The following notes deal mainly with the Arithmetic of the primary school, but the subject under consideration is only a single aspect of a very wide question.

It is a common remark that Oral (or Mental) and Written Arithmetic should be as nearly as possible identical: that pupils ought to be able to do mentally with small numbers whatever they can do in writing with larger numbers, and vice versa. Unfortunately, experience shows that, as a rule, they are not able to do so; that the child fails to identify written calculation completely with mental work. It is here proposed to try to discover some of the reasons why this is so.