This study of rewards and recognition in the mathematical sciences in higher education utilized data gathered from site visits to 26 institutions, 3 open forums, and a survey of a sample of faculty and department chairs in mathematical sciences departments. Results found: (1) a substantial gap between what faculty think the reward structure should be and what it actually is; (2) an increased emphasis on research and scholarship; (3) a perception that research in the discipline is very important; (4) ambiguity and uncertainty about what should be included in the definition of scholarship; (5) lack of effective communication between various organizational levels; (6) vital role of the department chair for departmental well-being; (7) dissatisfaction with teaching evaluation methods; (8) discomfort with evaluation of faculty duties; (9) quality of life issues of major importance in rewards structures; and (10) interest in a combination of across-the-board and merit increases. The major recommendation is that departments ensure that their reward structure is broad enough to encompass the full array of activity required to fulfill the departmental and institutional missions. Six guiding principles for the recognition and rewards system are also suggested. An appendix discusses the definition of mathematical scholarship. A supplementary data report that accompanies this document reports on survey methodology, shows selected data, and contains a copy of the survey questionnaire. (Contains 21 references.) (JB)