Two Sigma Problem

The two sigma problem is a finding reported by educational psychologist Benjamin Bloom in a 1984 paper, describing the result of a series of studies in which students who received one-to-one tutoring, combined with mastery-learning methods, performed on average about two standard deviations, or two sigma, better on tests than students taught the same material through conventional classroom instruction, a gap large enough to move an average tutored student to roughly the 98th percentile of a conventionally taught class. Bloom framed the finding as a problem rather than a solution because one-to-one tutoring at that scale is far too costly and labor-intensive to deliver to every student in a typical school system, and he posed the two sigma problem as a challenge to researchers to identify more affordable classroom-based methods capable of approaching tutoring's effectiveness at ordinary classroom scale. The finding has become one of the most frequently cited results in education research and is regularly invoked in discussions of tutoring programs and adaptive learning software as a benchmark for how large an effect individualized instruction can, in principle, produce.