The Ising on the Tree: The Master Model for Learning, Assessment, and Navigation

Learning and assessment are intrinsically linked. However, the research, tools, and statistical models used within the two fields differ greatly. This has created a disconnect: The goals and missions of educational institutions are codified in the language and ideas of learning, but evaluated, monitored, and administered with the tools of assessment. We propose a novel statistical model, the Master model, capable of being the engine behind a modern learning and assessment system. The Master model combines three key concepts from the assessment and learning literature from the past century: A learning model should be multidimensional and hierarchical and should incorporate learning progressions. The Master model is a multidimensional latent variable model, more specifically a latent class model, that not only ranks learners from best to worst but also provides detailed diagnostic feedback to tell learners what they know, and more importantly, what they don't know. By incorporating a hierarchical structure of the latent variables, the Master model reproduces the positive manifold, a phenomenon that continues to be replicated in assessment data where scores between cognitive tests correlate positively. Finally, expert and data-driven annotation can incorporate learning progressions directly into the latent variables. With these three key concepts, the Master model can track the estimate of a learner’s latent skills, track the efficacy of various educational resources such as videos, and recommend which resources the learner should next focus on in order to maximize their learning.