Exercise or Problem? An Epistemological Analysis of Primary and Secondary Teachers’ Conceptions Through Task Design

Abstract

This study examines how practicing Panamanian primary teachers distinguish between a routine mathematical exercise and a genuine problem when asked to justify their decision in writing. The analysis is framed through the Ontosemiotic Approach to Mathematical Knowledge and Instruction, specifically the epistemic suitability criterion and its four components: errors, ambiguities, richness of processes, and representativeness of complexity. The data set comprises 25 written responses drawn from a diagnostic activity administered within the EDEM diploma programme for in-service teachers. Teachers classified a contextualized subtraction task involving money and were required to explain whether the task should be considered an exercise or a problem. Responses were examined with a rubric scored from 0 to 3 on each epistemic component. The overall distribution reveals heterogeneous performance: 40% of participants reached the high level, 24% the medium level, 32% the low level, and only one teacher achieved the excellent level. At component level, representativeness of complexity showed the strongest performance (M = 2.44), whereas richness of processes was the weakest dimension (M = 1.28). These findings suggest that teachers frequently identify the task correctly but do not always justify their decisions with conceptually precise or sufficiently elaborated arguments. The study contributes a fine-grained account of teacher discourse about mathematical tasks and highlights the need for teacher education that connects epistemic analysis, task design, and reflective pedagogical reasoning.