The study involved the collection of (1) research reports, published through 1968, including journal articles and dissertation abstracts, and (2) information on developmental projects, supplemented by ERIC documents on funded research and Title III project reports. The journal articles were analyzed, categorized on ten aspects, evaluated, and summarized. Two instruments developed and tested for this purpose were used to evaluate; reports of tests of reliability on both instruments are included in this report. Dissertation abstracts, ERIC documents, and other project reports are summarized. Information derived from on-site visits to ten major projects is briefly summarized, and is followed by a taped interview with each project director. The research information about elementary school mathematics for 1900 through 1968 is synthesized, using the most valid of the findings of research to answer specific questions collected from editors of elementary school mathematics textbooks and college teachers of mathematics education courses. A list of the most applicable findings of research is also included. In a summary chapter, key research and developmental trends are discussed. (Authors)