This study compares and contrasts the status of the three main areas of mathematics in the secondary school and the education of mathematics teachers in the United States with that in Great Britain. Seven questions are posed at the start of the study. Comparisons are drawn between the two countries in view of these questions, and a chapter near the end summarizes the findings. Nine principles are stated as a basis for a method of training, and the final chapter evaluates the strengths and weaknesses of the training programs in both countries with regard to the stated principles. (LS)