This study has three major strands: the framing and general acceptability of a functional definition of numeracy, the development, application and analysis of criterion referenced tests of some of the domains of numeracy, and the use of these tests in identifying individual student difficulties in numeracy. Detailed information on the perceived importance of a range of 13 numeracy tasks and items was obtained by a questionnaire administered to small numbers of randomly selected members of groups such as employee and employer organisations, primary and secondary teachers, college lecturers and parents. Two age levels were selected to provide information on student performance in numeracy. More than 6600 students aged 10 years and 6200 students aged 14 years in normal schooling were tested throughout Australia to determine whether they could master tasks based on specific content areas, abilities and usages related to numeracy. Careless errors and algorithm errors were also major causes of difficulty for these students. It was clear that the students needed constant encouragement if they were to attempt to use and practise the algorithms they had been taught in place of the inefficient, error prone methods they seemed to prefer.