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A Reciprocal-Practice-Success (RPS) Model of Free Practice

Creative Commons 'BY' version 4.0 license
Abstract

Understanding how humans learn by themselves is crucial to develop interventions to prevent dropout and improve learner engagement. Classical learning curves were proposed to fit and describe experimental data involving enforced learning. However in real-world learning contexts such as MOOCs and hobbies, learners may quit - and often do. Even in formal settings such as college success typically requires intensive self-study outside lectures. Previous research in educational psychology supports a positive reciprocal relationship between motivation and achievement. Integrating insights from learning curves, forgetting curves and motivation-achievement cycles, we propose a formal Reciprocal-Practice-Success (RPS) model of learning ‘in the wild'. First, we describe the different components of the basic RPS model. Using simulations, we then show how long term learning outcomes critically depend on the shape of the learning curve. Concave curves lead to more consistent learning outcomes whereas S-shaped curves lead to either expertise or dropout. We also provide a dynamical systems version for the RPS model which shows similar qualitative behaviour. Through a bifurcation analysis of two controllable learning parameters - minimum practice rate and success sensitivity, we show which learner-specific interventions may be effective to preventing dropout. We also discuss theorized mechanisms which affect the inflection point of S-shaped learning curves such as task-complexity and relative feedback from failures vs. successes. These provide more task-specific interventions to lower quitting rates. Finally, we discuss possible extensions to the basic RPS model which will allow capturing spacing effects and insights from other motivation theories.

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