This guide has been designed to help teachers, supervisors, and administrators set up a science or mathematics research program which should provide students with a set of basic "tools" for use in problem solving situations. The guide is organized into 17 chapters. The first 15 chapters focus on: organizing a research program; recruiting students; using the library; using outside agencies; writing the research paper; teaching laboratory skills; selecting the problem; stating the hypothesis; designing and implementing the research project; recording and interpreting results; stating the conclusion; discussion and implications for future research; presenting the oral report; competing at science and mathematics fairs; and evaluating science and mathematics projects. Chapter 16 provides a sample research project in biology, chemistry, physics, earth science, and mathematics. Chapter 17 provides lists of textbooks and references (for both teachers and students) arranged by science and mathematic topic areas. Many chapters have been divided into separate sections for science and mathematics, with information germane to both areas integrated into the separate sections. However, teachers are encouraged to read both sections to make sure important concepts or suggestions are not missed. (JN)