Es muß [...] geprüft werden, ob die Beherrschung von Rechentechniken noch zu den wichtigsten Qualifikationen eines mündigen Erwachsenen des 21. Jahrhunderts gehört

In elementary mathematics instruction four types of calculation should be distinguished from each other: mental calculation, informal strategies, written algorithms, and the use of calculators. Each of these methods is connected with a specific degree of importance, but written algorithms traditionally are given priority over the other ones. The present paper pleads for a new reflection and reexamination of the four types that takes the specific features, intentions and strengths of each method into account. The essential suggestion is to reduce written algorithms in favor of mental calculation and informal strategies. This point of view is both theoretically founded and illustrated by means of typical examples.