Parents differing along a concreteness-abstractness dimension of conceptual development, as defined by the model of Harvey, Hunt, and Schroder, described their attitudes and practices regarding their children's home play environment. This was done using structured questionnaires. Potential creativity of the 3- and 4-year-old children themselves was measured by indicators of complexity and variety of performance on a laboratory play task. Parents' questionnaire responses were analyzed in terms of the complexity, novelty, autonomy, and explorativeness of the home play environment. Parents' levels of conceptual development were than compared on the questionnaire responses and the children's performance scores. The results for fathers showed no significant differences. The results for mothers indicated that more abstract mothers had more positive attitudes toward and were more likely than more concrete mothers to provide complex, novel, autonomous, and explorative play situations for their children. The children of more abstract mothers also showed more complex and varied behavior on the preformance task. These results were unrelated to differences among parents on certain demographic variables--age, income, education, and occupational prestige. The results were discussed in terms of the roles of parental conceptual development and the home play environment in affecting potential creativity. (Author)