Rechenschritte

Rechenschritte are the step-by-step procedures used to solve arithmetic problems. They encompass the sequence of operations, the identification of operands and operators, and the logical order in which calculations are carried out. In German-speaking education, students are often taught to write down the individual steps to show their reasoning and to ensure accuracy. Rechenschritte apply to basic arithmetic—addition, subtraction, multiplication, and division—as well as to more complex operations and problem solving.

In written arithmetic, typical Rechenschritte appear as columnar calculations. They involve aligning digits by place value, performing additions with carries and subtractions with borrows, and combining partial results in multiplication. For division, steps include estimating the quotient, carrying out long division, and subtracting products. Mental arithmetic relies on internal steps, but these are not always written down. The concept also covers applying procedures to multi-digit numbers, fractions, decimals, and simple algebraic expressions in a transparent, checkable manner.

The explicit presentation of Rechenschritte supports understanding, error detection, and progressive mastery of calculation skills. It helps teachers diagnose misconceptions and provide targeted feedback. At the same time, there is a balance to strike: an overemphasis on procedures can hinder conceptual understanding unless it is complemented by explanations of why the steps work and by tasks that emphasize meaning and problem solving.