This report is intended to provide attention to issues that the Cambridge Conference feels are related to the mathematical training of elementary school teachers. The document is divided into three parts. Part I, titled "The Problems and Proposals Towards the Solution," contains the following chapters: (1) Introduction to the Report; (2) The Preservice Training of Elementary School Teachers; (3) The In-Service Environment of Elementary School Teachers; and (4) Recommendations. Part II, "Details of the Mathematics Curriculum," contains: (5) Details of Proposal One; and (6) Details of Proposal Two. The third part is titled "Essays on Some Aspects of Elementary School Training," and contains six essays. It is hoped that this document will inspire debate, controversy, and experiment, and that out of these will eventually emerge guidelines which can actually be used. (MP)