ABSTRACT
Errors can be informative. They can show what a learner does not understand and sometimes hint at a reason why. This chapter presents examples which illustrate how mathematics develops and how much care has to be taken not to simplify explanations in a way that creates future errors and misconceptions. Some errors have a logic which exposes an imperfect understanding of a procedure, or a confusion created by the inconsistencies of mathematics. The norm-referenced 15 minute mathematics test can provide evidence of error patterns, as can almost any written mathematics work. Many of the items included in the 15 minute test were designed to expose error patterns. Some were designed to avoid some error patterns, for example, item 33 uses basic multiplication facts that should be in most subjects’ repertoire, thus reducing the incidence of basic fact errors. Some errors give useful diagnostic evidence about which concepts are understood or which pre-requisite skills are missing.
