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This paper presents a part of a research whose objective was to present and discuss aspects of the use of proof-writing-in-phases with cheating as a teacher strategy in initial teacher training. For that, Realistic Mathematics Education was taken as an approach to teaching. The interventions inherent to the stages reduce the utility of cheating because they individualize the exam. Within the context of that teacher strategy, cheating misses its purpose, since the exam carried out in stages eliminates the rule of noncommunication. [ABSTRACT FROM AUTHOR]

This paper aims to present part of a Case Study carried out in an Initial Training for Teachers of Mathematics, in the years 2010-2011, in order to contribute to the many actions done by those involved in the initial teacher's training in order to better prepare these professionals, in this important stage of formation. Having reformulated the course, Problem Solving (RP) came to be one of the new subjects, where the curriculum claimed to work with Trends in the Teaching of Mathematics. In this research, emphasis will be given to working with future teachers in this subject, focusing on Problem Solving as a teaching methodology in its theoretical and practical aspects. It is believed that teaching is a reflection of the experience of the teacher throughout his career and it is expected that experiencing different working methodologies in this stage of training future teachers are better prepared to work as teachers. After three semesters of work on the subject, it was found that prospective teachers were able to work with the methodology by extending it even to other contexts. [ABSTRACT FROM AUTHOR]