This thesis is a record of experiments in the education of mathematics
teachers for Irish Secondary schools conducted at Thomond College of
Education, Limerick during the years 1975–77 inclusive. But it is more
than a mere record of successes and failures. In its analyses and syntheses,
based on experiments and programmes conducted under actual conditions,
it endeavours in a true spirit of research in mathematical
education to provide new insights. The research culminates in the redefinition
of an old problem in mathematical education, and a first
step towards a viable solution to the redefined problem is presented
