Problem solving has become a focus of mathematics programs in Australia in recent years, necessitating the assessment of students' problem-solving abilities. This manual provides a problem-solving assessment and teaching resource package containing four elements: (1) profiles assessment items; (2) profiles diagnostic forms for recording individual and group information; (3) guidelines for using profiles for diagnostic assessment; and (4) suggestions for further teaching based on the student's current level of understanding. Two forms of the instrument measure the problem-solving abilities of Juniors (9-13 years) and Seniors (13-17 years) on the topics of algebra, chance and data, measurement, number, and space. Instructions are given for administering both versions of the instrument and for completing and interpreting an individual diagnostic profile. Suggestions for future learning activities are provided according to the student's SOLO level (unistructural, multistructural, relational, or extended abstract) as determined in the profile. A lengthy section is devoted to explaining the underlying theory of the SOLO Taxonomy and describing the development of the instrument. Separate documents provide the Profile A and Profile B forms of the instrument that can be used for pre- and posttest measures. Contains 32 references. (MDH)