Counting Squares or Measuring Length? Mathematics Teachers’ Hermeneutical Competence

This study explores the processes through which primary school teachers identify and interpret Grade 5 students’ errors in relation to the INVALSI swordfish item. In the responses to this item, which was administered in an open-ended format to a sample of 100 students, a misconception confounding one-dimensional and two-dimensional quantities (length and area) appears recurrent. Representative student protocols of this error type were subsequently used as prompts during semi-structured interviews conducted individually with two primary school teachers; their responses were analyzed through the new theoretical lens of hermeneutical competence. The findings highlight different modes of expression of this competence and reveal how teachers’ professional backgrounds can influence their processes of error identification and interpretation. Furthermore, the study shows how the guided analysis of student protocols and large-scale assessment data constitutes a promising formative tool to foster the development of teachers’ hermeneutical competence.