Mathematical working spaces in the mathematical modeling cycle: the case of preservice elementary mathematics teachers

Abstract

Mathematical modeling is a dynamic process through which real-life situations are explored and explained via mathematical knowledge and reasoning. The theory of Mathematical Working Spaces (MWS) ofers a robust framework for analyzing the cognitive process involved in modeling, emphasizing the roles of components of representation, artifacts, and theoretical reference. This study investigates the mathematical works of preservice mathematics teachers as they engage in a modeling task, using the MWS as an analytical lens. Adopting a qualitative case study design, data were collected from 34 preservice teachers selected via criterion sampling. Sources included written responses to guided exploratory questions and video recordings of group work. The modeling actions were examined through descriptive analysis grounded in the components of MWS. The fndings reveal that the diversity and depth of actions initiated in the early phases of the modeling cycle—particularly within the genesis processes—are critical for the successful completion of the task. The study highlights that engaging with the genesis processes meaningfully, beyond merely operating at the epistemological level, supports richer mathematical reasoning and more complete modeling outcomes.