How To Improve Pre-Service Mathematics Teachers' Problem-Solving Competencies (Case Study).

Lower and upper secondary school mathematics offers a few tools for solving mathematical problems (e. g., equational strategy or other algorithmic ones). At the beginning of the university study our students (pre-service mathematics teachers) know how to use them, but they have no experience with solving strategies such as systematic experimentation or drawing a picture. This paper presents our lesson plan to improve their solving competencies and its results. The special attention is given to the process of mathematics problem-solving and its fourth phase 'looking back' that we understand in a broader sense, not only as a test of correctness. The results of this case study aim to show and understand how students learn and use various solving strategies in problem-solving and how they pose other word problems with the same solution as the solution of the given word problems. The analysis finds that even though students understand the importance of non-standard strategies (e.g., trial and error or estimationverification-correction), they still understand the school equational strategy as the most advantageous. For problem-posing to contribute to the improvement of problem-solving competences, it must be more often involved in the problem-solving process. [ABSTRACT FROM AUTHOR]