Many of the errors that occur in children' subtraction are due to the use of incorrect strategies rather than to the incorrect recall of number facts. A production system is presented for performing written subtraction which is consistent with an earlier analysis of the nature of such a cognitive skill. Most of the incorrect strategies used by schoolchildren can be accounted for in a principled way by simple changes in the production system, such as the omission of individual rules or the inclusion of rules appropriate to other arithmetical tasks. The production system model is evaluated against a corpus of over 1500 subtraction problems done by 10‐year olds and is shown to account for about two‐thirds of the (nonnumber fact) errors. It also provides an alternative, simpler interpretation of the subtraction errors analysed by Brown and Burton (1978). Some implications for teaching are discussed.