Validation of a Learning Trajectory-Based Diagnostic Mathematics Assessment System as a Trading Zone

Abstract

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This study reports how a validation argument for a learning trajectory (LT) is constituted from test design, empirical recovery, and data use through a collaborative process, described as a “trading zone” among learning scientists, psychometricians, and practitioners. The validation argument is tied to a learning theory about learning trajectories and a framework (LT-based data-driven decision-making, or LT-DDDM) to guide instructional modifications. A validation study was conducted on a middle school LT on “Relations and Functions” using a Rasch model and stepwise regression. Of five potentially non-conforming items, three were adjusted, one retained to collect more data, and one was flagged as a discussion item. One LT level description was revised. A linear logistic test model (LLTM) revealed that LT level and item type explained substantial variance in item difficulty. Using the LT-DDDM framework, a hypothesized teacher analysis of a class report led to three conjectures for interventions, demonstrating the LT assessment’s potential to inform instructional decision-making.

Keywords

• validation
• learning trajectories
• diagnostic
• mathematics
• middle grades
• formative assessment