PROBLEM POSING AND SOLVING IN MATHEMATICS EDUCATION: AN ANALYSIS OF TEACHING CASES

Abstract

This article analyzes the implications of teachers’ decisions when planning and conducting problem-posing activities in the classroom, with particular attention to triggering elements, prompts, and connections to problem solving. To this end, a qualitative study was conducted involving three teaching cases developed from the implementation of problem-posing activities with students in the 5th grade, 6th grade of elementary school, and the 3rd year of high school, depicting the pedagogical objectives defined by the teachers and how these objectives influence the choice of the triggering element, the prompt, and the discussion and solving of the problems. The results show that, although it is possible to identify a recurring structure in these activities, there is no single way to implement them. The teacher’s intentionality and active listening, choices, and decisions are determining factors in transforming students’ productions into formative opportunities. In addition, problem posing supports the development of cognitive and metacognitive skills, and its connection to problem solving broadens the potential for learning.