This book, written on the recommendation of the Task Force on Mathematically Promising Students, investigates issues involving the development of promising mathematics students. Recommendations are made concerning topics such as the definition of promising students; the identification of such students; appropriate curriculum, instruction, and assessment; cultural influences; teacher preparation and enhancement; and appropriate next steps. Chapters include: (1) "Promises, Promises, Promises" (Peggy A. House); (2) "Definition and Identification of Mathematical Promise" (Richard Wertheimer); (3) "Mathematically Promising Students: National Trends and International Comparisons" (Judith Lynn Gieger and Jeremy Kilpatrick); (4) "Serving the Needs of the Mathematically Promising" (Linda Jensen Sheffield); (5) "The Mathematically Promising and the Mathematically Gifted" (Zalman Usiskin); (6) "Effective Learning Environments for Promising Elementary and Middle School Students" (Grayson H. Wheatley); (7) "A Community of Scholars: Working with Students of High Ability in the High School" (Mark Saul); (8) "Helping Students See the World Mathematically" (Solomon Garfunkel and Gary Froelich); (9) "The Open Approach to Teaching Mathematics--Creating a Culture of Mathematics in the Classroom: Japan" (Yoshihiko Hashimoto and Jerry Becker); (10) "Empowering Teachers to Discover, Challenge, and Support Students with Mathematical Promise" (Carole Greenes and Maggie Mode); (11) "Why Jane Doesn't Think She Can Do Math: How Teachers Can Encourage Talented Girls in Mathematics" (Sally M. Reis and M. Katherine Gavin); (12) "Building Programs for Promising Students Beyond the Classroom" (Harvey Keynes, Andrea Olson, Doug Shaw, and Karen Singer); (13) "The Missing Link: Connecting Parents of Mathematically Promising Students to Schools" (Jennie Bennett); (14) "Organizational Alternatives for the Mathematically Promising" (Betty J. Krist); (15) "Providing Opportunities through Competitions" (George Berzsenyi); (16) "International Perspectives on Cultivating Talent in Mathematics" (Frances R. Curcio); (17) "Making Children Count: Fostering Mathematical Literacy" (Mary Anne Anthony-Smith); (18) "The Gifted Dozen As They Move from Grades 2 through 4" (Gerald Elgarten); (19) "Ronnie Taught Us While We Mentored Him" (Marcia Nicol and James Fitzsimmons); (20) "A Boy Named Billy" (Linda Hall); (21) "You'll Do Better Next Time--You Can!" (Thomasenia Lott Adams); (22) "Everybody Counts--Including the Mathematically Promising" (Christian R. Hirsch and Marcia Weinhold); (23) "Instituting a Mathematics Research Program for Your School's Promising Mathematics Enthusiasts" (Robert Gerver); (24) "Nurturing Mathematical Promise during the School Day" (Paul Eenigenburg and Carol McCarthy); (25) "Project-Based Calculus 1 Students: A Case Study" (Cynthia Ramey); (26) "Identifying and Developing Mathematically Promising Students through Honors Calculus and the University Scholars Program" (John Douglas Faires, John Paul Holcomb, and Nathan Paul Ritchey); (27) "Supporting Students as Emerging Scholars" (James A. Mendoza Epperson); (28) "The Young Scholars Program at Ohio State University" (Arnold E. Ross); (29) "Developing Mathematically Promising Students Outside of Formal Education" (Richard Alvarez); (30) "The Charlotte Mathematics Club: A Greenhouse for Talent" (Ashley Reiter); (31) "Addiction to Mathematics: How Can We Cause It?" (William E. Geeslin); (32) "Nurturing the Growth of Young Mathematicians through Mathematics Contests" (Richard Grassl and Tabitha Mingus); (33) "MATHCOUNTS" (Madeline J. Bauer and Joseph P. Fagan); and (34) "Enriched Students Need Enriching Teachers: The Australian Mathematics Teacher Enrichment Project" (Steve Thornton and Francesca Peel). (ASK)