This first volume of a review prepared for the Cockcroft Committee of Inquiry into the Teaching of Mathematics in Schools in Great Britain, and its main conclusions were incorporated in their report, "Mathematics Counts." Its aim was to display the main outcomes of research relevant to the teaching and learning of mathematics. The introduction of this first volume was intended to highlight some of the main points of the review, as well as to put it into the context of questions currently of concern. The 14 chapters of the document synthesize the research on the following particular topics in mathematics education: (1) the mathematics curriculum; (2) background psychology; (3) stages of general intellectual development; (4) skills, concepts, and strategies; (5) the teaching of facts and skills; (6) understanding of concepts in specific topic areas; (7) teaching methods; (8) process aspects; (9) attitudes; (10) individual differences; (11) language; (12) evaluation and assessment; (13) calculators and computers; and (14) using research. A supplement has been added to take account of work published since the original review was compiled. (MNS)