Teacher’s actions to promote students’ justifications

Abstract

Justification is a mathematical reasoning process that relies on concepts, properties or mathematical ideas and, in certain situations, particular cases, being a fundamental part of the proof. The teacher needs to promote justification in the classroom, as it is essential to the development of students’ mathematical knowledge. This study aims to understand how a set of design principles regarding tasks and teacher’s actions contributes to enhance students’ justifications in whole-class mathematical discussions and to understand what kinds of justifications emerge in those discussions. The intervention, part of a design-based research, occurs in a grade 7 class of an experienced teacher, in nine classes about linear equations. The data collection includes classroom observations (video and audio recorded) and a logbook. Data analysis considers a set of design principles, a conceptual framework for teacher actions, and a conceptual framework for student justifications. The results show that certain sequences of teacher actions based on the design principles allow students to present quite complete justifications based on logical coherence and mathematical aspects of the situation.