Procedural documentation is presented for administering, scoring and analyzing data gathered to examine the construct validity of a set of superitems developed to assess student levels of mathematical reasoning ability. Each superitem includes a mathematical situation and a structured set of questions about that situation. The questions were based on Collis and Biggs' recently-developed taxonomy on the structure of the observed learning outcomes (SOLO). The assumption underlying this report is that the response patterns of students to the superitems would be interpretable. To judge interpretability, three primary questions about the response patterns were raised. For each question the data strongly support the validity of the construct. The response patterns of the majority of items matched the assumed latent hierarchical and cumulative cognitive dimension. The question profiles for student clusters were interpreted in terms of developmental base stages and the spiral notions of equilibration. These findings give support to the validity of the sequence of SOLO levels. The SOLO interpretation of responses appears useful for educators and researchers in describing the level of reasoning on school related tasks. Item analyses tables are appended. (Author/PN)