Abstract:

In mathematics education, research interest in formulating problems has been growing and consolidating since the 1980. After several decades of studies focused on problem solving, researchers began to realize that developing in our students the ability to propose mathematical problems is as important as developing the ability to solve them, from an educational point of view. Then, several works emerged where the relationship between formulation and problem solving, the problem formulation skills and processes involved in their formulation or even the formulation of problems and creativity stand out. Kilpatrick (1987) specified that “problem formulating is an important companion to problem solving” (p. 123). Stoyanova and Ellerton (1996) define the formulation of problems as being “the process by which, on the basis of mathematical experience, students construct personal interpretations of concrete situations and formulate them as meaningful mathematical problems” (p. 1).

We teach future teachers of the elementary school (ages 6 to 10) and from the second cycle (ages 11 to 12) and we believe that “preservice teachers can be encouraged to develop their own capacity for posing problems, moving from posing single-step, traditional problems to more cognitively complex and open-ended problems, and developing richer understandings of what problems are ‘good’ problems” (Xu, et al. 2020).

Given the problem solving and the posing problems importance, the aim of this paper is to present the analysis of the errors and difficulties of the future teachers in a task of posing mathematical problems for the elementary school level.

The study involved 28 students attending the first-year course of “Logic and problem solving” from Basic Education graduation in a Northern Portuguese University. A task of mathematical problem posing is analyzed. The first question refers only to a mathematical basic operation, the multiplication, and students were asked to invent the context that the operation models, to formulate a problem that could be solved through the presented operation. In the second, the student had an image that illustrated a real-life context, and based in it they had to pose the mathematical problem intended for 1st or 2nd years students’ elementary school. After analyzing the results, we found that all the students were able to pose the problem for the first question. In this question, students revealed no difficulties in wording the problem, because they considered very easy to find a real situation that could be described by the presented mathematical expression. In the next question some of the students showed some difficulties in wording the problem because some of the wrote it and didn’t even mention the figure they were using. We also asked the students to write the difficulties they felt doing the task and the general opinion reflects the students’ sense that they still have a lot to learn in order to be able to write good mathematical problems and also problems suitable to the different mathematical school levels.

Keywords:

Mathematics, posing problem, training, future teachers.