Designing and Developing Assessments of Complex Thinking in Mathematics for the Middle Grades

Abstract

Designing an assessment system for complex thinking in mathematics involves decisions at every stage, from how to represent the target competencies to how to interpret evidence from student performances. Beyond learning to solve particular problems in a particular area, learning mathematics with understanding involves comprehending connections among mathematical ideas and applying them in ways that may not have been taught directly. A challenge in characterizing mathematical competency is to capture not only the variety of skills and concepts, but also their connections. Designing assessments based on learning progressions may be one way to respond to this challenge. We discuss our experience developing a learning progression and an associated task model for mathetical functions.