Understanding and Responding to Students' Mathematical Thinking: A Study in Measurement and Theory Building

• In Event: 42.083 - Roundtable Session 17
  In Roundtable Session: 42.083-3 - Investigations in Mathematics Teachers' Learning and Practice

Abstract

We are developing theory around aspects of mathematical knowledge for teaching in conjunction with assessment items we designed to measure those aspects. This effort is part of an ongoing validation process for investigating the construct of analyzing and responding to students’ mathematical work. We report on how we used Rasch modeling to investigate the difficulty of two types of assessment items, those that require teachers to 1) infer what a student understands based on that student’s work versus 2) respond to a student based on that student’s work. The data suggest that items requiring pedagogical responses from teachers are more difficult than items that require inferences about student understanding, suggesting a hierarchical relationship between these aspects of teacher knowledge.

Authors

• Laurie O. Cavey, Boise State University

• Michele Carney, Boise State University

• Gwyneth Hughes, University of Wisconsin - Madison