The objective of this paper is to explain the need for and defend the sufficiency of the child's-play method of teaching the place value notation concept to preschool and elementary school children. Discussion first illustrates error patterns of school children in the use and interpretation of place value notation, arguing that the errors reflect counting principles learned in preschool and that such errors are the natural consequence of children's assimilation of information concerning digit symbols into their cognitive structures. Subsequent discussion suggests that future research will show that the inadequacy of the preschool principles is a major, if not the root, cause of mathematics anxiety in children, and that the harmonious integration of the preschool counting principles with number representation rules will lessen, perhaps eliminate, math anxiety. Discussion then explores the problem of integrating the rule systems, focusing on cognitive conflict and the task of instruction. The extensive concluding section presents five arguments supporting the child's-play method; these center on: (1) the simplicity of the method and the need for that simplicity; (2) the completeness of the concrete demonstrations and the sufficiency of the confirmations afforded by them; (3) the method's connection to a proven model; (4) evidence of the method's value from preliminary findings; and (5) minimal cost of the materials. (RH)