This report is a summary of research in the teaching of mathematics as reported to the U.S. Office of Education for the years 1959 and 1960. This analysis of research in mathematics education is designed to help both research workers and classroom teachers improve mathematics instruction. One hundred and five reported research studies are included in this publication. The selected reports include doctoral dissertations, master's theses, and nondegree studies which deal with such aspects as methods, content, teacher education, evaluation and psychology of learning mathematics. For convenience to the reader, the studies are grouped under the areas of elementary school, secondary school, and college mathematics. (FL)