Two Different Subtraction Algorithms-An Explorative Study Examining Typical Errors and Conceptual Understanding

Abstract

There are different ways to carry out written subtraction. The algorithms differ in determining the difference between minuend and subtrahend and in crossing the tens boundary. In the discussion to deliberate out, which procedure has to be chosen, the error-proneness of a procedure and children's understanding of the algorithm are involved as decision criteria-depending on the aims of instruction. To improve the knowledge regarding specific patterns in wrong solutions and error sources and children's understanding for ``subtraction with regrouping'' and ``indirect addition with equal addition'' an explorative study was conducted. 6 classes per procedure ``subtraction with regrouping'' (n = 113) and ``indirect addition with equal addition'' (n = 109) were examined through a test with written subtraction tasks and tasks to describe and explain the used procedure. We found specific patterns in wrong solutions and error sources, e.g. crossing the tens boundary several times in one task for ``subtraction with regrouping'' or ``minuend smaller than subtrahend'' for ``indirect addition with equal addition''. The analysis of the tasks concerning children's understanding based on a new developed detailed coding scheme showed that children could explain regrouping much better than equal addition. Our findings can be used as basis for the development of a balanced test instrument for studies comparing the procedures.