Proving processes in classrooms follow their own peculiar rationale. Reconstructing structures of argumentations in these processes reveals elements of this rationale. This article provides theoretical and methodological tools to reconstruct argumentation structures in proving processes and to shed light to their rationale. Toulmin's functional model of argumentation is used for reconstructing local arguments, and it is extended to provide a 'global' model of argumentation for reconstructing proving processes in the classroom.

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Complementary to existing normative models, in this paper we suggest a descriptive phase model of problem solving. Real, not ideal, problem-solving processes contain errors, detours, and cycles, and they do not follow a predetermined sequence, as is presumed in normative models. To represent and emphasize the non-linearity of empirical processes, a descriptive model seemed essential. The juxtaposition of models from the literature and our empirical analyses enabled us to generate such a descriptive model of problem-solving processes. For the generation of our model, we reflected on the following questions: (1) Which elements of existing models for problem-solving processes can be used for a descriptive model? (2) Can the model be used to describe and discriminate different types of processes? Our descriptive model allows one not only to capture the idiosyncratic sequencing of real problem-solving processes, but simultaneously to compare different processes, by means of accumulation. In particular, our model allows discrimination between problem-solving and routine processes. Also, successful and unsuccessful problem-solving processes as well as processes in paper-and-pencil versus dynamic-geometry environments can be characterised and compared with our model.

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This paper looks at sources of frustration in students of ''prerequisite'' mathematics courses (PMC), that is, courses required for admission into undergraduate programs in a large, urban, North American university. The research was based on responses to a questionnaire addressed to students and interviews with students and instructors. In the design of the questionnaire and the analysis of responses, an ''institutional'' theoretical perspective was taken, where frustration was conceived not only as a psychological process but also as a situation experienced by participants in a concrete educational institution. Several sources of frustration were identified as important in the group of respondents: the fast pace of the courses, inefficient learning strategies, the need to change previously acquired ways of thinking, difficult rapport with truth and reasoning in mathematics, being forced to take PMC, insufficient academic and moral support on the part of teachers, and poor achievement. These sources of frustration are discussed from the point of view of their impact on the quality of the mathematical knowledge that students develop in the PMC. Consideration is also given to the possibilities of improving the quality of this knowledge, given the institutional constraints implicated in the sources of students' frustration.

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