AbstractThe popular idea that mental calculation involves covert operations as counterparts to the scribblings, sayings or manipulations involved in classroom calculation is rejected by familiar arguments in Section I. Philosophers do not readily agree on an alternative account. Section II considers reasons why they are puzzled, reasons which encourage a return to the discredited position. The currently fashionable Causal or Functionalist view is criticised in Section III. Section IV reconsiders the stubborn fact that when someone calculates in their head they do something at the time which explains their arithmetical successes or failures. Some dispositional descriptions are rejected as inadequate. Though a restrained dispositionalism is finally supported, it does not have the implication that nothing was going on in the silence.