The purpose of this study was to explore among first grade children the relationship between achievement in mathematics and the understanding of the principles of conservation, seriation, and categorization as these are defined by Jean Piaget. Research instruments included those designed by Piaget and the Greater Cleveland Mathematics Tests. Conclusions included the following: (1) In the first grade there are many children who do not have the ability to conserve, to seriate, and to categorize; (2) Children who conserve when dealing with one type of material do not necessarily do so when dealing with another type of material; (3) In general, first grade children are more successful in tasks relating to conservation than those relating to ordering and classifying; (4) In general, a significant relationship exists between a child's ability to conserve, to seriate, to classify, and his level of achievement in mathematics; however, the degree of relationship varies from negligible to substantial, depending upon the tasks included in the comparisons. (Author/RS)