Assessing Mathematical Argumentation and Algebraic Reasoning Through Automated Conversations

• In Event: 49.057 - Conversation-Based Assessments

Abstract

Mathematical Argumentation has taken a more prominent role in mathematics classrooms in recent years, and this trend is only expected to rise given its presence in the Common Core State Standards as one of the “Standards of Mathematical Practice.” Given this movement, the assessment of mathematical argumentation has grown in importance, yet is still in its infancy with regards to methods of eliciting and assessing argumentation skills of an individual outside of the classroom. One reason this is the case is that mathematical argumentation is traditionally elicited through discourse, which is typically only possible in a classroom or small-group context. In this project, we use a dialogue-based assessment system (e.g., Graesser, Person, & Harter, 2001) to elicit evidence of student mathematical reasoning in a context of linear algebra (using a teacher avatar and peer avatar to interact with a human student).
This poster will present results from “trialogues” conversations involving three humans (two middle school students and one teacher) and those gathered from the dialogue-based assessment system involving a single middle school student interacting with two avatars. In both cases, students worked towards a solution of the same linear algebra problem allowing us to compare the two processes and to demonstrate the benefits of the automated “trialogues” in eliciting greater evidence of mathematical argumentation from students while preserving the natural flow of conversation and mathematical discourse.
The poster will also discuss the sequence of development of the automated trialogue, challenges faced in the use of automated conversation engines when dealing with arguments containing mathematical formulae or equations, and small-scale pilot studies used toward the iterative development of the assessment system. This study has a significant impact on the future assessments of mathematical argumentation outside of classroom observation protocols.

Authors

• Gabrielle Alexis Cayton-Hodges, Educational Testing Service

• Malcolm Bauer, ETS

• Maria Bertling, Harvard University

• Irvin R. Katz, Educational Testing Service

• E. Caroline Wylie, ETS