Abstract

This article reports on a qualitative research approach that used learners’ test items as data collecting instruments. It presents 132 South African Grade 4 learners’ work on the addition and subtraction of ten multiple-digit test items and calculation strategies, as well as the documentation of the errors and the misconceptions they displayed. The Grade 4 learners’ work illustrates expansion, alteration, and mentalization strategies that enable them to add and subtract numbers correctly. The knowledge and use of the concept of place value enable learners to add and subtract multi-digit whole numbers at elementary level. The learners’ work also indicates their conceptual and procedural knowledge of the zero effect, carrying procedure, and the errors thereof due to specific misconceptions. Interlinking learners’ invented calculation strategies and their computational errors is critical in informing their computational sequential development and allows teachers to make inferences on appropriate numerical teaching and instructional strategies. The key findings led to the formulation of a multi-digit addition and subtraction model.