Mathematical Discoveries in BASIC is based on the result that students of all ages can learn significant, important mathematics from very short programs in BASIC. Each page begins with a short program which, nevertheless, illustrates important, big ideas in mathematics. None of the programs are silly, or just examples-to show how commands work. All programs do real work. Using these short programs will allow you to give every student a successful starting point. Each program can be entered into any computer and will do interesting work when run. Subsequent questions and suggestions help students explore the mathematics involved and add lines to the program to create new mathematical programs. We believe such an approach allows students to learn good programming habits, develop their ~ programs, and learn mathematics appropriate for today and the future.