. Gaidoschik 2006, p 12)
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