The purpose of the two studies reported was to develop and validate clinical assessment instruments designed to identify both the progress of learners through a hierarchy of mathematics content and the mode of presentation through which learners can best handle the content. In Study 1, 73 second graders were given one of two forms of a 15-item instrument assessing knowledge of place value through three-digit numbers. Five modes of symbolic representation were used, ranging from concrete to abstract. When students handled materials or drew pictures, performance was significantly better than when they watched the examiner. No significant differences were found at the concrete-abstract, pictorial-abstract, and abstract levels. In Study 2, 45 sixth graders were given a 48-item instrument assessing knowledge of subtraction of fractions and mixed numbers, using concrete, pictorial, or abstract representations, or all three. The content hierarchy was found to become increasingly difficult from beginning to end of the test. Approximately 92% of the variance was accounted for by itmes using the pictorial mode. Performance was significantly related to ability level. (MNS)