This pilot study examined the form or nature of the more highly organized knowledge structures used by successful problem solvers and whether there are experiences that would encourage their development. Previous related research and a theoretical framework are discussed. The small-group problem solving mode was used, with "A Problem with Cards" chosen because it provided contexts and materials through which groups of children working together could construct various representations and use different strategies. One of five homogeneously-grouped grade 6 classes in Princeton Day School, with 15 students, was selected. A profile of each student was developed; two problem solving sessions for which students were divided into groups of 2, 3, and 4 were conducted; and each student was interviewed about the sessions. The protocol results are presented and analyzed in some detail, with a focus on commutativity, inverse, and generalizing. Comments from the interviews are also presented. It was concluded that several problem-solving strategies emerged as important. Group problem solving appeared to be an effective means of helping students develop the ability to analyze and solve problems. An appendix contains the card problem and questions. (MNS)