Mathematics items developed to measure concept attainment for the topics of set theory, division, and expressing relationships were studied. A completely crossed design with 30 concepts and 12 tasks was used. The items were administered to 196 girls who had just completed the fifth grade and to 195 boys who had just begun the sixth grade. Conventional factor analyses were performed, separately for boys and girls, for concept scores and for task scores; these showed that all 30 of the concepts were measures of a single functional relationship existing among the concepts and that all 12 tasks were measures of a single underlying ability or latent trait. Three-mode factor analyses indicated that there were no important concept-task interactions for the idealized person and thus the concepts and the tasks can be regarded as being two independent modes. For related documents in this series, see SE 015 462 and SE 015 468. (Author/DT)