This study documented the spontaneously derived strategies that children use which may play a key role in the transition from counting to recall of number facts. For these strategies, the child uses a small set of known number facts to derive the solution to unknown number facts. How training in the use of derived strategies influences the solution strategies used was also studied, with special note of changes in solution strategies from counting to strategies based on relations among facts. A teaching experiment was conducted with one second-grade class (N=23) for eight weeks beginning in early September. Four interviews were conducted with each child, involving a pretest, a mid-instruction interview, a posttest, and a long-range effects test, in addition to short daily interviews and three group timed tests. The instructional unit and strategies taught are described, as are the interviews, observations, timed test, and student workbooks. Derived fact strategies accounted for about 20 percent of the children's responses on the pretest, and for one-half of the responses to addition combinations and over one-fourth of the answers to subtraction combinations following instruction. (MNS)