Defining Productive Struggle in ST Math: Implications for Developing Indicators of Learning Behaviors and Strategies in Digital Learning Environments

This paper describes a process for operationally defining productive struggle in a widely used digital learning environment called ST Math. The process for developing an operational definition involved examining the existing literature for ways in which researchers have previously quantified productive struggle in digital learning environments. Using prior research, we defined productive struggle as a student persisting in a digital learning task while maintaining a likelihood of future success. To develop a machine-executable definition of productive struggle, we identified the typical number of attempts learners needed to complete a level in ST Math and applied a modified Performance Factors Analysis algorithm to estimate learners’ probability of success on a subsequent puzzle attempt within a level. Using definitions that differentially combined re-attempts and predicted probabilities, we examined the proportion of level attempts that could be newly classified as instances of productive struggle. The pragmatic approach described in this paper is intended to serve as an example for other digital learning environments seeking to develop indicators of productive struggle.