Findings about the nature of adult motivation and the rapid expansion of knowledge about mathematics and its pedagogy, suggested that teacher training in mathematics should be planned and executed under two major guidelines. Further, a school mathematics programme should be concerned, in the first place, with children learning mathematics usefully and meaningfully. A second concern, which derived its importance mainly from the first, should be the preparation of teachers to teach mathematics so that the pupils could learn it in a 'non-arbitrary substantive fashion. In developing countries like the Caribbean territories, teacher training in mathematics must also attend to the high percentage of undertrained and undereducated teachers in mathematics and the high failure rates in mathematics among pupils. The findings and data obtained from mathematics projects in the Caribbean, in particular the St. Lucia Mathematics Project, indicated possible approaches to teacher training in mathematics. Three main strategies were described as successful strategies to constitute teacher training in mathematics: Curriculum Development Strategies, Mathematics Curriculum Strategies, and Mathematics Strategies. It was suggested that these strategies allowed the activities of classroom teachers, of teachers of teachers, and of curriculum workers, to be brought together, organizationally and philosophically.