The realization tree assessment tool - examining explorative participation in mathematics lessons

摘要

In this paper we offer a new tool for assessing explorative participation in mathematics lessons, namely participation where students focus on constructing narratives about mathematical objects based on their own authority and on previously established mathematical narratives. This tool, named the Realization Tree Assessment tool (RTA), aims to record opportunities for objectification and the level of students' authority in whole classroom discussions. Inspired by the commognitive theory of mathematical objectification, the RTA visualizes the realizations of mathematical objects that arise during classroom discussions and the extent to which students authored the different realizations. We exemplify the tool on 14 lessons, all of which were based on an identical task - the Hexagons Task. The exemplification shows how the tool captures narratives about realizations and connections between these realizations offered by students and the teacher. We discuss the affordances of the tool for analysing and evaluating instruction that aims towards explorative participation.