Experiences of problem solving in whole class interactions

Abstract

Problem solving is often considered to be an essential part of learning mathematics. In this paper we examine the whole class interactions around problems and problem solving as they naturally occur in mathematics classrooms. Thus, we are examining students’ ordinary experiences of problem solving in their everyday mathematics lessons. Our analysis shows how students’ participate in a very narrow range of problem solving actions and that the actions that they do participate in are controlled by the teacher. This raises implications for what students perceive and interpret problem solving to be in mathematics.

Interactions Promoted by Teacher Educators Based on an Erroneous Approach to the Subject of Fractions

“…F2 raises open questions that allow diversifying responses, seeking to explore the thinking of participating teachers. This attitude of F2 contrasts with F1 and the same with the results of the aforementioned studies (Leguizamón, 2017;Pagés et al, 2018;Ingram andRiser , 2019 andDonoso et al, 2020). However, the way of asking the F2 questions coincides with what was reported by Borssoi et al (2021) who analyze the interactions promoted by a teacher at the time of a mathematical modeling class in a differential equations course.…”

“…A second aspect is in relation to the type of responses of the participating teachers based on the questions formulated by the trainers. As a logical consequence of the type of questions, it is observed that when faced with the questions formulated by F1, the answers of the teachers in the training session are generally brief, coinciding with what was reported by Leguizamón (2017), Pagés et al (2018), Ingram and Riser (2019) and Donoso et al ( 2020). On the contrary, the questions posed by F2 mostly correspond to broader answers, which are accompanied by arguments, as also reported by the studies by Borssoi et al (2021) and from Schleppenbach et al (2007), the latter in the case of teachers in China.…”

“…Similar results coincide with those of Leguizamón (2017) who reports the same attitude in three professors belonging to the Mathematics Degree at the Pedagogical and Technological University of Colombia (UPTC). It is an attitude that assumes control on the part of the person who directs the activity in order to focus attention on the subject he wants, leaving aside any other type of response that diverts his attention, as stated by Ingram andRiser . (2019) andDonoso et al (2020) in their studies, when inquiring about the behavior and interactions derived from the performance of teachers in their classes.…”

“…The study of interactions also revolves around their characteristics. For example, Ingram and Riser (2019) address the interactions that are generated in mathematics classes from problem solving, showing that students participate in a very limited range of problem-solving actions, generally controlled by the teacher.…”