This study explored student mathematical activity in open problem-solving situations, derived from the work of Polya on problem solving and Skemp on intelligent learning and teaching. Assignment projects with problems for ninth-grade students were developed, whether they elicit the desired cognitive and cogno-affective goals was investigated, and their effectiveness in enhancing mathematical activity was evaluated. Student responses were analyzed on quality-of-answer and quality-of-procedure scales. Improvement is exhibited in a quality of solution table. Assignment tests were developed, validated, and used to compare changes in mathematical activity in a pre-post control-experimental setting. The results indicate that the assignment projects were effective. It also became clear that teachers needed more support in a practical form. A clinical study was undertaken; students in one class were interviewed about their work on assignments. The researcher's premise was that if he could categorize student difficulties and the guidance into some sort of hierarchy, then he would have a model and a language which would help teachers in their work. The applicability of the diagnostic guidance hierarchy was examined successfully in a regular classroom setting. (MNS)