This paper presents a framework for understanding conditions of discovery learning in computer-based microworlds. It begins with a short discussion of problems related to a traditional type of microworld--i.e., learning tools for mathematics--using the Dienes Multibase Arithmetic blocks as an example. In this discussion, hypotheses are developed about characteristics of task environments that seem to be necessary for discovery learning. The design of a microworld in which students are challenged to acquire algorithms for mental addition of two-digit numbers is then proposed, in a discussion that advances two general principles for the design of computational microworlds in which procedural skills can be acquired by discovery learning and that identifies two conditions that can be expected to foster problem solving behavior. The project in which the 10-square microworld was designed is then described, together with a first experiment conducted to determine whether second grade students would be able to acquire the target algorithms without the help of a teacher; the problem solving methods they utilized in reaching the goal are also described. It is noted that a prototype of the 10-square microworld implemented for a Macintosh SE/30 computer system was used in the experiment, which consisted of a sequence of five microworlds with different sets of constraints and a sixth microworld without constraints. Analyses of the study data indicate that continuing experience with the task turned the process of solving addition problems into a routine action, and that the 10-square microworld was effective in narrowing down the number of student choices. The desirability of further study of the transfer from the 10-square model to mental problem solving is indicated. Eight figures are provided. (Contains 16 references.) (ALF)