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Game-based assessment (GBA) offers a powerful alternative to traditional assessment methods. The ease with which evidence can be collected from gameplay and displayed via dashboards shows promise for offering in the moment communications about where each student is in their learning. However, the ultimate value of GBA relies on alignment between what the assessment measures and what teachers value. In this study, we operationalized teacher definitions of persistence in mathematics to develop a descriptive, nuanced assessment algorithm in Shadowspect, a mathematics educational game. We uncover the potential for teacher definitions to directly inform log data processing and modeling methods. These models in turn allow grounded storytelling that provide rich descriptions of student behaviors in line with teacher values and practices.