The goal of Minicourse 5 is to increase the skill of inservice teachers (grades 4-6) in tutoring students whose understanding of mathematical concepts and procedures is weak. Emphasis is on actively involving the student in the tutoring process and developing his understanding, rather than rote learning, of mathematical concepts. The course consists of five lessons on different sets of tutoring skills: (1) prompting questions and verbal praise, (2) diagnostic questions, (3) demonstration techniques (estimation, the number line, expanded notation, manipulative materials, diagrams and pictures, and number sentences), (4) evaluation and practice examples, and (5) organizing the classroom for increased tutoring time. In the main field test of the course 49 teachers (volunteers) were videotaped during two tutoring sessions (one for a student having difficulty with number operations, one with verbal reasoning problems) before and after the course. Each tape was scored by two trained raters on six variables. A replication study was also conducted using 17 inservice teachers. Results demonstrate that the course accomplishes its objective. Major gains were in use of demonstration techniques, diagnostic questioning, and verbal praise. An operational field test with 290 teachers is under way to determine whether course materials contain all the information needed by school districts to use the course independent of supervision. (JS)