The Realization Tree Assessment tool: Assessing the exposure to mathematical objects during a lesson

Abstract

International audienceWe present a new tool-Realization Tree Assessment (RTA) for assessing the mathematical quality of lessons and the ways in which the whole classroom discussion expose students to mathematical concepts. The tool, built upon the commognitive framework, depicts the different realizations of a mathematical object treated in a lesson, and then uses different shades to signify who articulated the realization-the teacher or the students. We exemplify the tool on two lessons implementing an identical Hexagon pattern generalization task. The RTA visualizes the manner in which one lesson gave students sufficient opportunities to "same" different algebraic expressions, while the other lesson did not. We show how this visual presentation of the mathematical ideas complements existing assessment tools, particularly, the Instructional Quality Assessment and Accountable Talk. We conclude by discussing the potential of the tool as an aid for lesson planning