Abstract:

After several decades of studies focused on problem-solving, researchers realized that developing in students the ability to pose mathematical problems is, from an educational point of view, as important as developing the ability to solve them. Thus, from the 1980s onwards, research interest in problem formulation has been growing and consolidating. Currently, problem-posing is seen as an activity that can and should be considered in Mathematics classes and problem-solving. Aware of the importance of posing problems in the training of mathematics teachers of the first years, we carried out a study with 28 future teachers of the degree in Basic Education of a university in the north of Portugal. In the study's first part, students were asked to solve a task: pose a problem based on an arithmetic operation and another based on an image illustrating a context of life. In the study's second part, after collecting the students' task resolutions, each was randomly distributed to a student to act as a task reviewer. As a reviewer, each student was asked to analyze the posed problem, correct it, and give feedback to the colleague. The use of peer review as a learning facilitator is not new and has been widely applied in various scientific domains and collaborative learning contexts. As a tool that active learning, it helps build capacities related to diagnosis, evaluation, promotion, synthesis and communication, development of new ideas and critical thinking. Collaborative activities with Google-Drive, such as peer review, on the Internet, can help develop effective written and oral communication skills. At the same time, students provide peer feedback. They perceive how their colleagues posed and solved the problems as they did and learn to think critically and the rules of well-written feedback. For instance, among others, written feedback should be presented in a positive, tactful and non-threatening manner; it should avoid judgmental language; it should provide changes and suggestions instead of only pointing out errors.

In this work, we detail the phases of this task, and we analyze the peer feedback of four of the students as authors and their peer feedback (students acting as reviewers). After analyzing the peer reviews, we can conclude that students have many difficulties in the task of posing problems. In general, really creative posed-problems were unusual. In addition, despite the anonymity, it was noted that students do not like to "comment" about their colleagues' work. They view it as criticism instead of a critical peer-review analysis. These results point to the potential of problem-solving - creation and peer-review - which proved to be a strategy to be implemented regularly. To feel comfortable in the criticism between peers has the advantage of giving another person's perspective, given the problem-posed that the author might believe to be the "perfect" problem. Regularity of the course's task will make students more autonomous and confident when acting as student-reviewers and teachers.

Keywords:

Mathematics, posing problems, peer-review, feedback, future teachers.